TSTP Solution File: SYN583-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SYN583-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 23:56:31 EDT 2022
% Result : Unsatisfiable 3.89s 2.81s
% Output : Proof 4.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SYN583-1 : TPTP v8.1.0. Released v2.5.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % 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 : Mon Sep 5 06:02:46 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.
% 3.89/2.81 % SZS status Unsatisfiable
% 3.89/2.81 % SZS output start Proof
% 3.89/2.81 tff(p2_type, type, (
% 3.89/2.81 p2: ( $i * $i ) > $o)).
% 3.89/2.81 tff(c16_type, type, (
% 3.89/2.81 c16: $i)).
% 3.89/2.81 tff(f4_type, type, (
% 3.89/2.81 f4: $i > $i)).
% 3.89/2.81 tff(f6_type, type, (
% 3.89/2.81 f6: ( $i * $i ) > $i)).
% 3.89/2.81 tff(c18_type, type, (
% 3.89/2.81 c18: $i)).
% 3.89/2.81 tff(c15_type, type, (
% 3.89/2.81 c15: $i)).
% 3.89/2.81 tff(c13_type, type, (
% 3.89/2.81 c13: $i)).
% 3.89/2.81 tff(p5_type, type, (
% 3.89/2.81 p5: ( $i * $i ) > $o)).
% 3.89/2.81 tff(p12_type, type, (
% 3.89/2.81 p12: ( $i * $i ) > $o)).
% 3.89/2.81 tff(p11_type, type, (
% 3.89/2.81 p11: ( $i * $i ) > $o)).
% 3.89/2.81 tff(1,plain,
% 3.89/2.81 (^[X18: $i] : refl(p2(X18, X18) <=> p2(X18, X18))),
% 3.89/2.81 inference(bind,[status(th)],[])).
% 3.89/2.81 tff(2,plain,
% 3.89/2.81 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 3.89/2.81 inference(quant_intro,[status(thm)],[1])).
% 3.89/2.81 tff(3,plain,
% 3.89/2.81 (![X18: $i] : p2(X18, X18) <=> ![X18: $i] : p2(X18, X18)),
% 3.89/2.81 inference(rewrite,[status(thm)],[])).
% 3.89/2.81 tff(4,axiom,(![X18: $i] : p2(X18, X18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_2')).
% 3.89/2.81 tff(5,plain,
% 3.89/2.81 (![X18: $i] : p2(X18, X18)),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.89/2.81 tff(6,plain,(
% 3.89/2.81 ![X18: $i] : p2(X18, X18)),
% 3.89/2.81 inference(skolemize,[status(sab)],[5])).
% 3.89/2.81 tff(7,plain,
% 3.89/2.81 (![X18: $i] : p2(X18, X18)),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.89/2.81 tff(8,plain,
% 3.89/2.81 ((~![X18: $i] : p2(X18, X18)) | p2(c16, c16)),
% 3.89/2.81 inference(quant_inst,[status(thm)],[])).
% 3.89/2.81 tff(9,plain,
% 3.89/2.81 (p2(c16, c16)),
% 3.89/2.81 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.89/2.81 tff(10,assumption,(~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))), introduced(assumption)).
% 3.89/2.81 tff(11,assumption,(~p2(f6(c15, c13), f6(c15, c18))), introduced(assumption)).
% 3.89/2.81 tff(12,assumption,(~p5(c15, c15)), introduced(assumption)).
% 3.89/2.81 tff(13,plain,
% 3.89/2.81 (^[X31: $i] : refl(p5(X31, X31) <=> p5(X31, X31))),
% 3.89/2.81 inference(bind,[status(th)],[])).
% 3.89/2.81 tff(14,plain,
% 3.89/2.81 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 3.89/2.81 inference(quant_intro,[status(thm)],[13])).
% 3.89/2.81 tff(15,plain,
% 3.89/2.81 (![X31: $i] : p5(X31, X31) <=> ![X31: $i] : p5(X31, X31)),
% 3.89/2.81 inference(rewrite,[status(thm)],[])).
% 3.89/2.81 tff(16,axiom,(![X31: $i] : p5(X31, X31)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p5_3')).
% 3.89/2.81 tff(17,plain,
% 3.89/2.81 (![X31: $i] : p5(X31, X31)),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[16, 15])).
% 3.89/2.81 tff(18,plain,(
% 3.89/2.81 ![X31: $i] : p5(X31, X31)),
% 3.89/2.81 inference(skolemize,[status(sab)],[17])).
