%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU126+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:26:57 AM UTC 2025
% Result : Theorem 0.13s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU126+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:07:46 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.13/0.39 % SZS status Theorem
% 0.13/0.39 % SZS output start Proof
% 0.13/0.39 tff(tptp_fun_B_4_type, type, (
% 0.13/0.39 tptp_fun_B_4: $i)).
% 0.13/0.39 tff(set_union2_type, type, (
% 0.13/0.39 set_union2: ( $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_A_5_type, type, (
% 0.13/0.39 tptp_fun_A_5: $i)).
% 0.13/0.39 tff(in_type, type, (
% 0.13/0.39 in: ( $i * $i ) > $o)).
% 0.13/0.39 tff(tptp_fun_D_0_type, type, (
% 0.13/0.39 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.13/0.39 tff(tptp_fun_C_1_type, type, (
% 0.13/0.39 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.13/0.39 tff(subset_type, type, (
% 0.13/0.39 subset: ( $i * $i ) > $o)).
% 0.13/0.39 tff(1,plain,
% 0.13/0.39 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(2,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.39 tff(3,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(pull_quant,[status(thm)],[])).
% 0.13/0.39 tff(4,plain,
% 0.13/0.39 (^[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, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(5,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[4])).
% 0.13/0.39 tff(6,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[5, 3])).
% 0.13/0.39 tff(7,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[6, 2])).
% 0.13/0.39 tff(8,plain,
% 0.13/0.39 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(9,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[8])).
% 0.13/0.39 tff(10,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(transitivity,[status(thm)],[9, 7])).
% 0.13/0.39 tff(11,plain,
% 0.13/0.39 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 0.13/0.39 inference(bind,[status(th)],[])).
% 0.13/0.39 tff(12,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.39 inference(quant_intro,[status(thm)],[11])).
% 0.13/0.39 tff(13,plain,
% 0.13/0.39 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.13/0.39 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(14,plain,
% 0.13/0.40 (^[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)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(15,plain,
% 0.13/0.40 (![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, B) | in(D, A))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.13/0.40 tff(16,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/sandbox/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.13/0.40 tff(17,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.13/0.40 tff(18,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.13/0.40 tff(19,plain,(
% 0.13/0.40 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 0.13/0.40 inference(skolemize,[status(sab)],[18])).
% 0.13/0.40 tff(20,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.13/0.40 tff(21,plain,
% 0.13/0.40 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.13/0.40 tff(22,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(B!4 = set_union2(B!4, A!5))) | (in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))) | (~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(23,plain,
% 0.13/0.40 (~((~((~(B!4 = set_union2(B!4, A!5))) | (in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))) | (~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.13/0.40 tff(24,plain,
% 0.13/0.40 (((~((~(B!4 = set_union2(B!4, A!5))) | (in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))) | (~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))))) | ((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(25,plain,
% 0.13/0.40 ((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.13/0.40 tff(26,plain,
% 0.13/0.40 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(B!4 = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(A!5, B!4), B!4) <=> (in(tptp_fun_C_1(A!5, B!4), A!5) | in(tptp_fun_C_1(A!5, B!4), B!4))))) | (~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))))))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(27,plain,
% 0.13/0.40 (~((~((~(B!4 = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(A!5, B!4), B!4) <=> (in(tptp_fun_C_1(A!5, B!4), A!5) | in(tptp_fun_C_1(A!5, B!4), B!4))))) | (~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[26, 21])).
% 0.13/0.40 tff(28,plain,
% 0.13/0.40 (((~((~(B!4 = set_union2(B!4, A!5))) | (in(tptp_fun_C_1(A!5, B!4), B!4) <=> (in(tptp_fun_C_1(A!5, B!4), A!5) | in(tptp_fun_C_1(A!5, B!4), B!4))))) | (~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))))) | ((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(29,plain,
% 0.13/0.40 ((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.13/0.40 tff(30,plain,
% 0.13/0.40 ((B!4 = set_union2(A!5, B!4)) <=> (set_union2(A!5, B!4) = B!4)),
% 0.13/0.40 inference(commutativity,[status(thm)],[])).
% 0.13/0.40 tff(31,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(32,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[31])).
% 0.13/0.40 tff(33,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(34,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.13/0.40 tff(35,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.13/0.40 tff(36,plain,(
% 0.13/0.40 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.40 inference(skolemize,[status(sab)],[35])).
