%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL106-2 : TPTP v9.0.0. Released v3.2.0.
% 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 05:00:50 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : COL106-2 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Jun 19 12:17:11 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% 0.21/0.39 tff(c_in_type, type, (
% 0.21/0.39 c_in: ( $i * $i * $i ) > $o)).
% 0.21/0.39 tff(tc_prod_type, type, (
% 0.21/0.39 tc_prod: ( $i * $i ) > $i)).
% 0.21/0.39 tff(tc_Comb_Ocomb_type, type, (
% 0.21/0.39 tc_Comb_Ocomb: $i)).
% 0.21/0.39 tff(c_Comb_Oparcontract_type, type, (
% 0.21/0.39 c_Comb_Oparcontract: $i)).
% 0.21/0.39 tff(c_Pair_type, type, (
% 0.21/0.39 c_Pair: ( $i * $i * $i * $i ) > $i)).
% 0.21/0.39 tff(v_sko__uTE_type, type, (
% 0.21/0.39 v_sko__uTE: ( $i * $i ) > $i)).
% 0.21/0.39 tff(v_sko__uTI_type, type, (
% 0.21/0.39 v_sko__uTI: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(v_xb_type, type, (
% 0.21/0.39 v_xb: $i)).
% 0.21/0.39 tff(v_ya_type, type, (
% 0.21/0.39 v_ya: $i)).
% 0.21/0.39 tff(c_Comb_Ocomb_Oop_A_D_D_type, type, (
% 0.21/0.39 c_Comb_Ocomb_Oop_A_D_D: ( $i * $i ) > $i)).
% 0.21/0.39 tff(v_x_type, type, (
% 0.21/0.39 v_x: $i)).
% 0.21/0.39 tff(c_Comb_Ocomb_OK_type, type, (
% 0.21/0.39 c_Comb_Ocomb_OK: $i)).
% 0.21/0.39 tff(v_sko__uTG_type, type, (
% 0.21/0.39 v_sko__uTG: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(v_sko__uTF_type, type, (
% 0.21/0.39 v_sko__uTF: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(c_Comb_Ocomb_OS_type, type, (
% 0.21/0.39 c_Comb_Ocomb_OS: $i)).
% 0.21/0.39 tff(v_sko__uTH_type, type, (
% 0.21/0.39 v_sko__uTH: ( $i * $i * $i ) > $i)).
% 0.21/0.39 tff(1,assumption,(~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), introduced(assumption)).
% 0.21/0.39 tff(2,plain,
% 0.21/0.39 (^[V_x: $i] : refl(c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.39 inference(bind,[status(th)],[])).
% 0.21/0.39 tff(3,plain,
% 0.21/0.39 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.39 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.39 tff(4,plain,
% 0.21/0.39 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.39 inference(rewrite,[status(thm)],[])).
% 0.21/0.39 tff(5,axiom,(![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Oparcontract_Ointros__1_0')).
% 0.21/0.39 tff(6,plain,
% 0.21/0.39 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.39 tff(7,plain,(
% 0.21/0.39 ![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.39 inference(skolemize,[status(sab)],[6])).
% 0.21/0.39 tff(8,plain,
% 0.21/0.39 (![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.39 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.21/0.39 tff(9,plain,
% 0.21/0.39 ((~![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(10,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.21/0.39 tff(11,plain,(c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.39 tff(12,assumption,(~c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), introduced(assumption)).
% 0.21/0.39 tff(13,plain,
% 0.21/0.39 ((~![V_x: $i] : c_in(c_Pair(V_x, V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.39 inference(quant_inst,[status(thm)],[])).
% 0.21/0.39 tff(14,plain,
% 0.21/0.39 ($false),
% 0.21/0.39 inference(unit_resolution,[status(thm)],[13, 8, 12])).
% 0.21/0.40 tff(15,plain,(c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.40 tff(16,plain,
% 0.21/0.40 (^[V_x: $i, V_w: $i, V_z: $i, V_y: $i] : refl((c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(17,plain,
% 0.21/0.40 (![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.21/0.40 tff(18,plain,
% 0.21/0.40 (![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(19,plain,
% 0.21/0.40 (^[V_x: $i, V_w: $i, V_z: $i, V_y: $i] : rewrite((((~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(20,plain,
% 0.21/0.40 (![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (((~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[19])).
% 0.21/0.40 tff(21,axiom,(![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (((~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Oparcontract_Ointros__4_0')).
% 0.21/0.40 tff(22,plain,
% 0.21/0.40 (![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.21/0.40 tff(23,plain,
% 0.21/0.40 (![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.40 tff(24,plain,(
% 0.21/0.40 ![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[23])).
