%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU120+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:26:55 AM UTC 2025
% Result : Theorem 87.14s 87.31s
% Output : Proof 87.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU120+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n006.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 06:05:20 EDT 2025
% 0.11/0.33 % CPUTime :
% 87.14/87.31 % SZS status Theorem
% 87.14/87.31 % SZS output start Proof
% 87.14/87.31 tff(in_type, type, (
% 87.14/87.31 in: ( $i * $i ) > $o)).
% 87.14/87.31 tff(set_intersection2_type, type, (
% 87.14/87.31 set_intersection2: ( $i * $i ) > $i)).
% 87.14/87.31 tff(tptp_fun_A_6_type, type, (
% 87.14/87.31 tptp_fun_A_6: $i)).
% 87.14/87.31 tff(tptp_fun_B_5_type, type, (
% 87.14/87.31 tptp_fun_B_5: $i)).
% 87.14/87.31 tff(tptp_fun_B_0_type, type, (
% 87.14/87.31 tptp_fun_B_0: $i > $i)).
% 87.14/87.31 tff(empty_set_type, type, (
% 87.14/87.31 empty_set: $i)).
% 87.14/87.31 tff(disjoint_type, type, (
% 87.14/87.31 disjoint: ( $i * $i ) > $o)).
% 87.14/87.31 tff(tptp_fun_C_7_type, type, (
% 87.14/87.31 tptp_fun_C_7: $i)).
% 87.14/87.31 tff(1,plain,
% 87.14/87.31 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 87.14/87.31 inference(bind,[status(th)],[])).
% 87.14/87.31 tff(2,plain,
% 87.14/87.31 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 87.14/87.31 inference(quant_intro,[status(thm)],[1])).
% 87.14/87.31 tff(3,plain,
% 87.14/87.31 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 87.14/87.31 tff(5,plain,
% 87.14/87.31 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[4, 3])).
% 87.14/87.31 tff(6,plain,(
% 87.14/87.31 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 87.14/87.31 inference(skolemize,[status(sab)],[5])).
% 87.14/87.31 tff(7,plain,
% 87.14/87.31 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[6, 2])).
% 87.14/87.31 tff(8,plain,
% 87.14/87.31 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!6, B!5) = set_intersection2(B!5, A!6))),
% 87.14/87.31 inference(quant_inst,[status(thm)],[])).
% 87.14/87.31 tff(9,plain,
% 87.14/87.31 (set_intersection2(A!6, B!5) = set_intersection2(B!5, A!6)),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[8, 7])).
% 87.14/87.31 tff(10,plain,
% 87.14/87.31 (in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5)) <=> in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))),
% 87.14/87.31 inference(monotonicity,[status(thm)],[9])).
% 87.14/87.31 tff(11,plain,
% 87.14/87.31 (in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)) <=> in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5))),
% 87.14/87.31 inference(symmetry,[status(thm)],[10])).
% 87.14/87.31 tff(12,assumption,(in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))), introduced(assumption)).
% 87.14/87.31 tff(13,plain,
% 87.14/87.31 (in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[12, 11])).
% 87.14/87.31 tff(14,plain,
% 87.14/87.31 (^[A: $i, B: $i] : refl((~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 87.14/87.31 inference(bind,[status(th)],[])).
% 87.14/87.31 tff(15,plain,
% 87.14/87.31 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(quant_intro,[status(thm)],[14])).
% 87.14/87.31 tff(16,plain,
% 87.14/87.31 (![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(pull_quant,[status(thm)],[])).
% 87.14/87.31 tff(17,plain,
% 87.14/87.31 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ![B: $i] : ((~(A = empty_set)) | (~in(B, A)))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> (~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))))), pull_quant((~![B: $i] : ((~(A = empty_set)) | (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A))))), ((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) <=> ?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> (?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), pull_quant((?[B: $i] : (~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))), (((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))) <=> ?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))), pull_quant((~?[B: $i] : ((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 87.14/87.31 inference(bind,[status(th)],[])).
% 87.14/87.31 tff(18,plain,
% 87.14/87.31 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : ![B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(quant_intro,[status(thm)],[17])).
