%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU120+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.22s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU120+1 : TPTP v9.0.0. Released v3.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:05:56 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.40 % SZS status Theorem
% 0.22/0.40 % SZS output start Proof
% 0.22/0.40 tff(in_type, type, (
% 0.22/0.40 in: ( $i * $i ) > $o)).
% 0.22/0.40 tff(set_intersection2_type, type, (
% 0.22/0.40 set_intersection2: ( $i * $i ) > $i)).
% 0.22/0.40 tff(tptp_fun_A_4_type, type, (
% 0.22/0.40 tptp_fun_A_4: $i)).
% 0.22/0.40 tff(tptp_fun_B_3_type, type, (
% 0.22/0.40 tptp_fun_B_3: $i)).
% 0.22/0.40 tff(tptp_fun_C_5_type, type, (
% 0.22/0.40 tptp_fun_C_5: $i)).
% 0.22/0.40 tff(disjoint_type, type, (
% 0.22/0.40 disjoint: ( $i * $i ) > $o)).
% 0.22/0.40 tff(tptp_fun_B_0_type, type, (
% 0.22/0.40 tptp_fun_B_0: $i > $i)).
% 0.22/0.40 tff(empty_set_type, type, (
% 0.22/0.40 empty_set: $i)).
% 0.22/0.40 tff(1,plain,
% 0.22/0.40 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(2,plain,
% 0.22/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.40 tff(3,plain,
% 0.22/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 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')).
% 0.22/0.40 tff(5,plain,
% 0.22/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.22/0.40 tff(6,plain,(
% 0.22/0.40 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.40 inference(skolemize,[status(sab)],[5])).
% 0.22/0.40 tff(7,plain,
% 0.22/0.40 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.22/0.40 tff(8,plain,
% 0.22/0.40 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!4, B!3) = set_intersection2(B!3, A!4))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(9,plain,
% 0.22/0.40 (set_intersection2(A!4, B!3) = set_intersection2(B!3, A!4)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.22/0.40 tff(10,plain,
% 0.22/0.40 (set_intersection2(B!3, A!4) = set_intersection2(A!4, B!3)),
% 0.22/0.40 inference(symmetry,[status(thm)],[9])).
% 0.22/0.40 tff(11,plain,
% 0.22/0.40 (in(C!5, set_intersection2(B!3, A!4)) <=> in(C!5, set_intersection2(A!4, B!3))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[10])).
% 0.22/0.40 tff(12,plain,
% 0.22/0.40 (in(C!5, set_intersection2(A!4, B!3)) <=> in(C!5, set_intersection2(B!3, A!4))),
% 0.22/0.40 inference(symmetry,[status(thm)],[11])).
% 0.22/0.40 tff(13,plain,
% 0.22/0.40 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3)) <=> in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.22/0.40 inference(monotonicity,[status(thm)],[9])).
% 0.22/0.40 tff(14,plain,
% 0.22/0.40 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)) <=> in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3))),
% 0.22/0.40 inference(symmetry,[status(thm)],[13])).
% 0.22/0.40 tff(15,plain,
% 0.22/0.40 (^[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))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(16,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[15])).
% 0.22/0.40 tff(17,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(pull_quant,[status(thm)],[])).
% 0.22/0.40 tff(18,plain,
% 0.22/0.40 (^[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)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(19,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.40 tff(20,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[19, 17])).
% 0.22/0.40 tff(21,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[20, 16])).
% 0.22/0.40 tff(22,plain,
% 0.22/0.40 (^[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))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(23,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.22/0.40 tff(24,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(transitivity,[status(thm)],[23, 21])).
% 0.22/0.40 tff(25,plain,
% 0.22/0.40 (^[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)))))))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(26,plain,
% 0.22/0.40 (![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)))))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[25])).
% 0.22/0.40 tff(27,plain,
% 0.22/0.40 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A))) <=> ![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(28,axiom,(![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_xboole_0')).
