%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU172+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : SEU172+2 : TPTP v9.0.0. Released v3.3.0.
% 0.02/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 06:12:56 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% 0.19/0.49 tff(in_type, type, (
% 0.19/0.49 in: ( $i * $i ) > $o)).
% 0.19/0.49 tff(tptp_fun_C_25_type, type, (
% 0.19/0.49 tptp_fun_C_25: $i)).
% 0.19/0.49 tff(tptp_fun_D_15_type, type, (
% 0.19/0.49 tptp_fun_D_15: ( $i * $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_A_27_type, type, (
% 0.19/0.49 tptp_fun_A_27: $i)).
% 0.19/0.49 tff(subset_complement_type, type, (
% 0.19/0.49 subset_complement: ( $i * $i ) > $i)).
% 0.19/0.49 tff(set_difference_type, type, (
% 0.19/0.49 set_difference: ( $i * $i ) > $i)).
% 0.19/0.49 tff(tptp_fun_B_26_type, type, (
% 0.19/0.49 tptp_fun_B_26: $i)).
% 0.19/0.49 tff(element_type, type, (
% 0.19/0.49 element: ( $i * $i ) > $o)).
% 0.19/0.49 tff(powerset_type, type, (
% 0.19/0.49 powerset: $i > $i)).
% 0.19/0.49 tff(1,plain,
% 0.19/0.49 ((~![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))) <=> (~![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(2,plain,
% 0.19/0.49 ((~![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C))))) <=> (~![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(3,axiom,(~![A: $i, B: $i, C: $i] : (element(C, powerset(A)) => (~(in(B, subset_complement(A, C)) & in(B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t54_subset_1')).
% 0.19/0.49 tff(4,plain,
% 0.19/0.49 (~![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.19/0.49 tff(5,plain,
% 0.19/0.49 (~![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.19/0.49 tff(6,plain,
% 0.19/0.49 (~![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.19/0.49 tff(7,plain,
% 0.19/0.49 (~![A: $i, B: $i, C: $i] : ((~element(C, powerset(A))) | (~(in(B, subset_complement(A, C)) & in(B, C))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.19/0.49 tff(8,plain,(
% 0.19/0.49 ~((~element(C!25, powerset(A!27))) | (~(in(B!26, subset_complement(A!27, C!25)) & in(B!26, C!25))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[7])).
% 0.19/0.49 tff(9,plain,
% 0.19/0.49 (in(B!26, subset_complement(A!27, C!25)) & in(B!26, C!25)),
% 0.19/0.49 inference(or_elim,[status(thm)],[8])).
% 0.19/0.49 tff(10,plain,
% 0.19/0.49 (in(B!26, subset_complement(A!27, C!25))),
% 0.19/0.49 inference(and_elim,[status(thm)],[9])).
% 0.19/0.49 tff(11,plain,
% 0.19/0.49 (((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) | (~in(B!26, subset_complement(A!27, C!25)))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(12,plain,
% 0.19/0.49 ((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.19/0.49 tff(13,plain,
% 0.19/0.49 (in(B!26, C!25)),
% 0.19/0.49 inference(and_elim,[status(thm)],[9])).
% 0.19/0.49 tff(14,plain,
% 0.19/0.49 ((((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25)) | (~((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25)))) | (~in(B!26, C!25))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(15,plain,
% 0.19/0.49 (((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[14, 13, 12])).
% 0.19/0.49 tff(16,plain,
% 0.19/0.49 (element(C!25, powerset(A!27))),
% 0.19/0.49 inference(or_elim,[status(thm)],[8])).
% 0.19/0.49 tff(17,plain,
% 0.19/0.49 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(18,plain,
% 0.19/0.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[17])).
% 0.19/0.49 tff(19,plain,
% 0.19/0.49 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(20,plain,
% 0.19/0.49 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(21,plain,
% 0.19/0.50 (![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[20])).
% 0.19/0.50 tff(22,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_subset_1')).
% 0.19/0.50 tff(23,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.50 tff(24,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.19/0.50 tff(25,plain,(
% 0.19/0.50 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[24])).