% 87.14/87.31 tff(19,plain,
% 87.14/87.31 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(transitivity,[status(thm)],[18, 16])).
% 87.14/87.31 tff(20,plain,
% 87.14/87.31 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(transitivity,[status(thm)],[19, 15])).
% 87.14/87.31 tff(21,plain,
% 87.14/87.31 (^[A: $i] : rewrite((~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))))),
% 87.14/87.31 inference(bind,[status(th)],[])).
% 87.14/87.31 tff(22,plain,
% 87.14/87.31 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(quant_intro,[status(thm)],[21])).
% 87.14/87.31 tff(23,plain,
% 87.14/87.31 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A))))) <=> ![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(transitivity,[status(thm)],[22, 20])).
% 87.14/87.31 tff(24,plain,
% 87.14/87.31 (^[A: $i] : trans(monotonicity(rewrite(((~(A = empty_set)) | ![B: $i] : (~in(B, A))) <=> ((~(A = empty_set)) | ![B: $i] : (~in(B, A)))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))))), rewrite((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))), ((((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))))),
% 87.14/87.31 inference(bind,[status(th)],[])).
% 87.14/87.31 tff(25,plain,
% 87.14/87.31 (![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A))) <=> ![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(quant_intro,[status(thm)],[24])).
% 87.14/87.31 tff(26,plain,
% 87.14/87.31 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(27,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_xboole_0')).
% 87.14/87.31 tff(28,plain,
% 87.14/87.31 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[27, 26])).
% 87.14/87.31 tff(29,plain,(
% 87.14/87.31 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 87.14/87.31 inference(skolemize,[status(sab)],[28])).
% 87.14/87.31 tff(30,plain,
% 87.14/87.31 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[29, 25])).
% 87.14/87.31 tff(31,plain,
% 87.14/87.31 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[30, 23])).
% 87.14/87.31 tff(32,plain,
% 87.14/87.31 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~((set_intersection2(A!6, B!5) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!6, B!5)), set_intersection2(A!6, B!5))))))),
% 87.14/87.31 inference(quant_inst,[status(thm)],[])).
% 87.14/87.31 tff(33,plain,
% 87.14/87.31 (~((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~((set_intersection2(A!6, B!5) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!6, B!5)), set_intersection2(A!6, B!5)))))),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[32, 31])).
% 87.14/87.31 tff(34,plain,
% 87.14/87.31 (((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~((set_intersection2(A!6, B!5) = empty_set) | in(tptp_fun_B_0(set_intersection2(A!6, B!5)), set_intersection2(A!6, B!5))))) | ((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))),
% 87.14/87.31 inference(tautology,[status(thm)],[])).
% 87.14/87.31 tff(35,plain,
% 87.14/87.31 ((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5)))),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[34, 33])).
% 87.14/87.31 tff(36,plain,
% 87.14/87.31 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 87.14/87.31 inference(bind,[status(th)],[])).
% 87.14/87.31 tff(37,plain,
% 87.14/87.31 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 87.14/87.31 inference(quant_intro,[status(thm)],[36])).
% 87.14/87.31 tff(38,plain,
% 87.14/87.31 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(39,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_xboole_0')).
% 87.14/87.31 tff(40,plain,
% 87.14/87.31 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[39, 38])).
% 87.14/87.31 tff(41,plain,(
% 87.14/87.31 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 87.14/87.31 inference(skolemize,[status(sab)],[40])).
% 87.14/87.31 tff(42,plain,
% 87.14/87.31 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 87.14/87.31 inference(modus_ponens,[status(thm)],[41, 37])).
% 87.14/87.31 tff(43,plain,
% 87.14/87.31 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set))),
% 87.14/87.31 inference(quant_inst,[status(thm)],[])).
% 87.14/87.31 tff(44,plain,
% 87.14/87.31 (disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set)),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[43, 42])).
% 87.14/87.31 tff(45,assumption,(~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))), introduced(assumption)).
