%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU171+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 1.38s 1.55s
% Output : Proof 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU171+2 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n012.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % 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 06:11:10 EDT 2025
% 0.13/0.36 % CPUTime :
% 1.38/1.55 % SZS status Theorem
% 1.38/1.55 % SZS output start Proof
% 1.38/1.55 tff(in_type, type, (
% 1.38/1.55 in: ( $i * $i ) > $o)).
% 1.38/1.55 tff(tptp_fun_A_25_type, type, (
% 1.38/1.55 tptp_fun_A_25: $i)).
% 1.38/1.55 tff(tptp_fun_C_27_type, type, (
% 1.38/1.55 tptp_fun_C_27: $i)).
% 1.38/1.55 tff(subset_type, type, (
% 1.38/1.55 subset: ( $i * $i ) > $o)).
% 1.38/1.55 tff(singleton_type, type, (
% 1.38/1.55 singleton: $i > $i)).
% 1.38/1.55 tff(set_difference_type, type, (
% 1.38/1.55 set_difference: ( $i * $i ) > $i)).
% 1.38/1.55 tff(tptp_fun_B_26_type, type, (
% 1.38/1.55 tptp_fun_B_26: $i)).
% 1.38/1.55 tff(subset_complement_type, type, (
% 1.38/1.55 subset_complement: ( $i * $i ) > $i)).
% 1.38/1.55 tff(element_type, type, (
% 1.38/1.55 element: ( $i * $i ) > $o)).
% 1.38/1.55 tff(powerset_type, type, (
% 1.38/1.55 powerset: $i > $i)).
% 1.38/1.55 tff(empty_set_type, type, (
% 1.38/1.55 empty_set: $i)).
% 1.38/1.55 tff(disjoint_type, type, (
% 1.38/1.55 disjoint: ( $i * $i ) > $o)).
% 1.38/1.55 tff(empty_type, type, (
% 1.38/1.55 empty: $i > $o)).
% 1.38/1.55 tff(tptp_fun_C_10_type, type, (
% 1.38/1.55 tptp_fun_C_10: ( $i * $i ) > $i)).
% 1.38/1.55 tff(1,plain,
% 1.38/1.55 (^[A: $i, B: $i] : refl((subset(singleton(A), B) <=> in(A, B)) <=> (subset(singleton(A), B) <=> in(A, B)))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(2,plain,
% 1.38/1.55 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[1])).
% 1.38/1.55 tff(3,plain,
% 1.38/1.55 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B)) <=> ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(4,axiom,(![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l2_zfmisc_1')).
% 1.38/1.55 tff(5,plain,
% 1.38/1.55 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.38/1.55 tff(6,plain,(
% 1.38/1.55 ![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 1.38/1.55 inference(skolemize,[status(sab)],[5])).
% 1.38/1.55 tff(7,plain,
% 1.38/1.55 (![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.38/1.55 tff(8,plain,
% 1.38/1.55 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(C!27), A!25) <=> in(C!27, A!25))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(9,plain,
% 1.38/1.55 (subset(singleton(C!27), A!25) <=> in(C!27, A!25)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[8, 7])).
% 1.38/1.55 tff(10,plain,
% 1.38/1.55 (((~(A!25 = empty_set)) & (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))) <=> ((~(A!25 = empty_set)) & element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(11,plain,
% 1.38/1.55 ((~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))) <=> (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25))))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(12,plain,
% 1.38/1.55 ((element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25))))) <=> (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[11])).
% 1.38/1.55 tff(13,plain,
% 1.38/1.55 (((~(A!25 = empty_set)) & (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))) <=> ((~(A!25 = empty_set)) & (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25))))))),
% 1.38/1.55 inference(monotonicity,[status(thm)],[12])).
% 1.38/1.55 tff(14,plain,
% 1.38/1.55 (((~(A!25 = empty_set)) & (element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))) <=> ((~(A!25 = empty_set)) & element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))))),
% 1.38/1.55 inference(transitivity,[status(thm)],[13, 10])).