% 0.22/0.40 tff(29,plain,
% 0.22/0.40 (![A: $i] : ((A = empty_set) <=> ![B: $i] : (~in(B, A)))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.22/0.40 tff(30,plain,(
% 0.22/0.40 ![A: $i] : (((~(A = empty_set)) | ![B: $i] : (~in(B, A))) & ((A = empty_set) | in(tptp_fun_B_0(A), A)))),
% 0.22/0.40 inference(skolemize,[status(sab)],[29])).
% 0.22/0.40 tff(31,plain,
% 0.22/0.40 (![A: $i] : (~((~((~(A = empty_set)) | ![B: $i] : (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.22/0.40 tff(32,plain,
% 0.22/0.40 (![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.22/0.40 tff(33,plain,
% 0.22/0.40 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(empty_set, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))))))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(34,plain,
% 0.22/0.40 (~((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(empty_set, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.22/0.40 tff(35,plain,
% 0.22/0.40 (((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(empty_set, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))))) | ((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(36,plain,
% 0.22/0.40 ((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.22/0.40 tff(37,assumption,(~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))), introduced(assumption)).
% 0.22/0.40 tff(38,plain,
% 0.22/0.40 ((disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))) | (~disjoint(A!4, B!3))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(39,plain,
% 0.22/0.40 (~disjoint(A!4, B!3)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.22/0.40 tff(40,plain,
% 0.22/0.40 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(41,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.40 tff(42,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(43,plain,
% 0.22/0.40 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(44,plain,
% 0.22/0.40 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.40 tff(45,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 0.22/0.40 tff(46,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.40 tff(47,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.22/0.40 tff(48,plain,(
% 0.22/0.40 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.22/0.40 inference(skolemize,[status(sab)],[47])).
% 0.22/0.40 tff(49,plain,
% 0.22/0.40 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.22/0.40 tff(50,plain,
% 0.22/0.40 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!3, A!4)) | disjoint(A!4, B!3))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!3, A!4)) | disjoint(A!4, B!3))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(51,plain,
% 0.22/0.40 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!3, A!4)) | disjoint(A!4, B!3))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(52,plain,
% 0.22/0.40 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!3, A!4)) | disjoint(A!4, B!3)),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.22/0.40 tff(53,plain,
% 0.22/0.40 ((~disjoint(B!3, A!4)) | disjoint(A!4, B!3)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.22/0.40 tff(54,plain,
% 0.22/0.40 (~disjoint(B!3, A!4)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[53, 39])).
% 0.22/0.40 tff(55,plain,
% 0.22/0.40 (^[A: $i, B: $i] : refl((disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)) <=> (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set)))),
% 0.22/0.40 inference(bind,[status(th)],[])).
% 0.22/0.40 tff(56,plain,
% 0.22/0.40 (![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))),
% 0.22/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.22/0.40 tff(57,plain,
% 0.22/0.40 (![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))),
% 0.22/0.40 inference(rewrite,[status(thm)],[])).
% 0.22/0.40 tff(58,axiom,(![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_xboole_0')).
% 0.22/0.40 tff(59,plain,
% 0.22/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.22/0.40 tff(60,plain,(
% 0.22/0.40 ![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.40 inference(skolemize,[status(sab)],[59])).
% 0.22/0.40 tff(61,plain,
% 0.22/0.40 (![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))),
% 0.22/0.40 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.22/0.40 tff(62,plain,
% 0.22/0.40 ((~![A: $i, B: $i] : (disjoint(A, B) <=> (set_intersection2(A, B) = empty_set))) | (disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set))),
% 0.22/0.40 inference(quant_inst,[status(thm)],[])).
% 0.22/0.40 tff(63,plain,
% 0.22/0.40 (disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.22/0.40 tff(64,plain,
% 0.22/0.40 ((~(disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set))) | disjoint(B!3, A!4) | (~(set_intersection2(B!3, A!4) = empty_set))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(65,plain,
% 0.22/0.40 (disjoint(B!3, A!4) | (~(set_intersection2(B!3, A!4) = empty_set))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.22/0.40 tff(66,plain,
% 0.22/0.40 (~(set_intersection2(B!3, A!4) = empty_set)),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[65, 54])).
