%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : ITP006_2 : TPTP v9.0.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:11:17 AM UTC 2025
% Result : Theorem 12.22s 12.39s
% Output : Proof 12.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP006_2 : TPTP v9.0.0. Bugfixed v7.5.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 18:06:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 12.22/12.39 % SZS status Theorem
% 12.22/12.39 % SZS output start Proof
% 12.22/12.39 tff(p_type, type, (
% 12.22/12.39 p: $i > $o)).
% 12.22/12.39 tff(ap_type, type, (
% 12.22/12.39 ap: ( $i * $i ) > $i)).
% 12.22/12.39 tff(tptp_fun_V11fv_8_type, type, (
% 12.22/12.39 tptp_fun_V11fv_8: ( $i * $i * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_A_27b_14_type, type, (
% 12.22/12.39 tptp_fun_A_27b_14: del)).
% 12.22/12.39 tff(tptp_fun_V0i_13_type, type, (
% 12.22/12.39 tptp_fun_V0i_13: $i)).
% 12.22/12.39 tff(tptp_fun_V2Q_17_type, type, (
% 12.22/12.39 tptp_fun_V2Q_17: $i)).
% 12.22/12.39 tff(tptp_fun_V1P_16_type, type, (
% 12.22/12.39 tptp_fun_V1P_16: $i)).
% 12.22/12.39 tff(mem_type, type, (
% 12.22/12.39 mem: ( $i * del ) > $o)).
% 12.22/12.39 tff(c_2EquantHeuristics_2EGUESS__FORALL__POINT_type, type, (
% 12.22/12.39 c_2EquantHeuristics_2EGUESS__FORALL__POINT: ( del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_A_27a_15_type, type, (
% 12.22/12.39 tptp_fun_A_27a_15: del)).
% 12.22/12.39 tff(arr_type, type, (
% 12.22/12.39 arr: ( del * del ) > del)).
% 12.22/12.39 tff(bool_type, type, (
% 12.22/12.39 bool: del)).
% 12.22/12.39 tff(tptp_fun_V3fv_3_type, type, (
% 12.22/12.39 tptp_fun_V3fv_3: ( $i * $i * del ) > $i)).
% 12.22/12.39 tff(c_2EquantHeuristics_2EGUESS__EXISTS_type, type, (
% 12.22/12.39 c_2EquantHeuristics_2EGUESS__EXISTS: ( del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V5fv_5_type, type, (
% 12.22/12.39 tptp_fun_V5fv_5: ( $i * $i * del ) > $i)).
% 12.22/12.39 tff(c_2EquantHeuristics_2EGUESS__FORALL_type, type, (
% 12.22/12.39 c_2EquantHeuristics_2EGUESS__FORALL: ( del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V4v_6_type, type, (
% 12.22/12.39 tptp_fun_V4v_6: ( $i * $i * del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V2v_4_type, type, (
% 12.22/12.39 tptp_fun_V2v_4: ( $i * $i * del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V15fv_9_type, type, (
% 12.22/12.39 tptp_fun_V15fv_9: ( $i * $i * del ) > $i)).
% 12.22/12.39 tff(c_2EquantHeuristics_2EGUESS__EXISTS__GAP_type, type, (
% 12.22/12.39 c_2EquantHeuristics_2EGUESS__EXISTS__GAP: ( del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V14v_10_type, type, (
% 12.22/12.39 tptp_fun_V14v_10: ( $i * $i * del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V19fv_11_type, type, (
% 12.22/12.39 tptp_fun_V19fv_11: ( $i * $i * del ) > $i)).
% 12.22/12.39 tff(c_2EquantHeuristics_2EGUESS__FORALL__GAP_type, type, (
% 12.22/12.39 c_2EquantHeuristics_2EGUESS__FORALL__GAP: ( del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V18v_12_type, type, (
% 12.22/12.39 tptp_fun_V18v_12: ( $i * $i * del * del ) > $i)).
% 12.22/12.39 tff(tptp_fun_V8fv_7_type, type, (
% 12.22/12.39 tptp_fun_V8fv_7: ( $i * $i * del ) > $i)).
% 12.22/12.39 tff(c_2EquantHeuristics_2EGUESS__EXISTS__POINT_type, type, (
% 12.22/12.39 c_2EquantHeuristics_2EGUESS__EXISTS__POINT: ( del * del ) > $i)).
% 12.22/12.39 tff(1,plain,
% 12.22/12.39 ((mem(V0i!13, arr(A_27b!14, A_27a!15)) & (mem(V1P!16, arr(A_27a!15, bool)) & (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))) <=> (mem(V0i!13, arr(A_27b!14, A_27a!15)) & mem(V1P!16, arr(A_27a!15, bool)) & (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))),
% 12.22/12.39 inference(rewrite,[status(thm)],[])).
% 12.22/12.39 tff(2,plain,
% 12.22/12.39 ((mem(V1P!16, arr(A_27a!15, bool)) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))) <=> (mem(V1P!16, arr(A_27a!15, bool)) & (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))),
% 12.22/12.39 inference(rewrite,[status(thm)],[])).
% 12.22/12.39 tff(3,plain,
% 12.22/12.39 (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~p(ap(V2Q!17, V3x))) | p(ap(V1P!16, V3x)) | (~mem(V3x, A_27a!15)))) <=> ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))),
% 12.22/12.39 inference(rewrite,[status(thm)],[])).
