%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU170+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:08 AM UTC 2025
% Result : Theorem 0.47s 0.72s
% Output : Proof 0.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU170+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Jun 20 06:11:16 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.47/0.72 % SZS status Theorem
% 0.47/0.72 % SZS output start Proof
% 0.47/0.72 tff(in_type, type, (
% 0.47/0.72 in: ( $i * $i ) > $o)).
% 0.47/0.72 tff(set_difference_type, type, (
% 0.47/0.72 set_difference: ( $i * $i ) > $i)).
% 0.47/0.72 tff(tptp_fun_C_10_type, type, (
% 0.47/0.72 tptp_fun_C_10: $i)).
% 0.47/0.72 tff(tptp_fun_A_9_type, type, (
% 0.47/0.72 tptp_fun_A_9: $i)).
% 0.47/0.72 tff(tptp_fun_C_7_type, type, (
% 0.47/0.72 tptp_fun_C_7: ( $i * $i ) > $i)).
% 0.47/0.72 tff(tptp_fun_B_8_type, type, (
% 0.47/0.72 tptp_fun_B_8: $i)).
% 0.47/0.72 tff(subset_complement_type, type, (
% 0.47/0.72 subset_complement: ( $i * $i ) > $i)).
% 0.47/0.72 tff(element_type, type, (
% 0.47/0.72 element: ( $i * $i ) > $o)).
% 0.47/0.72 tff(powerset_type, type, (
% 0.47/0.72 powerset: $i > $i)).
% 0.47/0.72 tff(subset_type, type, (
% 0.47/0.72 subset: ( $i * $i ) > $o)).
% 0.47/0.72 tff(disjoint_type, type, (
% 0.47/0.72 disjoint: ( $i * $i ) > $o)).
% 0.47/0.72 tff(tptp_fun_C_0_type, type, (
% 0.47/0.72 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.47/0.72 tff(tptp_fun_B_5_type, type, (
% 0.47/0.72 tptp_fun_B_5: $i > $i)).
% 0.47/0.72 tff(tptp_fun_D_1_type, type, (
% 0.47/0.72 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.47/0.72 tff(empty_set_type, type, (
% 0.47/0.72 empty_set: $i)).
% 0.47/0.72 tff(empty_type, type, (
% 0.47/0.72 empty: $i > $o)).
% 0.47/0.72 tff(1,plain,
% 0.47/0.72 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) <=> (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(2,plain,
% 0.47/0.72 ((~![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))) <=> (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C))))))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(3,axiom,(~![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, powerset(A)) => (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t43_subset_1')).
% 0.47/0.72 tff(4,plain,
% 0.47/0.72 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.47/0.72 tff(5,plain,
% 0.47/0.72 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.47/0.72 tff(6,plain,
% 0.47/0.72 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.47/0.72 tff(7,plain,
% 0.47/0.72 (~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~element(C, powerset(A))) | (disjoint(B, C) <=> subset(B, subset_complement(A, C)))))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.47/0.72 tff(8,plain,
% 0.47/0.72 (~((~element(C!10, powerset(A!9))) | (disjoint(B!8, C!10) <=> subset(B!8, subset_complement(A!9, C!10))))),
% 0.47/0.72 inference(and_elim,[status(thm)],[7])).
% 0.47/0.72 tff(9,plain,
% 0.47/0.72 (element(C!10, powerset(A!9))),
% 0.47/0.72 inference(or_elim,[status(thm)],[8])).
% 0.47/0.72 tff(10,plain,
% 0.47/0.72 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 0.47/0.72 inference(bind,[status(th)],[])).
% 0.47/0.72 tff(11,plain,
% 0.47/0.72 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.47/0.72 inference(quant_intro,[status(thm)],[10])).
% 0.47/0.72 tff(12,plain,
% 0.47/0.72 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(13,plain,
% 0.47/0.72 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B))))),
% 0.47/0.72 inference(bind,[status(th)],[])).
% 0.47/0.72 tff(14,plain,
% 0.47/0.72 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.47/0.72 inference(quant_intro,[status(thm)],[13])).
% 0.47/0.72 tff(15,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, B) = set_difference(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d5_subset_1')).
% 0.47/0.72 tff(16,plain,
% 0.47/0.72 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.47/0.72 tff(17,plain,
% 0.47/0.72 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.47/0.72 tff(18,plain,(
% 0.47/0.72 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.47/0.72 inference(skolemize,[status(sab)],[17])).
% 0.47/0.72 tff(19,plain,
% 0.47/0.72 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.47/0.72 tff(20,plain,
% 0.47/0.72 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(C!10, powerset(A!9))) | (subset_complement(A!9, C!10) = set_difference(A!9, C!10)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(C!10, powerset(A!9))) | (subset_complement(A!9, C!10) = set_difference(A!9, C!10)))),
% 0.47/0.72 inference(rewrite,[status(thm)],[])).