% 0.13/0.40 tff(37,plain,
% 0.13/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.13/0.40 tff(38,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!5, B!4) = set_union2(B!4, A!5))),
% 0.13/0.40 inference(quant_inst,[status(thm)],[])).
% 0.13/0.40 tff(39,plain,
% 0.13/0.40 (set_union2(A!5, B!4) = set_union2(B!4, A!5)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.13/0.40 tff(40,plain,
% 0.13/0.40 (set_union2(B!4, A!5) = set_union2(A!5, B!4)),
% 0.13/0.40 inference(symmetry,[status(thm)],[39])).
% 0.13/0.40 tff(41,plain,
% 0.13/0.40 ((B!4 = set_union2(B!4, A!5)) <=> (B!4 = set_union2(A!5, B!4))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[40])).
% 0.13/0.40 tff(42,plain,
% 0.13/0.40 ((B!4 = set_union2(B!4, A!5)) <=> (set_union2(A!5, B!4) = B!4)),
% 0.13/0.40 inference(transitivity,[status(thm)],[41, 30])).
% 0.13/0.40 tff(43,plain,
% 0.13/0.40 ((set_union2(A!5, B!4) = B!4) <=> (B!4 = set_union2(B!4, A!5))),
% 0.13/0.40 inference(symmetry,[status(thm)],[42])).
% 0.13/0.40 tff(44,plain,
% 0.13/0.40 ((~(set_union2(A!5, B!4) = B!4)) <=> (~(B!4 = set_union2(B!4, A!5)))),
% 0.13/0.40 inference(monotonicity,[status(thm)],[43])).
% 0.13/0.40 tff(45,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(46,plain,
% 0.13/0.40 ((~![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.13/0.40 inference(rewrite,[status(thm)],[])).
% 0.13/0.40 tff(47,axiom,(~![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.13/0.40 tff(48,plain,
% 0.13/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.13/0.40 tff(49,plain,
% 0.13/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[48, 45])).
% 0.13/0.40 tff(50,plain,
% 0.13/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.13/0.40 tff(51,plain,
% 0.13/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[50, 45])).
% 0.13/0.40 tff(52,plain,(
% 0.13/0.40 ~((~subset(A!5, B!4)) | (set_union2(A!5, B!4) = B!4))),
% 0.13/0.40 inference(skolemize,[status(sab)],[51])).
% 0.13/0.40 tff(53,plain,
% 0.13/0.40 (~(set_union2(A!5, B!4) = B!4)),
% 0.13/0.40 inference(or_elim,[status(thm)],[52])).
% 0.13/0.40 tff(54,plain,
% 0.13/0.40 (~(B!4 = set_union2(B!4, A!5))),
% 0.13/0.40 inference(modus_ponens,[status(thm)],[53, 44])).
% 0.13/0.40 tff(55,plain,
% 0.13/0.40 ((~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))))) | (B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(56,plain,
% 0.13/0.40 (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[55, 54, 29])).
% 0.13/0.40 tff(57,assumption,(~(in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))), introduced(assumption)).
% 0.13/0.40 tff(58,plain,
% 0.13/0.40 ((in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)) | (~in(tptp_fun_D_0(B!4, A!5, B!4), B!4))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(59,plain,
% 0.13/0.40 (~in(tptp_fun_D_0(B!4, A!5, B!4), B!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.13/0.40 tff(60,plain,
% 0.13/0.40 ((in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4) | (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(61,plain,
% 0.13/0.40 ($false),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[60, 59, 57, 56])).
% 0.13/0.40 tff(62,plain,(in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.13/0.40 tff(63,assumption,(~in(tptp_fun_D_0(B!4, A!5, B!4), B!4)), introduced(assumption)).
% 0.13/0.40 tff(64,plain,
% 0.13/0.40 ((~(in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))) | in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)),
% 0.13/0.40 inference(tautology,[status(thm)],[])).
% 0.13/0.40 tff(65,plain,
% 0.13/0.40 (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[64, 62])).
% 0.13/0.40 tff(66,plain,
% 0.13/0.40 (in(tptp_fun_D_0(B!4, A!5, B!4), A!5)),
% 0.13/0.40 inference(unit_resolution,[status(thm)],[65, 63])).
