%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT032+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:00:28 AM UTC 2025
% Result : Theorem 0.54s 0.73s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT032+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 11:56:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.54/0.73 % SZS status Theorem
% 0.54/0.73 % SZS output start Proof
% 0.54/0.73 tff(v8_cat_1_type, type, (
% 0.54/0.73 v8_cat_1: ( $i * $i * $i ) > $o)).
% 0.54/0.73 tff(k11_cat_2_type, type, (
% 0.54/0.73 k11_cat_2: ( $i * $i ) > $i)).
% 0.54/0.73 tff(k12_nattra_1_type, type, (
% 0.54/0.73 k12_nattra_1: ( $i * $i ) > $i)).
% 0.54/0.73 tff(tptp_fun_C_2_type, type, (
% 0.54/0.73 tptp_fun_C_2: $i)).
% 0.54/0.73 tff(tptp_fun_A_0_type, type, (
% 0.54/0.73 tptp_fun_A_0: $i)).
% 0.54/0.73 tff(tptp_fun_B_1_type, type, (
% 0.54/0.73 tptp_fun_B_1: $i)).
% 0.54/0.73 tff(m2_cat_1_type, type, (
% 0.54/0.73 m2_cat_1: ( $i * $i * $i ) > $o)).
% 0.54/0.73 tff(r1_isocat_1_type, type, (
% 0.54/0.73 r1_isocat_1: ( $i * $i ) > $o)).
% 0.54/0.73 tff(tptp_fun_C_3_type, type, (
% 0.54/0.73 tptp_fun_C_3: ( $i * $i ) > $i)).
% 0.54/0.73 tff(v2_cat_1_type, type, (
% 0.54/0.73 v2_cat_1: $i > $o)).
% 0.54/0.73 tff(l1_cat_1_type, type, (
% 0.54/0.73 l1_cat_1: $i > $o)).
% 0.54/0.73 tff(v1_cat_1_type, type, (
% 0.54/0.73 v1_cat_1: $i > $o)).
% 0.54/0.73 tff(k17_isocat_2_type, type, (
% 0.54/0.73 k17_isocat_2: ( $i * $i * $i ) > $i)).
% 0.54/0.73 tff(1,plain,
% 0.54/0.73 (^[A: $i, B: $i] : refl(((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(2,plain,
% 0.54/0.73 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[1])).
% 0.54/0.73 tff(3,plain,
% 0.54/0.73 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))), rewrite((v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))) <=> (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))))),
% 0.54/0.73 inference(bind,[status(th)],[])).
% 0.54/0.73 tff(4,plain,
% 0.54/0.73 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.54/0.73 inference(quant_intro,[status(thm)],[3])).
% 0.54/0.73 tff(5,plain,
% 0.54/0.73 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.54/0.73 inference(rewrite,[status(thm)],[])).
% 0.54/0.73 tff(6,plain,
% 0.54/0.73 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(7,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[6])).
% 0.54/0.74 tff(8,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k11_cat_2')).
% 0.54/0.74 tff(9,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.54/0.74 tff(10,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.54/0.74 tff(11,plain,(
% 0.54/0.74 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v2_cat_1(k11_cat_2(A, B)) & l1_cat_1(k11_cat_2(A, B))))),
% 0.54/0.74 inference(skolemize,[status(sab)],[10])).
% 0.54/0.74 tff(12,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.54/0.74 tff(13,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.54/0.74 tff(14,plain,
% 0.54/0.74 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & (v2_cat_1(B!1) & l1_cat_1(B!1) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(15,plain,
% 0.54/0.74 (((v2_cat_1(B!1) & l1_cat_1(B!1)) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))) <=> (v2_cat_1(B!1) & l1_cat_1(B!1) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(16,plain,
% 0.54/0.74 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & ((v2_cat_1(B!1) & l1_cat_1(B!1)) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) <=> ((v2_cat_1(A!0) & l1_cat_1(A!0)) & (v2_cat_1(B!1) & l1_cat_1(B!1) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[15])).