% 3.89/2.81 tff(19,plain,
% 3.89/2.81 (![X31: $i] : p5(X31, X31)),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.89/2.81 tff(20,plain,
% 3.89/2.81 ((~![X31: $i] : p5(X31, X31)) | p5(c15, c15)),
% 3.89/2.81 inference(quant_inst,[status(thm)],[])).
% 3.89/2.81 tff(21,plain,
% 3.89/2.81 ($false),
% 3.89/2.81 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 3.89/2.81 tff(22,plain,(p5(c15, c15)), inference(lemma,lemma(discharge,[]))).
% 3.89/2.81 tff(23,plain,
% 3.89/2.81 (^[X25: $i, X27: $i, X28: $i, X26: $i] : refl(((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))))),
% 3.89/2.81 inference(bind,[status(th)],[])).
% 3.89/2.81 tff(24,plain,
% 3.89/2.81 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 3.89/2.81 inference(quant_intro,[status(thm)],[23])).
% 3.89/2.81 tff(25,plain,
% 3.89/2.81 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 3.89/2.81 inference(rewrite,[status(thm)],[])).
% 3.89/2.81 tff(26,plain,
% 3.89/2.81 (^[X25: $i, X27: $i, X28: $i, X26: $i] : trans(monotonicity(rewrite((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) <=> ((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28)))), (((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> (((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28))) | (~p5(X25, X27))))), rewrite((((~p2(X26, X28)) | p2(f6(X25, X26), f6(X27, X28))) | (~p5(X25, X27))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))), (((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))))),
% 3.89/2.81 inference(bind,[status(th)],[])).
% 3.89/2.81 tff(27,plain,
% 3.89/2.81 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27))) <=> ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 3.89/2.81 inference(quant_intro,[status(thm)],[26])).
% 3.89/2.81 tff(28,axiom,(![X25: $i, X27: $i, X28: $i, X26: $i] : ((p2(f6(X25, X26), f6(X27, X28)) | (~p2(X26, X28))) | (~p5(X25, X27)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_23')).
% 3.89/2.81 tff(29,plain,
% 3.89/2.81 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[28, 27])).
% 3.89/2.81 tff(30,plain,
% 3.89/2.81 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[29, 25])).
% 3.89/2.81 tff(31,plain,(
% 3.89/2.81 ![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 3.89/2.81 inference(skolemize,[status(sab)],[30])).
% 3.89/2.81 tff(32,plain,
% 3.89/2.81 (![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[31, 24])).
% 3.89/2.81 tff(33,plain,
% 3.89/2.81 (p2(c13, c18) <=> p2(c13, c18)),
% 3.89/2.81 inference(rewrite,[status(thm)],[])).
% 3.89/2.81 tff(34,axiom,(p2(c13, c18)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_4')).
% 3.89/2.81 tff(35,plain,
% 3.89/2.81 (p2(c13, c18)),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[34, 33])).
% 3.89/2.81 tff(36,plain,
% 3.89/2.81 (((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18)))) <=> ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18)))),
% 3.89/2.81 inference(rewrite,[status(thm)],[])).
% 3.89/2.81 tff(37,plain,
% 3.89/2.81 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | ((~p2(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18)))),
% 3.89/2.81 inference(quant_inst,[status(thm)],[])).
% 3.89/2.81 tff(38,plain,
% 3.89/2.81 ((~![X25: $i, X27: $i, X28: $i, X26: $i] : ((~p2(X26, X28)) | (~p5(X25, X27)) | p2(f6(X25, X26), f6(X27, X28)))) | (~p2(c13, c18)) | (~p5(c15, c15)) | p2(f6(c15, c13), f6(c15, c18))),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[37, 36])).
% 3.89/2.81 tff(39,plain,
% 3.89/2.81 ($false),
% 3.89/2.81 inference(unit_resolution,[status(thm)],[38, 35, 32, 22, 11])).
% 3.89/2.81 tff(40,plain,(p2(f6(c15, c13), f6(c15, c18))), inference(lemma,lemma(discharge,[]))).
% 3.89/2.81 tff(41,plain,
% 3.89/2.81 (^[X23: $i, X24: $i] : refl(((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 3.89/2.81 inference(bind,[status(th)],[])).
% 3.89/2.81 tff(42,plain,
% 3.89/2.81 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 3.89/2.81 inference(quant_intro,[status(thm)],[41])).