% 0.19/0.50 tff(26,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.19/0.50 tff(27,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(C!25, powerset(A!27))) | element(subset_complement(A!27, C!25), powerset(A!27)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(C!25, powerset(A!27))) | element(subset_complement(A!27, C!25), powerset(A!27)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(28,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(C!25, powerset(A!27))) | element(subset_complement(A!27, C!25), powerset(A!27)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(29,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(C!25, powerset(A!27))) | element(subset_complement(A!27, C!25), powerset(A!27))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.19/0.50 tff(30,plain,
% 0.19/0.50 (element(subset_complement(A!27, C!25), powerset(A!27))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[29, 26, 16])).
% 0.19/0.50 tff(31,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(32,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[31])).
% 0.19/0.50 tff(33,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(34,plain,
% 0.19/0.50 (^[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))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(35,plain,
% 0.19/0.50 (![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)))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[34])).
% 0.19/0.50 tff(36,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')).
% 0.19/0.50 tff(37,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.50 tff(38,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.19/0.50 tff(39,plain,(
% 0.19/0.50 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.19/0.50 inference(skolemize,[status(sab)],[38])).
% 0.19/0.50 tff(40,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[39, 32])).
% 0.19/0.50 tff(41,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(subset_complement(A!27, C!25), powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = set_difference(A!27, subset_complement(A!27, C!25))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(subset_complement(A!27, C!25), powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = set_difference(A!27, subset_complement(A!27, C!25))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(42,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | ((~element(subset_complement(A!27, C!25), powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = set_difference(A!27, subset_complement(A!27, C!25))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(43,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, B) = set_difference(A, B)))) | (~element(subset_complement(A!27, C!25), powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = set_difference(A!27, subset_complement(A!27, C!25)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.50 tff(44,plain,
% 0.19/0.50 (subset_complement(A!27, subset_complement(A!27, C!25)) = set_difference(A!27, subset_complement(A!27, C!25))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[43, 40, 30])).
% 0.19/0.50 tff(45,plain,
% 0.19/0.50 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(46,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.50 tff(47,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(48,plain,
% 0.19/0.50 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B)))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(49,plain,
% 0.19/0.50 (![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.50 tff(50,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => (subset_complement(A, subset_complement(A, B)) = B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','involutiveness_k3_subset_1')).
% 0.19/0.50 tff(51,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.19/0.50 tff(52,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.19/0.50 tff(53,plain,(
% 0.19/0.50 ![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.19/0.50 inference(skolemize,[status(sab)],[52])).
% 0.19/0.50 tff(54,plain,
% 0.19/0.50 (![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[53, 46])).
% 0.19/0.50 tff(55,plain,
% 0.19/0.50 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(C!25, powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = C!25))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(C!25, powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = C!25))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(56,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | ((~element(C!25, powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = C!25))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(57,plain,
% 0.19/0.50 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | (subset_complement(A, subset_complement(A, B)) = B))) | (~element(C!25, powerset(A!27))) | (subset_complement(A!27, subset_complement(A!27, C!25)) = C!25)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.19/0.50 tff(58,plain,
% 0.19/0.50 (subset_complement(A!27, subset_complement(A!27, C!25)) = C!25),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[57, 54, 16])).
% 0.19/0.50 tff(59,plain,
% 0.19/0.50 (C!25 = subset_complement(A!27, subset_complement(A!27, C!25))),
% 0.19/0.50 inference(symmetry,[status(thm)],[58])).
% 0.19/0.50 tff(60,plain,
% 0.19/0.50 (C!25 = set_difference(A!27, subset_complement(A!27, C!25))),
% 0.19/0.50 inference(transitivity,[status(thm)],[59, 44])).
% 0.19/0.50 tff(61,plain,
% 0.19/0.50 ((~((~(C!25 = set_difference(A!27, subset_complement(A!27, C!25)))) | (~(((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25))))) | (~(C!25 = set_difference(A!27, subset_complement(A!27, C!25)))) | (~(((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25)))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(62,plain,
% 0.19/0.50 (~((~(C!25 = set_difference(A!27, subset_complement(A!27, C!25)))) | (~(((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[61, 60, 15])).
