TSTP Solution File: SYN726-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN726-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Thu Sep 29 23:57:06 EDT 2022
% Result : Unsatisfiable 0.21s 0.42s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYN726-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % 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 : Mon Sep 5 06:44:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 0.21/0.42 % SZS status Unsatisfiable
% 0.21/0.42 % SZS output start Proof
% 0.21/0.42 tff(q_type, type, (
% 0.21/0.42 q: ( $i * $i ) > $o)).
% 0.21/0.42 tff(sk2_type, type, (
% 0.21/0.42 sk2: $i)).
% 0.21/0.42 tff(sk4_type, type, (
% 0.21/0.42 sk4: $i)).
% 0.21/0.42 tff(p_type, type, (
% 0.21/0.42 p: ( $i * $i ) > $o)).
% 0.21/0.42 tff(sk3_type, type, (
% 0.21/0.42 sk3: $i)).
% 0.21/0.42 tff(sk1_type, type, (
% 0.21/0.42 sk1: $i)).
% 0.21/0.42 tff(1,assumption,(p(sk4, sk2)), introduced(assumption)).
% 0.21/0.42 tff(2,assumption,(~q(sk1, sk3)), introduced(assumption)).
% 0.21/0.42 tff(3,assumption,(q(sk2, sk3)), introduced(assumption)).
% 0.21/0.42 tff(4,plain,
% 0.21/0.42 ((~p(sk1, sk2)) <=> (~p(sk1, sk2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(5,axiom,(~p(sk1, sk2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm400_5')).
% 0.21/0.42 tff(6,plain,
% 0.21/0.42 (~p(sk1, sk2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.21/0.42 tff(7,plain,
% 0.21/0.42 (^[B: $i, A: $i] : refl((p(A, B) | q(A, B)) <=> (p(A, B) | q(A, B)))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(8,plain,
% 0.21/0.42 (![B: $i, A: $i] : (p(A, B) | q(A, B)) <=> ![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.42 tff(9,plain,
% 0.21/0.42 (![B: $i, A: $i] : (p(A, B) | q(A, B)) <=> ![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(10,axiom,(![B: $i, A: $i] : (p(A, B) | q(A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm400_4')).
% 0.21/0.42 tff(11,plain,
% 0.21/0.42 (![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.42 tff(12,plain,(
% 0.21/0.42 ![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.21/0.42 inference(skolemize,[status(sab)],[11])).
% 0.21/0.42 tff(13,plain,
% 0.21/0.42 (![B: $i, A: $i] : (p(A, B) | q(A, B))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.42 tff(14,plain,
% 0.21/0.42 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk2) | q(sk1, sk2))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk2) | q(sk1, sk2))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(15,plain,
% 0.21/0.42 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk2) | q(sk1, sk2))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(16,plain,
% 0.21/0.42 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk2) | q(sk1, sk2)),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.42 tff(17,plain,
% 0.21/0.42 (q(sk1, sk2)),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[16, 13, 6])).
% 0.21/0.42 tff(18,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(19,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(20,plain,
% 0.21/0.42 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((q(A, C) | (~q(A, B))) <=> ((~q(A, B)) | q(A, C))), (((q(A, C) | (~q(A, B))) | (~q(B, C))) <=> (((~q(A, B)) | q(A, C)) | (~q(B, C))))), rewrite((((~q(A, B)) | q(A, C)) | (~q(B, C))) <=> ((~q(B, C)) | (~q(A, B)) | q(A, C))), (((q(A, C) | (~q(A, B))) | (~q(B, C))) <=> ((~q(B, C)) | (~q(A, B)) | q(A, C))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(21,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : ((q(A, C) | (~q(A, B))) | (~q(B, C))) <=> ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.42 tff(22,axiom,(![B: $i, A: $i, C: $i] : ((q(A, C) | (~q(A, B))) | (~q(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm400_2')).
% 0.21/0.42 tff(23,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.42 tff(24,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.21/0.42 tff(25,plain,(
% 0.21/0.42 ![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.21/0.42 inference(skolemize,[status(sab)],[24])).
