%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU137+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.55s 0.73s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU137+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:07:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.55/0.73 % SZS status Theorem
% 0.55/0.73 % SZS output start Proof
% 0.55/0.73 tff(in_type, type, (
% 0.55/0.73 in: ( $i * $i ) > $o)).
% 0.55/0.73 tff(set_difference_type, type, (
% 0.55/0.73 set_difference: ( $i * $i ) > $i)).
% 0.55/0.73 tff(tptp_fun_A_7_type, type, (
% 0.55/0.73 tptp_fun_A_7: $i)).
% 0.55/0.73 tff(tptp_fun_B_6_type, type, (
% 0.55/0.73 tptp_fun_B_6: $i)).
% 0.55/0.73 tff(tptp_fun_D_0_type, type, (
% 0.55/0.73 tptp_fun_D_0: ( $i * $i * $i ) > $i)).
% 0.55/0.73 tff(set_union2_type, type, (
% 0.55/0.73 set_union2: ( $i * $i ) > $i)).
% 0.55/0.73 tff(subset_type, type, (
% 0.55/0.73 subset: ( $i * $i ) > $o)).
% 0.55/0.73 tff(tptp_fun_C_1_type, type, (
% 0.55/0.73 tptp_fun_C_1: ( $i * $i ) > $i)).
% 0.55/0.73 tff(tptp_fun_D_2_type, type, (
% 0.55/0.73 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.55/0.73 tff(1,assumption,(~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)), introduced(assumption)).
% 0.55/0.73 tff(2,plain,
% 0.55/0.73 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(3,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[2])).
% 0.55/0.73 tff(4,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(pull_quant,[status(thm)],[])).
% 0.55/0.73 tff(5,plain,
% 0.55/0.73 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> (~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), pull_quant((~![D: $i] : ((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A)))))), ((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) <=> ?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> (?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), pull_quant((?[D: $i] : (~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), (((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))) <=> ?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))), pull_quant((~?[D: $i] : ((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(6,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[5])).
% 0.55/0.73 tff(7,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[6, 4])).
% 0.55/0.73 tff(8,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[7, 3])).
% 0.55/0.73 tff(9,plain,
% 0.55/0.73 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(10,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[9])).
% 0.55/0.73 tff(11,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))) <=> ![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[10, 8])).
% 0.55/0.73 tff(12,plain,
% 0.55/0.73 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) <=> ((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))), trans(monotonicity(rewrite((~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))) <=> (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), rewrite(((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))), (((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))) <=> ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))))), rewrite((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))), ((((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(13,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A)))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[12])).
% 0.55/0.73 tff(14,plain,
% 0.55/0.73 (![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))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(15,plain,
% 0.55/0.73 (^[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)))))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(16,plain,
% 0.55/0.73 (![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))))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[15])).
% 0.55/0.73 tff(17,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')).
% 0.55/0.73 tff(18,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.55/0.73 tff(19,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : ((C = set_union2(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.55/0.73 tff(20,plain,(
% 0.55/0.73 ![A: $i, B: $i, C: $i] : (((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A)))) & ((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))),
% 0.55/0.73 inference(skolemize,[status(sab)],[19])).
% 0.55/0.73 tff(21,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_union2(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.55/0.73 tff(22,plain,
% 0.55/0.73 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.55/0.73 tff(23,plain,
% 0.55/0.73 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_union2(A, B))) | (in(D, C) <=> (in(D, B) | in(D, A))))) | (~((C = set_union2(A, B)) | (~(in(tptp_fun_D_0(C, B, A), C) <=> (in(tptp_fun_D_0(C, B, A), B) | in(tptp_fun_D_0(C, B, A), A))))))))) | (~((~((~(B!6 = set_union2(set_difference(B!6, A!7), A!7))) | (in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((B!6 = set_union2(set_difference(B!6, A!7), A!7)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(24,plain,
% 0.55/0.73 (~((~((~(B!6 = set_union2(set_difference(B!6, A!7), A!7))) | (in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((B!6 = set_union2(set_difference(B!6, A!7), A!7)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.55/0.73 tff(25,plain,
% 0.55/0.73 (((~((~(B!6 = set_union2(set_difference(B!6, A!7), A!7))) | (in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(set_difference(B!6, A!7), A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((B!6 = set_union2(set_difference(B!6, A!7), A!7)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))))) | ((B!6 = set_union2(set_difference(B!6, A!7), A!7)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))))),
% 0.55/0.73 inference(tautology,[status(thm)],[])).
