TSTP Solution File: SEU130+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.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 : Tue Sep 20 07:27:38 EDT 2022
% Result : Theorem 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n020.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 : Sat Sep 3 09:36:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Theorem
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(subset_type, type, (
% 0.21/0.42 subset: ( $i * $i ) > $o)).
% 0.21/0.42 tff(tptp_fun_A_7_type, type, (
% 0.21/0.42 tptp_fun_A_7: $i)).
% 0.21/0.42 tff(set_intersection2_type, type, (
% 0.21/0.42 set_intersection2: ( $i * $i ) > $i)).
% 0.21/0.42 tff(tptp_fun_B_6_type, type, (
% 0.21/0.42 tptp_fun_B_6: $i)).
% 0.21/0.42 tff(1,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(2,plain,
% 0.21/0.42 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.42 tff(3,plain,
% 0.21/0.42 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(4,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 0.21/0.42 tff(5,plain,
% 0.21/0.42 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.21/0.42 tff(6,plain,(
% 0.21/0.42 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.42 inference(skolemize,[status(sab)],[5])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!7, B!6) = set_intersection2(B!6, A!7))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (set_intersection2(A!7, B!6) = set_intersection2(B!6, A!7)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.21/0.42 tff(10,plain,
% 0.21/0.42 (set_intersection2(B!6, A!7) = set_intersection2(A!7, B!6)),
% 0.21/0.42 inference(symmetry,[status(thm)],[9])).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (subset(set_intersection2(B!6, A!7), A!7) <=> subset(set_intersection2(A!7, B!6), A!7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.42 tff(12,plain,
% 0.21/0.42 (subset(set_intersection2(A!7, B!6), A!7) <=> subset(set_intersection2(B!6, A!7), A!7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[11])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(16,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.42 tff(18,plain,(
% 0.21/0.42 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.21/0.42 inference(skolemize,[status(sab)],[17])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(A!7, B!6), A!7)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (subset(set_intersection2(A!7, B!6), A!7)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.42 tff(22,plain,
% 0.21/0.42 (subset(set_intersection2(B!6, A!7), A!7)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[21, 12])).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.21/0.42 tff(25,plain,
% 0.21/0.42 (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[25])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(28,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.21/0.42 tff(29,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.42 tff(30,plain,(
% 0.21/0.42 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[29])).
% 0.21/0.42 tff(31,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.42 tff(32,plain,
% 0.21/0.42 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.21/0.42 tff(33,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((set_intersection2(B!6, A!7) = A!7) <=> (~((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(34,plain,
% 0.21/0.42 ((set_intersection2(B!6, A!7) = A!7) <=> (~((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 ((set_intersection2(B!6, A!7) = A!7) <=> (set_intersection2(A!7, B!6) = A!7)),
% 0.21/0.42 inference(monotonicity,[status(thm)],[10])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 ((set_intersection2(A!7, B!6) = A!7) <=> (set_intersection2(B!6, A!7) = A!7)),
% 0.21/0.42 inference(symmetry,[status(thm)],[35])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 ((~(set_intersection2(A!7, B!6) = A!7)) <=> (~(set_intersection2(B!6, A!7) = A!7))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 ((~![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(40,axiom,(~![A: $i, B: $i] : (subset(A, B) => (set_intersection2(A, B) = A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t28_xboole_1')).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[41, 38])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[43, 38])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[44, 38])).
% 0.21/0.42 tff(46,plain,
% 0.21/0.42 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_intersection2(A, B) = A))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[46, 38])).
% 0.21/0.42 tff(48,plain,(
% 0.21/0.42 ~((~subset(A!7, B!6)) | (set_intersection2(A!7, B!6) = A!7))),
% 0.21/0.42 inference(skolemize,[status(sab)],[47])).
% 0.21/0.42 tff(49,plain,
% 0.21/0.42 (~(set_intersection2(A!7, B!6) = A!7)),
% 0.21/0.42 inference(or_elim,[status(thm)],[48])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (~(set_intersection2(B!6, A!7) = A!7)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 37])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 ((~((set_intersection2(B!6, A!7) = A!7) <=> (~((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7))))))) | (set_intersection2(B!6, A!7) = A!7) | ((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7))))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 ((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[51, 50, 34])).