% 12.22/12.39 tff(4,plain,
% 12.22/12.39 ((mem(V1P!16, arr(A_27a!15, bool)) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~p(ap(V2Q!17, V3x))) | p(ap(V1P!16, V3x)) | (~mem(V3x, A_27a!15))))) <=> (mem(V1P!16, arr(A_27a!15, bool)) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))))),
% 12.22/12.39 inference(monotonicity,[status(thm)],[3])).
% 12.22/12.39 tff(5,plain,
% 12.22/12.39 ((mem(V1P!16, arr(A_27a!15, bool)) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~p(ap(V2Q!17, V3x))) | p(ap(V1P!16, V3x)) | (~mem(V3x, A_27a!15))))) <=> (mem(V1P!16, arr(A_27a!15, bool)) & (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))),
% 12.22/12.39 inference(transitivity,[status(thm)],[4, 2])).
% 12.22/12.39 tff(6,plain,
% 12.22/12.39 ((mem(V0i!13, arr(A_27b!14, A_27a!15)) & (mem(V1P!16, arr(A_27a!15, bool)) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~p(ap(V2Q!17, V3x))) | p(ap(V1P!16, V3x)) | (~mem(V3x, A_27a!15)))))) <=> (mem(V0i!13, arr(A_27b!14, A_27a!15)) & (mem(V1P!16, arr(A_27a!15, bool)) & (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))))),
% 12.22/12.39 inference(monotonicity,[status(thm)],[5])).
% 12.22/12.39 tff(7,plain,
% 12.22/12.39 ((mem(V0i!13, arr(A_27b!14, A_27a!15)) & (mem(V1P!16, arr(A_27a!15, bool)) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~p(ap(V2Q!17, V3x))) | p(ap(V1P!16, V3x)) | (~mem(V3x, A_27a!15)))))) <=> (mem(V0i!13, arr(A_27b!14, A_27a!15)) & mem(V1P!16, arr(A_27a!15, bool)) & (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))),
% 12.22/12.39 inference(transitivity,[status(thm)],[6, 1])).
% 12.22/12.39 tff(8,plain,
% 12.22/12.39 ((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27b, A_27a))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a, bool))) | ![V2Q: $i] : (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)) | (~mem(V2Q, arr(A_27a, bool))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P))) | (~![V3x: $i] : ((~p(ap(V2Q, V3x))) | p(ap(V1P, V3x)) | (~mem(V3x, A_27a)))))))) <=> (~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27b, A_27a))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a, bool))) | ![V2Q: $i] : (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)) | (~mem(V2Q, arr(A_27a, bool))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P))) | (~![V3x: $i] : ((~p(ap(V2Q, V3x))) | p(ap(V1P, V3x)) | (~mem(V3x, A_27a))))))))),
% 12.22/12.39 inference(rewrite,[status(thm)],[])).
% 12.22/12.39 tff(9,plain,
% 12.22/12.39 ((~![A_27a: del, A_27b: del, V0i: $i] : (mem(V0i, arr(A_27b, A_27a)) => ![V1P: $i] : (mem(V1P, arr(A_27a, bool)) => ![V2Q: $i] : (mem(V2Q, arr(A_27a, bool)) => (![V3x: $i] : (mem(V3x, A_27a) => (p(ap(V2Q, V3x)) => p(ap(V1P, V3x)))) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)))))))) <=> (~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27b, A_27a))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a, bool))) | ![V2Q: $i] : (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)) | (~mem(V2Q, arr(A_27a, bool))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P))) | (~![V3x: $i] : ((~p(ap(V2Q, V3x))) | p(ap(V1P, V3x)) | (~mem(V3x, A_27a))))))))),
% 12.22/12.39 inference(rewrite,[status(thm)],[])).
% 12.22/12.39 tff(10,axiom,(~![A_27a: del, A_27b: del, V0i: $i] : (mem(V0i, arr(A_27b, A_27a)) => ![V1P: $i] : (mem(V1P, arr(A_27a, bool)) => ![V2Q: $i] : (mem(V2Q, arr(A_27a, bool)) => (![V3x: $i] : (mem(V3x, A_27a) => (p(ap(V2Q, V3x)) => p(ap(V1P, V3x)))) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P)) => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT')).
% 12.22/12.39 tff(11,plain,
% 12.22/12.39 (~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27b, A_27a))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a, bool))) | ![V2Q: $i] : (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)) | (~mem(V2Q, arr(A_27a, bool))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P))) | (~![V3x: $i] : ((~p(ap(V2Q, V3x))) | p(ap(V1P, V3x)) | (~mem(V3x, A_27a)))))))),
% 12.22/12.39 inference(modus_ponens,[status(thm)],[10, 9])).
% 12.22/12.39 tff(12,plain,
% 12.22/12.39 (~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27b, A_27a))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a, bool))) | ![V2Q: $i] : (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)) | (~mem(V2Q, arr(A_27a, bool))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P))) | (~![V3x: $i] : ((~p(ap(V2Q, V3x))) | p(ap(V1P, V3x)) | (~mem(V3x, A_27a)))))))),
% 12.22/12.39 inference(modus_ponens,[status(thm)],[11, 8])).
% 12.22/12.39 tff(13,plain,
% 12.22/12.39 (~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27b, A_27a))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a, bool))) | ![V2Q: $i] : (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)) | (~mem(V2Q, arr(A_27a, bool))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P))) | (~![V3x: $i] : ((~p(ap(V2Q, V3x))) | p(ap(V1P, V3x)) | (~mem(V3x, A_27a)))))))),
% 12.22/12.39 inference(modus_ponens,[status(thm)],[12, 8])).
