%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET906+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:38 AM UTC 2025
% Result : Theorem 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET906+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n016.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 05:50:47 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.36 % SZS status Theorem
% 0.19/0.36 % SZS output start Proof
% 0.19/0.36 tff(tptp_fun_A_7_type, type, (
% 0.19/0.36 tptp_fun_A_7: $i)).
% 0.19/0.36 tff(tptp_fun_D_0_type, type, (
% 0.19/0.36 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.19/0.36 tff(tptp_fun_B_6_type, type, (
% 0.19/0.36 tptp_fun_B_6: $i)).
% 0.19/0.36 tff(unordered_pair_type, type, (
% 0.19/0.36 unordered_pair: ( $i * $i ) > $i)).
% 0.19/0.36 tff(in_type, type, (
% 0.19/0.36 in: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_C_5_type, type, (
% 0.19/0.36 tptp_fun_C_5: $i)).
% 0.19/0.36 tff(set_union2_type, type, (
% 0.19/0.36 set_union2: ( $i * $i ) > $i)).
% 0.19/0.36 tff(tptp_fun_D_1_type, type, (
% 0.19/0.36 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.19/0.36 tff(subset_type, type, (
% 0.19/0.36 subset: ( $i * $i ) > $o)).
% 0.19/0.36 tff(tptp_fun_C_2_type, type, (
% 0.19/0.36 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.19/0.36 tff(1,plain,
% 0.19/0.36 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.19/0.36 inference(bind,[status(th)],[])).
% 0.19/0.36 tff(2,plain,
% 0.19/0.36 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.36 tff(3,plain,
% 0.19/0.36 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.36 inference(pull_quant,[status(thm)],[])).
% 0.19/0.36 tff(4,plain,
% 0.19/0.36 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(5,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[4])).
% 0.19/0.37 tff(6,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[5, 3])).
% 0.19/0.37 tff(7,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[6, 2])).
% 0.19/0.37 tff(8,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(9,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.37 tff(10,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(transitivity,[status(thm)],[9, 7])).
% 0.19/0.37 tff(11,plain,
% 0.19/0.37 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))) <=> (in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))), ((~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), rewrite((~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))), ((~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))))),
% 0.19/0.37 inference(bind,[status(th)],[])).
% 0.19/0.37 tff(12,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.37 tff(13,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(14,axiom,(![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.19/0.37 tff(15,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.19/0.37 tff(16,plain,(
% 0.19/0.37 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))),
% 0.19/0.37 inference(skolemize,[status(sab)],[15])).
% 0.19/0.37 tff(17,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.37 tff(18,plain,
% 0.19/0.37 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))),
% 0.19/0.37 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.19/0.37 tff(19,plain,
% 0.19/0.37 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))))),
% 0.19/0.37 inference(rewrite,[status(thm)],[])).
% 0.19/0.37 tff(20,plain,
% 0.19/0.37 ((~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))) <=> (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[20])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[21, 19])).
% 0.19/0.38 tff(23,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, unordered_pair(B!6, A!7)) | in(A!7, C!5))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(24,plain,
% 0.19/0.38 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, A) | in(D, B))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) | in(tptp_fun_D_1(C, B, A), B))))))))) | (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.38 tff(25,plain,
% 0.19/0.38 (~((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5)))))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[24, 18])).
% 0.19/0.38 tff(26,plain,
% 0.19/0.38 (((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~((set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)) | (~(in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), unordered_pair(B!6, A!7)) | in(tptp_fun_D_1(set_union2(C!5, unordered_pair(A!7, B!6)), C!5, unordered_pair(B!6, A!7)), C!5))))))) | ((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(27,plain,
% 0.19/0.38 ((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.19/0.38 tff(28,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((unordered_pair(A, B) = unordered_pair(B, A)) <=> (unordered_pair(A, B) = unordered_pair(B, A)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(29,plain,
% 0.19/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[28])).
% 0.19/0.38 tff(30,plain,
% 0.19/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A)) <=> ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(31,axiom,(![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_tarski')).
% 0.19/0.38 tff(32,plain,
% 0.19/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.38 tff(33,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.38 inference(skolemize,[status(sab)],[32])).
% 0.19/0.38 tff(34,plain,
% 0.19/0.38 (![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.38 tff(35,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(36,plain,
% 0.19/0.38 (unordered_pair(A!7, B!6) = unordered_pair(B!6, A!7)),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.19/0.38 tff(37,plain,
% 0.19/0.38 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 0.19/0.38 inference(symmetry,[status(thm)],[36])).
% 0.19/0.38 tff(38,plain,
% 0.19/0.38 (set_union2(unordered_pair(B!6, A!7), C!5) = set_union2(unordered_pair(A!7, B!6), C!5)),
% 0.19/0.38 inference(monotonicity,[status(thm)],[37])).