% 87.14/87.31 tff(46,plain,
% 87.14/87.31 (((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))) | disjoint(A!6, B!5)),
% 87.14/87.31 inference(tautology,[status(thm)],[])).
% 87.14/87.31 tff(47,plain,
% 87.14/87.31 (disjoint(A!6, B!5)),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[46, 45])).
% 87.14/87.31 tff(48,plain,
% 87.14/87.31 ((~(disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set))) | (~disjoint(A!6, B!5)) | (set_intersection2(A!6, B!5) = empty_set)),
% 87.14/87.31 inference(tautology,[status(thm)],[])).
% 87.14/87.31 tff(49,plain,
% 87.14/87.31 ((~(disjoint(A!6, B!5) <=> (set_intersection2(A!6, B!5) = empty_set))) | (set_intersection2(A!6, B!5) = empty_set)),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[48, 47])).
% 87.14/87.31 tff(50,plain,
% 87.14/87.31 (set_intersection2(A!6, B!5) = empty_set),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[49, 44])).
% 87.14/87.31 tff(51,plain,
% 87.14/87.31 (((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))) | in(C!7, set_intersection2(A!6, B!5))),
% 87.14/87.31 inference(tautology,[status(thm)],[])).
% 87.14/87.31 tff(52,plain,
% 87.14/87.31 (in(C!7, set_intersection2(A!6, B!5))),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[51, 45])).
% 87.14/87.31 tff(53,plain,
% 87.14/87.31 ((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5)))),
% 87.14/87.31 inference(tautology,[status(thm)],[])).
% 87.14/87.31 tff(54,plain,
% 87.14/87.31 ((~((~(set_intersection2(A!6, B!5) = empty_set)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(set_intersection2(A!6, B!5) = empty_set))),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[53, 52])).
% 87.14/87.31 tff(55,plain,
% 87.14/87.31 ($false),
% 87.14/87.31 inference(unit_resolution,[status(thm)],[54, 50, 35])).
% 87.14/87.31 tff(56,plain,((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))), inference(lemma,lemma(discharge,[]))).
% 87.14/87.31 tff(57,plain,
% 87.14/87.31 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(58,plain,
% 87.14/87.31 ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) <=> (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(59,plain,
% 87.14/87.31 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 87.14/87.31 inference(monotonicity,[status(thm)],[58])).
% 87.14/87.31 tff(60,plain,
% 87.14/87.31 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))))),
% 87.14/87.31 inference(transitivity,[status(thm)],[59, 57])).
% 87.14/87.31 tff(61,plain,
% 87.14/87.31 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(62,plain,
% 87.14/87.31 (((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(63,plain,
% 87.14/87.31 ((in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)) <=> (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))),
% 87.14/87.31 inference(rewrite,[status(thm)],[])).
% 87.14/87.31 tff(64,plain,
% 87.14/87.31 (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) <=> (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))))),
% 87.14/87.32 inference(rewrite,[status(thm)],[])).
% 87.14/87.32 tff(65,plain,
% 87.14/87.32 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 87.14/87.32 inference(monotonicity,[status(thm)],[64, 63])).
% 87.14/87.32 tff(66,plain,
% 87.14/87.32 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))))),
% 87.14/87.32 inference(transitivity,[status(thm)],[65, 62])).
% 87.14/87.32 tff(67,plain,
% 87.14/87.32 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)))),
% 87.14/87.32 inference(rewrite,[status(thm)],[])).
% 87.14/87.32 tff(68,plain,
% 87.14/87.32 (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) <=> ((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5))))),
% 87.14/87.32 inference(rewrite,[status(thm)],[])).
% 87.14/87.32 tff(69,plain,
% 87.14/87.32 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)))),
% 87.14/87.32 inference(monotonicity,[status(thm)],[68])).
% 87.14/87.32 tff(70,plain,
% 87.14/87.32 ((((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))) <=> (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5)))),
% 87.14/87.32 inference(transitivity,[status(thm)],[69, 67])).
% 87.14/87.32 tff(71,plain,
% 87.14/87.32 ((~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))) <=> (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B)))))),
% 87.14/87.32 inference(rewrite,[status(thm)],[])).
