TSTP Solution File: SEU126+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 07:27:36 EDT 2022
% Result : Theorem 0.18s 0.40s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 09:54:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.18/0.40 % SZS status Theorem
% 0.18/0.40 % SZS output start Proof
% 0.18/0.40 tff(subset_type, type, (
% 0.18/0.40 subset: ( $i * $i ) > $o)).
% 0.18/0.40 tff(tptp_fun_B_6_type, type, (
% 0.18/0.40 tptp_fun_B_6: $i)).
% 0.18/0.40 tff(set_union2_type, type, (
% 0.18/0.40 set_union2: ( $i * $i ) > $i)).
% 0.18/0.40 tff(tptp_fun_A_7_type, type, (
% 0.18/0.40 tptp_fun_A_7: $i)).
% 0.18/0.40 tff(1,plain,
% 0.18/0.40 (^[A: $i, B: $i] : refl(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(2,plain,
% 0.18/0.40 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.40 tff(3,plain,
% 0.18/0.40 (^[A: $i, B: $i] : rewrite(((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(4,plain,
% 0.18/0.40 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.40 tff(5,plain,
% 0.18/0.40 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(6,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.18/0.40 tff(7,plain,
% 0.18/0.40 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.40 tff(8,plain,(
% 0.18/0.40 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.18/0.40 inference(skolemize,[status(sab)],[7])).
% 0.18/0.40 tff(9,plain,
% 0.18/0.40 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.40 tff(10,plain,
% 0.18/0.40 (![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.40 tff(11,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A)))))) | ((B!6 = set_union2(B!6, A!7)) <=> (~((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(12,plain,
% 0.18/0.40 ((B!6 = set_union2(B!6, A!7)) <=> (~((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.40 tff(13,plain,
% 0.18/0.40 ((B!6 = set_union2(A!7, B!6)) <=> (set_union2(A!7, B!6) = B!6)),
% 0.18/0.40 inference(commutativity,[status(thm)],[])).
% 0.18/0.40 tff(14,plain,
% 0.18/0.40 (^[A: $i, B: $i] : refl((set_union2(A, B) = set_union2(B, A)) <=> (set_union2(A, B) = set_union2(B, A)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(15,plain,
% 0.18/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.40 tff(16,plain,
% 0.18/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A)) <=> ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(17,axiom,(![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k2_xboole_0')).
% 0.18/0.40 tff(18,plain,
% 0.18/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.18/0.40 tff(19,plain,(
% 0.18/0.40 ![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.18/0.40 inference(skolemize,[status(sab)],[18])).
% 0.18/0.40 tff(20,plain,
% 0.18/0.40 (![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.18/0.40 tff(21,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : (set_union2(A, B) = set_union2(B, A))) | (set_union2(A!7, B!6) = set_union2(B!6, A!7))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(22,plain,
% 0.18/0.40 (set_union2(A!7, B!6) = set_union2(B!6, A!7)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.18/0.40 tff(23,plain,
% 0.18/0.40 (set_union2(B!6, A!7) = set_union2(A!7, B!6)),
% 0.18/0.40 inference(symmetry,[status(thm)],[22])).
% 0.18/0.40 tff(24,plain,
% 0.18/0.40 ((B!6 = set_union2(B!6, A!7)) <=> (B!6 = set_union2(A!7, B!6))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[23])).
% 0.18/0.40 tff(25,plain,
% 0.18/0.40 ((B!6 = set_union2(B!6, A!7)) <=> (set_union2(A!7, B!6) = B!6)),
% 0.18/0.40 inference(transitivity,[status(thm)],[24, 13])).
% 0.18/0.40 tff(26,plain,
% 0.18/0.40 ((set_union2(A!7, B!6) = B!6) <=> (B!6 = set_union2(B!6, A!7))),
% 0.18/0.40 inference(symmetry,[status(thm)],[25])).
% 0.18/0.40 tff(27,plain,
% 0.18/0.40 ((~(set_union2(A!7, B!6) = B!6)) <=> (~(B!6 = set_union2(B!6, A!7)))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[26])).
% 0.18/0.40 tff(28,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(29,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))) <=> (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(30,axiom,(~![A: $i, B: $i] : (subset(A, B) => (set_union2(A, B) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_xboole_1')).
% 0.18/0.40 tff(31,plain,
% 0.18/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[31, 28])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[33, 28])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (~![A: $i, B: $i] : ((~subset(A, B)) | (set_union2(A, B) = B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[36, 28])).