% 0.54/0.74 tff(17,plain,
% 0.54/0.74 (((v2_cat_1(A!0) & l1_cat_1(A!0)) & ((v2_cat_1(B!1) & l1_cat_1(B!1)) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) <=> (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[16, 14])).
% 0.54/0.74 tff(18,plain,
% 0.54/0.74 ((~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(19,plain,
% 0.54/0.74 ((~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))) <=> (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(20,axiom,(~![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t49_isocat_2')).
% 0.54/0.74 tff(21,plain,
% 0.54/0.74 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.54/0.74 tff(22,plain,
% 0.54/0.74 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.54/0.74 tff(23,plain,
% 0.54/0.74 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.54/0.74 tff(24,plain,
% 0.54/0.74 (~![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | r1_isocat_1(k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.54/0.74 tff(25,plain,
% 0.54/0.74 (v2_cat_1(A!0) & l1_cat_1(A!0) & v2_cat_1(B!1) & l1_cat_1(B!1) & (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.54/0.74 tff(26,plain,
% 0.54/0.74 (~((~(v2_cat_1(C!2) & l1_cat_1(C!2))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))),
% 0.54/0.74 inference(and_elim,[status(thm)],[25])).
% 0.54/0.74 tff(27,plain,
% 0.54/0.74 (v2_cat_1(C!2) & l1_cat_1(C!2)),
% 0.54/0.74 inference(or_elim,[status(thm)],[26])).
% 0.54/0.74 tff(28,plain,
% 0.54/0.74 (l1_cat_1(C!2)),
% 0.54/0.74 inference(and_elim,[status(thm)],[27])).
% 0.54/0.74 tff(29,plain,
% 0.54/0.74 (v2_cat_1(C!2)),
% 0.54/0.74 inference(and_elim,[status(thm)],[27])).
% 0.54/0.74 tff(30,plain,
% 0.54/0.74 (l1_cat_1(B!1)),
% 0.54/0.74 inference(and_elim,[status(thm)],[25])).
% 0.54/0.74 tff(31,plain,
% 0.54/0.74 (v2_cat_1(B!1)),
% 0.54/0.74 inference(and_elim,[status(thm)],[25])).
% 0.54/0.74 tff(32,plain,
% 0.54/0.74 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(33,plain,
% 0.54/0.74 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))) <=> ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(34,plain,
% 0.54/0.74 ((~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))) <=> (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(35,plain,
% 0.54/0.74 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[34])).
% 0.54/0.74 tff(36,plain,
% 0.54/0.74 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))) <=> ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[35, 33])).
% 0.54/0.74 tff(37,plain,
% 0.54/0.74 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[36])).
% 0.54/0.74 tff(38,plain,
% 0.54/0.74 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[37, 32])).
% 0.54/0.74 tff(39,plain,
% 0.54/0.74 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(40,plain,
% 0.54/0.74 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.54/0.74 tff(41,plain,
% 0.54/0.74 (~((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[40, 31, 30, 29, 28, 13])).
% 0.54/0.74 tff(42,plain,
% 0.54/0.74 (((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))) | v2_cat_1(k11_cat_2(B!1, C!2))),
% 0.54/0.74 inference(tautology,[status(thm)],[])).
% 0.54/0.74 tff(43,plain,
% 0.54/0.74 (v2_cat_1(k11_cat_2(B!1, C!2))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.54/0.74 tff(44,plain,
% 0.54/0.74 (((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2)))) | l1_cat_1(k11_cat_2(B!1, C!2))),
% 0.54/0.74 inference(tautology,[status(thm)],[])).
% 0.54/0.74 tff(45,plain,
% 0.54/0.74 (l1_cat_1(k11_cat_2(B!1, C!2))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.54/0.74 tff(46,plain,
% 0.54/0.74 (^[A: $i, B: $i] : refl(((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B)))))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(47,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B)))))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[46])).