% 1.38/1.55 tff(15,plain,
% 1.38/1.55 ((~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(16,plain,
% 1.38/1.55 ((~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))) <=> (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A))))))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(17,axiom,(~![A: $i] : ((~(A = empty_set)) => ![B: $i] : (element(B, powerset(A)) => ![C: $i] : (element(C, A) => ((~in(C, B)) => in(C, subset_complement(A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t50_subset_1')).
% 1.38/1.55 tff(18,plain,
% 1.38/1.55 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.38/1.55 tff(19,plain,
% 1.38/1.55 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[18, 15])).
% 1.38/1.55 tff(20,plain,
% 1.38/1.55 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.38/1.55 tff(21,plain,
% 1.38/1.55 (~![A: $i] : ((A = empty_set) | ![B: $i] : ((~element(B, powerset(A))) | ![C: $i] : (in(C, B) | in(C, subset_complement(A, B)) | (~element(C, A)))))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[20, 15])).
% 1.38/1.55 tff(22,plain,
% 1.38/1.55 ((~(A!25 = empty_set)) & element(B!26, powerset(A!25)) & (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25))))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.38/1.55 tff(23,plain,
% 1.38/1.55 (element(B!26, powerset(A!25))),
% 1.38/1.55 inference(and_elim,[status(thm)],[22])).
% 1.38/1.55 tff(24,plain,
% 1.38/1.55 (^[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))))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(25,plain,
% 1.38/1.55 (![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)))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[24])).
% 1.38/1.55 tff(26,plain,
% 1.38/1.55 (![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)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(27,plain,
% 1.38/1.55 (^[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))))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(28,plain,
% 1.38/1.55 (![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)))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[27])).
% 1.38/1.55 tff(29,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')).
% 1.38/1.55 tff(30,plain,
% 1.38/1.55 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[29, 28])).
% 1.38/1.55 tff(31,plain,
% 1.38/1.55 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[30, 26])).
% 1.38/1.55 tff(32,plain,(
% 1.38/1.55 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.38/1.55 inference(skolemize,[status(sab)],[31])).
% 1.38/1.55 tff(33,plain,
% 1.38/1.55 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[32, 25])).
% 1.38/1.55 tff(34,plain,
% 1.38/1.55 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26)))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(35,plain,
% 1.38/1.55 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(36,plain,
% 1.38/1.55 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(B!26, powerset(A!25))) | (subset_complement(A!25, B!26) = set_difference(A!25, B!26))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[35, 34])).
% 1.38/1.55 tff(37,plain,
% 1.38/1.55 (subset_complement(A!25, B!26) = set_difference(A!25, B!26)),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[36, 33, 23])).
% 1.38/1.55 tff(38,plain,
% 1.38/1.55 (set_difference(A!25, B!26) = subset_complement(A!25, B!26)),
% 1.38/1.55 inference(symmetry,[status(thm)],[37])).
% 1.38/1.55 tff(39,plain,
% 1.38/1.55 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_difference(A, B) = A)) <=> (disjoint(A, B) <=> (set_difference(A, B) = A)))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(40,plain,
% 1.38/1.55 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[39])).
% 1.38/1.55 tff(41,plain,
% 1.38/1.55 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(42,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t83_xboole_1')).
% 1.38/1.55 tff(43,plain,
% 1.38/1.55 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[42, 41])).
% 1.38/1.55 tff(44,plain,(
% 1.38/1.55 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 1.38/1.55 inference(skolemize,[status(sab)],[43])).
% 1.38/1.55 tff(45,plain,
% 1.38/1.55 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))),
% 1.38/1.55 inference(modus_ponens,[status(thm)],[44, 40])).
% 1.38/1.55 tff(46,plain,
% 1.38/1.55 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_difference(A, B) = A))) | (disjoint(singleton(C!27), B!26) <=> (set_difference(singleton(C!27), B!26) = singleton(C!27)))),
% 1.38/1.55 inference(quant_inst,[status(thm)],[])).