% 12.22/12.39 tff(14,plain,
% 12.22/12.39 (~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27b, A_27a))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a, bool))) | ![V2Q: $i] : (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V2Q)) | (~mem(V2Q, arr(A_27a, bool))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b, A_27a), V0i), V1P))) | (~![V3x: $i] : ((~p(ap(V2Q, V3x))) | p(ap(V1P, V3x)) | (~mem(V3x, A_27a)))))))),
% 12.22/12.39 inference(modus_ponens,[status(thm)],[13, 8])).
% 12.22/12.39 tff(15,plain,
% 12.22/12.39 (mem(V0i!13, arr(A_27b!14, A_27a!15)) & mem(V1P!16, arr(A_27a!15, bool)) & (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) & mem(V2Q!17, arr(A_27a!15, bool)) & p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) & ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))),
% 12.22/12.39 inference(modus_ponens,[status(thm)],[14, 7])).
% 12.22/12.39 tff(16,plain,
% 12.22/12.39 (mem(V0i!13, arr(A_27b!14, A_27a!15))),
% 12.22/12.39 inference(and_elim,[status(thm)],[15])).
% 12.22/12.39 tff(17,plain,
% 12.22/12.39 (^[A_27a: del, A_27b: del, V0i: $i] : rewrite(((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))) <=> ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))))),
% 12.22/12.39 inference(bind,[status(th)],[])).
% 12.22/12.39 tff(18,plain,
% 12.22/12.39 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.39 inference(quant_intro,[status(thm)],[17])).
% 12.22/12.39 tff(19,plain,
% 12.22/12.39 (^[A_27a: del, A_27b: del, V0i: $i] : refl(((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))) <=> ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))))),
% 12.22/12.40 inference(bind,[status(th)],[])).
% 12.22/12.40 tff(20,plain,
% 12.22/12.40 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.40 inference(quant_intro,[status(thm)],[19])).
% 12.22/12.40 tff(21,plain,
% 12.22/12.40 (^[A_27a: del, A_27b: del, V0i: $i] : rewrite(((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))) <=> ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))))),
% 12.22/12.40 inference(bind,[status(th)],[])).
% 12.22/12.40 tff(22,plain,
% 12.22/12.40 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.40 inference(quant_intro,[status(thm)],[21])).
% 12.22/12.40 tff(23,plain,
% 12.22/12.40 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.40 inference(transitivity,[status(thm)],[22, 20])).
% 12.22/12.40 tff(24,plain,
% 12.22/12.40 (^[A_27a: del, A_27b: del, V0i: $i] : rewrite(((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b))) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b))))))))) <=> ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))))))))))))))))))),
% 12.22/12.40 inference(bind,[status(th)],[])).
% 12.22/12.40 tff(25,plain,
% 12.22/12.40 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b))) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.40 inference(quant_intro,[status(thm)],[24])).
% 12.22/12.40 tff(26,plain,
% 12.22/12.40 (^[A_27a: del, A_27b: del, V0i: $i] : rewrite(((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)))) & (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))) | (~mem(V4v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))) | (~mem(V18v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b))))))))) <=> ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b))) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b))))))))))),
% 12.22/12.40 inference(bind,[status(th)],[])).
% 12.22/12.40 tff(27,plain,
% 12.22/12.40 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)))) & (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))) | (~mem(V4v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))) | (~mem(V18v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b))) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)))))))))),
% 12.22/12.41 inference(quant_intro,[status(thm)],[26])).
% 12.22/12.41 tff(28,plain,
% 12.22/12.41 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))),
% 12.22/12.41 inference(rewrite,[status(thm)],[])).
% 12.22/12.41 tff(29,plain,
% 12.22/12.41 (^[A_27a: del, A_27b: del, V0i: $i] : trans(monotonicity(quant_intro(proof_bind(^[V1P: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))))), quant_intro(proof_bind(^[V6i: $i] : trans(monotonicity(quant_intro(proof_bind(^[V7P: $i] : trans(monotonicity(rewrite((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv))))) <=> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))), ((mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))) <=> (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))), rewrite((mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) <=> ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))), ((mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))) <=> ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))))), (![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))) <=> ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))), ((mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv))))))) <=> (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))))), rewrite((mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) <=> ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))), ((mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv))))))) <=> ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))))), (![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv))))))) <=> ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))))), ((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) <=> (((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b))))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))))), rewrite((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b))))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))))), ((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))))), quant_intro(proof_bind(^[V9i: $i] : trans(monotonicity(quant_intro(proof_bind(^[V10P: $i] : trans(monotonicity(rewrite((p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv)))))) <=> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))), ((mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))) <=> (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))), rewrite((mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) <=> ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))), ((mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))) <=> ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))))), (![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))) <=> ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))), ((mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv)))))))) <=> (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))))), rewrite((mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) <=> ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))), ((mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv)))))))) <=> ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))))), (![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv)))))))) <=> ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))))), (((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) <=> (((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))))), rewrite((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))))), (((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))))), quant_intro(proof_bind(^[V12i: $i] : trans(monotonicity(quant_intro(proof_bind(^[V13P: $i] : trans(monotonicity(rewrite((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv)))))) <=> (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))), ((mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))) <=> (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))), rewrite((mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))) <=> ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))), ((mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))) <=> ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))))), (![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))) <=> ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))), ((mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv)))))))) <=> (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))))), rewrite((mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) <=> ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))), ((mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv)))))))) <=> ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))))), (![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv)))))))) <=> ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))))), ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) <=> (((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))))), rewrite((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))))), ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))))), quant_intro(proof_bind(^[V16i: $i] : trans(monotonicity(quant_intro(proof_bind(^[V17P: $i] : trans(monotonicity(rewrite((p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))) <=> (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))), ((mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))) <=> (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))), rewrite((mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))) <=> ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))), ((mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))) <=> ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))), (![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))) <=> ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))), ((mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))))) <=> (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))), rewrite((mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))) <=> ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))), ((mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))))) <=> ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))), (![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))))) <=> ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))), (((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))))) <=> (((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))), rewrite((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b))))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))), (((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))))) <=> ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))), ((mem(V1P, arr(A_27b, bool)) => ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))))))) <=> (mem(V1P, arr(A_27b, bool)) => ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))), rewrite((mem(V1P, arr(A_27b, bool)) => ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))) <=> ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))), ((mem(V1P, arr(A_27b, bool)) => ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))))))) <=> ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))))), (![V1P: $i] : (mem(V1P, arr(A_27b, bool)) => ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))))))) <=> ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))), ((mem(V0i, arr(A_27a, A_27b)) => ![V1P: $i] : (mem(V1P, arr(A_27b, bool)) => ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))))))) <=> (mem(V0i, arr(A_27a, A_27b)) => ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))))), rewrite((mem(V0i, arr(A_27a, A_27b)) => ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b))))))))) <=> ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))), ((mem(V0i, arr(A_27a, A_27b)) => ![V1P: $i] : (mem(V1P, arr(A_27b, bool)) => ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))))))) <=> ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))))),
% 12.22/12.42 inference(bind,[status(th)],[])).