% 0.47/0.72 tff(21,plain,
% 0.47/0.72 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(C!10, powerset(A!9))) | (subset_complement(A!9, C!10) = set_difference(A!9, C!10)))),
% 0.47/0.72 inference(quant_inst,[status(thm)],[])).
% 0.47/0.72 tff(22,plain,
% 0.47/0.72 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(C!10, powerset(A!9))) | (subset_complement(A!9, C!10) = set_difference(A!9, C!10))),
% 0.47/0.72 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.47/0.72 tff(23,plain,
% 0.47/0.72 (subset_complement(A!9, C!10) = set_difference(A!9, C!10)),
% 0.47/0.72 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.47/0.72 tff(24,plain,
% 0.47/0.72 (set_difference(A!9, C!10) = subset_complement(A!9, C!10)),
% 0.47/0.72 inference(symmetry,[status(thm)],[23])).
% 0.47/0.72 tff(25,plain,
% 0.47/0.72 (in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)) <=> in(tptp_fun_C_7(C!10, B!8), subset_complement(A!9, C!10))),
% 0.47/0.72 inference(monotonicity,[status(thm)],[24])).
% 0.47/0.72 tff(26,plain,
% 0.47/0.72 (in(tptp_fun_C_7(C!10, B!8), subset_complement(A!9, C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10))),
% 0.47/0.72 inference(symmetry,[status(thm)],[25])).
% 0.47/0.72 tff(27,plain,
% 0.47/0.72 (^[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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.47/0.72 inference(bind,[status(th)],[])).
% 0.47/0.72 tff(28,plain,
% 0.47/0.72 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.72 inference(quant_intro,[status(thm)],[27])).
% 0.47/0.72 tff(29,plain,
% 0.47/0.72 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(pull_quant,[status(thm)],[])).
% 0.47/0.73 tff(30,plain,
% 0.47/0.73 (^[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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(31,plain,
% 0.47/0.73 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[30])).
% 0.47/0.73 tff(32,plain,
% 0.47/0.73 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(transitivity,[status(thm)],[31, 29])).
% 0.47/0.73 tff(33,plain,
% 0.47/0.73 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(transitivity,[status(thm)],[32, 28])).
% 0.47/0.73 tff(34,plain,
% 0.47/0.73 (^[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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(35,plain,
% 0.47/0.73 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[34])).
% 0.47/0.73 tff(36,plain,
% 0.47/0.73 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(transitivity,[status(thm)],[35, 33])).
% 0.47/0.73 tff(37,plain,
% 0.47/0.73 (^[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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))), ((((~(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> (((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) & ((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C)))))), 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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(38,plain,
% 0.47/0.73 (![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B))))))) <=> ![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[37])).
% 0.47/0.73 tff(39,plain,
% 0.47/0.73 (![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)))))),
% 0.47/0.73 inference(rewrite,[status(thm)],[])).
% 0.47/0.73 tff(40,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/sandbox/benchmark/theBenchmark.p','d4_xboole_0')).
% 0.47/0.73 tff(41,plain,
% 0.47/0.73 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.47/0.73 tff(42,plain,(
% 0.47/0.73 ![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_1(C, B, A), C) <=> (in(tptp_fun_D_1(C, B, A), A) & (~in(tptp_fun_D_1(C, B, A), B)))))))),
% 0.47/0.73 inference(skolemize,[status(sab)],[41])).
% 0.47/0.73 tff(43,plain,
% 0.47/0.73 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.47/0.73 tff(44,plain,
% 0.47/0.73 (![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.47/0.73 tff(45,plain,
% 0.47/0.73 ((~![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)))))) | (~((set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10)) | (((~in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), C!10)) <=> in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, C!10)))))))),
% 0.47/0.73 inference(quant_inst,[status(thm)],[])).
% 0.47/0.73 tff(46,plain,
% 0.47/0.73 (~((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)))))) | (~((set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10)) | (((~in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), C!10)) <=> in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, C!10))))))),
% 0.47/0.73 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.47/0.73 tff(47,plain,
% 0.47/0.73 (((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)))))) | (~((set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10)) | (((~in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), C!10)) <=> in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, C!10)))))) | ((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)))))),
% 0.47/0.73 inference(tautology,[status(thm)],[])).
% 0.47/0.73 tff(48,plain,
% 0.47/0.73 ((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10))))),
% 0.47/0.73 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.47/0.73 tff(49,plain,
% 0.47/0.73 (^[A: $i] : refl((set_difference(A, empty_set) = A) <=> (set_difference(A, empty_set) = A))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(50,plain,
% 0.47/0.73 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 0.47/0.73 inference(quant_intro,[status(thm)],[49])).
% 0.47/0.73 tff(51,plain,
% 0.47/0.73 (![A: $i] : (set_difference(A, empty_set) = A) <=> ![A: $i] : (set_difference(A, empty_set) = A)),
% 0.47/0.73 inference(rewrite,[status(thm)],[])).
% 0.47/0.73 tff(52,axiom,(![A: $i] : (set_difference(A, empty_set) = A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_boole')).