% 0.19/0.50 tff(63,plain,
% 0.19/0.50 (((~((~(C!25 = set_difference(A!27, subset_complement(A!27, C!25)))) | (~(((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25))))) | (~((C!25 = set_difference(A!27, subset_complement(A!27, C!25))) | (((~in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), A!27)) | in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), subset_complement(A!27, C!25))) <=> in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), C!25))))) | ((~(C!25 = set_difference(A!27, subset_complement(A!27, C!25)))) | (~(((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25))))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(64,plain,
% 0.19/0.50 ((~((~(C!25 = set_difference(A!27, subset_complement(A!27, C!25)))) | (~(((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25))))) | (~((C!25 = set_difference(A!27, subset_complement(A!27, C!25))) | (((~in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), A!27)) | in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), subset_complement(A!27, C!25))) <=> in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), C!25))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.19/0.50 tff(65,plain,
% 0.19/0.50 (^[A: $i, B: $i, C: $i, D: $i] : refl((~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C)))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(66,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.50 tff(67,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : ![D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(pull_quant,[status(thm)],[])).
% 0.19/0.50 tff(68,plain,
% 0.19/0.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))) <=> ![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> (~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), pull_quant((~![D: $i] : ((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C)))))), ((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) <=> ?[D: $i] : (~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))))), (((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(69,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.50 tff(70,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[69, 67])).
% 0.19/0.50 tff(71,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[70, 66])).
% 0.19/0.50 tff(72,plain,
% 0.19/0.50 (^[A: $i, B: $i, C: $i] : rewrite((~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C)))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(73,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.50 tff(74,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[73, 71])).
% 0.19/0.50 tff(75,plain,
% 0.19/0.50 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite(((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))), rewrite(((C = set_difference(A, B)) | (~(in(tptp_fun_D_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B)))))) <=> ((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(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_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))))),
% 0.19/0.50 inference(bind,[status(th)],[])).
% 0.19/0.50 tff(76,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(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_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.50 tff(77,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) <=> ![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(78,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')).
% 0.19/0.50 tff(79,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : ((C = set_difference(A, B)) <=> ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.50 tff(80,plain,(
% 0.19/0.50 ![A: $i, B: $i, C: $i] : (((~(C = set_difference(A, B))) | ![D: $i] : (in(D, C) <=> (in(D, A) & (~in(D, B))))) & ((C = set_difference(A, B)) | (~(in(tptp_fun_D_15(C, B, A), C) <=> (in(tptp_fun_D_15(C, B, A), A) & (~in(tptp_fun_D_15(C, B, A), B)))))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[79])).
% 0.19/0.50 tff(81,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i] : (~((~((~(C = set_difference(A, B))) | ![D: $i] : (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.19/0.50 tff(82,plain,
% 0.19/0.50 (![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.19/0.51 tff(83,plain,
% 0.19/0.51 ((~![A: $i, B: $i, C: $i, D: $i] : (~((~((~(C = set_difference(A, B))) | (~(((~in(D, A)) | in(D, B)) <=> in(D, C))))) | (~((C = set_difference(A, B)) | (((~in(tptp_fun_D_15(C, B, A), A)) | in(tptp_fun_D_15(C, B, A), B)) <=> in(tptp_fun_D_15(C, B, A), C))))))) | (~((~((~(C!25 = set_difference(A!27, subset_complement(A!27, C!25)))) | (~(((~in(B!26, A!27)) | in(B!26, subset_complement(A!27, C!25))) <=> in(B!26, C!25))))) | (~((C!25 = set_difference(A!27, subset_complement(A!27, C!25))) | (((~in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), A!27)) | in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), subset_complement(A!27, C!25))) <=> in(tptp_fun_D_15(C!25, subset_complement(A!27, C!25), A!27), C!25))))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(84,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[83, 82, 64])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------