% 0.55/0.73 tff(26,plain,
% 0.55/0.73 ((B!6 = set_union2(set_difference(B!6, A!7), A!7)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[25, 24])).
% 0.55/0.73 tff(27,plain,
% 0.55/0.73 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.55/0.73 inference(bind,[status(th)],[])).
% 0.55/0.73 tff(28,plain,
% 0.55/0.73 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.55/0.73 inference(quant_intro,[status(thm)],[27])).
% 0.55/0.73 tff(29,plain,
% 0.55/0.73 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(30,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.55/0.73 tff(31,plain,
% 0.55/0.73 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.55/0.73 tff(32,plain,(
% 0.55/0.73 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.55/0.73 inference(skolemize,[status(sab)],[31])).
% 0.55/0.73 tff(33,plain,
% 0.55/0.73 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.55/0.73 tff(34,plain,
% 0.55/0.73 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!7, set_difference(B!6, A!7)) = set_union2(set_difference(B!6, A!7), A!7))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(35,plain,
% 0.55/0.73 (set_union2(A!7, set_difference(B!6, A!7)) = set_union2(set_difference(B!6, A!7), A!7)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.55/0.73 tff(36,plain,
% 0.55/0.73 (set_union2(set_difference(B!6, A!7), A!7) = set_union2(A!7, set_difference(B!6, A!7))),
% 0.55/0.73 inference(symmetry,[status(thm)],[35])).
% 0.55/0.73 tff(37,plain,
% 0.55/0.73 ((B!6 = set_union2(set_difference(B!6, A!7), A!7)) <=> (B!6 = set_union2(A!7, set_difference(B!6, A!7)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[36])).
% 0.55/0.73 tff(38,plain,
% 0.55/0.73 ((B!6 = set_union2(A!7, set_difference(B!6, A!7))) <=> (B!6 = set_union2(set_difference(B!6, A!7), A!7))),
% 0.55/0.73 inference(symmetry,[status(thm)],[37])).
% 0.55/0.73 tff(39,plain,
% 0.55/0.73 ((~(B!6 = set_union2(A!7, set_difference(B!6, A!7)))) <=> (~(B!6 = set_union2(set_difference(B!6, A!7), A!7)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[38])).
% 0.55/0.73 tff(40,plain,
% 0.55/0.73 ((~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(41,plain,
% 0.55/0.73 ((~![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A)))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(42,axiom,(~![A: $i, B: $i] : (subset(A, B) => (B = set_union2(A, set_difference(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_xboole_1')).
% 0.55/0.73 tff(43,plain,
% 0.55/0.73 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.55/0.73 tff(44,plain,
% 0.55/0.73 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[43, 40])).
% 0.55/0.74 tff(45,plain,
% 0.55/0.74 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.55/0.74 tff(46,plain,
% 0.55/0.74 (~![A: $i, B: $i] : ((~subset(A, B)) | (B = set_union2(A, set_difference(B, A))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[45, 40])).
% 0.55/0.74 tff(47,plain,(
% 0.55/0.74 ~((~subset(A!7, B!6)) | (B!6 = set_union2(A!7, set_difference(B!6, A!7))))),
% 0.55/0.74 inference(skolemize,[status(sab)],[46])).
% 0.55/0.74 tff(48,plain,
% 0.55/0.74 (~(B!6 = set_union2(A!7, set_difference(B!6, A!7)))),
% 0.55/0.74 inference(or_elim,[status(thm)],[47])).