% 0.22/0.40 tff(67,plain,
% 0.22/0.40 ((~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))) | (set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.22/0.40 inference(tautology,[status(thm)],[])).
% 0.22/0.40 tff(68,plain,
% 0.22/0.40 ((~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.22/0.40 tff(69,plain,
% 0.22/0.40 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))),
% 0.22/0.40 inference(unit_resolution,[status(thm)],[68, 36])).
% 0.22/0.40 tff(70,plain,
% 0.22/0.40 (in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[69, 14])).
% 0.22/0.41 tff(71,plain,
% 0.22/0.41 ((disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))) | ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))),
% 0.22/0.41 inference(tautology,[status(thm)],[])).
% 0.22/0.41 tff(72,plain,
% 0.22/0.41 (![C: $i] : (~in(C, set_intersection2(A!4, B!3)))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[71, 37])).
% 0.22/0.41 tff(73,plain,
% 0.22/0.41 ((~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (~in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3)))),
% 0.22/0.41 inference(quant_inst,[status(thm)],[])).
% 0.22/0.41 tff(74,plain,
% 0.22/0.41 (~in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(A!4, B!3))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.22/0.41 tff(75,plain,
% 0.22/0.41 ($false),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[74, 70])).
% 0.22/0.41 tff(76,plain,(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.41 tff(77,plain,
% 0.22/0.41 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(78,plain,
% 0.22/0.41 ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) <=> (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(79,plain,
% 0.22/0.41 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[78])).
% 0.22/0.41 tff(80,plain,
% 0.22/0.41 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[79, 77])).
% 0.22/0.41 tff(81,plain,
% 0.22/0.41 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(82,plain,
% 0.22/0.41 (((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(83,plain,
% 0.22/0.41 ((in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)) <=> (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(84,plain,
% 0.22/0.41 (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) <=> (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(85,plain,
% 0.22/0.41 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[84, 83])).
% 0.22/0.41 tff(86,plain,
% 0.22/0.41 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(transitivity,[status(thm)],[85, 82])).
% 0.22/0.41 tff(87,plain,
% 0.22/0.41 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(88,plain,
% 0.22/0.41 (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) <=> ((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(89,plain,
% 0.22/0.41 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)))),
% 0.22/0.41 inference(monotonicity,[status(thm)],[88])).
% 0.22/0.41 tff(90,plain,
% 0.22/0.41 ((((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))) <=> (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3)))),
% 0.22/0.41 inference(transitivity,[status(thm)],[89, 87])).
% 0.22/0.41 tff(91,plain,
% 0.22/0.41 ((~![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)))))),
% 0.22/0.41 inference(rewrite,[status(thm)],[])).
% 0.22/0.41 tff(92,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')).
% 0.22/0.41 tff(93,plain,
% 0.22/0.41 (~![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))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.22/0.41 tff(94,plain,
% 0.22/0.41 (~![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))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[93, 91])).
% 0.22/0.41 tff(95,plain,
% 0.22/0.41 (~![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))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.22/0.41 tff(96,plain,
% 0.22/0.41 (~![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))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.22/0.41 tff(97,plain,
% 0.22/0.41 (((~disjoint(A!4, B!3)) & ![C: $i] : (~in(C, set_intersection2(A!4, B!3)))) | (in(C!5, set_intersection2(A!4, B!3)) & disjoint(A!4, B!3))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[96, 90])).
% 0.22/0.41 tff(98,plain,
% 0.22/0.41 ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[97, 86])).
% 0.22/0.41 tff(99,plain,
% 0.22/0.41 ((~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3)))))) | (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[98, 81])).
% 0.22/0.41 tff(100,plain,
% 0.22/0.41 ((~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))) | (~(disjoint(A!4, B!3) | (~![C: $i] : (~in(C, set_intersection2(A!4, B!3))))))),
% 0.22/0.41 inference(modus_ponens,[status(thm)],[99, 80])).