% 0.21/0.42 tff(26,plain,
% 0.21/0.42 (![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.21/0.42 tff(27,plain,
% 0.21/0.42 (((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk1, sk2)) | q(sk1, sk3) | (~q(sk2, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk1, sk2)) | q(sk1, sk3) | (~q(sk2, sk3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (((~q(sk2, sk3)) | (~q(sk1, sk2)) | q(sk1, sk3)) <=> ((~q(sk1, sk2)) | q(sk1, sk3) | (~q(sk2, sk3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk2, sk3)) | (~q(sk1, sk2)) | q(sk1, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk1, sk2)) | q(sk1, sk3) | (~q(sk2, sk3))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[28])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk2, sk3)) | (~q(sk1, sk2)) | q(sk1, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk1, sk2)) | q(sk1, sk3) | (~q(sk2, sk3)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[29, 27])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk2, sk3)) | (~q(sk1, sk2)) | q(sk1, sk3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk1, sk2)) | q(sk1, sk3) | (~q(sk2, sk3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[32, 26, 17, 3, 2])).
% 0.21/0.43 tff(34,plain,((~q(sk2, sk3)) | q(sk1, sk3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (~q(sk2, sk3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[34, 2])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk3) | q(sk1, sk3))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk3) | q(sk1, sk3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk3) | q(sk1, sk3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk3) | q(sk1, sk3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (p(sk1, sk3) | q(sk1, sk3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[38, 13])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (p(sk1, sk3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[39, 2])).
% 0.21/0.43 tff(41,assumption,(p(sk1, sk3)), introduced(assumption)).
% 0.21/0.43 tff(42,assumption,(p(sk3, sk2)), introduced(assumption)).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(45,plain,
% 0.21/0.43 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((p(A, C) | (~p(A, B))) <=> ((~p(A, B)) | p(A, C))), (((p(A, C) | (~p(A, B))) | (~p(B, C))) <=> (((~p(A, B)) | p(A, C)) | (~p(B, C))))), rewrite((((~p(A, B)) | p(A, C)) | (~p(B, C))) <=> ((~p(B, C)) | (~p(A, B)) | p(A, C))), (((p(A, C) | (~p(A, B))) | (~p(B, C))) <=> ((~p(B, C)) | (~p(A, B)) | p(A, C))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : ((p(A, C) | (~p(A, B))) | (~p(B, C))) <=> ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.43 tff(47,axiom,(![B: $i, A: $i, C: $i] : ((p(A, C) | (~p(A, B))) | (~p(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm400_1')).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.43 tff(50,plain,(
% 0.21/0.43 ![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.21/0.43 inference(skolemize,[status(sab)],[49])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2)) <=> (p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3)))),
% 0.21/0.43 inference(transitivity,[status(thm)],[54, 52])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk2)) | (~p(sk1, sk3)) | p(sk1, sk2))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | p(sk1, sk2) | (~p(sk3, sk2)) | (~p(sk1, sk3))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[57, 51, 6, 42, 41])).
% 0.21/0.43 tff(59,plain,((~p(sk3, sk2)) | (~p(sk1, sk3))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (~p(sk3, sk2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[59, 40])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk2) | q(sk3, sk2))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk2) | q(sk3, sk2))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk2) | q(sk3, sk2))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk2) | q(sk3, sk2)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 (p(sk3, sk2) | q(sk3, sk2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[63, 13])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (q(sk3, sk2)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[64, 60])).
% 0.21/0.43 tff(66,plain,
% 0.21/0.43 (^[B: $i, A: $i] : refl(((~q(A, B)) | q(B, A)) <=> ((~q(A, B)) | q(B, A)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(67,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A)) <=> ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.43 tff(68,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A)) <=> ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(69,plain,
% 0.21/0.43 (^[B: $i, A: $i] : rewrite((q(B, A) | (~q(A, B))) <=> ((~q(A, B)) | q(B, A)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(70,plain,
% 0.21/0.43 (![B: $i, A: $i] : (q(B, A) | (~q(A, B))) <=> ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.43 tff(71,axiom,(![B: $i, A: $i] : (q(B, A) | (~q(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm400_3')).
% 0.21/0.43 tff(72,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.43 tff(73,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.21/0.43 tff(74,plain,(
% 0.21/0.43 ![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.21/0.43 inference(skolemize,[status(sab)],[73])).