% 0.55/0.74 tff(49,plain,
% 0.55/0.74 (~(B!6 = set_union2(set_difference(B!6, A!7), A!7))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[48, 39])).
% 0.55/0.74 tff(50,plain,
% 0.55/0.74 ((~((B!6 = set_union2(set_difference(B!6, A!7), A!7)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))))) | (B!6 = set_union2(set_difference(B!6, A!7), A!7)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))),
% 0.55/0.74 inference(tautology,[status(thm)],[])).
% 0.55/0.74 tff(51,plain,
% 0.55/0.74 (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[50, 49, 26])).
% 0.55/0.74 tff(52,plain,
% 0.55/0.74 ((in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) | (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.74 inference(tautology,[status(thm)],[])).
% 0.55/0.74 tff(53,plain,
% 0.55/0.74 (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) | (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.55/0.74 tff(54,plain,
% 0.55/0.74 (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[53, 1])).
% 0.55/0.74 tff(55,plain,
% 0.55/0.74 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(56,plain,
% 0.55/0.74 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[55])).
% 0.55/0.74 tff(57,plain,
% 0.55/0.74 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(58,plain,
% 0.55/0.74 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[57])).
% 0.55/0.74 tff(59,plain,
% 0.55/0.74 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[58, 56])).
% 0.55/0.74 tff(60,plain,
% 0.55/0.74 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(61,plain,
% 0.55/0.74 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[60])).
% 0.55/0.74 tff(62,plain,
% 0.55/0.74 (![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)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(63,plain,
% 0.55/0.74 (^[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))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(64,plain,
% 0.55/0.74 (![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)))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[63])).
% 0.55/0.74 tff(65,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')).
% 0.55/0.74 tff(66,plain,
% 0.55/0.74 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.55/0.74 tff(67,plain,
% 0.55/0.74 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.55/0.74 tff(68,plain,(
% 0.55/0.74 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))),
% 0.55/0.74 inference(skolemize,[status(sab)],[67])).
% 0.55/0.74 tff(69,plain,
% 0.55/0.74 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.55/0.74 tff(70,plain,
% 0.55/0.74 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.55/0.74 tff(71,plain,
% 0.55/0.74 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_1(B, A), A)) | in(tptp_fun_C_1(B, A), B)))))))) | (~((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~(subset(A!7, B!6) | (~((~in(tptp_fun_C_1(B!6, A!7), A!7)) | in(tptp_fun_C_1(B!6, A!7), B!6)))))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(72,plain,
% 0.55/0.74 (~((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~(subset(A!7, B!6) | (~((~in(tptp_fun_C_1(B!6, A!7), A!7)) | in(tptp_fun_C_1(B!6, A!7), B!6))))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.55/0.74 tff(73,plain,
% 0.55/0.74 (((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~(subset(A!7, B!6) | (~((~in(tptp_fun_C_1(B!6, A!7), A!7)) | in(tptp_fun_C_1(B!6, A!7), B!6)))))) | ((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))),
% 0.55/0.74 inference(tautology,[status(thm)],[])).
% 0.55/0.74 tff(74,plain,
% 0.55/0.74 ((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.55/0.74 tff(75,plain,
% 0.55/0.74 (subset(A!7, B!6)),
% 0.55/0.74 inference(or_elim,[status(thm)],[47])).
% 0.55/0.74 tff(76,plain,
% 0.55/0.74 ((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | (~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 0.55/0.74 inference(tautology,[status(thm)],[])).
% 0.55/0.74 tff(77,plain,
% 0.55/0.74 ((~((~subset(A!7, B!6)) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6)))) | ![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.55/0.74 tff(78,plain,
% 0.55/0.74 (![C: $i] : ((~in(C, A!7)) | in(C, B!6))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[77, 74])).