% 0.22/0.41 tff(101,plain,
% 0.22/0.41 (~((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3))))),
% 0.22/0.41 inference(unit_resolution,[status(thm)],[100, 76])).
% 0.22/0.41 tff(102,plain,
% 0.22/0.41 (((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))) | in(C!5, set_intersection2(A!4, B!3))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(103,plain,
% 0.22/0.42 (in(C!5, set_intersection2(A!4, B!3))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.22/0.42 tff(104,plain,
% 0.22/0.42 (in(C!5, set_intersection2(B!3, A!4))),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[103, 12])).
% 0.22/0.42 tff(105,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : (~((~((~(A = empty_set)) | (~in(B, A)))) | (~((A = empty_set) | in(tptp_fun_B_0(A), A)))))) | (~((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))))))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(106,plain,
% 0.22/0.42 (~((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4)))))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[105, 32])).
% 0.22/0.42 tff(107,plain,
% 0.22/0.42 (((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4))))) | (~((set_intersection2(B!3, A!4) = empty_set) | in(tptp_fun_B_0(set_intersection2(B!3, A!4)), set_intersection2(B!3, A!4))))) | ((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4))))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(108,plain,
% 0.22/0.42 ((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.22/0.42 tff(109,plain,
% 0.22/0.42 (((~disjoint(A!4, B!3)) | (~in(C!5, set_intersection2(A!4, B!3)))) | disjoint(A!4, B!3)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(110,plain,
% 0.22/0.42 (disjoint(A!4, B!3)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[109, 101])).
% 0.22/0.42 tff(111,plain,
% 0.22/0.42 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(A!4, B!3)) | disjoint(B!3, A!4))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(A!4, B!3)) | disjoint(B!3, A!4))),
% 0.22/0.42 inference(rewrite,[status(thm)],[])).
% 0.22/0.42 tff(112,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(A!4, B!3)) | disjoint(B!3, A!4))),
% 0.22/0.42 inference(quant_inst,[status(thm)],[])).
% 0.22/0.42 tff(113,plain,
% 0.22/0.42 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(A!4, B!3)) | disjoint(B!3, A!4)),
% 0.22/0.42 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.22/0.42 tff(114,plain,
% 0.22/0.42 ((~disjoint(A!4, B!3)) | disjoint(B!3, A!4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[113, 49])).
% 0.22/0.42 tff(115,plain,
% 0.22/0.42 (disjoint(B!3, A!4)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[114, 110])).
% 0.22/0.42 tff(116,plain,
% 0.22/0.42 ((~(disjoint(B!3, A!4) <=> (set_intersection2(B!3, A!4) = empty_set))) | (~disjoint(B!3, A!4)) | (set_intersection2(B!3, A!4) = empty_set)),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(117,plain,
% 0.22/0.42 ((~disjoint(B!3, A!4)) | (set_intersection2(B!3, A!4) = empty_set)),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[116, 63])).
% 0.22/0.42 tff(118,plain,
% 0.22/0.42 (set_intersection2(B!3, A!4) = empty_set),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[117, 115])).
% 0.22/0.42 tff(119,plain,
% 0.22/0.42 ((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4))))) | (~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4)))),
% 0.22/0.42 inference(tautology,[status(thm)],[])).
% 0.22/0.42 tff(120,plain,
% 0.22/0.42 ((~((~(set_intersection2(B!3, A!4) = empty_set)) | (~in(C!5, set_intersection2(B!3, A!4))))) | (~in(C!5, set_intersection2(B!3, A!4)))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.22/0.42 tff(121,plain,
% 0.22/0.42 (~in(C!5, set_intersection2(B!3, A!4))),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[120, 108])).
% 0.22/0.42 tff(122,plain,
% 0.22/0.42 ($false),
% 0.22/0.42 inference(unit_resolution,[status(thm)],[121, 104])).
% 0.22/0.42 % SZS output end Proof
% 0.22/0.42 % E exiting
%------------------------------------------------------------------------------