% 0.54/0.74 tff(48,plain,
% 0.54/0.74 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))), rewrite((v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))) <=> (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B)))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B)))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B)))))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(49,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B)))) <=> ![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[48])).
% 0.54/0.74 tff(50,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(51,plain,
% 0.54/0.74 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), rewrite(((v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B))) & l1_cat_1(k12_nattra_1(A, B))) <=> (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => ((v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B))) & l1_cat_1(k12_nattra_1(A, B)))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B)))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) => (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => ((v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B))) & l1_cat_1(k12_nattra_1(A, B)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(52,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => ((v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B))) & l1_cat_1(k12_nattra_1(A, B)))) <=> ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[51])).
% 0.54/0.74 tff(53,axiom,(![A: $i, B: $i] : ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) => ((v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B))) & l1_cat_1(k12_nattra_1(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k12_nattra_1')).
% 0.54/0.74 tff(54,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.54/0.74 tff(55,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.54/0.74 tff(56,plain,(
% 0.54/0.74 ![A: $i, B: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))) | (v1_cat_1(k12_nattra_1(A, B)) & v2_cat_1(k12_nattra_1(A, B)) & l1_cat_1(k12_nattra_1(A, B))))),
% 0.54/0.74 inference(skolemize,[status(sab)],[55])).
% 0.54/0.74 tff(57,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.54/0.74 tff(58,plain,
% 0.54/0.74 (![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.54/0.74 tff(59,plain,
% 0.54/0.74 (l1_cat_1(A!0)),
% 0.54/0.74 inference(and_elim,[status(thm)],[25])).
% 0.54/0.74 tff(60,plain,
% 0.54/0.74 (v2_cat_1(A!0)),
% 0.54/0.74 inference(and_elim,[status(thm)],[25])).
% 0.54/0.74 tff(61,plain,
% 0.54/0.74 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(62,plain,
% 0.54/0.74 (((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))))) <=> ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(63,plain,
% 0.54/0.74 ((~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))) <=> (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(rewrite,[status(thm)],[])).
% 0.54/0.74 tff(64,plain,
% 0.54/0.74 (((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))))) <=> ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[63])).
% 0.54/0.74 tff(65,plain,
% 0.54/0.74 (((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))))) <=> ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[64, 62])).
% 0.54/0.74 tff(66,plain,
% 0.54/0.74 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))))))),
% 0.54/0.74 inference(monotonicity,[status(thm)],[65])).
% 0.54/0.74 tff(67,plain,
% 0.54/0.74 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[66, 61])).
% 0.54/0.74 tff(68,plain,
% 0.54/0.74 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))))),
% 0.54/0.74 inference(quant_inst,[status(thm)],[])).
% 0.54/0.74 tff(69,plain,
% 0.54/0.74 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.54/0.74 tff(70,plain,
% 0.54/0.74 ((~v2_cat_1(k11_cat_2(B!1, C!2))) | (~l1_cat_1(k11_cat_2(B!1, C!2))) | (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[69, 60, 59, 58])).
% 0.54/0.74 tff(71,plain,
% 0.54/0.74 (~((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[70, 45, 43])).
% 0.54/0.74 tff(72,plain,
% 0.54/0.74 (((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))) | l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))),
% 0.54/0.74 inference(tautology,[status(thm)],[])).
% 0.54/0.74 tff(73,plain,
% 0.54/0.74 (l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.54/0.74 tff(74,plain,
% 0.54/0.74 (((~v1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2))))) | v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))),
% 0.54/0.74 inference(tautology,[status(thm)],[])).
% 0.54/0.74 tff(75,plain,
% 0.54/0.74 (v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))),
% 0.54/0.74 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.54/0.74 tff(76,plain,
% 0.54/0.74 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(77,plain,
% 0.54/0.74 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[76])).
% 0.54/0.74 tff(78,plain,
% 0.54/0.74 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))))),
% 0.54/0.74 inference(bind,[status(th)],[])).