% 1.38/1.55 tff(47,plain,
% 1.38/1.55 (disjoint(singleton(C!27), B!26) <=> (set_difference(singleton(C!27), B!26) = singleton(C!27))),
% 1.38/1.55 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.38/1.55 tff(48,plain,
% 1.38/1.55 (~(in(C!27, B!26) | in(C!27, subset_complement(A!25, B!26)) | (~element(C!27, A!25)))),
% 1.38/1.55 inference(and_elim,[status(thm)],[22])).
% 1.38/1.55 tff(49,plain,
% 1.38/1.55 (~in(C!27, B!26)),
% 1.38/1.55 inference(or_elim,[status(thm)],[48])).
% 1.38/1.55 tff(50,plain,
% 1.38/1.55 (^[A: $i, B: $i] : refl((in(A, B) | disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(51,plain,
% 1.38/1.55 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[50])).
% 1.38/1.55 tff(52,plain,
% 1.38/1.55 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 1.38/1.55 inference(rewrite,[status(thm)],[])).
% 1.38/1.55 tff(53,plain,
% 1.38/1.55 (^[A: $i, B: $i] : rewrite(((~in(A, B)) => disjoint(singleton(A), B)) <=> (in(A, B) | disjoint(singleton(A), B)))),
% 1.38/1.55 inference(bind,[status(th)],[])).
% 1.38/1.55 tff(54,plain,
% 1.38/1.55 (![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B)) <=> ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 1.38/1.55 inference(quant_intro,[status(thm)],[53])).
% 1.38/1.55 tff(55,axiom,(![A: $i, B: $i] : ((~in(A, B)) => disjoint(singleton(A), B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l28_zfmisc_1')).
% 1.38/1.56 tff(56,plain,
% 1.38/1.56 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[55, 54])).
% 1.38/1.56 tff(57,plain,
% 1.38/1.56 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[56, 52])).
% 1.38/1.56 tff(58,plain,(
% 1.38/1.56 ![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 1.38/1.56 inference(skolemize,[status(sab)],[57])).
% 1.38/1.56 tff(59,plain,
% 1.38/1.56 (![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[58, 51])).
% 1.38/1.56 tff(60,plain,
% 1.38/1.56 (((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(C!27, B!26) | disjoint(singleton(C!27), B!26))) <=> ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(C!27, B!26) | disjoint(singleton(C!27), B!26))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(61,plain,
% 1.38/1.56 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | (in(C!27, B!26) | disjoint(singleton(C!27), B!26))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(62,plain,
% 1.38/1.56 ((~![A: $i, B: $i] : (in(A, B) | disjoint(singleton(A), B))) | in(C!27, B!26) | disjoint(singleton(C!27), B!26)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[61, 60])).
% 1.38/1.56 tff(63,plain,
% 1.38/1.56 (disjoint(singleton(C!27), B!26)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[62, 59, 49])).
% 1.38/1.56 tff(64,plain,
% 1.38/1.56 ((~(disjoint(singleton(C!27), B!26) <=> (set_difference(singleton(C!27), B!26) = singleton(C!27)))) | (~disjoint(singleton(C!27), B!26)) | (set_difference(singleton(C!27), B!26) = singleton(C!27))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(65,plain,
% 1.38/1.56 ((~(disjoint(singleton(C!27), B!26) <=> (set_difference(singleton(C!27), B!26) = singleton(C!27)))) | (set_difference(singleton(C!27), B!26) = singleton(C!27))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[64, 63])).
% 1.38/1.56 tff(66,plain,
% 1.38/1.56 (set_difference(singleton(C!27), B!26) = singleton(C!27)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[65, 47])).
% 1.38/1.56 tff(67,plain,
% 1.38/1.56 (subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26)) <=> subset(singleton(C!27), subset_complement(A!25, B!26))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[66, 38])).
% 1.38/1.56 tff(68,plain,
% 1.38/1.56 (subset(singleton(C!27), subset_complement(A!25, B!26)) <=> subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26))),
% 1.38/1.56 inference(symmetry,[status(thm)],[67])).
% 1.38/1.56 tff(69,plain,
% 1.38/1.56 ((~subset(singleton(C!27), subset_complement(A!25, B!26))) <=> (~subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26)))),
% 1.38/1.56 inference(monotonicity,[status(thm)],[68])).