% 0.18/0.40 tff(38,plain,(
% 0.18/0.40 ~((~subset(A!7, B!6)) | (set_union2(A!7, B!6) = B!6))),
% 0.18/0.40 inference(skolemize,[status(sab)],[37])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 (~(set_union2(A!7, B!6) = B!6)),
% 0.18/0.40 inference(or_elim,[status(thm)],[38])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 (~(B!6 = set_union2(B!6, A!7))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 27])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 ((~((B!6 = set_union2(B!6, A!7)) <=> (~((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6)))))) | (B!6 = set_union2(B!6, A!7)) | ((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 ((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[41, 40, 12])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (^[A: $i, B: $i] : refl(subset(A, set_union2(A, B)) <=> subset(A, set_union2(A, B)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (![A: $i, B: $i] : subset(A, set_union2(A, B)) <=> ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(46,axiom,(![A: $i, B: $i] : subset(A, set_union2(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_xboole_1')).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.18/0.40 tff(48,plain,(
% 0.18/0.40 ![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.40 inference(skolemize,[status(sab)],[47])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (![A: $i, B: $i] : subset(A, set_union2(A, B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 ((~![A: $i, B: $i] : subset(A, set_union2(A, B))) | subset(B!6, set_union2(B!6, A!7))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (subset(B!6, set_union2(B!6, A!7))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 ((~((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6)))) | (~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 ((~((~subset(B!6, set_union2(B!6, A!7))) | (~subset(set_union2(B!6, A!7), B!6)))) | (~subset(set_union2(B!6, A!7), B!6))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (~subset(set_union2(B!6, A!7), B!6)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[53, 42])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i] : refl((subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B))) <=> (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(C, B)) <=> (~((~subset(C, B)) | (~subset(A, B))))), ((~(subset(A, B) & subset(C, B))) <=> (~(~((~subset(C, B)) | (~subset(A, B))))))), rewrite((~(~((~subset(C, B)) | (~subset(A, B))))) <=> ((~subset(C, B)) | (~subset(A, B)))), ((~(subset(A, B) & subset(C, B))) <=> ((~subset(C, B)) | (~subset(A, B))))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (((~subset(C, B)) | (~subset(A, B))) | subset(set_union2(A, C), B)))), rewrite((((~subset(C, B)) | (~subset(A, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))), (((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[57])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B)))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[60])).
% 0.18/0.40 tff(62,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(C, B)) => subset(set_union2(A, C), B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_xboole_1')).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.18/0.40 tff(65,plain,(
% 0.18/0.40 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(C, B))) | subset(set_union2(A, C), B))),
% 0.18/0.40 inference(skolemize,[status(sab)],[64])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[66, 56])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (subset(A!7, B!6)),
% 0.18/0.40 inference(or_elim,[status(thm)],[38])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | ((~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(70,plain,
% 0.18/0.41 ((subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6))) <=> ((~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(71,plain,
% 0.18/0.41 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | ((~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[70])).
% 0.18/0.41 tff(72,plain,
% 0.18/0.41 (((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6)))),
% 0.18/0.41 inference(transitivity,[status(thm)],[71, 69])).
% 0.18/0.41 tff(73,plain,
% 0.18/0.41 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (subset(set_union2(B!6, A!7), B!6) | (~subset(A!7, B!6)) | (~subset(B!6, B!6)))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(74,plain,
% 0.18/0.41 ((~![A: $i, B: $i, C: $i] : (subset(set_union2(A, C), B) | (~subset(C, B)) | (~subset(A, B)))) | (~subset(A!7, B!6)) | subset(set_union2(B!6, A!7), B!6) | (~subset(B!6, B!6))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 (~subset(B!6, B!6)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[74, 68, 67, 54])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.18/0.41 inference(quant_intro,[status(thm)],[76])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 0.18/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.18/0.41 tff(80,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 0.18/0.41 tff(81,plain,
% 0.18/0.41 (![A: $i] : subset(A, A)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 (![A: $i] : subset(A, A)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[81, 78])).
% 0.18/0.41 tff(83,plain,(
% 0.18/0.41 ![A: $i] : subset(A, A)),
% 0.18/0.41 inference(skolemize,[status(sab)],[82])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (![A: $i] : subset(A, A)),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[83, 77])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 ((~![A: $i] : subset(A, A)) | subset(B!6, B!6)),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 ($false),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[85, 84, 75])).
% 0.18/0.41 % SZS output end Proof
%------------------------------------------------------------------------------