%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU136+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:26:59 AM UTC 2025
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU136+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:07:18 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(in_type, type, (
% 0.20/0.47 in: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_B_9_type, type, (
% 0.20/0.47 tptp_fun_B_9: $i)).
% 0.20/0.47 tff(tptp_fun_C_2_type, type, (
% 0.20/0.47 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.20/0.47 tff(set_difference_type, type, (
% 0.20/0.47 set_difference: ( $i * $i ) > $i)).
% 0.20/0.47 tff(set_union2_type, type, (
% 0.20/0.47 set_union2: ( $i * $i ) > $i)).
% 0.20/0.47 tff(tptp_fun_A_10_type, type, (
% 0.20/0.47 tptp_fun_A_10: $i)).
% 0.20/0.47 tff(tptp_fun_D_1_type, type, (
% 0.20/0.47 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(subset_type, type, (
% 0.20/0.47 subset: ( $i * $i ) > $o)).
% 0.20/0.47 tff(tptp_fun_D_4_type, type, (
% 0.20/0.47 tptp_fun_D_4: ( $i * $i * $i ) > $i)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(pull_quant,[status(thm)],[])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (^[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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[6, 2])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 (^[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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[8])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[9, 7])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (^[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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))) <=> (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (^[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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.47 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/sandbox2/benchmark/theBenchmark.p','d2_xboole_0')).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.20/0.47 tff(19,plain,(
% 0.20/0.47 ![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[18])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 ((~![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), B) | in(tptp_fun_D_1(C, B, A), A))))))))) | (~((~((~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))))) | (~((set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9))) | (~(in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), set_union2(B!9, A!10)) <=> (in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), set_difference(A!10, B!9)) | in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), B!9))))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (~((~((~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))))) | (~((set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9))) | (~(in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), set_union2(B!9, A!10)) <=> (in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), set_difference(A!10, B!9)) | in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), B!9)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.48 tff(24,plain,
% 0.20/0.48 (((~((~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))))) | (~((set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9))) | (~(in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), set_union2(B!9, A!10)) <=> (in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), set_difference(A!10, B!9)) | in(tptp_fun_D_1(set_union2(B!9, A!10), set_difference(A!10, B!9), B!9), B!9))))))) | ((~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(25,plain,
% 0.20/0.48 ((~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.48 tff(26,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl((set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> (set_union2(A, set_difference(B, A)) = set_union2(A, B)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(27,plain,
% 0.20/0.48 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.48 tff(28,plain,
% 0.20/0.48 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B)) <=> ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(29,axiom,(![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t39_xboole_1')).
% 0.20/0.48 tff(30,plain,
% 0.20/0.48 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.48 tff(31,plain,(
% 0.20/0.48 ![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.20/0.48 inference(skolemize,[status(sab)],[30])).
% 0.20/0.48 tff(32,plain,
% 0.20/0.48 (![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.48 tff(33,plain,
% 0.20/0.48 ((~![A: $i, B: $i] : (set_union2(A, set_difference(B, A)) = set_union2(A, B))) | (set_union2(B!9, set_difference(A!10, B!9)) = set_union2(B!9, A!10))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(34,plain,
% 0.20/0.48 (set_union2(B!9, set_difference(A!10, B!9)) = set_union2(B!9, A!10)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.48 tff(35,plain,
% 0.20/0.48 (set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9))),
% 0.20/0.48 inference(symmetry,[status(thm)],[34])).