% 12.22/12.42 tff(30,plain,
% 12.22/12.42 (![A_27a: del, A_27b: del, V0i: $i] : (mem(V0i, arr(A_27a, A_27b)) => ![V1P: $i] : (mem(V1P, arr(A_27b, bool)) => ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))))))))))) <=> ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))),
% 12.22/12.42 inference(quant_intro,[status(thm)],[29])).
% 12.22/12.42 tff(31,axiom,(![A_27a: del, A_27b: del, V0i: $i] : (mem(V0i, arr(A_27a, A_27b)) => ![V1P: $i] : (mem(V1P, arr(A_27b, bool)) => ((((((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : (mem(V2v, A_27b) => (p(ap(V1P, V2v)) => ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (mem(V4v, A_27b) => ((~p(ap(V1P, V4v))) => ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))))))) & ![V6i: $i] : (mem(V6i, arr(A_27a, A_27b)) => ![V7P: $i] : (mem(V7P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : (mem(V8fv, A_27a) => p(ap(V7P, ap(V6i, V8fv)))))))) & ![V9i: $i] : (mem(V9i, arr(A_27a, A_27b)) => ![V10P: $i] : (mem(V10P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : (mem(V11fv, A_27a) => (~p(ap(V10P, ap(V9i, V11fv))))))))) & ![V12i: $i] : (mem(V12i, arr(A_27a, A_27b)) => ![V13P: $i] : (mem(V13P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (mem(V14v, A_27b) => (p(ap(V13P, V14v)) => ?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))))))))) & ![V16i: $i] : (mem(V16i, arr(A_27a, A_27b)) => ![V17P: $i] : (mem(V17P, arr(A_27b, bool)) => (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (mem(V18v, A_27b) => ((~p(ap(V17P, V18v))) => ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','conj_thm_2EquantHeuristics_2EGUESS__REWRITES')).
% 12.22/12.42 tff(32,plain,
% 12.22/12.42 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))),
% 12.22/12.42 inference(modus_ponens,[status(thm)],[31, 30])).
% 12.22/12.42 tff(33,plain,
% 12.22/12.42 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) <=> ![V2v: $i] : ((~p(ap(V1P, V2v))) | ?[V3fv: $i] : (mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv)))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) <=> ![V4v: $i] : (p(ap(V1P, V4v)) | ?[V5fv: $i] : (mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv))))) | (~mem(V4v, A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) <=> ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) <=> ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) <=> ![V14v: $i] : (?[V15fv: $i] : (mem(V15fv, A_27a) & (V14v = ap(V12i, V15fv))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) <=> ![V18v: $i] : (p(ap(V17P, V18v)) | ?[V19fv: $i] : (mem(V19fv, A_27a) & (V18v = ap(V16i, V19fv))) | (~mem(V18v, A_27b)))))))))),
% 12.22/12.42 inference(modus_ponens,[status(thm)],[32, 28])).
% 12.22/12.42 tff(34,plain,(
% 12.22/12.42 ![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | ((((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))) | (~mem(V2v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)))) & (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))) | (~mem(V4v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))) | (~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))) | (~mem(V18v, A_27b)))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)))))))))),
% 12.22/12.42 inference(skolemize,[status(sab)],[33])).
% 12.22/12.42 tff(35,plain,
% 12.22/12.42 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a) & p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a))) & ![V3fv: $i] : (~(mem(V3fv, A_27a) & p(ap(V1P, ap(V0i, V3fv))))) & mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b))) & ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a) & (~p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a)))))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | ((~p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a)))) & ![V5fv: $i] : (~(mem(V5fv, A_27a) & (~p(ap(V1P, ap(V0i, V5fv)))))) & mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b))) & ![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a)))))))))) & ![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a))))))))))) & ![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a) & (V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (![V15fv: $i] : (~(mem(V15fv, A_27a) & (tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))) & p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a))) & mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)))))) & ![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a) & (V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a)))))) & (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | ((~p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a)))) & ![V19fv: $i] : (~(mem(V19fv, A_27a) & (tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv)))) & mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)))))))))),
% 12.22/12.42 inference(modus_ponens,[status(thm)],[34, 27])).