% 0.54/0.74 tff(79,plain,
% 0.54/0.74 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))),
% 0.54/0.74 inference(quant_intro,[status(thm)],[78])).
% 0.54/0.74 tff(80,plain,
% 0.54/0.74 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))),
% 0.54/0.74 inference(transitivity,[status(thm)],[79, 77])).
% 0.54/0.74 tff(81,plain,
% 0.54/0.74 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), trans(monotonicity(rewrite(((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) <=> ((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))), rewrite((r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))) <=> (r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))), ((((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))) <=> (((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B))))) & (r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))), rewrite((((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B))))) & (r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))) <=> (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))), ((((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))) <=> (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | (((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | (((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B))))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(82,plain,
% 0.54/0.75 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[81])).
% 0.54/0.75 tff(83,plain,
% 0.54/0.75 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(84,plain,
% 0.54/0.75 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))) <=> (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))), (((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))), (((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))))),
% 0.54/0.75 inference(bind,[status(th)],[])).
% 0.54/0.75 tff(85,plain,
% 0.54/0.75 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))),
% 0.54/0.75 inference(quant_intro,[status(thm)],[84])).
% 0.54/0.75 tff(86,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_isocat_1')).
% 0.54/0.75 tff(87,plain,
% 0.54/0.75 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.54/0.75 tff(88,plain,
% 0.54/0.75 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (r1_isocat_1(A, B) <=> ?[C: $i] : (m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.54/0.75 tff(89,plain,(
% 0.54/0.75 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | (((~r1_isocat_1(A, B)) | (m2_cat_1(tptp_fun_C_3(B, A), A, B) & v8_cat_1(tptp_fun_C_3(B, A), A, B))) & (r1_isocat_1(A, B) | ![C: $i] : (~(m2_cat_1(C, A, B) & v8_cat_1(C, A, B)))))))),
% 0.54/0.75 inference(skolemize,[status(sab)],[88])).
% 0.54/0.75 tff(90,plain,
% 0.54/0.75 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[89, 82])).
% 0.54/0.75 tff(91,plain,
% 0.54/0.75 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[90, 80])).
% 0.54/0.75 tff(92,plain,
% 0.54/0.75 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | ((~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(93,plain,
% 0.54/0.75 (((~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))) | (~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))))))) <=> ((~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(94,plain,
% 0.54/0.75 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | ((~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))) | (~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | ((~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[93])).
% 0.54/0.75 tff(95,plain,
% 0.54/0.75 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | ((~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))) | (~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))))))))),
% 0.54/0.75 inference(transitivity,[status(thm)],[94, 92])).
% 0.54/0.75 tff(96,plain,
% 0.54/0.75 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | ((~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))) | (~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))),
% 0.54/0.75 inference(quant_inst,[status(thm)],[])).
% 0.54/0.75 tff(97,plain,
% 0.54/0.75 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~((~r1_isocat_1(A, B)) | (~((~m2_cat_1(tptp_fun_C_3(B, A), A, B)) | (~v8_cat_1(tptp_fun_C_3(B, A), A, B)))))) | (~(r1_isocat_1(A, B) | ![C: $i] : ((~m2_cat_1(C, A, B)) | (~v8_cat_1(C, A, B)))))))))) | (~l1_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | (~v2_cat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))),
% 0.54/0.75 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.54/0.75 tff(98,plain,
% 0.54/0.75 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))),
% 0.54/0.75 inference(unit_resolution,[status(thm)],[97, 91, 75, 73])).
% 0.54/0.75 tff(99,plain,
% 0.54/0.75 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(100,plain,
% 0.54/0.75 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2)))))) <=> ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2))))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(101,plain,
% 0.54/0.75 ((~((~v1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~l1_cat_1(k12_nattra_1(A!0, C!2))))) <=> (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2)))))),
% 0.54/0.75 inference(rewrite,[status(thm)],[])).
% 0.54/0.75 tff(102,plain,
% 0.54/0.75 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~l1_cat_1(k12_nattra_1(A!0, C!2)))))) <=> ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[101])).