% 0.21/0.43 tff(75,plain,
% 0.21/0.43 (![B: $i, A: $i] : ((~q(A, B)) | q(B, A))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.21/0.43 tff(76,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk3, sk2)) | q(sk2, sk3))) <=> ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk3, sk2)) | q(sk2, sk3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(77,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk3, sk2)) | q(sk2, sk3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(78,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk3, sk2)) | q(sk2, sk3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.43 tff(79,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[78, 75, 65, 35])).
% 0.21/0.43 tff(80,plain,(q(sk1, sk3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(81,assumption,(q(sk4, sk1)), introduced(assumption)).
% 0.21/0.43 tff(82,assumption,(q(sk1, sk3)), introduced(assumption)).
% 0.21/0.43 tff(83,plain,
% 0.21/0.43 ((~q(sk3, sk4)) <=> (~q(sk3, sk4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(84,axiom,(~q(sk3, sk4)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm400_6')).
% 0.21/0.43 tff(85,plain,
% 0.21/0.43 (~q(sk3, sk4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.21/0.43 tff(86,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk4, sk3)) | q(sk3, sk4))) <=> ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk4, sk3)) | q(sk3, sk4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(87,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk4, sk3)) | q(sk3, sk4))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(88,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk4, sk3)) | q(sk3, sk4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.43 tff(89,plain,
% 0.21/0.43 (~q(sk4, sk3)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[88, 75, 85])).
% 0.21/0.43 tff(90,plain,
% 0.21/0.43 (((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk1, sk3)) | (~q(sk4, sk1)) | q(sk4, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk1, sk3)) | (~q(sk4, sk1)) | q(sk4, sk3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(91,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk1, sk3)) | (~q(sk4, sk1)) | q(sk4, sk3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(92,plain,
% 0.21/0.43 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk1, sk3)) | (~q(sk4, sk1)) | q(sk4, sk3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.21/0.43 tff(93,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[92, 26, 89, 82, 81])).
% 0.21/0.43 tff(94,plain,((~q(sk1, sk3)) | (~q(sk4, sk1))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(95,plain,
% 0.21/0.43 (~q(sk4, sk1)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[94, 80])).
% 0.21/0.43 tff(96,assumption,(q(sk1, sk4)), introduced(assumption)).
% 0.21/0.43 tff(97,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk1, sk4)) | q(sk4, sk1))) <=> ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk1, sk4)) | q(sk4, sk1))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(98,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk1, sk4)) | q(sk4, sk1))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(99,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk1, sk4)) | q(sk4, sk1)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.21/0.43 tff(100,plain,
% 0.21/0.43 ($false),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[99, 75, 96, 95])).
% 0.21/0.43 tff(101,plain,(~q(sk1, sk4)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.43 tff(102,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk4) | q(sk1, sk4))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk4) | q(sk1, sk4))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(103,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk1, sk4) | q(sk1, sk4))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(104,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk1, sk4) | q(sk1, sk4)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.43 tff(105,plain,
% 0.21/0.43 (p(sk1, sk4) | q(sk1, sk4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[104, 13])).
% 0.21/0.43 tff(106,plain,
% 0.21/0.43 (p(sk1, sk4)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[105, 101])).
% 0.21/0.43 tff(107,assumption,(~p(sk1, sk3)), introduced(assumption)).
% 0.21/0.43 tff(108,assumption,(p(sk1, sk4)), introduced(assumption)).
% 0.21/0.43 tff(109,plain,
% 0.21/0.43 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk3) | q(sk4, sk3))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk3) | q(sk4, sk3))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(110,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk3) | q(sk4, sk3))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(111,plain,
% 0.21/0.43 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk3) | q(sk4, sk3)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.44 tff(112,plain,
% 0.21/0.44 (p(sk4, sk3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[111, 13, 89])).
% 0.21/0.44 tff(113,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk3)) | p(sk1, sk3) | (~p(sk1, sk4)))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk4, sk3)) | p(sk1, sk3) | (~p(sk1, sk4)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(114,plain,
% 0.21/0.44 (((~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3)) <=> ((~p(sk4, sk3)) | p(sk1, sk3) | (~p(sk1, sk4)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(115,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk3)) | p(sk1, sk3) | (~p(sk1, sk4))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.44 tff(116,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk4, sk3)) | p(sk1, sk3) | (~p(sk1, sk4)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[115, 113])).
% 0.21/0.44 tff(117,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk3)) | (~p(sk1, sk4)) | p(sk1, sk3))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(118,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk4, sk3)) | p(sk1, sk3) | (~p(sk1, sk4))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.44 tff(119,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[118, 51, 112, 108, 107])).