% 0.55/0.74 tff(79,plain,
% 0.55/0.74 (((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | ((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6))) <=> ((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(80,plain,
% 0.55/0.74 ((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | ((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(81,plain,
% 0.55/0.74 ((~![C: $i] : ((~in(C, A!7)) | in(C, B!6))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.55/0.74 tff(82,plain,
% 0.55/0.74 ((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[81, 78])).
% 0.55/0.74 tff(83,plain,
% 0.55/0.74 (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[82, 1])).
% 0.55/0.74 tff(84,plain,
% 0.55/0.74 (((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)),
% 0.55/0.74 inference(tautology,[status(thm)],[])).
% 0.55/0.74 tff(85,plain,
% 0.55/0.74 ((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[84, 1])).
% 0.55/0.74 tff(86,assumption,(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))), introduced(assumption)).
% 0.55/0.74 tff(87,plain,
% 0.55/0.74 (^[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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(88,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[87])).
% 0.55/0.74 tff(89,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(pull_quant,[status(thm)],[])).
% 0.55/0.74 tff(90,plain,
% 0.55/0.74 (^[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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(91,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[90])).
% 0.55/0.74 tff(92,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[91, 89])).
% 0.55/0.74 tff(93,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[92, 88])).
% 0.55/0.74 tff(94,plain,
% 0.55/0.74 (^[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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C)))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(95,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[94])).
% 0.55/0.74 tff(96,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[95, 93])).
% 0.55/0.74 tff(97,plain,
% 0.55/0.74 (^[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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))))),
% 0.55/0.74 inference(bind,[status(th)],[])).
% 0.55/0.74 tff(98,plain,
% 0.55/0.74 (![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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(quant_intro,[status(thm)],[97])).
% 0.55/0.74 tff(99,plain,
% 0.55/0.74 (![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)))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(100,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')).
% 0.55/0.74 tff(101,plain,
% 0.55/0.74 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.55/0.74 tff(102,plain,(
% 0.55/0.74 ![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_2(C, B, A), C) <=> (in(tptp_fun_D_2(C, B, A), A) & (~in(tptp_fun_D_2(C, B, A), B)))))))),
% 0.55/0.74 inference(skolemize,[status(sab)],[101])).
% 0.55/0.74 tff(103,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.55/0.74 tff(104,plain,
% 0.55/0.74 (![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.55/0.74 tff(105,plain,
% 0.55/0.74 (((~![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))) <=> ((~![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(106,plain,
% 0.55/0.74 ((~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))) <=> (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(107,plain,
% 0.55/0.74 (((((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))) | $false) <=> (((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(108,plain,
% 0.55/0.74 ((~$true) <=> $false),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(109,plain,
% 0.55/0.74 (($true | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))) <=> $true),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(110,plain,
% 0.55/0.74 ((set_difference(B!6, A!7) = set_difference(B!6, A!7)) <=> $true),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(111,plain,
% 0.55/0.74 (((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))) <=> ($true | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[110])).
% 0.55/0.74 tff(112,plain,
% 0.55/0.74 (((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))) <=> $true),
% 0.55/0.74 inference(transitivity,[status(thm)],[111, 109])).
% 0.55/0.74 tff(113,plain,
% 0.55/0.74 ((~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7))))) <=> (~$true)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[112])).
% 0.55/0.74 tff(114,plain,
% 0.55/0.74 ((~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7))))) <=> $false),
% 0.55/0.75 inference(transitivity,[status(thm)],[113, 108])).
% 0.55/0.75 tff(115,plain,
% 0.55/0.75 ((~(~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))) <=> (((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(116,plain,
% 0.55/0.75 (($false | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))) <=> (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(117,plain,
% 0.55/0.75 ((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) <=> (~$true)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[110])).
% 0.55/0.75 tff(118,plain,
% 0.55/0.75 ((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) <=> $false),
% 0.55/0.75 inference(transitivity,[status(thm)],[117, 108])).
% 0.55/0.75 tff(119,plain,
% 0.55/0.75 (((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))) <=> ($false | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[118, 106])).