% 0.21/0.40 tff(25,plain,
% 0.21/0.40 (![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.21/0.40 tff(26,plain,
% 0.21/0.40 (((~![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) <=> ((~![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(27,plain,
% 0.21/0.40 ((~![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.40 inference(quant_inst,[status(thm)],[])).
% 0.21/0.40 tff(28,plain,
% 0.21/0.40 ((~![V_x: $i, V_w: $i, V_z: $i, V_y: $i] : (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_x, V_z), c_Comb_Ocomb_Oop_A_D_D(V_y, V_w), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(V_x, V_y, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(V_z, V_w, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.21/0.40 tff(29,plain,
% 0.21/0.40 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) | (~c_in(c_Pair(c_Comb_Ocomb_OK, c_Comb_Ocomb_OK, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.21/0.40 tff(30,plain,
% 0.21/0.40 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.40 inference(unit_resolution,[status(thm)],[29, 15, 11])).
% 0.21/0.40 tff(31,plain,
% 0.21/0.40 (^[V_x: $i, V_z: $i] : refl(((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))) <=> ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))))),
% 0.21/0.40 inference(bind,[status(th)],[])).
% 0.21/0.40 tff(32,plain,
% 0.21/0.40 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.21/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.40 tff(33,plain,
% 0.21/0.40 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z)))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.21/0.40 inference(rewrite,[status(thm)],[])).
% 0.21/0.40 tff(34,axiom,(![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OK1__parcontractD__dest_0')).
% 0.21/0.40 tff(35,plain,
% 0.21/0.40 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.40 tff(36,plain,(
% 0.21/0.40 ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.21/0.40 inference(skolemize,[status(sab)],[35])).
% 0.21/0.40 tff(37,plain,
% 0.21/0.40 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))),
% 0.21/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.40 tff(38,plain,
% 0.21/0.40 (((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)))))) <=> ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(40,plain,
% 0.21/0.41 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.41 tff(41,plain,
% 0.21/0.41 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[40, 37, 30])).
% 0.21/0.41 tff(42,plain,
% 0.21/0.41 (^[V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : refl(((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)) <=> ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(43,plain,
% 0.21/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[42])).
% 0.21/0.41 tff(44,plain,
% 0.21/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(45,axiom,(![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Ocomb_Oinject__iff1_1')).
% 0.21/0.41 tff(46,plain,
% 0.21/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.41 tff(47,plain,(
% 0.21/0.41 ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.21/0.41 inference(skolemize,[status(sab)],[46])).
% 0.21/0.41 tff(48,plain,
% 0.21/0.41 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.41 tff(49,plain,
% 0.21/0.41 (((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))) | (v_x = v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))) <=> ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))) | (v_x = v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(50,plain,
% 0.21/0.41 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))) | (v_x = v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(51,plain,
% 0.21/0.41 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))))) | (v_x = v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.41 tff(52,plain,
% 0.21/0.41 (v_x = v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[51, 48, 41])).
% 0.21/0.41 tff(53,plain,
% 0.21/0.41 (c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[52])).
% 0.21/0.41 tff(54,plain,
% 0.21/0.41 (c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.41 tff(55,plain,
% 0.21/0.41 (c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.41 inference(symmetry,[status(thm)],[54])).
% 0.21/0.41 tff(56,plain,
% 0.21/0.41 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)),
% 0.21/0.41 inference(symmetry,[status(thm)],[41])).
% 0.21/0.41 tff(57,plain,
% 0.21/0.41 (c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.41 tff(58,plain,
% 0.21/0.41 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.41 tff(59,plain,
% 0.21/0.41 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.41 inference(symmetry,[status(thm)],[58])).
% 0.21/0.41 tff(60,plain,
% 0.21/0.41 ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) <=> (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.41 tff(61,plain,
% 0.21/0.41 ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) <=> (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[60])).
% 0.21/0.41 tff(62,assumption,(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)), introduced(assumption)).
% 0.21/0.41 tff(63,plain,
% 0.21/0.41 (v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)) = v_x),
% 0.21/0.41 inference(symmetry,[status(thm)],[52])).
% 0.21/0.41 tff(64,assumption,(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)) = v_xb), introduced(assumption)).
% 0.21/0.41 tff(65,plain,
% 0.21/0.41 (v_xb = v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))),
% 0.21/0.41 inference(symmetry,[status(thm)],[64])).
% 0.21/0.41 tff(66,plain,
% 0.21/0.41 (v_xb = v_x),
% 0.21/0.41 inference(transitivity,[status(thm)],[65, 63])).
