TSTP Solution File: SEU129+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU129+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 0.11s 0.38s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU129+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 09:43:48 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.11/0.38 % SZS status Theorem
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(subset_type, type, (
% 0.11/0.38 subset: ( $i * $i ) > $o)).
% 0.11/0.38 tff(set_intersection2_type, type, (
% 0.11/0.38 set_intersection2: ( $i * $i ) > $i)).
% 0.11/0.38 tff(tptp_fun_B_7_type, type, (
% 0.11/0.38 tptp_fun_B_7: $i)).
% 0.11/0.38 tff(tptp_fun_C_6_type, type, (
% 0.11/0.38 tptp_fun_C_6: $i)).
% 0.11/0.38 tff(tptp_fun_A_8_type, type, (
% 0.11/0.38 tptp_fun_A_8: $i)).
% 0.11/0.38 tff(1,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 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')).
% 0.11/0.38 tff(5,plain,
% 0.11/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.11/0.38 tff(6,plain,(
% 0.11/0.38 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.11/0.38 inference(skolemize,[status(sab)],[5])).
% 0.11/0.38 tff(7,plain,
% 0.11/0.38 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(B!7, C!6) = set_intersection2(C!6, B!7))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 (set_intersection2(B!7, C!6) = set_intersection2(C!6, B!7)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 (set_intersection2(C!6, B!7) = set_intersection2(B!7, C!6)),
% 0.11/0.38 inference(symmetry,[status(thm)],[9])).
% 0.11/0.38 tff(11,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!8, C!6) = set_intersection2(C!6, A!8))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (set_intersection2(A!8, C!6) = set_intersection2(C!6, A!8)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[11, 7])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (set_intersection2(C!6, A!8) = set_intersection2(A!8, C!6)),
% 0.11/0.38 inference(symmetry,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7)) <=> subset(set_intersection2(A!8, C!6), set_intersection2(B!7, C!6))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[13, 10])).
% 0.11/0.38 tff(15,plain,
% 0.11/0.38 (subset(set_intersection2(A!8, C!6), set_intersection2(B!7, C!6)) <=> subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7))),
% 0.11/0.38 inference(symmetry,[status(thm)],[14])).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 ((~subset(set_intersection2(A!8, C!6), set_intersection2(B!7, C!6))) <=> (~subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7)))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[15])).
% 0.11/0.38 tff(17,plain,
% 0.11/0.38 ((~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 ((~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C)))) <=> (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C))))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(19,axiom,(~![A: $i, B: $i, C: $i] : (subset(A, B) => subset(set_intersection2(A, C), set_intersection2(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_xboole_1')).
% 0.11/0.38 tff(20,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.11/0.38 tff(21,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[20, 17])).
% 0.11/0.38 tff(22,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.11/0.38 tff(23,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[22, 17])).
% 0.11/0.38 tff(24,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[23, 17])).
% 0.11/0.38 tff(25,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.11/0.38 tff(26,plain,
% 0.11/0.38 (~![A: $i, B: $i, C: $i] : ((~subset(A, B)) | subset(set_intersection2(A, C), set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.11/0.38 tff(27,plain,(
% 0.11/0.38 ~((~subset(A!8, B!7)) | subset(set_intersection2(A!8, C!6), set_intersection2(B!7, C!6)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[26])).
% 0.11/0.38 tff(28,plain,
% 0.11/0.38 (~subset(set_intersection2(A!8, C!6), set_intersection2(B!7, C!6))),
% 0.11/0.38 inference(or_elim,[status(thm)],[27])).
% 0.11/0.38 tff(29,plain,
% 0.11/0.38 (~subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[28, 16])).
% 0.11/0.38 tff(30,plain,
% 0.11/0.38 (subset(set_intersection2(C!6, A!8), A!8) <=> subset(set_intersection2(A!8, C!6), A!8)),
% 0.11/0.38 inference(monotonicity,[status(thm)],[13])).