% 0.47/0.73 tff(53,plain,
% 0.47/0.73 (![A: $i] : (set_difference(A, empty_set) = A)),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.47/0.73 tff(54,plain,(
% 0.47/0.73 ![A: $i] : (set_difference(A, empty_set) = A)),
% 0.47/0.73 inference(skolemize,[status(sab)],[53])).
% 0.47/0.73 tff(55,plain,
% 0.47/0.73 (![A: $i] : (set_difference(A, empty_set) = A)),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.47/0.73 tff(56,plain,
% 0.47/0.73 ((~![A: $i] : (set_difference(A, empty_set) = A)) | (set_difference(A!9, empty_set) = A!9)),
% 0.47/0.73 inference(quant_inst,[status(thm)],[])).
% 0.47/0.73 tff(57,plain,
% 0.47/0.73 (set_difference(A!9, empty_set) = A!9),
% 0.47/0.73 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.47/0.73 tff(58,plain,
% 0.47/0.73 (^[A: $i] : refl((~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))) <=> (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(59,plain,
% 0.47/0.73 (![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))) <=> ![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[58])).
% 0.47/0.73 tff(60,plain,
% 0.47/0.73 (^[A: $i] : rewrite((element(tptp_fun_B_5(A), powerset(A)) & empty(tptp_fun_B_5(A))) <=> (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(61,plain,
% 0.47/0.73 (![A: $i] : (element(tptp_fun_B_5(A), powerset(A)) & empty(tptp_fun_B_5(A))) <=> ![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[60])).
% 0.47/0.73 tff(62,plain,
% 0.47/0.73 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B)) <=> ![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 0.47/0.73 inference(rewrite,[status(thm)],[])).
% 0.47/0.73 tff(63,axiom,(![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc2_subset_1')).
% 0.47/0.73 tff(64,plain,
% 0.47/0.73 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.47/0.73 tff(65,plain,(
% 0.47/0.73 ![A: $i] : (element(tptp_fun_B_5(A), powerset(A)) & empty(tptp_fun_B_5(A)))),
% 0.47/0.73 inference(skolemize,[status(sab)],[64])).
% 0.47/0.73 tff(66,plain,
% 0.47/0.73 (![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.47/0.73 tff(67,plain,
% 0.47/0.73 (![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.47/0.73 tff(68,plain,
% 0.47/0.73 ((~![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))) | (~((~element(tptp_fun_B_5(A!9), powerset(A!9))) | (~empty(tptp_fun_B_5(A!9)))))),
% 0.47/0.73 inference(quant_inst,[status(thm)],[])).
% 0.47/0.73 tff(69,plain,
% 0.47/0.73 (~((~element(tptp_fun_B_5(A!9), powerset(A!9))) | (~empty(tptp_fun_B_5(A!9))))),
% 0.47/0.73 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.47/0.73 tff(70,plain,
% 0.47/0.73 (((~element(tptp_fun_B_5(A!9), powerset(A!9))) | (~empty(tptp_fun_B_5(A!9)))) | empty(tptp_fun_B_5(A!9))),
% 0.47/0.73 inference(tautology,[status(thm)],[])).
% 0.47/0.73 tff(71,plain,
% 0.47/0.73 (empty(tptp_fun_B_5(A!9))),
% 0.47/0.73 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.47/0.73 tff(72,plain,
% 0.47/0.73 (^[A: $i, B: $i] : refl(((~empty(B)) | (A = B) | (~empty(A))) <=> ((~empty(B)) | (A = B) | (~empty(A))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(73,plain,
% 0.47/0.73 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[72])).
% 0.47/0.73 tff(74,plain,
% 0.47/0.73 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(B)) | (A = B) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(B)) | (A = B) | (~empty(A))))))), rewrite((~(~((~empty(B)) | (A = B) | (~empty(A))))) <=> ((~empty(B)) | (A = B) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(B)) | (A = B) | (~empty(A)))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(75,plain,
% 0.47/0.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[74])).
% 0.47/0.73 tff(76,plain,
% 0.47/0.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.47/0.73 inference(rewrite,[status(thm)],[])).
% 0.47/0.73 tff(77,plain,
% 0.47/0.73 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.47/0.73 inference(bind,[status(th)],[])).
% 0.47/0.73 tff(78,plain,
% 0.47/0.73 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.47/0.73 inference(quant_intro,[status(thm)],[77])).
% 0.47/0.73 tff(79,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 0.47/0.73 tff(80,plain,
% 0.47/0.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.47/0.73 tff(81,plain,
% 0.47/0.73 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.47/0.73 tff(82,plain,(
% 0.47/0.73 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.47/0.73 inference(skolemize,[status(sab)],[81])).
% 0.47/0.73 tff(83,plain,
% 0.47/0.73 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.47/0.73 tff(84,plain,
% 0.47/0.73 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[83, 73])).