% 0.21/0.41 tff(67,plain,
% 0.21/0.41 (c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.21/0.41 inference(monotonicity,[status(thm)],[66, 63])).
% 0.21/0.41 tff(68,plain,
% 0.21/0.41 (c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.41 tff(69,plain,
% 0.21/0.41 (c_in(c_Pair(v_x, v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.41 inference(symmetry,[status(thm)],[68])).
% 0.21/0.41 tff(70,plain,
% 0.21/0.41 (c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[11, 69])).
% 0.21/0.41 tff(71,plain,
% 0.21/0.41 (^[V_x: $i, V_z: $i] : refl(((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(72,plain,
% 0.21/0.41 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.41 tff(73,plain,
% 0.21/0.41 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(74,axiom,(![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OK1__parcontractD__dest_1')).
% 0.21/0.41 tff(75,plain,
% 0.21/0.41 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.41 tff(76,plain,(
% 0.21/0.41 ![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.41 inference(skolemize,[status(sab)],[75])).
% 0.21/0.41 tff(77,plain,
% 0.21/0.41 (![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.21/0.41 tff(78,plain,
% 0.21/0.41 (((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(80,plain,
% 0.21/0.42 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[80, 77, 30])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (^[V_U: $i] : refl(((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(83,plain,
% 0.21/0.42 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[82])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 (^[V_U: $i] : rewrite(((~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 (![V_U: $i] : ((~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[85])).
% 0.21/0.42 tff(87,axiom,(![V_U: $i] : ((~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 0.21/0.42 tff(88,plain,
% 0.21/0.42 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.42 tff(89,plain,
% 0.21/0.42 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.21/0.42 tff(90,plain,(
% 0.21/0.42 ![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[89])).
% 0.21/0.42 tff(91,plain,
% 0.21/0.42 (![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.21/0.42 tff(92,plain,
% 0.21/0.42 (((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) <=> ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(93,plain,
% 0.21/0.42 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(94,plain,
% 0.21/0.42 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.42 tff(95,plain,
% 0.21/0.42 (~c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[94, 91, 81])).
% 0.21/0.42 tff(96,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[95, 70])).
% 0.21/0.42 tff(97,plain,(~(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)) = v_xb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(98,plain,
% 0.21/0.42 (((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)) = v_xb))) <=> ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)) = v_xb))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(99,plain,
% 0.21/0.42 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)) = v_xb))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(100,plain,
% 0.21/0.42 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb2 = V_comb2_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))) | (v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)) = v_xb)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.21/0.42 tff(101,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[100, 48, 97, 62])).
% 0.21/0.42 tff(102,plain,(~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.42 tff(103,plain,
% 0.21/0.42 (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[102, 61])).
% 0.21/0.42 tff(104,assumption,(v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)), introduced(assumption)).
% 0.21/0.42 tff(105,plain,
% 0.21/0.42 (c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[104, 63])).
% 0.21/0.42 tff(106,plain,
% 0.21/0.42 (c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[105])).
% 0.21/0.42 tff(107,plain,
% 0.21/0.42 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.42 inference(symmetry,[status(thm)],[106])).
% 0.21/0.42 tff(108,plain,
% 0.21/0.42 (^[V_x: $i, V_y: $i] : refl(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(109,plain,
% 0.21/0.42 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[108])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> ![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(111,axiom,(![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Oparcontract_Ointros__2_0')).
% 0.21/0.43 tff(112,plain,
% 0.21/0.43 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.21/0.43 tff(113,plain,(
% 0.21/0.43 ![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(skolemize,[status(sab)],[112])).
% 0.21/0.43 tff(114,plain,
% 0.21/0.43 (![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.21/0.43 tff(115,plain,
% 0.21/0.43 ((~![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(116,plain,
% 0.21/0.43 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.21/0.43 tff(117,plain,
% 0.21/0.43 (c_in(c_Pair(v_xb, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[116, 107])).
% 0.21/0.43 tff(118,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[95, 117])).
% 0.21/0.43 tff(119,plain,(~(v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(120,plain,
% 0.21/0.43 ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) <=> (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[56])).
% 0.21/0.43 tff(121,plain,
% 0.21/0.43 ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) <=> (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[120])).
% 0.21/0.43 tff(122,assumption,(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), introduced(assumption)).
% 0.21/0.43 tff(123,assumption,(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), introduced(assumption)).
% 0.21/0.43 tff(124,plain,
% 0.21/0.43 (^[V_comb1_H: $i, V_comb2_H: $i] : refl((~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) <=> (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(125,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) <=> ![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[124])).