% 0.54/0.75 tff(103,plain,
% 0.54/0.75 (((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~l1_cat_1(k12_nattra_1(A!0, C!2)))))) <=> ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2))))))),
% 0.54/0.75 inference(transitivity,[status(thm)],[102, 100])).
% 0.54/0.75 tff(104,plain,
% 0.54/0.75 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~l1_cat_1(k12_nattra_1(A!0, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2)))))))),
% 0.54/0.75 inference(monotonicity,[status(thm)],[103])).
% 0.54/0.75 tff(105,plain,
% 0.54/0.75 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~l1_cat_1(k12_nattra_1(A!0, C!2))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2))))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[104, 99])).
% 0.54/0.76 tff(106,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~l1_cat_1(k12_nattra_1(A!0, C!2))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(107,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2)))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.54/0.76 tff(108,plain,
% 0.54/0.76 (~((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[107, 60, 59, 29, 28, 58])).
% 0.54/0.76 tff(109,plain,
% 0.54/0.76 (((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2)))) | l1_cat_1(k12_nattra_1(A!0, C!2))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(110,plain,
% 0.54/0.76 (l1_cat_1(k12_nattra_1(A!0, C!2))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.54/0.76 tff(111,plain,
% 0.54/0.76 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(112,plain,
% 0.54/0.76 (((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1)))))) <=> ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(113,plain,
% 0.54/0.76 ((~((~v1_cat_1(k12_nattra_1(A!0, B!1))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))))) <=> (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1)))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(114,plain,
% 0.54/0.76 (((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, B!1))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1)))))) <=> ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1))))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[113])).
% 0.54/0.76 tff(115,plain,
% 0.54/0.76 (((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, B!1))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1)))))) <=> ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1))))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[114, 112])).
% 0.54/0.76 tff(116,plain,
% 0.54/0.76 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, B!1))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1)))))))),
% 0.54/0.76 inference(monotonicity,[status(thm)],[115])).
% 0.54/0.76 tff(117,plain,
% 0.54/0.76 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, B!1))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1))))))),
% 0.54/0.76 inference(transitivity,[status(thm)],[116, 111])).
% 0.54/0.76 tff(118,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~((~v1_cat_1(k12_nattra_1(A!0, B!1))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(119,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v1_cat_1(k12_nattra_1(A, B))) | (~v2_cat_1(k12_nattra_1(A, B))) | (~l1_cat_1(k12_nattra_1(A, B))))))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1)))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.54/0.76 tff(120,plain,
% 0.54/0.76 (~((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[119, 60, 59, 31, 30, 58])).
% 0.54/0.76 tff(121,plain,
% 0.54/0.76 (((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1)))) | l1_cat_1(k12_nattra_1(A!0, B!1))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(122,plain,
% 0.54/0.76 (l1_cat_1(k12_nattra_1(A!0, B!1))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.54/0.76 tff(123,plain,
% 0.54/0.76 (((~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~v1_cat_1(k12_nattra_1(A!0, B!1)))) | v2_cat_1(k12_nattra_1(A!0, B!1))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(124,plain,
% 0.54/0.76 (v2_cat_1(k12_nattra_1(A!0, B!1))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[123, 120])).
% 0.54/0.76 tff(125,plain,
% 0.54/0.76 (((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v1_cat_1(k12_nattra_1(A!0, C!2)))) | v2_cat_1(k12_nattra_1(A!0, C!2))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(126,plain,
% 0.54/0.76 (v2_cat_1(k12_nattra_1(A!0, C!2))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[125, 108])).
% 0.54/0.76 tff(127,plain,
% 0.54/0.76 (((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))) <=> ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(128,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | ((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(129,plain,
% 0.54/0.76 ((~![A: $i, B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)) | (~((~v2_cat_1(k11_cat_2(A, B))) | (~l1_cat_1(k11_cat_2(A, B))))))) | (~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.54/0.76 tff(130,plain,
% 0.54/0.76 ((~l1_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, C!2))) | (~v2_cat_1(k12_nattra_1(A!0, B!1))) | (~l1_cat_1(k12_nattra_1(A!0, B!1))) | (~((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[129, 13])).