% 0.11/0.38 tff(31,plain,
% 0.11/0.38 (subset(set_intersection2(A!8, C!6), A!8) <=> subset(set_intersection2(C!6, A!8), A!8)),
% 0.11/0.38 inference(symmetry,[status(thm)],[30])).
% 0.11/0.38 tff(32,plain,
% 0.11/0.38 (^[A: $i, B: $i] : refl(subset(set_intersection2(A, B), A) <=> subset(set_intersection2(A, B), A))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(33,plain,
% 0.11/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.11/0.38 inference(quant_intro,[status(thm)],[32])).
% 0.11/0.38 tff(34,plain,
% 0.11/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A) <=> ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(35,axiom,(![A: $i, B: $i] : subset(set_intersection2(A, B), A)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t17_xboole_1')).
% 0.11/0.38 tff(36,plain,
% 0.11/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.11/0.38 tff(37,plain,(
% 0.11/0.38 ![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.11/0.38 inference(skolemize,[status(sab)],[36])).
% 0.11/0.38 tff(38,plain,
% 0.11/0.38 (![A: $i, B: $i] : subset(set_intersection2(A, B), A)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.11/0.38 tff(39,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(A!8, C!6), A!8)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(40,plain,
% 0.11/0.38 (subset(set_intersection2(A!8, C!6), A!8)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.11/0.38 tff(41,plain,
% 0.11/0.38 (subset(set_intersection2(C!6, A!8), A!8)),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[40, 31])).
% 0.11/0.38 tff(42,plain,
% 0.11/0.38 (subset(A!8, B!7)),
% 0.11/0.38 inference(or_elim,[status(thm)],[27])).
% 0.11/0.38 tff(43,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(44,plain,
% 0.11/0.38 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & subset(B, C)) <=> (~((~subset(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & subset(B, C))) <=> (~(~((~subset(B, C)) | (~subset(A, B))))))), rewrite((~(~((~subset(B, C)) | (~subset(A, B))))) <=> ((~subset(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & subset(B, C))) <=> ((~subset(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (((~subset(B, C)) | (~subset(A, B))) | subset(A, C)))), rewrite((((~subset(B, C)) | (~subset(A, B))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(45,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[44])).
% 0.11/0.38 tff(46,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(47,plain,
% 0.11/0.38 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ((~(subset(A, B) & subset(B, C))) | subset(A, C)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(48,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.38 tff(49,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(B, C)) => subset(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t1_xboole_1')).
% 0.11/0.38 tff(50,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.11/0.38 tff(51,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.11/0.38 tff(52,plain,(
% 0.11/0.38 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(B, C))) | subset(A, C))),
% 0.11/0.38 inference(skolemize,[status(sab)],[51])).
% 0.11/0.38 tff(53,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.11/0.38 tff(54,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.11/0.38 tff(55,plain,
% 0.11/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!8, B!7)) | subset(set_intersection2(C!6, A!8), B!7) | (~subset(set_intersection2(C!6, A!8), A!8)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!8, B!7)) | subset(set_intersection2(C!6, A!8), B!7) | (~subset(set_intersection2(C!6, A!8), A!8)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(56,plain,
% 0.11/0.38 ((subset(set_intersection2(C!6, A!8), B!7) | (~subset(A!8, B!7)) | (~subset(set_intersection2(C!6, A!8), A!8))) <=> ((~subset(A!8, B!7)) | subset(set_intersection2(C!6, A!8), B!7) | (~subset(set_intersection2(C!6, A!8), A!8)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(57,plain,
% 0.11/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_intersection2(C!6, A!8), B!7) | (~subset(A!8, B!7)) | (~subset(set_intersection2(C!6, A!8), A!8)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | ((~subset(A!8, B!7)) | subset(set_intersection2(C!6, A!8), B!7) | (~subset(set_intersection2(C!6, A!8), A!8))))),
% 0.11/0.38 inference(monotonicity,[status(thm)],[56])).