% 0.47/0.73 tff(85,plain,
% 0.47/0.73 (empty(empty_set) <=> empty(empty_set)),
% 0.47/0.73 inference(rewrite,[status(thm)],[])).
% 0.47/0.73 tff(86,axiom,(empty(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.47/0.73 tff(87,plain,
% 0.47/0.73 (empty(empty_set)),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.47/0.73 tff(88,plain,
% 0.47/0.73 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(A!9))) | (~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!9))) | (~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set))),
% 0.47/0.73 inference(rewrite,[status(thm)],[])).
% 0.47/0.73 tff(89,plain,
% 0.47/0.73 (((~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set) | (~empty(tptp_fun_B_5(A!9)))) <=> ((~empty(tptp_fun_B_5(A!9))) | (~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set))),
% 0.47/0.73 inference(rewrite,[status(thm)],[])).
% 0.47/0.73 tff(90,plain,
% 0.47/0.73 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set) | (~empty(tptp_fun_B_5(A!9))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(A!9))) | (~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set)))),
% 0.47/0.73 inference(monotonicity,[status(thm)],[89])).
% 0.47/0.73 tff(91,plain,
% 0.47/0.73 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set) | (~empty(tptp_fun_B_5(A!9))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!9))) | (~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set))),
% 0.47/0.73 inference(transitivity,[status(thm)],[90, 88])).
% 0.47/0.73 tff(92,plain,
% 0.47/0.73 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set) | (~empty(tptp_fun_B_5(A!9))))),
% 0.47/0.73 inference(quant_inst,[status(thm)],[])).
% 0.47/0.73 tff(93,plain,
% 0.47/0.73 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!9))) | (~empty(empty_set)) | (tptp_fun_B_5(A!9) = empty_set)),
% 0.47/0.73 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.47/0.73 tff(94,plain,
% 0.47/0.73 (tptp_fun_B_5(A!9) = empty_set),
% 0.47/0.73 inference(unit_resolution,[status(thm)],[93, 87, 84, 71])).
% 0.47/0.73 tff(95,plain,
% 0.47/0.73 (empty_set = tptp_fun_B_5(A!9)),
% 0.47/0.73 inference(symmetry,[status(thm)],[94])).
% 0.47/0.73 tff(96,plain,
% 0.47/0.73 (set_difference(A!9, empty_set) = set_difference(A!9, tptp_fun_B_5(A!9))),
% 0.47/0.73 inference(monotonicity,[status(thm)],[95])).
% 0.47/0.73 tff(97,plain,
% 0.47/0.73 (set_difference(A!9, tptp_fun_B_5(A!9)) = set_difference(A!9, empty_set)),
% 0.47/0.73 inference(symmetry,[status(thm)],[96])).
% 0.47/0.73 tff(98,plain,
% 0.47/0.73 (set_difference(A!9, tptp_fun_B_5(A!9)) = A!9),
% 0.47/0.73 inference(transitivity,[status(thm)],[97, 57])).
% 0.47/0.73 tff(99,plain,
% 0.47/0.73 (set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10) = set_difference(A!9, C!10)),
% 0.47/0.73 inference(monotonicity,[status(thm)],[98])).
% 0.47/0.73 tff(100,plain,
% 0.47/0.73 (set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10)),
% 0.47/0.73 inference(symmetry,[status(thm)],[99])).
% 0.47/0.73 tff(101,plain,
% 0.47/0.73 ((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)))))) | (~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10))))),
% 0.58/0.73 inference(tautology,[status(thm)],[])).
% 0.58/0.73 tff(102,plain,
% 0.58/0.73 (~(((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)))),
% 0.58/0.73 inference(unit_resolution,[status(thm)],[101, 100, 48])).
% 0.58/0.73 tff(103,plain,
% 0.58/0.73 (in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[24])).
% 0.58/0.73 tff(104,plain,
% 0.58/0.73 (in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10))),
% 0.58/0.73 inference(symmetry,[status(thm)],[103])).
% 0.58/0.73 tff(105,plain,
% 0.58/0.73 ((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))) <=> (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10)))),
% 0.58/0.73 inference(monotonicity,[status(thm)],[104])).
% 0.58/0.73 tff(106,assumption,(~subset(B!8, subset_complement(A!9, C!10))), introduced(assumption)).
% 0.58/0.73 tff(107,plain,
% 0.58/0.73 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.58/0.73 inference(bind,[status(th)],[])).
% 0.58/0.73 tff(108,plain,
% 0.58/0.73 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.58/0.73 inference(quant_intro,[status(thm)],[107])).
% 0.58/0.73 tff(109,plain,
% 0.58/0.73 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.58/0.73 inference(bind,[status(th)],[])).
% 0.58/0.73 tff(110,plain,
% 0.58/0.73 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.58/0.73 inference(quant_intro,[status(thm)],[109])).
% 0.58/0.73 tff(111,plain,
% 0.58/0.73 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.58/0.73 inference(transitivity,[status(thm)],[110, 108])).