% 0.54/0.76 tff(131,plain,
% 0.54/0.76 (~((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[130, 126, 124, 122, 110])).
% 0.54/0.76 tff(132,plain,
% 0.54/0.76 (((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))) | l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(133,plain,
% 0.54/0.76 (l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.54/0.76 tff(134,plain,
% 0.54/0.76 (((~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))) | v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(135,plain,
% 0.54/0.76 (v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.54/0.76 tff(136,plain,
% 0.54/0.76 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))) | ((~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~m2_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~m2_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))))))),
% 0.54/0.76 inference(rewrite,[status(thm)],[])).
% 0.54/0.76 tff(137,plain,
% 0.54/0.76 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))) | ((~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~m2_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))))))),
% 0.54/0.76 inference(quant_inst,[status(thm)],[])).
% 0.54/0.76 tff(138,plain,
% 0.54/0.76 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~((~m2_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)) | (~v8_cat_1(tptp_fun_C_3(B, k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), B)))))))))) | (~l1_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v2_cat_1(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~m2_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))))))),
% 0.54/0.76 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.54/0.76 tff(139,plain,
% 0.54/0.76 (~((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~m2_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[138, 135, 133, 98])).
% 0.54/0.76 tff(140,plain,
% 0.54/0.76 (((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | (~((~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~((~m2_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(tptp_fun_C_3(k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)), k12_nattra_1(A!0, k11_cat_2(B!1, C!2))), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))))) | (r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(141,plain,
% 0.54/0.76 (r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.54/0.76 tff(142,plain,
% 0.54/0.76 (~r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.54/0.76 inference(or_elim,[status(thm)],[26])).
% 0.54/0.76 tff(143,plain,
% 0.54/0.76 ((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.54/0.76 inference(tautology,[status(thm)],[])).
% 0.54/0.76 tff(144,plain,
% 0.54/0.76 ((~(r1_isocat_1(k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))))) | ![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.54/0.76 tff(145,plain,
% 0.54/0.76 (![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.54/0.76 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.54/0.76 tff(146,plain,
% 0.54/0.76 (^[A: $i] : refl(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))))),
% 0.54/0.76 inference(bind,[status(th)],[])).
% 0.54/0.76 tff(147,plain,
% 0.54/0.76 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))),
% 0.54/0.76 inference(quant_intro,[status(thm)],[146])).
% 0.54/0.76 tff(148,plain,
% 0.54/0.76 (^[A: $i] : rewrite(((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))))),
% 0.54/0.77 inference(bind,[status(th)],[])).
% 0.54/0.77 tff(149,plain,
% 0.54/0.77 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))),
% 0.54/0.77 inference(quant_intro,[status(thm)],[148])).
% 0.54/0.77 tff(150,plain,
% 0.54/0.77 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))),
% 0.54/0.77 inference(transitivity,[status(thm)],[149, 147])).
% 0.54/0.77 tff(151,plain,
% 0.54/0.77 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A)) <=> (~((~l1_cat_1(A)) | (~v2_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> (~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))))), rewrite((~(~((~l1_cat_1(A)) | (~v2_cat_1(A))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(B) & l1_cat_1(B)) <=> (~((~l1_cat_1(B)) | (~v2_cat_1(B))))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> (~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))))), rewrite((~(~((~l1_cat_1(B)) | (~v2_cat_1(B))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)))), ((~(v2_cat_1(B) & l1_cat_1(B))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C))))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)))), ((~(v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C))))), (((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))), (((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))), (![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))) <=> (((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))), rewrite((((~l1_cat_1(B)) | (~v2_cat_1(B))) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))), (((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))) <=> ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))))), (![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))) <=> ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> (((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))))), rewrite((((~l1_cat_1(A)) | (~v2_cat_1(A))) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))), (((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(152,plain,
% 0.61/0.77 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> ![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[151])).