% 0.21/0.43 tff(126,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) <=> ![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(127,axiom,(![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Ocomb_Odistinct__3__iff1_0')).
% 0.21/0.43 tff(128,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.43 tff(129,plain,(
% 0.21/0.43 ![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[128])).
% 0.21/0.43 tff(130,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.21/0.43 tff(131,plain,
% 0.21/0.43 ((~![V_comb1_H: $i, V_comb2_H: $i] : (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H)))) | (~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(132,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[131, 130, 123])).
% 0.21/0.43 tff(133,plain,(~(c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(134,plain,
% 0.21/0.43 (^[V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : refl(((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)) <=> ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(135,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.43 tff(136,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H)) <=> ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(137,axiom,(![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_Ocomb_Oinject__iff1_0')).
% 0.21/0.43 tff(138,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.21/0.43 tff(139,plain,(
% 0.21/0.43 ![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.21/0.43 inference(skolemize,[status(sab)],[138])).
% 0.21/0.43 tff(140,plain,
% 0.21/0.43 (![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.21/0.43 tff(141,plain,
% 0.21/0.43 (((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))) <=> ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(142,plain,
% 0.21/0.43 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | ((~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(143,plain,
% 0.21/0.43 ((~![V_comb1_H: $i, V_comb2_H: $i, V_comb1: $i, V_comb2: $i] : ((~(c_Comb_Ocomb_Oop_A_D_D(V_comb1, V_comb2) = c_Comb_Ocomb_Oop_A_D_D(V_comb1_H, V_comb2_H))) | (V_comb1 = V_comb1_H))) | (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))) | (c_Comb_Ocomb_OK = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.21/0.43 tff(144,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[143, 140, 133, 122])).
% 0.21/0.43 tff(145,plain,(~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(146,plain,
% 0.21/0.43 (~(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[145, 121])).
% 0.21/0.43 tff(147,plain,
% 0.21/0.43 (^[V_q: $i, V_r: $i, V_p: $i] : refl(((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(148,plain,
% 0.21/0.43 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[147])).
% 0.21/0.43 tff(149,plain,
% 0.21/0.43 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(150,plain,
% 0.21/0.43 (^[V_q: $i, V_r: $i, V_p: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> (((V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))))), rewrite((((V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> (((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))))), rewrite((((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(151,plain,
% 0.21/0.44 (![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.44 tff(152,axiom,(![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OAp__parcontractE_2')).
% 0.21/0.44 tff(153,plain,
% 0.21/0.44 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.44 tff(154,plain,
% 0.21/0.44 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.21/0.44 tff(155,plain,(
% 0.21/0.44 ![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.44 inference(skolemize,[status(sab)],[154])).
% 0.21/0.44 tff(156,plain,
% 0.21/0.44 (![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[155, 148])).
% 0.21/0.44 tff(157,plain,
% 0.21/0.44 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(158,axiom,(c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 0.21/0.44 tff(159,plain,
% 0.21/0.44 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.44 tff(160,plain,
% 0.21/0.44 (((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(161,plain,
% 0.21/0.44 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(162,plain,
% 0.21/0.44 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_p, v_sko__uTI(V_p, V_q, V_r), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.44 tff(163,plain,
% 0.21/0.44 ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[162, 159, 156])).
% 0.21/0.44 tff(164,plain,
% 0.21/0.44 ((c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[163, 146, 119])).
% 0.21/0.45 tff(165,plain,
% 0.21/0.45 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[164, 103])).
% 0.21/0.45 tff(166,plain,
% 0.21/0.45 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[165, 59])).
% 0.21/0.45 tff(167,plain,
% 0.21/0.45 (((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(168,plain,
% 0.21/0.45 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(169,plain,
% 0.21/0.45 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(V_x, v_sko__uTE(V_x, V_z), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.21/0.45 tff(170,plain,
% 0.21/0.45 ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[169, 77])).
% 0.21/0.45 tff(171,plain,
% 0.21/0.45 (c_in(c_Pair(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[170, 166])).
% 0.21/0.45 tff(172,plain,
% 0.21/0.45 (c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[171, 55])).
% 0.21/0.45 tff(173,plain,
% 0.21/0.45 (^[V_q: $i, V_r: $i, V_p: $i] : refl(((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(174,plain,
% 0.21/0.45 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[173])).