% 0.58/0.73 tff(112,plain,
% 0.58/0.73 (^[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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.58/0.73 inference(bind,[status(th)],[])).
% 0.58/0.73 tff(113,plain,
% 0.58/0.73 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(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_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.58/0.73 inference(quant_intro,[status(thm)],[112])).
% 0.58/0.73 tff(114,plain,
% 0.58/0.73 (![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)))),
% 0.58/0.73 inference(rewrite,[status(thm)],[])).
% 0.58/0.73 tff(115,plain,
% 0.58/0.73 (^[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))))),
% 0.58/0.73 inference(bind,[status(th)],[])).
% 0.58/0.73 tff(116,plain,
% 0.58/0.73 (![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)))),
% 0.58/0.73 inference(quant_intro,[status(thm)],[115])).
% 0.58/0.73 tff(117,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d3_tarski')).
% 0.58/0.73 tff(118,plain,
% 0.58/0.73 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.58/0.73 tff(119,plain,
% 0.58/0.73 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.58/0.73 tff(120,plain,(
% 0.58/0.73 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.58/0.73 inference(skolemize,[status(sab)],[119])).
% 0.58/0.73 tff(121,plain,
% 0.58/0.73 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.58/0.73 tff(122,plain,
% 0.58/0.73 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.58/0.73 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.58/0.73 tff(123,plain,
% 0.58/0.73 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10))))) | (~(subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))))))))),
% 0.58/0.73 inference(quant_inst,[status(thm)],[])).
% 0.58/0.73 tff(124,plain,
% 0.58/0.73 (~((~((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10))))) | (~(subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10)))))))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.58/0.74 tff(125,plain,
% 0.58/0.74 (((~((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10))))) | (~(subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))))))) | (subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10)))))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(126,plain,
% 0.58/0.74 (subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.58/0.74 tff(127,plain,
% 0.58/0.74 ((~(subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10)))))) | subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(128,plain,
% 0.58/0.74 (subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.58/0.74 tff(129,plain,
% 0.58/0.74 (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10)))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[128, 106])).
% 0.58/0.74 tff(130,plain,
% 0.58/0.74 (((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10)))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(131,plain,
% 0.58/0.74 (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.58/0.74 tff(132,plain,
% 0.58/0.74 (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[131, 105])).
% 0.58/0.74 tff(133,plain,
% 0.58/0.74 (in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9))) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), A!9)),
% 0.58/0.74 inference(monotonicity,[status(thm)],[98])).
% 0.58/0.74 tff(134,plain,
% 0.58/0.74 (in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), A!9) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))),
% 0.58/0.74 inference(symmetry,[status(thm)],[133])).
% 0.58/0.74 tff(135,plain,
% 0.58/0.74 (element(B!8, powerset(A!9))),
% 0.58/0.74 inference(and_elim,[status(thm)],[7])).
% 0.58/0.74 tff(136,plain,
% 0.58/0.74 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(137,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[136])).
% 0.58/0.74 tff(138,plain,
% 0.58/0.74 (^[A: $i, B: $i] : rewrite(((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(139,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[138])).
% 0.58/0.74 tff(140,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(transitivity,[status(thm)],[139, 137])).
% 0.58/0.74 tff(141,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(142,plain,
% 0.58/0.74 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((in(C, B) => in(C, A)) <=> ((~in(C, B)) | in(C, A)))), (![C: $i] : (in(C, B) => in(C, A)) <=> ![C: $i] : ((~in(C, B)) | in(C, A)))), ((element(B, powerset(A)) => ![C: $i] : (in(C, B) => in(C, A))) <=> (element(B, powerset(A)) => ![C: $i] : ((~in(C, B)) | in(C, A))))), rewrite((element(B, powerset(A)) => ![C: $i] : ((~in(C, B)) | in(C, A))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))), ((element(B, powerset(A)) => ![C: $i] : (in(C, B) => in(C, A))) <=> ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(143,plain,
% 0.58/0.74 (![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (in(C, B) => in(C, A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[142])).
% 0.58/0.74 tff(144,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => ![C: $i] : (in(C, B) => in(C, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l3_subset_1')).
% 0.58/0.74 tff(145,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.58/0.74 tff(146,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.58/0.74 tff(147,plain,(
% 0.58/0.74 ![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(skolemize,[status(sab)],[146])).
% 0.58/0.74 tff(148,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.58/0.74 tff(149,plain,
% 0.58/0.74 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))) | ((~element(B!8, powerset(A!9))) | ![C: $i] : ((~in(C, B!8)) | in(C, A!9)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))) | (~element(B!8, powerset(A!9))) | ![C: $i] : ((~in(C, B!8)) | in(C, A!9)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(150,plain,
% 0.58/0.74 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))) | ((~element(B!8, powerset(A!9))) | ![C: $i] : ((~in(C, B!8)) | in(C, A!9)))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(151,plain,
% 0.58/0.74 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | ![C: $i] : ((~in(C, B)) | in(C, A)))) | (~element(B!8, powerset(A!9))) | ![C: $i] : ((~in(C, B!8)) | in(C, A!9))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.58/0.74 tff(152,plain,
% 0.58/0.74 (![C: $i] : ((~in(C, B!8)) | in(C, A!9))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[151, 148, 135])).