% 0.11/0.38 tff(58,plain,
% 0.11/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_intersection2(C!6, A!8), B!7) | (~subset(A!8, B!7)) | (~subset(set_intersection2(C!6, A!8), A!8)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!8, B!7)) | subset(set_intersection2(C!6, A!8), B!7) | (~subset(set_intersection2(C!6, A!8), A!8)))),
% 0.11/0.38 inference(transitivity,[status(thm)],[57, 55])).
% 0.11/0.38 tff(59,plain,
% 0.11/0.38 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (subset(set_intersection2(C!6, A!8), B!7) | (~subset(A!8, B!7)) | (~subset(set_intersection2(C!6, A!8), A!8)))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(60,plain,
% 0.11/0.38 ((~![A: $i, B: $i, C: $i] : (subset(A, C) | (~subset(B, C)) | (~subset(A, B)))) | (~subset(A!8, B!7)) | subset(set_intersection2(C!6, A!8), B!7) | (~subset(set_intersection2(C!6, A!8), A!8))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.11/0.38 tff(61,plain,
% 0.11/0.38 (subset(set_intersection2(C!6, A!8), B!7) | (~subset(set_intersection2(C!6, A!8), A!8))),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[60, 54, 42])).
% 0.11/0.38 tff(62,plain,
% 0.11/0.38 (subset(set_intersection2(C!6, A!8), B!7)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[61, 41])).
% 0.11/0.38 tff(63,plain,
% 0.11/0.38 ((~![A: $i, B: $i] : subset(set_intersection2(A, B), A)) | subset(set_intersection2(C!6, A!8), C!6)),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(64,plain,
% 0.11/0.38 (subset(set_intersection2(C!6, A!8), C!6)),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[63, 38])).
% 0.11/0.38 tff(65,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(66,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[65])).
% 0.11/0.38 tff(67,plain,
% 0.11/0.38 (^[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)))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(68,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[67])).
% 0.11/0.38 tff(69,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(70,plain,
% 0.11/0.38 (^[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))))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(71,plain,
% 0.11/0.38 (![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)))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[70])).
% 0.11/0.38 tff(72,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & subset(A, C)) => subset(A, set_intersection2(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t19_xboole_1')).
% 0.11/0.38 tff(73,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.11/0.38 tff(74,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.11/0.38 tff(75,plain,(
% 0.11/0.38 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & subset(A, C))) | subset(A, set_intersection2(B, C)))),
% 0.11/0.38 inference(skolemize,[status(sab)],[74])).
% 0.11/0.38 tff(76,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.11/0.38 tff(77,plain,
% 0.11/0.38 (![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.11/0.38 tff(78,plain,
% 0.11/0.38 (((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7)) | (~subset(set_intersection2(C!6, A!8), C!6)) | (~subset(set_intersection2(C!6, A!8), B!7)))) <=> ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7)) | (~subset(set_intersection2(C!6, A!8), C!6)) | (~subset(set_intersection2(C!6, A!8), B!7)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(79,plain,
% 0.11/0.39 ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | (subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7)) | (~subset(set_intersection2(C!6, A!8), C!6)) | (~subset(set_intersection2(C!6, A!8), B!7)))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(80,plain,
% 0.11/0.39 ((~![A: $i, B: $i, C: $i] : (subset(A, set_intersection2(B, C)) | (~subset(A, B)) | (~subset(A, C)))) | subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7)) | (~subset(set_intersection2(C!6, A!8), C!6)) | (~subset(set_intersection2(C!6, A!8), B!7))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 (subset(set_intersection2(C!6, A!8), set_intersection2(C!6, B!7)) | (~subset(set_intersection2(C!6, A!8), B!7))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[80, 77, 64])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[81, 62, 29])).
% 0.11/0.39 % SZS output end Proof
%------------------------------------------------------------------------------