% 1.38/1.56 tff(70,plain,
% 1.38/1.56 ((~![A: $i, B: $i] : (subset(singleton(A), B) <=> in(A, B))) | (subset(singleton(C!27), subset_complement(A!25, B!26)) <=> in(C!27, subset_complement(A!25, B!26)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(71,plain,
% 1.38/1.56 (subset(singleton(C!27), subset_complement(A!25, B!26)) <=> in(C!27, subset_complement(A!25, B!26))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[70, 7])).
% 1.38/1.56 tff(72,plain,
% 1.38/1.56 (~in(C!27, subset_complement(A!25, B!26))),
% 1.38/1.56 inference(or_elim,[status(thm)],[48])).
% 1.38/1.56 tff(73,plain,
% 1.38/1.56 ((~(subset(singleton(C!27), subset_complement(A!25, B!26)) <=> in(C!27, subset_complement(A!25, B!26)))) | (~subset(singleton(C!27), subset_complement(A!25, B!26))) | in(C!27, subset_complement(A!25, B!26))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(74,plain,
% 1.38/1.56 ((~(subset(singleton(C!27), subset_complement(A!25, B!26)) <=> in(C!27, subset_complement(A!25, B!26)))) | (~subset(singleton(C!27), subset_complement(A!25, B!26)))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[73, 72])).
% 1.38/1.56 tff(75,plain,
% 1.38/1.56 (~subset(singleton(C!27), subset_complement(A!25, B!26))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[74, 71])).
% 1.38/1.56 tff(76,plain,
% 1.38/1.56 (~subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[75, 69])).
% 1.38/1.56 tff(77,plain,
% 1.38/1.56 (^[A: $i, B: $i, C: $i] : refl(((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))) <=> ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(78,plain,
% 1.38/1.56 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[77])).
% 1.38/1.56 tff(79,plain,
% 1.38/1.56 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(80,plain,
% 1.38/1.56 (^[A: $i, B: $i, C: $i] : rewrite((subset(A, B) => subset(set_difference(A, C), set_difference(B, C))) <=> ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(81,plain,
% 1.38/1.56 (![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[80])).
% 1.38/1.56 tff(82,axiom,(![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_difference(A, C), set_difference(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_xboole_1')).
% 1.38/1.56 tff(83,plain,
% 1.38/1.56 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[82, 81])).
% 1.38/1.56 tff(84,plain,
% 1.38/1.56 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[83, 79])).
% 1.38/1.56 tff(85,plain,(
% 1.38/1.56 ![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.38/1.56 inference(skolemize,[status(sab)],[84])).
% 1.38/1.56 tff(86,plain,
% 1.38/1.56 (![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[85, 78])).
% 1.38/1.56 tff(87,plain,
% 1.38/1.56 (((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | ((~subset(singleton(C!27), A!25)) | subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26)))) <=> ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | (~subset(singleton(C!27), A!25)) | subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(88,plain,
% 1.38/1.56 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | ((~subset(singleton(C!27), A!25)) | subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26)))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(89,plain,
% 1.38/1.56 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_difference(A, C), set_difference(B, C)))) | (~subset(singleton(C!27), A!25)) | subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[88, 87])).
% 1.38/1.56 tff(90,plain,
% 1.38/1.56 ((~subset(singleton(C!27), A!25)) | subset(set_difference(singleton(C!27), B!26), set_difference(A!25, B!26))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[89, 86])).
% 1.38/1.56 tff(91,plain,
% 1.38/1.56 (~subset(singleton(C!27), A!25)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[90, 76])).
% 1.38/1.56 tff(92,plain,
% 1.38/1.56 ((~(subset(singleton(C!27), A!25) <=> in(C!27, A!25))) | subset(singleton(C!27), A!25) | (~in(C!27, A!25))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(93,plain,
% 1.38/1.56 ((~(subset(singleton(C!27), A!25) <=> in(C!27, A!25))) | (~in(C!27, A!25))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[92, 91])).