% 0.58/0.74 tff(153,plain,
% 0.58/0.74 (((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(154,plain,
% 0.58/0.74 (in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[153, 129])).
% 0.58/0.74 tff(155,plain,
% 0.58/0.74 (((~![C: $i] : ((~in(C, B!8)) | in(C, A!9))) | ((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), A!9))) <=> ((~![C: $i] : ((~in(C, B!8)) | in(C, A!9))) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), A!9))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(156,plain,
% 0.58/0.74 ((~![C: $i] : ((~in(C, B!8)) | in(C, A!9))) | ((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), A!9))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(157,plain,
% 0.58/0.74 ((~![C: $i] : ((~in(C, B!8)) | in(C, A!9))) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), A!9)),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.58/0.74 tff(158,plain,
% 0.58/0.74 (in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), A!9)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[157, 154, 152])).
% 0.58/0.74 tff(159,plain,
% 0.58/0.74 (in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[158, 134])).
% 0.58/0.74 tff(160,plain,
% 0.58/0.74 (~(disjoint(B!8, C!10) <=> subset(B!8, subset_complement(A!9, C!10)))),
% 0.58/0.74 inference(or_elim,[status(thm)],[8])).
% 0.58/0.74 tff(161,plain,
% 0.58/0.74 ((disjoint(B!8, C!10) <=> subset(B!8, subset_complement(A!9, C!10))) | disjoint(B!8, C!10) | subset(B!8, subset_complement(A!9, C!10))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(162,plain,
% 0.58/0.74 (disjoint(B!8, C!10) | subset(B!8, subset_complement(A!9, C!10))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.58/0.74 tff(163,plain,
% 0.58/0.74 (disjoint(B!8, C!10)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[162, 106])).
% 0.58/0.74 tff(164,plain,
% 0.58/0.74 (^[A: $i, B: $i] : refl((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(165,plain,
% 0.58/0.74 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[164])).
% 0.58/0.74 tff(166,plain,
% 0.58/0.74 (^[A: $i, B: $i] : rewrite((~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(167,plain,
% 0.58/0.74 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[166])).
% 0.58/0.74 tff(168,plain,
% 0.58/0.74 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))),
% 0.58/0.74 inference(transitivity,[status(thm)],[167, 165])).
% 0.58/0.74 tff(169,plain,
% 0.58/0.74 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((in(tptp_fun_C_7(B, A), A) & in(tptp_fun_C_7(B, A), B)) <=> (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B))))), ((disjoint(A, B) | (in(tptp_fun_C_7(B, A), A) & in(tptp_fun_C_7(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B))))))), rewrite((disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B))))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))), ((disjoint(A, B) | (in(tptp_fun_C_7(B, A), A) & in(tptp_fun_C_7(B, A), B))) <=> (disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B))))))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, A) & in(C, B)) <=> (~((~in(C, A)) | (~in(C, B))))), ((~(in(C, A) & in(C, B))) <=> (~(~((~in(C, A)) | (~in(C, B))))))), rewrite((~(~((~in(C, A)) | (~in(C, B))))) <=> ((~in(C, A)) | (~in(C, B)))), ((~(in(C, A) & in(C, B))) <=> ((~in(C, A)) | (~in(C, B)))))), (![C: $i] : (~(in(C, A) & in(C, B))) <=> ![C: $i] : ((~in(C, A)) | (~in(C, B))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> (![C: $i] : ((~in(C, A)) | (~in(C, B))) | (~disjoint(A, B))))), rewrite((![C: $i] : ((~in(C, A)) | (~in(C, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))), ((![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))) <=> ((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))), (((disjoint(A, B) | (in(tptp_fun_C_7(B, A), A) & in(tptp_fun_C_7(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ((disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))))), rewrite(((disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B))))) & ((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B))))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))), (((disjoint(A, B) | (in(tptp_fun_C_7(B, A), A) & in(tptp_fun_C_7(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))))),
% 0.58/0.74 inference(bind,[status(th)],[])).
% 0.58/0.74 tff(170,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_7(B, A), A) & in(tptp_fun_C_7(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B)))) <=> ![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))),
% 0.58/0.74 inference(quant_intro,[status(thm)],[169])).
% 0.58/0.74 tff(171,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B)))) <=> ![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(172,axiom,(![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_0')).
% 0.58/0.74 tff(173,plain,
% 0.58/0.74 (![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~(in(C, A) & in(C, B))))) & (~(?[C: $i] : (in(C, A) & in(C, B)) & disjoint(A, B))))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.58/0.74 tff(174,plain,(
% 0.58/0.74 ![A: $i, B: $i] : ((disjoint(A, B) | (in(tptp_fun_C_7(B, A), A) & in(tptp_fun_C_7(B, A), B))) & (![C: $i] : (~(in(C, A) & in(C, B))) | (~disjoint(A, B))))),
% 0.58/0.74 inference(skolemize,[status(sab)],[173])).