% 0.21/0.45 tff(175,plain,
% 0.21/0.45 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(176,plain,
% 0.21/0.45 (^[V_q: $i, V_r: $i, V_p: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> (((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))))), rewrite((((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) <=> ((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> (((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))))), rewrite((((V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))), ((((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(177,plain,
% 0.21/0.45 (![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r)))) <=> ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[176])).
% 0.21/0.45 tff(178,axiom,(![V_q: $i, V_r: $i, V_p: $i] : (((((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r)))) | (V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_Comb_OAp__parcontractE_0')).
% 0.21/0.45 tff(179,plain,
% 0.21/0.45 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.21/0.45 tff(180,plain,
% 0.21/0.45 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.21/0.45 tff(181,plain,(
% 0.21/0.45 ![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[180])).
% 0.21/0.45 tff(182,plain,
% 0.21/0.45 (![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.21/0.45 tff(183,plain,
% 0.21/0.45 (((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) <=> ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(184,plain,
% 0.21/0.46 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(185,plain,
% 0.21/0.46 ((~![V_q: $i, V_r: $i, V_p: $i] : ((V_r = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(V_p, V_q, V_r), v_sko__uTH(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(V_p, V_q, V_r)), v_sko__uTG(V_p, V_q, V_r))) | (V_p = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_r)) | (V_r = c_Comb_Ocomb_Oop_A_D_D(V_p, V_q)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(V_p, V_q), V_r, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya)) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya), v_xb, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.46 tff(186,plain,
% 0.21/0.46 ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OS, v_sko__uTF(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTG(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb)) | (v_xb = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[185, 159, 182])).
% 0.21/0.46 tff(187,plain,
% 0.21/0.46 ((v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) | (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_xb))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[186, 146, 119])).
% 0.21/0.46 tff(188,plain,
% 0.21/0.46 (v_xb = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[187, 103])).
% 0.21/0.46 tff(189,plain,
% 0.21/0.46 (c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)) = v_xb),
% 0.21/0.46 inference(symmetry,[status(thm)],[188])).
% 0.21/0.46 tff(190,plain,
% 0.21/0.46 (((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))))) <=> ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(191,plain,
% 0.21/0.46 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(192,plain,
% 0.21/0.46 ((~![V_x: $i, V_z: $i] : ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_z, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (V_z = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(V_x, V_z))))) | (~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.46 tff(193,plain,
% 0.21/0.46 ((~c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x))), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[192, 37])).
% 0.21/0.46 tff(194,plain,
% 0.21/0.46 (v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb) = c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[193, 166])).
% 0.21/0.46 tff(195,plain,
% 0.21/0.46 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))) = v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)),
% 0.21/0.46 inference(symmetry,[status(thm)],[194])).
% 0.21/0.46 tff(196,plain,
% 0.21/0.46 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)) = c_Comb_Ocomb_Oop_A_D_D(v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[195])).
% 0.21/0.46 tff(197,plain,
% 0.21/0.46 (c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)) = v_xb),
% 0.21/0.46 inference(transitivity,[status(thm)],[196, 189])).
% 0.21/0.46 tff(198,plain,
% 0.21/0.46 (c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb) = c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[197])).
% 0.21/0.46 tff(199,plain,
% 0.21/0.46 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)) <=> c_in(c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[198])).
% 0.21/0.47 tff(200,plain,
% 0.21/0.47 ((~![V_x: $i, V_y: $i] : c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, V_x), V_y), V_x, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(201,plain,
% 0.21/0.47 (c_in(c_Pair(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb))), v_sko__uTH(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[200, 114])).
% 0.21/0.47 tff(202,plain,
% 0.21/0.47 (c_in(c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[201, 199])).
% 0.21/0.47 tff(203,plain,
% 0.21/0.47 (((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) <=> ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(204,plain,
% 0.21/0.47 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | ((~c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(205,plain,
% 0.21/0.47 ((~![V_U: $i] : ((~c_in(c_Pair(v_x, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, V_U, tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))))) | (~c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.47 tff(206,plain,
% 0.21/0.47 ((~c_in(c_Pair(v_x, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb))) | (~c_in(c_Pair(v_xb, v_sko__uTE(v_sko__uTE(v_x, c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x)), v_sko__uTI(c_Comb_Ocomb_Oop_A_D_D(c_Comb_Ocomb_OK, v_x), v_ya, v_xb)), tc_Comb_Ocomb, tc_Comb_Ocomb), c_Comb_Oparcontract, tc_prod(tc_Comb_Ocomb, tc_Comb_Ocomb)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[205, 91])).
% 0.21/0.47 tff(207,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[206, 202, 172])).
% 0.21/0.47 % SZS output end Proof
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------