% 0.20/0.48 tff(36,plain,
% 0.20/0.48 ((~((~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))))) | (~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 ((~((~(set_union2(B!9, A!10) = set_union2(B!9, set_difference(A!10, B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[37, 25])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (^[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))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (^[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))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[42, 40])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 (^[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)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[44])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (^[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))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.48 tff(49,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')).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.20/0.48 tff(52,plain,(
% 0.20/0.48 ![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)))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[51])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((~![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_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_difference(A!10, B!9))))) | (~(subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (~((~((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_difference(A!10, B!9))))) | (~(subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (((~((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_difference(A!10, B!9))))) | (~(subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))))))) | (subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)))))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 (subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[59])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(64,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.48 tff(66,plain,(
% 0.20/0.48 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[65])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 ((~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))) <=> (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 ((((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))) <=> (((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 ((~(((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))) <=> (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[71])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 ((~(((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))) <=> (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[72, 70])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[73])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[74, 69])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 (~(((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[77, 68])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))) <=> (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(80,axiom,(~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t40_xboole_1')).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[81, 79])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[82, 79])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (~![A: $i, B: $i] : (set_difference(set_union2(A, B), B) = set_difference(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.20/0.49 tff(85,plain,(
% 0.20/0.49 ~(set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))),
% 0.20/0.49 inference(skolemize,[status(sab)],[84])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 ((((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))) | ((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) | (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 ((((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) <=> (set_difference(set_union2(A!10, B!9), B!9) = set_difference(A!10, B!9))) | ((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[86, 85])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[87, 78])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(92,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.49 tff(94,plain,(
% 0.20/0.49 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.20/0.49 inference(skolemize,[status(sab)],[93])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(A!10, set_union2(A!10, B!9))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (subset(A!10, set_union2(A!10, B!9))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (^[A: $i, B: $i, C: $i] : refl(((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))) <=> ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, B) => subset(set_difference(A, C), set_difference(B, C))) <=> ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.49 tff(103,axiom,(![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_xboole_1')).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.20/0.49 tff(106,plain,(
% 0.20/0.49 ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[105])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[106, 99])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | ((~subset(A!10, set_union2(A!10, B!9))) | subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | (~subset(A!10, set_union2(A!10, B!9))) | subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | ((~subset(A!10, set_union2(A!10, B!9))) | subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | (~subset(A!10, set_union2(A!10, B!9))) | subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[110, 107, 97])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 ((~((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 ((~((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (~subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[113, 88])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 ((~(subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)))))) | subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 ((~(subset(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)))))) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[116, 58])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 (((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 ((~![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_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10))))) | (~(subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10)) | (~((~in(tptp_fun_C_2(set_union2(B!9, A!10), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_union2(B!9, A!10), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 (~((~((~subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10))))) | (~(subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10)) | (~((~in(tptp_fun_C_2(set_union2(B!9, A!10), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_union2(B!9, A!10), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[120, 54])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (((~((~subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10))))) | (~(subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10)) | (~((~in(tptp_fun_C_2(set_union2(B!9, A!10), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_union2(B!9, A!10), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))))))) | ((~subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 ((~subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[124])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(127,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.50 tff(129,plain,(
% 0.20/0.50 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.50 inference(skolemize,[status(sab)],[128])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!10, B!9) = set_union2(B!9, A!10))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 (set_union2(A!10, B!9) = set_union2(B!9, A!10)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.20/0.50 tff(133,plain,
% 0.20/0.50 (set_union2(B!9, A!10) = set_union2(A!10, B!9)),
% 0.20/0.50 inference(symmetry,[status(thm)],[132])).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 (subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10)) <=> subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(A!10, B!9))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.50 tff(135,plain,
% 0.20/0.50 (subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(A!10, B!9)) <=> subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))),
% 0.20/0.50 inference(symmetry,[status(thm)],[134])).
% 0.20/0.50 tff(136,plain,
% 0.20/0.50 (^[A: $i, B: $i] : refl(subset(set_difference(A, B), A) <=> subset(set_difference(A, B), A))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.50 tff(138,plain,
% 0.20/0.50 (![A: $i, B: $i] : subset(set_difference(A, B), A) <=> ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(139,axiom,(![A: $i, B: $i] : subset(set_difference(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_xboole_1')).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.50 tff(141,plain,(