% 0.58/0.74 tff(175,plain,
% 0.58/0.74 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.58/0.74 tff(176,plain,
% 0.58/0.74 (![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.58/0.74 tff(177,plain,
% 0.58/0.74 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))))))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(178,plain,
% 0.58/0.74 ((~((~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))) | (~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))))) <=> (~((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))))))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(179,plain,
% 0.58/0.74 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))) | (~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))))))),
% 0.58/0.74 inference(monotonicity,[status(thm)],[178])).
% 0.58/0.74 tff(180,plain,
% 0.58/0.74 (((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))) | (~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))))))) <=> ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))))))),
% 0.58/0.74 inference(transitivity,[status(thm)],[179, 177])).
% 0.58/0.74 tff(181,plain,
% 0.58/0.74 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))) | (~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))))))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(182,plain,
% 0.58/0.74 ((~![A: $i, B: $i] : (~((~(disjoint(A, B) | (~((~in(tptp_fun_C_7(B, A), A)) | (~in(tptp_fun_C_7(B, A), B)))))) | (~((~disjoint(A, B)) | ![C: $i] : ((~in(C, A)) | (~in(C, B)))))))) | (~((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))))))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.58/0.74 tff(183,plain,
% 0.58/0.74 (~((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[182, 176])).
% 0.58/0.74 tff(184,plain,
% 0.58/0.74 (((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))))) | ((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(185,plain,
% 0.58/0.74 ((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.58/0.74 tff(186,plain,
% 0.58/0.74 ((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(187,plain,
% 0.58/0.74 ((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.58/0.74 tff(188,plain,
% 0.58/0.74 (![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[187, 163])).
% 0.58/0.74 tff(189,plain,
% 0.58/0.74 (((~![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))) | ((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)))) <=> ((~![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)))),
% 0.58/0.74 inference(rewrite,[status(thm)],[])).
% 0.58/0.74 tff(190,plain,
% 0.58/0.74 ((~![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))) | ((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)))),
% 0.58/0.74 inference(quant_inst,[status(thm)],[])).
% 0.58/0.74 tff(191,plain,
% 0.58/0.74 ((~![C: $i] : ((~in(C, B!8)) | (~in(C, C!10)))) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10))),
% 0.58/0.74 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.58/0.74 tff(192,plain,
% 0.58/0.74 (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[191, 154, 188])).
% 0.58/0.74 tff(193,plain,
% 0.58/0.74 ((~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10))) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(194,plain,
% 0.58/0.74 ((~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10))) | (~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9))))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.58/0.74 tff(195,plain,
% 0.58/0.74 (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[194, 159])).
% 0.58/0.74 tff(196,plain,
% 0.58/0.74 ((((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) <=> in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10))) | ((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), C!10)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), set_difference(A!9, C!10))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(197,plain,
% 0.58/0.74 ($false),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[196, 195, 132, 102])).
% 0.58/0.74 tff(198,plain,(subset(B!8, subset_complement(A!9, C!10))), inference(lemma,lemma(discharge,[]))).
% 0.58/0.74 tff(199,plain,
% 0.58/0.74 ((disjoint(B!8, C!10) <=> subset(B!8, subset_complement(A!9, C!10))) | (~disjoint(B!8, C!10)) | (~subset(B!8, subset_complement(A!9, C!10)))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(200,plain,
% 0.58/0.74 ((~disjoint(B!8, C!10)) | (~subset(B!8, subset_complement(A!9, C!10)))),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[199, 160])).
% 0.58/0.74 tff(201,plain,
% 0.58/0.74 (~disjoint(B!8, C!10)),
% 0.58/0.74 inference(unit_resolution,[status(thm)],[200, 198])).
% 0.58/0.74 tff(202,plain,
% 0.58/0.74 (((~((~disjoint(B!8, C!10)) | ![C: $i] : ((~in(C, B!8)) | (~in(C, C!10))))) | (~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))))) | (disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))),
% 0.58/0.74 inference(tautology,[status(thm)],[])).
% 0.58/0.74 tff(203,plain,
% 0.58/0.74 (disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[202, 183])).
% 0.58/0.75 tff(204,plain,
% 0.58/0.75 ((~(disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))))) | disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(205,plain,
% 0.58/0.75 (disjoint(B!8, C!10) | (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.58/0.75 tff(206,plain,
% 0.58/0.75 (~((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10)))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[205, 201])).
% 0.58/0.75 tff(207,plain,
% 0.58/0.75 (((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))) | in(tptp_fun_C_7(C!10, B!8), B!8)),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(208,plain,
% 0.58/0.75 (in(tptp_fun_C_7(C!10, B!8), B!8)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.58/0.75 tff(209,plain,
% 0.58/0.75 (((~((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10))))) | (~(subset(B!8, subset_complement(A!9, C!10)) | (~((~in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), B!8)) | in(tptp_fun_C_0(subset_complement(A!9, C!10), B!8), subset_complement(A!9, C!10))))))) | ((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10))))),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(210,plain,
% 0.58/0.75 ((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[209, 124])).