% 0.55/0.75 tff(120,plain,
% 0.55/0.75 (((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))) <=> (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[119, 116])).
% 0.55/0.75 tff(121,plain,
% 0.55/0.75 ((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) <=> (~(~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[120])).
% 0.55/0.75 tff(122,plain,
% 0.55/0.75 ((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) <=> (((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[121, 115])).
% 0.55/0.75 tff(123,plain,
% 0.55/0.75 (((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))))) <=> ((((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))) | $false)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[122, 114])).
% 0.55/0.75 tff(124,plain,
% 0.55/0.75 (((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))))) <=> (((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.75 inference(transitivity,[status(thm)],[123, 107])).
% 0.55/0.75 tff(125,plain,
% 0.55/0.75 ((~((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7))))))) <=> (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[124])).
% 0.55/0.75 tff(126,plain,
% 0.55/0.75 ((~((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7))))))) <=> (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[125, 106])).
% 0.55/0.75 tff(127,plain,
% 0.55/0.75 (((~![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))))))) <=> ((~![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[126])).
% 0.55/0.75 tff(128,plain,
% 0.55/0.75 (((~![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))))))) <=> ((~![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[127, 105])).
% 0.55/0.75 tff(129,plain,
% 0.55/0.75 ((~![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_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~((~((~(set_difference(B!6, A!7) = set_difference(B!6, A!7))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))))) | (~((set_difference(B!6, A!7) = set_difference(B!6, A!7)) | (((~in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), B!6)) | in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), A!7)) <=> in(tptp_fun_D_2(set_difference(B!6, A!7), A!7, B!6), set_difference(B!6, A!7)))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(130,plain,
% 0.55/0.75 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_2(C, B, A), A)) | in(tptp_fun_D_2(C, B, A), B)) <=> in(tptp_fun_D_2(C, B, A), C))))))) | (~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.55/0.75 tff(131,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[130, 104, 86])).
% 0.55/0.75 tff(132,plain,(~(((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(133,plain,
% 0.55/0.75 ((((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))) | (~((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.75 inference(tautology,[status(thm)],[])).
% 0.55/0.75 tff(134,plain,
% 0.55/0.75 ((~((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.55/0.75 tff(135,plain,
% 0.55/0.75 (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[134, 85])).
% 0.55/0.75 tff(136,plain,
% 0.55/0.75 ((~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))),
% 0.55/0.75 inference(tautology,[status(thm)],[])).
% 0.55/0.75 tff(137,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[136, 135, 83, 54])).
% 0.55/0.75 tff(138,plain,(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(139,plain,
% 0.55/0.75 ((in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6) <=> (in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(140,plain,
% 0.55/0.76 ((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[139, 51])).
% 0.55/0.76 tff(141,plain,
% 0.55/0.76 (~(in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[140, 138])).
% 0.55/0.76 tff(142,plain,
% 0.55/0.76 ((in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7)))),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(143,plain,
% 0.55/0.76 (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.55/0.76 tff(144,plain,
% 0.55/0.76 ((in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7))),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(145,plain,
% 0.55/0.76 (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[144, 141])).
% 0.55/0.76 tff(146,plain,
% 0.55/0.76 ((~((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7))) | (~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(147,plain,
% 0.55/0.76 (~((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[146, 145, 138])).
% 0.55/0.76 tff(148,plain,
% 0.55/0.76 ((((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) <=> in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))) | ((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))),
% 0.55/0.76 inference(tautology,[status(thm)],[])).
% 0.55/0.76 tff(149,plain,
% 0.55/0.76 (((~in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), B!6)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), A!7)) | in(tptp_fun_D_0(B!6, A!7, set_difference(B!6, A!7)), set_difference(B!6, A!7))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[148, 132])).
% 0.55/0.76 tff(150,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[149, 147, 143])).
% 0.55/0.76 % SZS output end Proof
% 0.55/0.76 % E exiting
%------------------------------------------------------------------------------