% 0.19/0.38 tff(39,plain,
% 0.19/0.38 (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(unordered_pair(B!6, A!7), C!5)),
% 0.19/0.38 inference(symmetry,[status(thm)],[38])).
% 0.19/0.38 tff(40,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(41,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[40])).
% 0.19/0.38 tff(42,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(rewrite,[status(thm)],[])).
% 0.19/0.38 tff(43,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.19/0.38 tff(44,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.38 tff(45,plain,(
% 0.19/0.38 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(skolemize,[status(sab)],[44])).
% 0.19/0.38 tff(46,plain,
% 0.19/0.38 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.19/0.38 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.19/0.38 tff(47,plain,
% 0.19/0.38 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(C!5, unordered_pair(A!7, B!6)))),
% 0.19/0.38 inference(quant_inst,[status(thm)],[])).
% 0.19/0.38 tff(48,plain,
% 0.19/0.38 (set_union2(unordered_pair(A!7, B!6), C!5) = set_union2(C!5, unordered_pair(A!7, B!6))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.38 tff(49,plain,
% 0.19/0.38 (set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(A!7, B!6), C!5)),
% 0.19/0.38 inference(symmetry,[status(thm)],[48])).
% 0.19/0.38 tff(50,plain,
% 0.19/0.38 (set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5)),
% 0.19/0.38 inference(transitivity,[status(thm)],[49, 39])).
% 0.19/0.38 tff(51,plain,
% 0.19/0.38 ((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.19/0.38 inference(tautology,[status(thm)],[])).
% 0.19/0.38 tff(52,plain,
% 0.19/0.38 ((~((~(set_union2(C!5, unordered_pair(A!7, B!6)) = set_union2(unordered_pair(B!6, A!7), C!5))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))))) | (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.19/0.38 tff(53,plain,
% 0.19/0.38 (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.19/0.38 inference(unit_resolution,[status(thm)],[52, 27])).
% 0.19/0.38 tff(54,plain,
% 0.19/0.38 (in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[49])).
% 0.19/0.38 tff(55,plain,
% 0.19/0.38 (in(A!7, set_union2(unordered_pair(A!7, B!6), C!5)) <=> in(A!7, set_union2(C!5, unordered_pair(A!7, B!6)))),
% 0.19/0.38 inference(symmetry,[status(thm)],[54])).
% 0.19/0.38 tff(56,plain,
% 0.19/0.38 ((~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) <=> (~in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))))),
% 0.19/0.38 inference(monotonicity,[status(thm)],[55])).
% 0.19/0.38 tff(57,plain,
% 0.19/0.38 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(58,plain,
% 0.19/0.38 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[57])).
% 0.19/0.38 tff(59,plain,
% 0.19/0.38 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(60,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[59])).
% 0.19/0.39 tff(61,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.39 inference(transitivity,[status(thm)],[60, 58])).
% 0.19/0.39 tff(62,plain,
% 0.19/0.39 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(63,plain,
% 0.19/0.39 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.39 tff(64,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(65,plain,
% 0.19/0.39 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(66,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.39 tff(67,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.19/0.39 tff(68,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.39 tff(69,plain,
% 0.19/0.39 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.19/0.39 tff(70,plain,(
% 0.19/0.39 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[69])).
% 0.19/0.39 tff(71,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.19/0.39 tff(72,plain,
% 0.19/0.39 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.19/0.39 tff(73,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_2(B, A), A)) | in(tptp_fun_C_2(B, A), B)))))))) | (~((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~(subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5) | (~((~in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), set_union2(unordered_pair(A!7, B!6), C!5))) | in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), C!5)))))))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(74,plain,
% 0.19/0.39 (~((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~(subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5) | (~((~in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), set_union2(unordered_pair(A!7, B!6), C!5))) | in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), C!5))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.19/0.39 tff(75,plain,
% 0.19/0.39 (((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~(subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5) | (~((~in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), set_union2(unordered_pair(A!7, B!6), C!5))) | in(tptp_fun_C_2(C!5, set_union2(unordered_pair(A!7, B!6), C!5)), C!5)))))) | ((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(76,plain,
% 0.19/0.39 ((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(unordered_pair(A, B), C), C) => in(A, C))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(79,axiom,(~![A: $i, B: $i, C: $i] : (subset(set_union2(unordered_pair(A, B), C), C) => in(A, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t47_zfmisc_1')).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.39 tff(81,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[80, 77])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (~![A: $i, B: $i, C: $i] : ((~subset(set_union2(unordered_pair(A, B), C), C)) | in(A, C))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[82, 77])).