% 12.22/12.42 tff(36,plain,
% 12.22/12.42 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.42 inference(modus_ponens,[status(thm)],[35, 25])).
% 12.22/12.42 tff(37,plain,
% 12.22/12.42 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.42 inference(modus_ponens,[status(thm)],[36, 23])).
% 12.22/12.42 tff(38,plain,
% 12.22/12.42 (![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))),
% 12.22/12.42 inference(modus_ponens,[status(thm)],[37, 18])).
% 12.22/12.42 tff(39,plain,
% 12.22/12.42 (((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))))))))))))) <=> ((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | (~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))))))))))))),
% 12.22/12.43 inference(rewrite,[status(thm)],[])).
% 12.22/12.43 tff(40,plain,
% 12.22/12.43 (((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv)))))))))))))))))) <=> ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))))))))))))),
% 12.22/12.43 inference(rewrite,[status(thm)],[])).
% 12.22/12.43 tff(41,plain,
% 12.22/12.43 (((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))))))))))))) <=> ((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))))),
% 12.28/12.43 inference(monotonicity,[status(thm)],[40])).
% 12.28/12.43 tff(42,plain,
% 12.28/12.43 (((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))))))))))))) <=> ((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | (~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))))))))))))),
% 12.28/12.44 inference(transitivity,[status(thm)],[41, 39])).
% 12.28/12.44 tff(43,plain,
% 12.28/12.44 ((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))))))))))))),
% 12.28/12.44 inference(quant_inst,[status(thm)],[])).
% 12.28/12.44 tff(44,plain,
% 12.28/12.44 ((~![A_27a: del, A_27b: del, V0i: $i] : ((~mem(V0i, arr(A_27a, A_27b))) | ![V1P: $i] : ((~mem(V1P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27b)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i, A_27a), A_27a)) | (~p(ap(V1P, ap(V0i, tptp_fun_V3fv_3(V1P, V0i, A_27a)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27b)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i, A_27a), A_27a)) | p(ap(V1P, ap(V0i, tptp_fun_V5fv_5(V1P, V0i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a), A_27b)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i, A_27b, A_27a)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27a)) | (~p(ap(V1P, ap(V0i, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a, A_27b), V0i), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a), A_27b)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i, A_27b, A_27a))) | (~![V5fv: $i] : ((~mem(V5fv, A_27a)) | p(ap(V1P, ap(V0i, V5fv))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27a, A_27b))) | ![V7P: $i] : ((~mem(V7P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27a)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a, A_27b), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27a), A_27a)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27a))))))))))))) | (~![V9i: $i] : ((~mem(V9i, arr(A_27a, A_27b))) | ![V10P: $i] : ((~mem(V10P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27a)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a, A_27b), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27a), A_27a)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27a)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27a, A_27b))) | ![V13P: $i] : ((~mem(V13P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27b)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27a), A_27a)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a, A_27b), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a), A_27b)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27a)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27b, A_27a) = ap(V12i, V15fv)))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27a, A_27b))) | ![V17P: $i] : ((~mem(V17P, arr(A_27b, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27b)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27a), A_27a)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27a))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a, A_27b), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a), A_27b)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a))) | (~![V19fv: $i] : ((~mem(V19fv, A_27a)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27b, A_27a) = ap(V16i, V19fv))))))))))))))))))) | (~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))),
% 12.28/12.44 inference(modus_ponens,[status(thm)],[43, 42])).
% 12.28/12.44 tff(45,plain,
% 12.28/12.44 (![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))),
% 12.28/12.44 inference(unit_resolution,[status(thm)],[44, 38, 16])).
% 12.28/12.44 tff(46,plain,
% 12.28/12.44 (mem(V1P!16, arr(A_27a!15, bool))),
% 12.28/12.44 inference(and_elim,[status(thm)],[15])).
% 12.28/12.44 tff(47,plain,
% 12.28/12.44 (((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))))))) <=> ((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | (~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))))))),
% 12.28/12.45 inference(rewrite,[status(thm)],[])).
% 12.28/12.45 tff(48,plain,
% 12.28/12.45 (((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : (p(ap(V1P!16, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~p(ap(V1P!16, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14))))))))))))))))) <=> ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))))))),
% 12.28/12.45 inference(rewrite,[status(thm)],[])).
% 12.28/12.45 tff(49,plain,
% 12.28/12.45 (((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : (p(ap(V1P!16, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~p(ap(V1P!16, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) <=> ((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14))))))))))))))),
% 12.30/12.46 inference(monotonicity,[status(thm)],[48])).
% 12.30/12.46 tff(50,plain,
% 12.30/12.46 (((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : (p(ap(V1P!16, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~p(ap(V1P!16, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) <=> ((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | (~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))))))),
% 12.30/12.46 inference(transitivity,[status(thm)],[49, 47])).
% 12.30/12.46 tff(51,plain,
% 12.30/12.46 ((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : (p(ap(V1P!16, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~p(ap(V1P!16, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))),
% 12.30/12.47 inference(quant_inst,[status(thm)],[])).