% 3.89/2.81 tff(43,plain,
% 3.89/2.81 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 3.89/2.81 inference(rewrite,[status(thm)],[])).
% 3.89/2.81 tff(44,plain,
% 3.89/2.81 (^[X23: $i, X24: $i] : rewrite((p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ((~p2(X23, X24)) | p2(f4(X23), f4(X24))))),
% 3.89/2.81 inference(bind,[status(th)],[])).
% 3.89/2.81 tff(45,plain,
% 3.89/2.81 (![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24))) <=> ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 3.89/2.81 inference(quant_intro,[status(thm)],[44])).
% 3.89/2.81 tff(46,axiom,(![X23: $i, X24: $i] : (p2(f4(X23), f4(X24)) | (~p2(X23, X24)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_14')).
% 3.89/2.81 tff(47,plain,
% 3.89/2.81 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.89/2.81 tff(48,plain,
% 3.89/2.81 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 3.89/2.81 inference(modus_ponens,[status(thm)],[47, 43])).
% 3.89/2.81 tff(49,plain,(
% 3.89/2.81 ![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 4.02/2.81 inference(skolemize,[status(sab)],[48])).
% 4.02/2.81 tff(50,plain,
% 4.02/2.81 (![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[49, 42])).
% 4.02/2.81 tff(51,plain,
% 4.02/2.81 (((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18))))) <=> ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18))))),
% 4.02/2.81 inference(rewrite,[status(thm)],[])).
% 4.02/2.81 tff(52,plain,
% 4.02/2.81 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | ((~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18))))),
% 4.02/2.81 inference(quant_inst,[status(thm)],[])).
% 4.02/2.81 tff(53,plain,
% 4.02/2.81 ((~![X23: $i, X24: $i] : ((~p2(X23, X24)) | p2(f4(X23), f4(X24)))) | (~p2(f6(c15, c13), f6(c15, c18))) | p2(f4(f6(c15, c13)), f4(f6(c15, c18)))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[52, 51])).
% 4.02/2.81 tff(54,plain,
% 4.02/2.81 ($false),
% 4.02/2.81 inference(unit_resolution,[status(thm)],[53, 50, 40, 10])).
% 4.02/2.81 tff(55,plain,(p2(f4(f6(c15, c13)), f4(f6(c15, c18)))), inference(lemma,lemma(discharge,[]))).
% 4.02/2.81 tff(56,plain,
% 4.02/2.81 (^[X12: $i, X11: $i] : refl(((~p12(X11, X12)) | p11(X11, X12)) <=> ((~p12(X11, X12)) | p11(X11, X12)))),
% 4.02/2.81 inference(bind,[status(th)],[])).
% 4.02/2.81 tff(57,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12)) <=> ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 4.02/2.81 inference(quant_intro,[status(thm)],[56])).
% 4.02/2.81 tff(58,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12)) <=> ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 4.02/2.81 inference(rewrite,[status(thm)],[])).
% 4.02/2.81 tff(59,plain,
% 4.02/2.81 (^[X12: $i, X11: $i] : rewrite((p11(X11, X12) | (~p12(X11, X12))) <=> ((~p12(X11, X12)) | p11(X11, X12)))),
% 4.02/2.81 inference(bind,[status(th)],[])).
% 4.02/2.81 tff(60,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p12(X11, X12))) <=> ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 4.02/2.81 inference(quant_intro,[status(thm)],[59])).
% 4.02/2.81 tff(61,axiom,(![X12: $i, X11: $i] : (p11(X11, X12) | (~p12(X11, X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_10')).
% 4.02/2.81 tff(62,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[61, 60])).
% 4.02/2.81 tff(63,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[62, 58])).
% 4.02/2.81 tff(64,plain,(
% 4.02/2.81 ![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 4.02/2.81 inference(skolemize,[status(sab)],[63])).
% 4.02/2.81 tff(65,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[64, 57])).
% 4.02/2.81 tff(66,plain,
% 4.02/2.81 ((~p11(f4(f6(c15, c18)), c16)) <=> (~p11(f4(f6(c15, c18)), c16))),
% 4.02/2.81 inference(rewrite,[status(thm)],[])).
% 4.02/2.81 tff(67,axiom,(~p11(f4(f6(c15, c18)), c16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','not_p11_9')).
% 4.02/2.81 tff(68,plain,
% 4.02/2.81 (~p11(f4(f6(c15, c18)), c16)),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[67, 66])).