% 0.19/0.39 tff(84,plain,(
% 0.19/0.39 ~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | in(A!7, C!5))),
% 0.19/0.39 inference(skolemize,[status(sab)],[83])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 (subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)),
% 0.19/0.39 inference(or_elim,[status(thm)],[84])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 ((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | (~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((~((~subset(set_union2(unordered_pair(A!7, B!6), C!5), C!5)) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5)))) | ![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[87, 76])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 (~in(A!7, C!5)),
% 0.19/0.39 inference(or_elim,[status(thm)],[84])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 (((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | ((~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5))) <=> ((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | (~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 ((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | ((~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 ((~![C: $i] : ((~in(C, set_union2(unordered_pair(A!7, B!6), C!5))) | in(C, C!5))) | (~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))) | in(A!7, C!5)),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 (~in(A!7, set_union2(unordered_pair(A!7, B!6), C!5))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[92, 89, 88])).
% 0.19/0.39 tff(94,plain,
% 0.19/0.39 (~in(A!7, set_union2(C!5, unordered_pair(A!7, B!6)))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[93, 56])).
% 0.19/0.39 tff(95,plain,
% 0.19/0.39 ((~(in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) <=> (in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))) | in(A!7, set_union2(C!5, unordered_pair(A!7, B!6))) | (~(in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(96,plain,
% 0.19/0.39 (~(in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[95, 94, 53])).
% 0.19/0.39 tff(97,plain,
% 0.19/0.39 ((in(A!7, C!5) | in(A!7, unordered_pair(B!6, A!7))) | (~in(A!7, unordered_pair(B!6, A!7)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(98,plain,
% 0.19/0.39 (~in(A!7, unordered_pair(B!6, A!7))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.19/0.39 tff(99,plain,
% 0.19/0.39 ((~![A: $i, B: $i] : (unordered_pair(A, B) = unordered_pair(B, A))) | (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))),
% 0.19/0.39 inference(quant_inst,[status(thm)],[])).
% 0.19/0.39 tff(100,plain,
% 0.19/0.39 (unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[99, 34])).
% 0.19/0.39 tff(101,plain,
% 0.19/0.39 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(102,plain,
% 0.19/0.39 (~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[101, 100, 98])).
% 0.19/0.39 tff(103,plain,
% 0.19/0.39 (((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))) | ((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))),
% 0.19/0.39 inference(tautology,[status(thm)],[])).
% 0.19/0.39 tff(104,plain,
% 0.19/0.39 ((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))),
% 0.19/0.39 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.39 tff(105,plain,
% 0.19/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(106,plain,
% 0.19/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[105])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(pull_quant,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> (~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), pull_quant((~![D: $i] : ((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A)))))), ((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) <=> ?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> (?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), pull_quant((?[D: $i] : (~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), (((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))) <=> ?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> (~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), ((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[108])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[110, 106])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), rewrite(((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))), (((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))) <=> ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))))), rewrite((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))), ((((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(116,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[115])).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(118,plain,
% 0.19/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B)))) <=> ![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[118])).
% 0.19/0.40 tff(120,axiom,(![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = A) | (D = B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_tarski')).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : ((C = unordered_pair(A, B)) <=> ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[121, 117])).
% 0.19/0.40 tff(123,plain,(
% 0.19/0.40 ![A: $i, B: $i, C: $i] : (((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A)))) & ((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))),
% 0.19/0.40 inference(skolemize,[status(sab)],[122])).
% 0.19/0.40 tff(124,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = unordered_pair(A, B))) | ![D: $i] : (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[123, 116])).
% 0.19/0.40 tff(125,plain,
% 0.19/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[124, 114])).
% 0.19/0.40 tff(126,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(127,plain,
% 0.19/0.40 ((~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))) <=> (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(128,plain,
% 0.19/0.40 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))) <=> ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7)))))))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[128, 126])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | (in(A!7, unordered_pair(B!6, A!7)) <=> ((A!7 = B!6) | (A!7 = A!7))))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = unordered_pair(A, B))) | (in(D, C) <=> ((D = B) | (D = A))))) | (~((C = unordered_pair(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> ((tptp_fun_D_0(C, B, A) = B) | (tptp_fun_D_0(C, B, A) = A))))))))) | (~((~((~(unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6))) | in(A!7, unordered_pair(B!6, A!7)))) | (~((unordered_pair(B!6, A!7) = unordered_pair(A!7, B!6)) | (~(in(tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7), unordered_pair(B!6, A!7)) <=> ((tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = B!6) | (tptp_fun_D_0(unordered_pair(B!6, A!7), B!6, A!7) = A!7))))))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[131, 125, 104])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------