% 12.30/12.47 tff(52,plain,
% 12.30/12.47 ((~![V1P: $i] : ((~mem(V1P, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P, tptp_fun_V4v_6(V1P, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P, ap(V0i!13, V5fv))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P)) | (~((~mem(tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P, tptp_fun_V2v_4(V1P, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P, ap(V0i!13, V3fv)))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V4v: $i] : (p(ap(V1P, V4v)) | (~mem(V4v, A_27a!15)) | (~((~mem(tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P, ap(V0i!13, tptp_fun_V5fv_5(V1P, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P))) | ![V2v: $i] : ((~p(ap(V1P, V2v))) | (~mem(V2v, A_27a!15)) | (~((~mem(tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P, ap(V0i!13, tptp_fun_V3fv_3(V1P, V0i!13, A_27b!14)))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))))))) | (~mem(V1P!16, arr(A_27a!15, bool))) | (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14))))))))))))),
% 12.30/12.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 12.30/12.47 tff(53,plain,
% 12.30/12.47 (~((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14)))))))))))),
% 12.30/12.47 inference(unit_resolution,[status(thm)],[52, 46, 45])).
% 12.30/12.47 tff(54,plain,
% 12.30/12.47 (((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~![V6i: $i] : ((~mem(V6i, arr(A_27b!14, A_27a!15))) | ![V7P: $i] : ((~mem(V7P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P))) | ![V8fv: $i] : ((~mem(V8fv, A_27b!14)) | p(ap(V7P, ap(V6i, V8fv)))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27b!14, A_27a!15), V6i), V7P)) | (~((~mem(tptp_fun_V8fv_7(V7P, V6i, A_27b!14), A_27b!14)) | p(ap(V7P, ap(V6i, tptp_fun_V8fv_7(V7P, V6i, A_27b!14))))))))))))) | (~![V16i: $i] : ((~mem(V16i, arr(A_27b!14, A_27a!15))) | ![V17P: $i] : ((~mem(V17P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P)) | (~((~mem(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V17P, tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14))) | (~![V19fv: $i] : ((~mem(V19fv, A_27b!14)) | (~(tptp_fun_V18v_12(V17P, V16i, A_27a!15, A_27b!14) = ap(V16i, V19fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27b!14, A_27a!15), V16i), V17P))) | ![V18v: $i] : (p(ap(V17P, V18v)) | (~mem(V18v, A_27a!15)) | (~((~mem(tptp_fun_V19fv_11(V18v, V16i, A_27b!14), A_27b!14)) | (~(V18v = ap(V16i, tptp_fun_V19fv_11(V18v, V16i, A_27b!14)))))))))))))) | (~![V12i: $i] : ((~mem(V12i, arr(A_27b!14, A_27a!15))) | ![V13P: $i] : ((~mem(V13P, arr(A_27a!15, bool))) | (~((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P)) | (~((~mem(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V13P, tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14)))) | (~![V15fv: $i] : ((~mem(V15fv, A_27b!14)) | (~(tptp_fun_V14v_10(V13P, V12i, A_27a!15, A_27b!14) = ap(V12i, V15fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27b!14, A_27a!15), V12i), V13P))) | ![V14v: $i] : ((~p(ap(V13P, V14v))) | (~mem(V14v, A_27a!15)) | (~((~mem(tptp_fun_V15fv_9(V14v, V12i, A_27b!14), A_27b!14)) | (~(V14v = ap(V12i, tptp_fun_V15fv_9(V14v, V12i, A_27b!14)))))))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | (~p(ap(V1P!16, tptp_fun_V2v_4(V1P!16, V0i!13, A_27a!15, A_27b!14)))) | (~![V3fv: $i] : ((~mem(V3fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V3fv)))))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14), A_27a!15)) | p(ap(V1P!16, tptp_fun_V4v_6(V1P!16, V0i!13, A_27a!15, A_27b!14))) | (~![V5fv: $i] : ((~mem(V5fv, A_27b!14)) | p(ap(V1P!16, ap(V0i!13, V5fv))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V4v: $i] : ((~mem(V4v, A_27a!15)) | p(ap(V1P!16, V4v)) | (~((~mem(tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14), A_27b!14)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V5fv_5(V1P!16, V0i!13, A_27b!14))))))))) | (~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V2v: $i] : ((~mem(V2v, A_27a!15)) | (~p(ap(V1P!16, V2v))) | (~((~mem(tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V3fv_3(V1P!16, V0i!13, A_27b!14))))))))))) | ![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))),
% 12.30/12.47 inference(tautology,[status(thm)],[])).
% 12.30/12.47 tff(55,plain,
% 12.30/12.47 (![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))),
% 12.30/12.47 inference(unit_resolution,[status(thm)],[54, 53])).
% 12.30/12.47 tff(56,plain,
% 12.30/12.47 (((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14)))))))))))))) <=> ((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14)))))))))))))),
% 12.30/12.47 inference(rewrite,[status(thm)],[])).
% 12.30/12.47 tff(57,plain,
% 12.30/12.47 ((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14)))))))))))))),
% 12.30/12.47 inference(quant_inst,[status(thm)],[])).
% 12.30/12.47 tff(58,plain,
% 12.30/12.47 ((~![V9i: $i] : ((~mem(V9i, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V9i, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V9i), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V9i, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V9i, tptp_fun_V11fv_8(V10P, V9i, A_27b!14)))))))))))))) | (~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))),
% 12.30/12.47 inference(modus_ponens,[status(thm)],[57, 56])).
% 12.30/12.47 tff(59,plain,
% 12.30/12.47 (![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))),
% 12.30/12.47 inference(unit_resolution,[status(thm)],[58, 16, 55])).