% 0.13/0.40 tff(67,plain,
% 0.13/0.40 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.13/0.40 inference(bind,[status(th)],[])).
% 0.13/0.40 tff(68,plain,
% 0.13/0.40 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.40 inference(quant_intro,[status(thm)],[67])).
% 0.13/0.40 tff(69,plain,
% 0.13/0.40 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(70,plain,
% 0.13/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.13/0.41 tff(71,plain,
% 0.13/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[70, 68])).
% 0.13/0.41 tff(72,plain,
% 0.13/0.41 (^[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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(73,plain,
% 0.13/0.41 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(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_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.41 tff(74,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(75,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(76,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[75])).
% 0.13/0.41 tff(77,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.13/0.41 tff(78,plain,
% 0.13/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.13/0.41 tff(79,plain,
% 0.13/0.41 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.13/0.41 tff(80,plain,(
% 0.13/0.41 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[79])).
% 0.13/0.41 tff(81,plain,
% 0.13/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.21/0.41 tff(82,plain,
% 0.21/0.41 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.21/0.41 tff(83,plain,
% 0.21/0.41 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_1(B!4, A!5), A!5)) | in(tptp_fun_C_1(B!4, A!5), B!4)))))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(84,plain,
% 0.21/0.41 (~((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_1(B!4, A!5), A!5)) | in(tptp_fun_C_1(B!4, A!5), B!4))))))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.41 tff(85,plain,
% 0.21/0.41 (((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~(subset(A!5, B!4) | (~((~in(tptp_fun_C_1(B!4, A!5), A!5)) | in(tptp_fun_C_1(B!4, A!5), B!4)))))) | ((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(86,plain,
% 0.21/0.41 ((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.21/0.41 tff(87,plain,
% 0.21/0.41 (subset(A!5, B!4)),
% 0.21/0.41 inference(or_elim,[status(thm)],[52])).
% 0.21/0.41 tff(88,plain,
% 0.21/0.41 ((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | (~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(89,plain,
% 0.21/0.41 ((~((~subset(A!5, B!4)) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4)))) | ![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.41 tff(90,plain,
% 0.21/0.41 (![C: $i] : ((~in(C, A!5)) | in(C, B!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[89, 86])).
% 0.21/0.41 tff(91,plain,
% 0.21/0.41 (((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | ((~in(tptp_fun_D_0(B!4, A!5, B!4), A!5)) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))) <=> ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | (~in(tptp_fun_D_0(B!4, A!5, B!4), A!5)) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(92,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | ((~in(tptp_fun_D_0(B!4, A!5, B!4), A!5)) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(93,plain,
% 0.21/0.41 ((~![C: $i] : ((~in(C, A!5)) | in(C, B!4))) | (~in(tptp_fun_D_0(B!4, A!5, B!4), A!5)) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.41 tff(94,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[93, 90, 66, 63])).
% 0.21/0.41 tff(95,plain,(in(tptp_fun_D_0(B!4, A!5, B!4), B!4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.41 tff(96,plain,
% 0.21/0.41 ((in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))) | (~in(tptp_fun_D_0(B!4, A!5, B!4), B!4)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(97,plain,
% 0.21/0.41 (in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[96, 95, 62])).
% 0.21/0.41 tff(98,plain,
% 0.21/0.41 ((~((B!4 = set_union2(B!4, A!5)) | (~(in(tptp_fun_D_0(B!4, A!5, B!4), B!4) <=> (in(tptp_fun_D_0(B!4, A!5, B!4), A!5) | in(tptp_fun_D_0(B!4, A!5, B!4), B!4)))))) | (B!4 = set_union2(B!4, A!5))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[55, 97])).
% 0.21/0.41 tff(99,plain,
% 0.21/0.41 (B!4 = set_union2(B!4, A!5)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[98, 25])).
% 0.21/0.41 tff(100,plain,
% 0.21/0.41 (set_union2(B!4, A!5) = B!4),
% 0.21/0.41 inference(symmetry,[status(thm)],[99])).
% 0.21/0.41 tff(101,plain,
% 0.21/0.41 (set_union2(A!5, B!4) = B!4),
% 0.21/0.41 inference(transitivity,[status(thm)],[39, 100])).
% 0.21/0.41 tff(102,plain,
% 0.21/0.41 ($false),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[53, 101])).
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------