% 87.14/87.32 tff(72,axiom,(~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t4_xboole_0')).
% 87.14/87.32 tff(73,plain,
% 87.14/87.32 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[72, 71])).
% 87.14/87.32 tff(74,plain,
% 87.14/87.32 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[73, 71])).
% 87.14/87.32 tff(75,plain,
% 87.14/87.32 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[74, 71])).
% 87.14/87.32 tff(76,plain,
% 87.14/87.32 (~![A: $i, B: $i] : ((~((~disjoint(A, B)) & ![C: $i] : (~in(C, set_intersection2(A, B))))) & (~(?[C: $i] : in(C, set_intersection2(A, B)) & disjoint(A, B))))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[75, 71])).
% 87.14/87.32 tff(77,plain,
% 87.14/87.32 (((~disjoint(A!6, B!5)) & ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (in(C!7, set_intersection2(A!6, B!5)) & disjoint(A!6, B!5))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[76, 70])).
% 87.14/87.32 tff(78,plain,
% 87.14/87.32 ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[77, 66])).
% 87.14/87.32 tff(79,plain,
% 87.14/87.32 ((~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))) | (~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5)))))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[78, 61])).
% 87.14/87.32 tff(80,plain,
% 87.14/87.32 ((~((~disjoint(A!6, B!5)) | (~in(C!7, set_intersection2(A!6, B!5))))) | (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[79, 60])).
% 87.14/87.32 tff(81,plain,
% 87.14/87.32 (~(disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))))),
% 87.14/87.32 inference(unit_resolution,[status(thm)],[80, 56])).
% 87.14/87.32 tff(82,plain,
% 87.14/87.32 ((disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))) | ![C: $i] : (~in(C, set_intersection2(A!6, B!5)))),
% 87.14/87.32 inference(tautology,[status(thm)],[])).
% 87.14/87.32 tff(83,plain,
% 87.14/87.32 (![C: $i] : (~in(C, set_intersection2(A!6, B!5)))),
% 87.14/87.32 inference(unit_resolution,[status(thm)],[82, 81])).
% 87.14/87.32 tff(84,plain,
% 87.14/87.32 ((~![C: $i] : (~in(C, set_intersection2(A!6, B!5)))) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5)))),
% 87.14/87.32 inference(quant_inst,[status(thm)],[])).
% 87.14/87.32 tff(85,plain,
% 87.14/87.32 (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(A!6, B!5))),
% 87.14/87.32 inference(unit_resolution,[status(thm)],[84, 83])).
% 87.14/87.32 tff(86,plain,
% 87.14/87.32 ($false),
% 87.14/87.32 inference(unit_resolution,[status(thm)],[85, 13])).
% 87.14/87.32 tff(87,plain,(~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))), inference(lemma,lemma(discharge,[]))).
% 87.14/87.32 tff(88,plain,
% 87.14/87.32 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set))),
% 87.14/87.32 inference(quant_inst,[status(thm)],[])).
% 87.14/87.32 tff(89,plain,
% 87.14/87.32 (disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set)),
% 87.14/87.32 inference(unit_resolution,[status(thm)],[88, 42])).
% 87.14/87.32 tff(90,plain,
% 87.14/87.32 ((disjoint(A!6, B!5) | (~![C: $i] : (~in(C, set_intersection2(A!6, B!5))))) | (~disjoint(A!6, B!5))),
% 87.14/87.32 inference(tautology,[status(thm)],[])).
% 87.14/87.32 tff(91,plain,
% 87.14/87.32 (~disjoint(A!6, B!5)),
% 87.14/87.32 inference(unit_resolution,[status(thm)],[90, 81])).
% 87.14/87.32 tff(92,plain,
% 87.14/87.32 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 87.14/87.32 inference(bind,[status(th)],[])).
% 87.14/87.32 tff(93,plain,
% 87.14/87.32 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 87.14/87.32 inference(quant_intro,[status(thm)],[92])).
% 87.14/87.32 tff(94,plain,
% 87.14/87.32 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 87.14/87.32 inference(rewrite,[status(thm)],[])).