% 12.30/12.47 tff(60,plain,
% 12.30/12.47 (mem(V2Q!17, arr(A_27a!15, bool))),
% 12.30/12.47 inference(and_elim,[status(thm)],[15])).
% 12.30/12.47 tff(61,plain,
% 12.30/12.47 (((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | ((~mem(V2Q!17, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))))))))) <=> ((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | (~mem(V2Q!17, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))))))))),
% 12.30/12.47 inference(rewrite,[status(thm)],[])).
% 12.30/12.47 tff(62,plain,
% 12.30/12.47 ((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | ((~mem(V2Q!17, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))))))))),
% 12.30/12.47 inference(quant_inst,[status(thm)],[])).
% 12.30/12.47 tff(63,plain,
% 12.30/12.47 ((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | (~mem(V2Q!17, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))))))))),
% 12.30/12.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 12.30/12.47 tff(64,plain,
% 12.30/12.47 (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))))))),
% 12.30/12.47 inference(unit_resolution,[status(thm)],[63, 60, 59])).
% 12.30/12.47 tff(65,plain,
% 12.30/12.47 (((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))))))) | (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))))),
% 12.30/12.47 inference(tautology,[status(thm)],[])).
% 12.30/12.47 tff(66,plain,
% 12.30/12.47 (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))))),
% 12.30/12.47 inference(unit_resolution,[status(thm)],[65, 64])).
% 12.30/12.47 tff(67,plain,
% 12.30/12.47 (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17))),
% 12.30/12.47 inference(and_elim,[status(thm)],[15])).
% 12.30/12.47 tff(68,plain,
% 12.30/12.47 ((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))))) | p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))))),
% 12.30/12.47 inference(tautology,[status(thm)],[])).
% 12.30/12.47 tff(69,plain,
% 12.30/12.47 ((~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V2Q!17)) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))))) | (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))))),
% 12.30/12.47 inference(unit_resolution,[status(thm)],[68, 67])).
% 12.30/12.47 tff(70,plain,
% 12.30/12.47 (~((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[69, 66])).
% 12.30/12.48 tff(71,plain,
% 12.30/12.48 (((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))) | mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)),
% 12.30/12.48 inference(tautology,[status(thm)],[])).
% 12.30/12.48 tff(72,plain,
% 12.30/12.48 (mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[71, 70])).
% 12.30/12.48 tff(73,plain,
% 12.30/12.48 (((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14))))))))))))) <=> ((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | (~mem(V1P!16, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14))))))))))))),
% 12.30/12.48 inference(rewrite,[status(thm)],[])).
% 12.30/12.48 tff(74,plain,
% 12.30/12.48 ((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | ((~mem(V1P!16, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14))))))))))))),
% 12.30/12.48 inference(quant_inst,[status(thm)],[])).
% 12.30/12.48 tff(75,plain,
% 12.30/12.48 ((~![V10P: $i] : ((~mem(V10P, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V10P, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V10P)) | (~((~mem(tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V10P, ap(V0i!13, tptp_fun_V11fv_8(V10P, V0i!13, A_27b!14))))))))))))) | (~mem(V1P!16, arr(A_27a!15, bool))) | (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14)))))))))))),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[74, 73])).
% 12.30/12.48 tff(76,plain,
% 12.30/12.48 (~((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14))))))))))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[75, 46, 59])).
% 12.30/12.48 tff(77,plain,
% 12.30/12.48 (((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | (~(p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16)) | (~((~mem(tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V1P!16, V0i!13, A_27b!14)))))))))) | ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))),
% 12.30/12.48 inference(tautology,[status(thm)],[])).
% 12.30/12.48 tff(78,plain,
% 12.30/12.48 ((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[77, 76])).
% 12.30/12.48 tff(79,plain,
% 12.30/12.48 (p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))),
% 12.30/12.48 inference(and_elim,[status(thm)],[15])).
% 12.30/12.48 tff(80,plain,
% 12.30/12.48 ((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | (~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))),
% 12.30/12.48 inference(tautology,[status(thm)],[])).
% 12.30/12.48 tff(81,plain,
% 12.30/12.48 ((~((~p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b!14, A_27a!15), V0i!13), V1P!16))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv))))))) | ![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[80, 79])).
% 12.30/12.48 tff(82,plain,
% 12.30/12.48 (![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[81, 78])).
% 12.30/12.48 tff(83,plain,
% 12.30/12.48 (((~![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))) | ((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))) <=> ((~![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))) | (~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))),
% 12.30/12.48 inference(rewrite,[status(thm)],[])).
% 12.30/12.48 tff(84,plain,
% 12.30/12.48 ((~![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))) | ((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))),
% 12.30/12.48 inference(quant_inst,[status(thm)],[])).
% 12.30/12.48 tff(85,plain,
% 12.30/12.48 ((~![V11fv: $i] : ((~mem(V11fv, A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, V11fv)))))) | (~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[84, 83])).
% 12.30/12.48 tff(86,plain,
% 12.30/12.48 (~p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[85, 82, 72])).
% 12.30/12.48 tff(87,plain,
% 12.30/12.48 (^[A: del, B: del, F: $i] : refl(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 12.30/12.48 inference(bind,[status(th)],[])).
% 12.30/12.48 tff(88,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(quant_intro,[status(thm)],[87])).
% 12.30/12.48 tff(89,plain,
% 12.30/12.48 (^[A: del, B: del, F: $i] : rewrite(((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))),
% 12.30/12.48 inference(bind,[status(th)],[])).