% 1.38/1.56 tff(94,plain,
% 1.38/1.56 (~in(C!27, A!25)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[93, 9])).
% 1.38/1.56 tff(95,plain,
% 1.38/1.56 (^[A: $i, B: $i] : refl((~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(96,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[95])).
% 1.38/1.56 tff(97,plain,
% 1.38/1.56 (^[A: $i, B: $i] : rewrite(((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B)))))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(98,plain,
% 1.38/1.56 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[97])).
% 1.38/1.56 tff(99,plain,
% 1.38/1.56 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(100,plain,
% 1.38/1.56 (^[A: $i, B: $i] : rewrite((((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B)))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(101,plain,
% 1.38/1.56 (![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B)))) <=> ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[100])).
% 1.38/1.56 tff(102,axiom,(![A: $i, B: $i] : (((~empty(A)) => (element(B, A) <=> in(B, A))) & (empty(A) => (element(B, A) <=> empty(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_subset_1')).
% 1.38/1.56 tff(103,plain,
% 1.38/1.56 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.38/1.56 tff(104,plain,
% 1.38/1.56 (![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.38/1.56 tff(105,plain,(
% 1.38/1.56 ![A: $i, B: $i] : ((empty(A) | (element(B, A) <=> in(B, A))) & ((~empty(A)) | (element(B, A) <=> empty(B))))),
% 1.38/1.56 inference(skolemize,[status(sab)],[104])).
% 1.38/1.56 tff(106,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.38/1.56 tff(107,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[106, 96])).
% 1.38/1.56 tff(108,plain,
% 1.38/1.56 ((~![A: $i, B: $i] : (~((~(empty(A) | (element(B, A) <=> in(B, A)))) | (~((~empty(A)) | (element(B, A) <=> empty(B))))))) | (~((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | (~((~empty(A!25)) | (element(C!27, A!25) <=> empty(C!27))))))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(109,plain,
% 1.38/1.56 (~((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | (~((~empty(A!25)) | (element(C!27, A!25) <=> empty(C!27)))))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[108, 107])).
% 1.38/1.56 tff(110,plain,
% 1.38/1.56 (((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | (~((~empty(A!25)) | (element(C!27, A!25) <=> empty(C!27))))) | (empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(111,plain,
% 1.38/1.56 (empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[110, 109])).
% 1.38/1.56 tff(112,plain,
% 1.38/1.56 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(113,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[112])).
% 1.38/1.56 tff(114,plain,
% 1.38/1.56 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(115,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[114])).
% 1.38/1.56 tff(116,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 1.38/1.56 inference(transitivity,[status(thm)],[115, 113])).
% 1.38/1.56 tff(117,plain,
% 1.38/1.56 (^[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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(118,plain,
% 1.38/1.56 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(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_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[117])).
% 1.38/1.56 tff(119,plain,
% 1.38/1.56 (![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)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(120,plain,
% 1.38/1.56 (^[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))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(121,plain,
% 1.38/1.56 (![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)))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[120])).
% 1.38/1.56 tff(122,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')).
% 1.38/1.56 tff(123,plain,
% 1.38/1.56 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[122, 121])).
% 1.38/1.56 tff(124,plain,
% 1.38/1.56 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[123, 119])).
% 1.38/1.56 tff(125,plain,(
% 1.38/1.56 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))),
% 1.38/1.56 inference(skolemize,[status(sab)],[124])).
% 1.38/1.56 tff(126,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[125, 118])).
% 1.38/1.56 tff(127,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[126, 116])).
% 1.38/1.56 tff(128,plain,
% 1.38/1.56 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_10(B, A), A)) | in(tptp_fun_C_10(B, A), B)))))))) | (~((~((~subset(A!25, empty_set)) | ![C: $i] : ((~in(C, A!25)) | in(C, empty_set)))) | (~(subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set)))))))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(129,plain,
% 1.38/1.56 (~((~((~subset(A!25, empty_set)) | ![C: $i] : ((~in(C, A!25)) | in(C, empty_set)))) | (~(subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set))))))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[128, 127])).