% 0.61/0.77 tff(153,plain,
% 0.61/0.77 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(154,plain,
% 0.61/0.77 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite(((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))), (![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))) <=> ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))), rewrite(((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))), (((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))) <=> ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))))), (![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))) <=> ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))))), rewrite(((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))), (((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(155,plain,
% 0.61/0.77 (![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))) <=> ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[154])).
% 0.61/0.77 tff(156,axiom,(![A: $i] : ((v2_cat_1(A) & l1_cat_1(A)) => ![B: $i] : ((v2_cat_1(B) & l1_cat_1(B)) => ![C: $i] : ((v2_cat_1(C) & l1_cat_1(C)) => v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t48_isocat_2')).
% 0.61/0.77 tff(157,plain,
% 0.61/0.77 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.61/0.77 tff(158,plain,
% 0.61/0.77 (![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[157, 153])).
% 0.61/0.77 tff(159,plain,(
% 0.61/0.77 ![A: $i] : ((~(v2_cat_1(A) & l1_cat_1(A))) | ![B: $i] : ((~(v2_cat_1(B) & l1_cat_1(B))) | ![C: $i] : ((~(v2_cat_1(C) & l1_cat_1(C))) | v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.61/0.77 inference(skolemize,[status(sab)],[158])).
% 0.61/0.77 tff(160,plain,
% 0.61/0.77 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[159, 152])).
% 0.61/0.77 tff(161,plain,
% 0.61/0.77 (![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[160, 150])).
% 0.61/0.77 tff(162,plain,
% 0.61/0.77 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(163,plain,
% 0.61/0.77 (((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C))))) <=> ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(164,plain,
% 0.61/0.77 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C)))))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[163])).
% 0.61/0.77 tff(165,plain,
% 0.61/0.77 (((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) <=> ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))))))),
% 0.61/0.77 inference(transitivity,[status(thm)],[164, 162])).
% 0.61/0.77 tff(166,plain,
% 0.61/0.77 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | ((~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(167,plain,
% 0.61/0.77 ((~![A: $i] : ((~l1_cat_1(A)) | (~v2_cat_1(A)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : (v8_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)))))) | (~l1_cat_1(A!0)) | (~v2_cat_1(A!0)) | ![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.61/0.77 tff(168,plain,
% 0.61/0.77 (![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C)))))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[167, 60, 59, 161])).
% 0.61/0.77 tff(169,plain,
% 0.61/0.77 (((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C)))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C)))))) <=> ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C)))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(170,plain,
% 0.61/0.77 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C)))))) | ((~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C)))))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(171,plain,
% 0.61/0.77 ((~![B: $i] : ((~l1_cat_1(B)) | (~v2_cat_1(B)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B, C), k12_nattra_1(A!0, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A!0, B), k12_nattra_1(A!0, C)))))) | (~l1_cat_1(B!1)) | (~v2_cat_1(B!1)) | ![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.61/0.77 tff(172,plain,
% 0.61/0.77 (![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C))))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[171, 31, 30, 168])).
% 0.61/0.77 tff(173,plain,
% 0.61/0.77 (((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))) <=> ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(174,plain,
% 0.61/0.77 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C))))) | ((~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(175,plain,
% 0.61/0.77 ((~![C: $i] : ((~l1_cat_1(C)) | (~v2_cat_1(C)) | v8_cat_1(k17_isocat_2(A!0, B!1, C), k12_nattra_1(A!0, k11_cat_2(B!1, C)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C))))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.61/0.77 tff(176,plain,
% 0.61/0.77 (v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[175, 29, 28, 172])).
% 0.61/0.77 tff(177,plain,
% 0.61/0.77 (^[A: $i, B: $i, C: $i] : refl((m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) <=> (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(178,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) <=> ![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[177])).