% 0.20/0.50 ![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.20/0.50 inference(skolemize,[status(sab)],[140])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (![A: $i, B: $i] : subset(set_difference(A, B), A)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[141, 137])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 ((~![A: $i, B: $i] : subset(set_difference(A, B), A)) | subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(A!10, B!9))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 (subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(A!10, B!9))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 (subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[144, 135])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 ((~((~subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10))))) | (~subset(set_difference(set_union2(A!10, B!9), B!9), set_union2(B!9, A!10))) | ![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[146, 145, 123])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (((~![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10)))) | ((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)))) <=> ((~![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10)))) | (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 ((~![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10)))) | ((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 ((~![C: $i] : ((~in(C, set_difference(set_union2(A!10, B!9), B!9))) | in(C, set_union2(B!9, A!10)))) | (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[150, 147, 119])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 ((~(in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)))) | (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 ((~(in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10)) <=> (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)))) | (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[153, 38])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[155])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(pull_quant,[status(thm)],[])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> (?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), pull_quant((?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))) <=> ?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))), pull_quant((~?[D: $i] : ((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[159, 157])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[160, 156])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[162])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[163, 161])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))))), rewrite((((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C)))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))), ((((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(168,axiom,(![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.50 tff(170,plain,(
% 0.20/0.50 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_4(C, B, A), C) <=> (in(tptp_fun_D_4(C, B, A), A) & (~in(tptp_fun_D_4(C, B, A), B)))))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[169])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[170, 166])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[171, 164])).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_4(C, B, A), A)) | in(tptp_fun_D_4(C, B, A), B)) <=> in(tptp_fun_D_4(C, B, A), C))))))) | (~((~((~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))) | (~((set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9)) | (((~in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), set_union2(B!9, A!10))) | in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), B!9)) <=> in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (~((~((~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))) | (~((set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9)) | (((~in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), set_union2(B!9, A!10))) | in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), B!9)) <=> in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.20/0.51 tff(175,plain,
% 0.20/0.51 (((~((~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))) | (~((set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9)) | (((~in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), set_union2(B!9, A!10))) | in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), B!9)) <=> in(tptp_fun_D_4(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)), B!9, set_union2(B!9, A!10)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))) | ((~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 ((~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[175, 174])).
% 0.20/0.51 tff(177,plain,
% 0.20/0.51 (set_difference(set_union2(B!9, A!10), B!9) = set_difference(set_union2(A!10, B!9), B!9)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[133])).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 (set_difference(set_union2(A!10, B!9), B!9) = set_difference(set_union2(B!9, A!10), B!9)),
% 0.20/0.51 inference(symmetry,[status(thm)],[177])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 (^[A: $i, B: $i] : refl(((~subset(A, B)) | (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[179])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 (^[A: $i, B: $i] : rewrite((subset(A, B) => (set_union2(A, B) = B)) <=> ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B)) <=> ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[182])).
% 0.20/0.51 tff(184,axiom,(![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.20/0.51 tff(187,plain,(
% 0.20/0.51 ![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.20/0.51 inference(skolemize,[status(sab)],[186])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 (![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.20/0.51 tff(189,plain,
% 0.20/0.51 (((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)) = set_difference(set_union2(A!10, B!9), B!9)))) <=> ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)) = set_difference(set_union2(A!10, B!9), B!9)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(190,plain,
% 0.20/0.51 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | ((~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)) = set_difference(set_union2(A!10, B!9), B!9)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(191,plain,
% 0.20/0.51 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) | (~subset(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))) | (set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)) = set_difference(set_union2(A!10, B!9), B!9))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 (set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)) = set_difference(set_union2(A!10, B!9), B!9)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[191, 188, 111])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)) = set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 (set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)) = set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[193, 130])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 (set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_union2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9))),
% 0.20/0.51 inference(symmetry,[status(thm)],[194])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 (set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9)),
% 0.20/0.51 inference(transitivity,[status(thm)],[195, 192, 178])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 ((~((~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))) | (~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.51 ((~((~(set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(B!9, A!10), B!9))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))))) | (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.20/0.51 tff(199,plain,
% 0.20/0.51 (~(((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[198, 176])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 (set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)) = set_difference(set_union2(A!10, B!9), B!9)),
% 0.20/0.51 inference(transitivity,[status(thm)],[195, 192])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[200])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[201])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 (in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[119, 202])).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 ((((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))) | (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 ((((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) <=> in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(set_difference(set_union2(A!10, B!9), B!9), set_difference(A!10, B!9)))) | (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 (~((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[205, 199])).
% 0.20/0.51 tff(207,plain,
% 0.20/0.51 (((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_union2(B!9, A!10))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)) | (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 (((~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(set_union2(A!10, B!9), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))) | (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(210,plain,
% 0.20/0.51 (~in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[209, 117])).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 ((~(in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 ((~(in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), set_difference(A!10, B!9)) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9))) | in(tptp_fun_C_2(set_difference(A!10, B!9), set_difference(set_union2(A!10, B!9), B!9)), B!9)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[212, 208, 154])).
% 0.20/0.51 % SZS output end Proof
% 0.20/0.51 % E exiting
%------------------------------------------------------------------------------