% 12.30/12.48 tff(90,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(quant_intro,[status(thm)],[89])).
% 12.30/12.48 tff(91,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(transitivity,[status(thm)],[90, 88])).
% 12.30/12.48 tff(92,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(rewrite,[status(thm)],[])).
% 12.30/12.48 tff(93,plain,
% 12.30/12.48 (^[A: del, B: del, F: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite((mem(X, A) => mem(ap(F, X), B)) <=> ((~mem(X, A)) | mem(ap(F, X), B)))), (![X: $i] : (mem(X, A) => mem(ap(F, X), B)) <=> ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> (mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))))), rewrite((mem(F, arr(A, B)) => ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))), ((mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))))),
% 12.30/12.48 inference(bind,[status(th)],[])).
% 12.30/12.48 tff(94,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B))) <=> ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(quant_intro,[status(thm)],[93])).
% 12.30/12.48 tff(95,axiom,(![A: del, B: del, F: $i] : (mem(F, arr(A, B)) => ![X: $i] : (mem(X, A) => mem(ap(F, X), B)))), file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001_2.ax','ap_tp')).
% 12.30/12.48 tff(96,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[95, 94])).
% 12.30/12.48 tff(97,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[96, 92])).
% 12.30/12.48 tff(98,plain,(
% 12.30/12.48 ![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(skolemize,[status(sab)],[97])).
% 12.30/12.48 tff(99,plain,
% 12.30/12.48 (![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[98, 91])).
% 12.30/12.48 tff(100,plain,
% 12.30/12.48 (((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15)))) <=> ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15)))),
% 12.30/12.48 inference(rewrite,[status(thm)],[])).
% 12.30/12.48 tff(101,plain,
% 12.30/12.48 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | ((~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15)))),
% 12.30/12.48 inference(quant_inst,[status(thm)],[])).
% 12.30/12.48 tff(102,plain,
% 12.30/12.48 ((~![A: del, B: del, F: $i] : ((~mem(F, arr(A, B))) | ![X: $i] : ((~mem(X, A)) | mem(ap(F, X), B)))) | (~mem(V0i!13, arr(A_27b!14, A_27a!15))) | ![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15))),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[101, 100])).
% 12.30/12.48 tff(103,plain,
% 12.30/12.48 (![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[102, 99, 16])).
% 12.30/12.48 tff(104,plain,
% 12.30/12.48 (((~![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15))) | ((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15))) <=> ((~![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15))) | (~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15))),
% 12.30/12.48 inference(rewrite,[status(thm)],[])).
% 12.30/12.48 tff(105,plain,
% 12.30/12.48 ((~![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15))) | ((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15))),
% 12.30/12.48 inference(quant_inst,[status(thm)],[])).
% 12.30/12.48 tff(106,plain,
% 12.30/12.48 ((~![X: $i] : ((~mem(X, A_27b!14)) | mem(ap(V0i!13, X), A_27a!15))) | (~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15)),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[105, 104])).
% 12.30/12.48 tff(107,plain,
% 12.30/12.48 (mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15)),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[106, 103, 72])).
% 12.30/12.48 tff(108,plain,
% 12.30/12.48 (((~mem(tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14), A_27b!14)) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))) | p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))),
% 12.30/12.48 inference(tautology,[status(thm)],[])).
% 12.30/12.48 tff(109,plain,
% 12.30/12.48 (p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))),
% 12.30/12.48 inference(unit_resolution,[status(thm)],[108, 70])).
% 12.30/12.48 tff(110,plain,
% 12.30/12.48 (^[V3x: $i] : refl(((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))) <=> ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))))),
% 12.30/12.48 inference(bind,[status(th)],[])).
% 12.30/12.48 tff(111,plain,
% 12.30/12.48 (![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x)))) <=> ![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))),
% 12.30/12.48 inference(quant_intro,[status(thm)],[110])).
% 12.30/12.48 tff(112,plain,
% 12.30/12.48 (![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))),
% 12.30/12.48 inference(and_elim,[status(thm)],[15])).
% 12.30/12.48 tff(113,plain,
% 12.30/12.48 (![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))),
% 12.30/12.48 inference(modus_ponens,[status(thm)],[112, 111])).
% 12.30/12.48 tff(114,plain,
% 12.30/12.48 (((~![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))) | ((~mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))) <=> ((~![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))) | (~mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))),
% 12.37/12.53 inference(rewrite,[status(thm)],[])).
% 12.37/12.53 tff(115,plain,
% 12.37/12.53 ((~![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))) | ((~mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14))))))),
% 12.37/12.53 inference(quant_inst,[status(thm)],[])).
% 12.37/12.53 tff(116,plain,
% 12.37/12.53 ((~![V3x: $i] : ((~mem(V3x, A_27a!15)) | p(ap(V1P!16, V3x)) | (~p(ap(V2Q!17, V3x))))) | (~mem(ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)), A_27a!15)) | p(ap(V1P!16, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))) | (~p(ap(V2Q!17, ap(V0i!13, tptp_fun_V11fv_8(V2Q!17, V0i!13, A_27b!14)))))),
% 12.37/12.53 inference(modus_ponens,[status(thm)],[115, 114])).
% 12.37/12.53 tff(117,plain,
% 12.37/12.53 ($false),
% 12.37/12.53 inference(unit_resolution,[status(thm)],[116, 113, 109, 107, 86])).
% 12.37/12.53 % SZS output end Proof
% 12.37/12.54 % E exiting
%------------------------------------------------------------------------------