% 0.21/0.44 tff(120,plain,((~p(sk1, sk4)) | p(sk1, sk3)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(121,plain,
% 0.21/0.44 (p(sk1, sk3)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[120, 106])).
% 0.21/0.44 tff(122,plain,
% 0.21/0.44 (~p(sk3, sk2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[59, 121])).
% 0.21/0.44 tff(123,plain,
% 0.21/0.44 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk4) | q(sk3, sk4))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk4) | q(sk3, sk4))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(124,plain,
% 0.21/0.44 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk3, sk4) | q(sk3, sk4))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(125,plain,
% 0.21/0.44 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk3, sk4) | q(sk3, sk4)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.21/0.44 tff(126,plain,
% 0.21/0.44 (p(sk3, sk4)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[125, 13, 85])).
% 0.21/0.44 tff(127,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk4)) | p(sk3, sk2) | (~p(sk4, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk3, sk4)) | p(sk3, sk2) | (~p(sk4, sk2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(128,plain,
% 0.21/0.44 (((~p(sk4, sk2)) | (~p(sk3, sk4)) | p(sk3, sk2)) <=> ((~p(sk3, sk4)) | p(sk3, sk2) | (~p(sk4, sk2)))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(129,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk2)) | (~p(sk3, sk4)) | p(sk3, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk3, sk4)) | p(sk3, sk2) | (~p(sk4, sk2))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[128])).
% 0.21/0.44 tff(130,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk2)) | (~p(sk3, sk4)) | p(sk3, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk3, sk4)) | p(sk3, sk2) | (~p(sk4, sk2)))),
% 0.21/0.44 inference(transitivity,[status(thm)],[129, 127])).
% 0.21/0.44 tff(131,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | ((~p(sk4, sk2)) | (~p(sk3, sk4)) | p(sk3, sk2))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(132,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : ((~p(B, C)) | (~p(A, B)) | p(A, C))) | (~p(sk3, sk4)) | p(sk3, sk2) | (~p(sk4, sk2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.44 tff(133,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[132, 51, 126, 122, 1])).
% 0.21/0.44 tff(134,plain,(~p(sk4, sk2)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(135,plain,
% 0.21/0.44 (((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk2) | q(sk4, sk2))) <=> ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk2) | q(sk4, sk2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(136,plain,
% 0.21/0.44 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | (p(sk4, sk2) | q(sk4, sk2))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(137,plain,
% 0.21/0.44 ((~![B: $i, A: $i] : (p(A, B) | q(A, B))) | p(sk4, sk2) | q(sk4, sk2)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.44 tff(138,plain,
% 0.21/0.44 (p(sk4, sk2) | q(sk4, sk2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[137, 13])).
% 0.21/0.44 tff(139,plain,
% 0.21/0.44 (q(sk4, sk2)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[138, 134])).
% 0.21/0.44 tff(140,plain,
% 0.21/0.44 (((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk1, sk2)) | q(sk2, sk1))) <=> ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk1, sk2)) | q(sk2, sk1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(141,plain,
% 0.21/0.44 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | ((~q(sk1, sk2)) | q(sk2, sk1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(142,plain,
% 0.21/0.44 ((~![B: $i, A: $i] : ((~q(A, B)) | q(B, A))) | (~q(sk1, sk2)) | q(sk2, sk1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.44 tff(143,plain,
% 0.21/0.44 (q(sk2, sk1)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[142, 75, 17])).
% 0.21/0.44 tff(144,plain,
% 0.21/0.44 (((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk2, sk1)) | (~q(sk4, sk2)) | q(sk4, sk1))) <=> ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk2, sk1)) | (~q(sk4, sk2)) | q(sk4, sk1))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(145,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | ((~q(sk2, sk1)) | (~q(sk4, sk2)) | q(sk4, sk1))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(146,plain,
% 0.21/0.44 ((~![B: $i, A: $i, C: $i] : ((~q(B, C)) | (~q(A, B)) | q(A, C))) | (~q(sk2, sk1)) | (~q(sk4, sk2)) | q(sk4, sk1)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.21/0.44 tff(147,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[146, 26, 143, 95, 139])).
% 0.21/0.44 % SZS output end Proof
%------------------------------------------------------------------------------