% 1.38/1.56 tff(130,plain,
% 1.38/1.56 (((~((~subset(A!25, empty_set)) | ![C: $i] : ((~in(C, A!25)) | in(C, empty_set)))) | (~(subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set)))))) | (subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set))))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(131,plain,
% 1.38/1.56 (subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set)))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[130, 129])).
% 1.38/1.56 tff(132,plain,
% 1.38/1.56 (~(A!25 = empty_set)),
% 1.38/1.56 inference(and_elim,[status(thm)],[22])).
% 1.38/1.56 tff(133,plain,
% 1.38/1.56 (^[A: $i] : refl(((~subset(A, empty_set)) | (A = empty_set)) <=> ((~subset(A, empty_set)) | (A = empty_set)))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(134,plain,
% 1.38/1.56 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[133])).
% 1.38/1.56 tff(135,plain,
% 1.38/1.56 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(136,plain,
% 1.38/1.56 (^[A: $i] : rewrite((subset(A, empty_set) => (A = empty_set)) <=> ((~subset(A, empty_set)) | (A = empty_set)))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(137,plain,
% 1.38/1.56 (![A: $i] : (subset(A, empty_set) => (A = empty_set)) <=> ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[136])).
% 1.38/1.56 tff(138,axiom,(![A: $i] : (subset(A, empty_set) => (A = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t3_xboole_1')).
% 1.38/1.56 tff(139,plain,
% 1.38/1.56 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[138, 137])).
% 1.38/1.56 tff(140,plain,
% 1.38/1.56 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[139, 135])).
% 1.38/1.56 tff(141,plain,(
% 1.38/1.56 ![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.38/1.56 inference(skolemize,[status(sab)],[140])).
% 1.38/1.56 tff(142,plain,
% 1.38/1.56 (![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[141, 134])).
% 1.38/1.56 tff(143,plain,
% 1.38/1.56 (((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | ((~subset(A!25, empty_set)) | (A!25 = empty_set))) <=> ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | (~subset(A!25, empty_set)) | (A!25 = empty_set))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(144,plain,
% 1.38/1.56 ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | ((~subset(A!25, empty_set)) | (A!25 = empty_set))),
% 1.38/1.56 inference(quant_inst,[status(thm)],[])).
% 1.38/1.56 tff(145,plain,
% 1.38/1.56 ((~![A: $i] : ((~subset(A, empty_set)) | (A = empty_set))) | (~subset(A!25, empty_set)) | (A!25 = empty_set)),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.38/1.56 tff(146,plain,
% 1.38/1.56 (~subset(A!25, empty_set)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[145, 142, 132])).
% 1.38/1.56 tff(147,plain,
% 1.38/1.56 ((~(subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set))))) | subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set)))),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(148,plain,
% 1.38/1.56 ((~(subset(A!25, empty_set) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set))))) | (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set)))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[147, 146])).
% 1.38/1.56 tff(149,plain,
% 1.38/1.56 (~((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set))),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[148, 131])).
% 1.38/1.56 tff(150,plain,
% 1.38/1.56 (((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | in(tptp_fun_C_10(empty_set, A!25), empty_set)) | in(tptp_fun_C_10(empty_set, A!25), A!25)),
% 1.38/1.56 inference(tautology,[status(thm)],[])).
% 1.38/1.56 tff(151,plain,
% 1.38/1.56 (in(tptp_fun_C_10(empty_set, A!25), A!25)),
% 1.38/1.56 inference(unit_resolution,[status(thm)],[150, 149])).
% 1.38/1.56 tff(152,plain,
% 1.38/1.56 (^[A: $i, B: $i] : refl(((~in(A, B)) | (~empty(B))) <=> ((~in(A, B)) | (~empty(B))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(153,plain,
% 1.38/1.56 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[152])).
% 1.38/1.56 tff(154,plain,
% 1.38/1.56 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~in(A, B)) | (~empty(B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~in(A, B)) | (~empty(B))))))), rewrite((~(~((~in(A, B)) | (~empty(B))))) <=> ((~in(A, B)) | (~empty(B)))), ((~(in(A, B) & empty(B))) <=> ((~in(A, B)) | (~empty(B)))))),
% 1.38/1.56 inference(bind,[status(th)],[])).