% 4.02/2.81 tff(69,plain,
% 4.02/2.81 (((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | ((~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16))) <=> ((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | (~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16))),
% 4.02/2.81 inference(rewrite,[status(thm)],[])).
% 4.02/2.81 tff(70,plain,
% 4.02/2.81 ((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | ((~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16))),
% 4.02/2.81 inference(quant_inst,[status(thm)],[])).
% 4.02/2.81 tff(71,plain,
% 4.02/2.81 ((~![X12: $i, X11: $i] : ((~p12(X11, X12)) | p11(X11, X12))) | (~p12(f4(f6(c15, c18)), c16)) | p11(f4(f6(c15, c18)), c16)),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[70, 69])).
% 4.02/2.81 tff(72,plain,
% 4.02/2.81 (~p12(f4(f6(c15, c18)), c16)),
% 4.02/2.81 inference(unit_resolution,[status(thm)],[71, 68, 65])).
% 4.02/2.81 tff(73,plain,
% 4.02/2.81 (^[X12: $i, X11: $i] : refl((p11(X11, X12) | (~p2(X11, X12))) <=> (p11(X11, X12) | (~p2(X11, X12))))),
% 4.02/2.81 inference(bind,[status(th)],[])).
% 4.02/2.81 tff(74,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12))) <=> ![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 4.02/2.81 inference(quant_intro,[status(thm)],[73])).
% 4.02/2.81 tff(75,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12))) <=> ![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 4.02/2.81 inference(rewrite,[status(thm)],[])).
% 4.02/2.81 tff(76,axiom,(![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_11')).
% 4.02/2.81 tff(77,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[76, 75])).
% 4.02/2.81 tff(78,plain,(
% 4.02/2.81 ![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 4.02/2.81 inference(skolemize,[status(sab)],[77])).
% 4.02/2.81 tff(79,plain,
% 4.02/2.81 (![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[78, 74])).
% 4.02/2.81 tff(80,plain,
% 4.02/2.81 (((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c18)), c16)))) <=> ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c18)), c16)))),
% 4.02/2.81 inference(rewrite,[status(thm)],[])).
% 4.02/2.81 tff(81,plain,
% 4.02/2.81 ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | (p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c18)), c16)))),
% 4.02/2.81 inference(quant_inst,[status(thm)],[])).
% 4.02/2.81 tff(82,plain,
% 4.02/2.81 ((~![X12: $i, X11: $i] : (p11(X11, X12) | (~p2(X11, X12)))) | p11(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c18)), c16))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[81, 80])).
% 4.02/2.81 tff(83,plain,
% 4.02/2.81 (~p2(f4(f6(c15, c18)), c16)),
% 4.02/2.81 inference(unit_resolution,[status(thm)],[82, 68, 79])).
% 4.02/2.81 tff(84,assumption,(p2(f4(f6(c15, c13)), c16)), introduced(assumption)).
% 4.02/2.81 tff(85,plain,
% 4.02/2.81 (^[X18: $i, X20: $i, X19: $i] : refl((p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))))),
% 4.02/2.81 inference(bind,[status(th)],[])).
% 4.02/2.81 tff(86,plain,
% 4.02/2.81 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 4.02/2.81 inference(quant_intro,[status(thm)],[85])).
% 4.02/2.81 tff(87,plain,
% 4.02/2.81 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 4.02/2.81 inference(rewrite,[status(thm)],[])).
% 4.02/2.81 tff(88,plain,
% 4.02/2.81 (^[X18: $i, X20: $i, X19: $i] : trans(monotonicity(rewrite((p2(X19, X20) | (~p2(X18, X19))) <=> (p2(X19, X20) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))))), rewrite(((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))), (((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))))),
% 4.02/2.81 inference(bind,[status(th)],[])).
% 4.02/2.81 tff(89,plain,
% 4.02/2.81 (![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20))) <=> ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 4.02/2.81 inference(quant_intro,[status(thm)],[88])).
% 4.02/2.81 tff(90,axiom,(![X18: $i, X20: $i, X19: $i] : ((p2(X19, X20) | (~p2(X18, X19))) | (~p2(X18, X20)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p2_18')).
% 4.02/2.81 tff(91,plain,
% 4.02/2.81 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[90, 89])).
% 4.02/2.81 tff(92,plain,
% 4.02/2.81 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[91, 87])).
% 4.02/2.81 tff(93,plain,(
% 4.02/2.81 ![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 4.02/2.81 inference(skolemize,[status(sab)],[92])).