% 0.61/0.77 tff(179,plain,
% 0.61/0.77 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C)) <=> (~((~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) <=> (~(~((~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))))), rewrite((~(~((~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))), ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) <=> ((~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> (((~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))), rewrite((((~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))), (((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(180,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[179])).
% 0.61/0.77 tff(181,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(182,plain,
% 0.61/0.77 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B))), ((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) & v2_cat_1(C)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B)) & v2_cat_1(C)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C))), (((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C)))), ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) & l1_cat_1(C)) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C)) & l1_cat_1(C)))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C)) & l1_cat_1(C)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))), ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) & l1_cat_1(C)) <=> (v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C)))), (((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) & l1_cat_1(C)) => m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C)) => m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))))), rewrite(((v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C)) => m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))), (((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) & l1_cat_1(C)) => m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(183,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) & l1_cat_1(C)) => m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[182])).
% 0.61/0.77 tff(184,axiom,(![A: $i, B: $i, C: $i] : ((((((v2_cat_1(A) & l1_cat_1(A)) & v2_cat_1(B)) & l1_cat_1(B)) & v2_cat_1(C)) & l1_cat_1(C)) => m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k17_isocat_2')).
% 0.61/0.77 tff(185,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.61/0.77 tff(186,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.61/0.77 tff(187,plain,(
% 0.61/0.77 ![A: $i, B: $i, C: $i] : ((~(v2_cat_1(A) & l1_cat_1(A) & v2_cat_1(B) & l1_cat_1(B) & v2_cat_1(C) & l1_cat_1(C))) | m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))))),
% 0.61/0.77 inference(skolemize,[status(sab)],[186])).
% 0.61/0.77 tff(188,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.61/0.77 tff(189,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[188, 178])).
% 0.61/0.77 tff(190,plain,
% 0.61/0.77 (((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))) <=> ((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(191,plain,
% 0.61/0.77 ((m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0))) <=> ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(192,plain,
% 0.61/0.77 (((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | (m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | ((~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[191])).
% 0.61/0.78 tff(193,plain,
% 0.61/0.78 (((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | (m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[192, 190])).
% 0.61/0.78 tff(194,plain,
% 0.61/0.78 ((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | (m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))) | (~l1_cat_1(C!2)) | (~v2_cat_1(C!2)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(195,plain,
% 0.61/0.78 ((~![A: $i, B: $i, C: $i] : (m2_cat_1(k17_isocat_2(A, B, C), k12_nattra_1(A, k11_cat_2(B, C)), k11_cat_2(k12_nattra_1(A, B), k12_nattra_1(A, C))) | (~l1_cat_1(C)) | (~v2_cat_1(C)) | (~v2_cat_1(B)) | (~l1_cat_1(B)) | (~v2_cat_1(A)) | (~l1_cat_1(A)))) | (~v2_cat_1(A!0)) | (~l1_cat_1(A!0)) | (~v2_cat_1(B!1)) | (~l1_cat_1(B!1)) | (~v2_cat_1(C!2)) | (~l1_cat_1(C!2)) | m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[194, 193])).
% 0.61/0.78 tff(196,plain,
% 0.61/0.78 (m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[195, 60, 59, 31, 30, 29, 28, 189])).
% 0.61/0.78 tff(197,plain,
% 0.61/0.78 (((~![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))) | ((~m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))) <=> ((~![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))) | (~m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(198,plain,
% 0.61/0.78 ((~![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))) | ((~m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(199,plain,
% 0.61/0.78 ((~![C: $i] : ((~m2_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(C, k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))))) | (~m2_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2)))) | (~v8_cat_1(k17_isocat_2(A!0, B!1, C!2), k12_nattra_1(A!0, k11_cat_2(B!1, C!2)), k11_cat_2(k12_nattra_1(A!0, B!1), k12_nattra_1(A!0, C!2))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.61/0.78 tff(200,plain,
% 0.61/0.78 ($false),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[199, 196, 176, 145])).
% 0.61/0.78 % SZS output end Proof
% 0.61/0.79 % E exiting
%------------------------------------------------------------------------------