% 1.38/1.56 tff(155,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.38/1.56 inference(quant_intro,[status(thm)],[154])).
% 1.38/1.56 tff(156,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(157,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t7_boole')).
% 1.38/1.56 tff(158,plain,
% 1.38/1.56 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[157, 156])).
% 1.38/1.56 tff(159,plain,(
% 1.38/1.56 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 1.38/1.56 inference(skolemize,[status(sab)],[158])).
% 1.38/1.56 tff(160,plain,
% 1.38/1.56 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[159, 155])).
% 1.38/1.56 tff(161,plain,
% 1.38/1.56 (![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))),
% 1.38/1.56 inference(modus_ponens,[status(thm)],[160, 153])).
% 1.38/1.56 tff(162,plain,
% 1.38/1.56 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(A!25)) | (~in(tptp_fun_C_10(empty_set, A!25), A!25)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(A!25)) | (~in(tptp_fun_C_10(empty_set, A!25), A!25)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(163,plain,
% 1.38/1.56 (((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | (~empty(A!25))) <=> ((~empty(A!25)) | (~in(tptp_fun_C_10(empty_set, A!25), A!25)))),
% 1.38/1.56 inference(rewrite,[status(thm)],[])).
% 1.38/1.56 tff(164,plain,
% 1.38/1.56 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | (~empty(A!25)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~empty(A!25)) | (~in(tptp_fun_C_10(empty_set, A!25), A!25))))),
% 1.38/1.57 inference(monotonicity,[status(thm)],[163])).
% 1.38/1.57 tff(165,plain,
% 1.38/1.57 (((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | (~empty(A!25)))) <=> ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(A!25)) | (~in(tptp_fun_C_10(empty_set, A!25), A!25)))),
% 1.38/1.57 inference(transitivity,[status(thm)],[164, 162])).
% 1.38/1.57 tff(166,plain,
% 1.38/1.57 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | ((~in(tptp_fun_C_10(empty_set, A!25), A!25)) | (~empty(A!25)))),
% 1.38/1.57 inference(quant_inst,[status(thm)],[])).
% 1.38/1.57 tff(167,plain,
% 1.38/1.57 ((~![A: $i, B: $i] : ((~in(A, B)) | (~empty(B)))) | (~empty(A!25)) | (~in(tptp_fun_C_10(empty_set, A!25), A!25))),
% 1.38/1.57 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.38/1.57 tff(168,plain,
% 1.38/1.57 (~empty(A!25)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[167, 161, 151])).
% 1.38/1.57 tff(169,plain,
% 1.38/1.57 ((~(empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25)))) | empty(A!25) | (element(C!27, A!25) <=> in(C!27, A!25))),
% 1.38/1.57 inference(tautology,[status(thm)],[])).
% 1.38/1.57 tff(170,plain,
% 1.38/1.57 (element(C!27, A!25) <=> in(C!27, A!25)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[169, 168, 111])).
% 1.38/1.57 tff(171,plain,
% 1.38/1.57 (element(C!27, A!25)),
% 1.38/1.57 inference(or_elim,[status(thm)],[48])).
% 1.38/1.57 tff(172,plain,
% 1.38/1.57 ((~(element(C!27, A!25) <=> in(C!27, A!25))) | (~element(C!27, A!25)) | in(C!27, A!25)),
% 1.38/1.57 inference(tautology,[status(thm)],[])).
% 1.38/1.57 tff(173,plain,
% 1.38/1.57 ((~(element(C!27, A!25) <=> in(C!27, A!25))) | in(C!27, A!25)),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[172, 171])).
% 1.38/1.57 tff(174,plain,
% 1.38/1.57 ($false),
% 1.38/1.57 inference(unit_resolution,[status(thm)],[173, 170, 94])).
% 1.38/1.57 % SZS output end Proof
% 1.38/1.57 % E exiting
%------------------------------------------------------------------------------