% 0.21/0.42 tff(53,plain,
% 0.21/0.42 ((~((~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7))))) | (~subset(set_intersection2(B!6, A!7), A!7)) | (~subset(A!7, set_intersection2(B!6, A!7)))),
% 0.21/0.42 inference(tautology,[status(thm)],[])).
% 0.21/0.42 tff(54,plain,
% 0.21/0.42 (~subset(A!7, set_intersection2(B!6, A!7))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[53, 52, 22])).
% 0.21/0.42 tff(55,plain,
% 0.21/0.42 (subset(A!7, B!6)),
% 0.21/0.42 inference(or_elim,[status(thm)],[48])).
% 0.21/0.42 tff(56,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i] : refl((subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C))) <=> (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(57,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.42 tff(58,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(A, C)) <=> (~((~subset(A, B)) | (~subset(A, C))))), ((~(subset(A, B) & subset(A, C))) <=> (~(~((~subset(A, B)) | (~subset(A, C))))))), rewrite((~(~((~subset(A, B)) | (~subset(A, C))))) <=> ((~subset(A, B)) | (~subset(A, C)))), ((~(subset(A, B) & subset(A, C))) <=> ((~subset(A, B)) | (~subset(A, C))))), (((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> (((~subset(A, B)) | (~subset(A, C))) | subset(A, set_intersection2(B, C))))), rewrite((((~subset(A, B)) | (~subset(A, C))) | subset(A, set_intersection2(B, C))) <=> (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))), (((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(59,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[58])).
% 0.21/0.42 tff(60,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(61,plain,
% 0.21/0.42 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C))) <=> ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(62,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.42 tff(63,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t19_xboole_1')).
% 0.21/0.42 tff(64,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.21/0.42 tff(65,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.21/0.42 tff(66,plain,(
% 0.21/0.42 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.21/0.42 inference(skolemize,[status(sab)],[65])).
% 0.21/0.42 tff(67,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[66, 59])).
% 0.21/0.42 tff(68,plain,
% 0.21/0.42 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[67, 57])).
% 0.21/0.42 tff(69,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | ((~subset(A!7, B!6)) | subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, A!7)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (~subset(A!7, B!6)) | subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, A!7)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(70,plain,
% 0.21/0.42 ((subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7))) <=> ((~subset(A!7, B!6)) | subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, A!7)))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(71,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | ((~subset(A!7, B!6)) | subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, A!7))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[70])).
% 0.21/0.42 tff(72,plain,
% 0.21/0.42 (((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (~subset(A!7, B!6)) | subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, A!7)))),
% 0.21/0.42 inference(transitivity,[status(thm)],[71, 69])).
% 0.21/0.42 tff(73,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, B!6)) | (~subset(A!7, A!7)))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(74,plain,
% 0.21/0.42 ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (~subset(A!7, B!6)) | subset(A!7, set_intersection2(B!6, A!7)) | (~subset(A!7, A!7))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.42 tff(75,plain,
% 0.21/0.42 (~subset(A!7, A!7)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[74, 68, 55, 54])).
% 0.21/0.42 tff(76,plain,
% 0.21/0.42 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(77,plain,
% 0.21/0.42 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.21/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.21/0.42 tff(78,plain,
% 0.21/0.42 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(79,plain,
% 0.21/0.42 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.21/0.42 inference(elim_unused_vars,[status(thm)],[])).
% 0.21/0.42 tff(80,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.21/0.42 tff(81,plain,
% 0.21/0.42 (![A: $i] : subset(A, A)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.42 tff(82,plain,
% 0.21/0.42 (![A: $i] : subset(A, A)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.21/0.42 tff(83,plain,(
% 0.21/0.42 ![A: $i] : subset(A, A)),
% 0.21/0.42 inference(skolemize,[status(sab)],[82])).
% 0.21/0.42 tff(84,plain,
% 0.21/0.42 (![A: $i] : subset(A, A)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[83, 77])).
% 0.21/0.42 tff(85,plain,
% 0.21/0.42 ((~![A: $i] : subset(A, A)) | subset(A!7, A!7)),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(86,plain,
% 0.21/0.42 ($false),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[85, 84, 75])).
% 0.21/0.42 % SZS output end Proof
%------------------------------------------------------------------------------