% 0.58/0.75 tff(211,plain,
% 0.58/0.75 ((~((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10))))) | (~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(212,plain,
% 0.58/0.75 ((~subset(B!8, subset_complement(A!9, C!10))) | ![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[211, 210])).
% 0.58/0.75 tff(213,plain,
% 0.58/0.75 (![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[212, 198])).
% 0.58/0.75 tff(214,plain,
% 0.58/0.75 (((~![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))) | ((~in(tptp_fun_C_7(C!10, B!8), B!8)) | in(tptp_fun_C_7(C!10, B!8), subset_complement(A!9, C!10)))) <=> ((~![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))) | (~in(tptp_fun_C_7(C!10, B!8), B!8)) | in(tptp_fun_C_7(C!10, B!8), subset_complement(A!9, C!10)))),
% 0.58/0.75 inference(rewrite,[status(thm)],[])).
% 0.58/0.75 tff(215,plain,
% 0.58/0.75 ((~![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))) | ((~in(tptp_fun_C_7(C!10, B!8), B!8)) | in(tptp_fun_C_7(C!10, B!8), subset_complement(A!9, C!10)))),
% 0.58/0.75 inference(quant_inst,[status(thm)],[])).
% 0.58/0.75 tff(216,plain,
% 0.58/0.75 ((~![C: $i] : ((~in(C, B!8)) | in(C, subset_complement(A!9, C!10)))) | (~in(tptp_fun_C_7(C!10, B!8), B!8)) | in(tptp_fun_C_7(C!10, B!8), subset_complement(A!9, C!10))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.58/0.75 tff(217,plain,
% 0.58/0.75 (in(tptp_fun_C_7(C!10, B!8), subset_complement(A!9, C!10))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[216, 213, 208])).
% 0.58/0.75 tff(218,plain,
% 0.58/0.75 (in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10))),
% 0.58/0.75 inference(modus_ponens,[status(thm)],[217, 26])).
% 0.58/0.75 tff(219,plain,
% 0.58/0.75 ((~![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_1(C, B, A), A)) | in(tptp_fun_D_1(C, B, A), B)) <=> in(tptp_fun_D_1(C, B, A), C))))))) | (~((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))))) | (~((set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10)) | (((~in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), C!10)) <=> in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, C!10)))))))),
% 0.58/0.75 inference(quant_inst,[status(thm)],[])).
% 0.58/0.75 tff(220,plain,
% 0.58/0.75 (~((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))))) | (~((set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10)) | (((~in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), C!10)) <=> in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, C!10))))))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[219, 44])).
% 0.58/0.75 tff(221,plain,
% 0.58/0.75 (((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))))) | (~((set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10)) | (((~in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), C!10)) <=> in(tptp_fun_D_1(set_difference(A!9, C!10), C!10, set_difference(A!9, tptp_fun_B_5(A!9))), set_difference(A!9, C!10)))))) | ((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))))),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(222,plain,
% 0.58/0.75 ((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10))))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.58/0.75 tff(223,plain,
% 0.58/0.75 ((~((~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))))) | (~(set_difference(A!9, C!10) = set_difference(set_difference(A!9, tptp_fun_B_5(A!9)), C!10))) | (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10))))),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(224,plain,
% 0.58/0.75 (~(((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[223, 100, 222])).
% 0.58/0.75 tff(225,plain,
% 0.58/0.75 (((~in(tptp_fun_C_7(C!10, B!8), B!8)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))) | in(tptp_fun_C_7(C!10, B!8), C!10)),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(226,plain,
% 0.58/0.75 (in(tptp_fun_C_7(C!10, B!8), C!10)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[225, 206])).
% 0.58/0.75 tff(227,plain,
% 0.58/0.75 (((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) | (~in(tptp_fun_C_7(C!10, B!8), C!10))),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(228,plain,
% 0.58/0.75 ((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.58/0.75 tff(229,plain,
% 0.58/0.75 ((((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10))) | (~((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10))) | (~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))),
% 0.58/0.75 inference(tautology,[status(thm)],[])).
% 0.58/0.75 tff(230,plain,
% 0.58/0.75 ((((~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, tptp_fun_B_5(A!9)))) | in(tptp_fun_C_7(C!10, B!8), C!10)) <=> in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10))) | (~in(tptp_fun_C_7(C!10, B!8), set_difference(A!9, C!10)))),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.58/0.75 tff(231,plain,
% 0.58/0.75 ($false),
% 0.58/0.75 inference(unit_resolution,[status(thm)],[230, 224, 218])).
% 0.58/0.75 % SZS output end Proof
% 0.58/0.75 % E exiting
%------------------------------------------------------------------------------