% 87.14/87.32 tff(95,plain,
% 87.14/87.32 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 87.14/87.32 inference(bind,[status(th)],[])).
% 87.14/87.32 tff(96,plain,
% 87.14/87.32 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 87.14/87.32 inference(quant_intro,[status(thm)],[95])).
% 87.14/87.32 tff(97,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 87.14/87.32 tff(98,plain,
% 87.14/87.32 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[97, 96])).
% 87.14/87.32 tff(99,plain,
% 87.14/87.32 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[98, 94])).
% 87.14/87.32 tff(100,plain,(
% 87.14/87.32 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 87.14/87.32 inference(skolemize,[status(sab)],[99])).
% 87.14/87.32 tff(101,plain,
% 87.14/87.32 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 87.14/87.32 inference(modus_ponens,[status(thm)],[100, 93])).
% 87.14/87.32 tff(102,plain,
% 87.14/87.32 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!5, A!6)) | disjoint(A!6, B!5))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!5, A!6)) | disjoint(A!6, B!5))),
% 87.14/87.32 inference(rewrite,[status(thm)],[])).
% 87.14/87.32 tff(103,plain,
% 87.14/87.32 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!5, A!6)) | disjoint(A!6, B!5))),
% 87.14/87.32 inference(quant_inst,[status(thm)],[])).
% 87.14/87.32 tff(104,plain,
% 87.14/87.33 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!5, A!6)) | disjoint(A!6, B!5)),
% 87.14/87.33 inference(modus_ponens,[status(thm)],[103, 102])).
% 87.14/87.33 tff(105,plain,
% 87.14/87.33 (~disjoint(B!5, A!6)),
% 87.14/87.33 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 87.14/87.33 tff(106,plain,
% 87.14/87.33 ((~(disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set))) | disjoint(B!5, A!6) | (~(set_intersection2(B!5, A!6) = empty_set))),
% 87.14/87.33 inference(tautology,[status(thm)],[])).
% 87.14/87.33 tff(107,plain,
% 87.14/87.33 ((~(disjoint(B!5, A!6) <=> (set_intersection2(B!5, A!6) = empty_set))) | (~(set_intersection2(B!5, A!6) = empty_set))),
% 87.14/87.33 inference(unit_resolution,[status(thm)],[106, 105])).
% 87.14/87.33 tff(108,plain,
% 87.14/87.33 (~(set_intersection2(B!5, A!6) = empty_set)),
% 87.14/87.33 inference(unit_resolution,[status(thm)],[107, 89])).
% 87.14/87.33 tff(109,plain,
% 87.14/87.33 ((~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)))) | (set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))),
% 87.14/87.33 inference(tautology,[status(thm)],[])).
% 87.14/87.33 tff(110,plain,
% 87.14/87.33 (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)))),
% 87.14/87.33 inference(unit_resolution,[status(thm)],[109, 108, 87])).
% 87.14/87.33 tff(111,plain,
% 87.14/87.33 (((~((~(set_intersection2(B!5, A!6) = empty_set)) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | ((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6)))),
% 87.14/87.33 inference(tautology,[status(thm)],[])).
% 87.14/87.33 tff(112,plain,
% 87.14/87.33 ((~((~(set_intersection2(B!5, A!6) = empty_set)) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))),
% 87.14/87.33 inference(unit_resolution,[status(thm)],[111, 110])).
% 87.14/87.33 tff(113,plain,
% 87.14/87.33 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(B!5, A!6) = empty_set)) | (~in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))) | (~((set_intersection2(B!5, A!6) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!5, A!6)), set_intersection2(B!5, A!6))))))),
% 87.14/87.33 inference(quant_inst,[status(thm)],[])).
% 87.14/87.33 tff(114,plain,
% 87.14/87.33 ($false),
% 87.14/87.33 inference(unit_resolution,[status(thm)],[113, 31, 112])).
% 87.14/87.33 % SZS output end Proof
% 87.14/87.34 % E exiting
%------------------------------------------------------------------------------