% 4.02/2.81 tff(94,plain,
% 4.02/2.81 (![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))),
% 4.02/2.81 inference(modus_ponens,[status(thm)],[93, 86])).
% 4.02/2.81 tff(95,plain,
% 4.02/2.81 (((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))))) <=> ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))))),
% 4.02/2.82 inference(rewrite,[status(thm)],[])).
% 4.02/2.82 tff(96,plain,
% 4.02/2.82 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | (p2(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))))),
% 4.02/2.82 inference(quant_inst,[status(thm)],[])).
% 4.02/2.82 tff(97,plain,
% 4.02/2.82 ((~![X18: $i, X20: $i, X19: $i] : (p2(X19, X20) | (~p2(X18, X20)) | (~p2(X18, X19)))) | p2(f4(f6(c15, c18)), c16) | (~p2(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18))))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[96, 95])).
% 4.02/2.82 tff(98,plain,
% 4.02/2.82 ($false),
% 4.02/2.82 inference(unit_resolution,[status(thm)],[97, 94, 84, 83, 55])).
% 4.02/2.82 tff(99,plain,(~p2(f4(f6(c15, c13)), c16)), inference(lemma,lemma(discharge,[]))).
% 4.02/2.82 tff(100,plain,
% 4.02/2.82 (^[X12: $i, X11: $i] : refl((p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))) <=> (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))))),
% 4.02/2.82 inference(bind,[status(th)],[])).
% 4.02/2.82 tff(101,plain,
% 4.02/2.82 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))) <=> ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 4.02/2.82 inference(quant_intro,[status(thm)],[100])).
% 4.02/2.82 tff(102,plain,
% 4.02/2.82 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))) <=> ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 4.02/2.82 inference(rewrite,[status(thm)],[])).
% 4.02/2.82 tff(103,plain,
% 4.02/2.82 (^[X12: $i, X11: $i] : rewrite(((p12(X11, X12) | p2(X11, X12)) | (~p11(X11, X12))) <=> (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12))))),
% 4.02/2.82 inference(bind,[status(th)],[])).
% 4.02/2.82 tff(104,plain,
% 4.02/2.82 (![X12: $i, X11: $i] : ((p12(X11, X12) | p2(X11, X12)) | (~p11(X11, X12))) <=> ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 4.02/2.82 inference(quant_intro,[status(thm)],[103])).
% 4.02/2.82 tff(105,axiom,(![X12: $i, X11: $i] : ((p12(X11, X12) | p2(X11, X12)) | (~p11(X11, X12)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_16')).
% 4.02/2.82 tff(106,plain,
% 4.02/2.82 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[105, 104])).
% 4.02/2.82 tff(107,plain,
% 4.02/2.82 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[106, 102])).
% 4.02/2.82 tff(108,plain,(
% 4.02/2.82 ![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 4.02/2.82 inference(skolemize,[status(sab)],[107])).
% 4.02/2.82 tff(109,plain,
% 4.02/2.82 (![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[108, 101])).
% 4.02/2.82 tff(110,plain,
% 4.02/2.82 (p11(f4(f6(c15, c13)), c16) <=> p11(f4(f6(c15, c13)), c16)),
% 4.02/2.82 inference(rewrite,[status(thm)],[])).
% 4.02/2.82 tff(111,axiom,(p11(f4(f6(c15, c13)), c16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p11_7')).
% 4.02/2.82 tff(112,plain,
% 4.02/2.82 (p11(f4(f6(c15, c13)), c16)),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[111, 110])).
% 4.02/2.82 tff(113,plain,
% 4.02/2.82 (((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | (p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16)))) <=> ((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16)))),
% 4.02/2.82 inference(rewrite,[status(thm)],[])).
% 4.02/2.82 tff(114,plain,
% 4.02/2.82 ((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | (p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16)))),
% 4.02/2.82 inference(quant_inst,[status(thm)],[])).
% 4.02/2.82 tff(115,plain,
% 4.02/2.82 ((~![X12: $i, X11: $i] : (p12(X11, X12) | p2(X11, X12) | (~p11(X11, X12)))) | p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16) | (~p11(f4(f6(c15, c13)), c16))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[114, 113])).
% 4.02/2.82 tff(116,plain,
% 4.02/2.82 (p12(f4(f6(c15, c13)), c16) | p2(f4(f6(c15, c13)), c16)),
% 4.02/2.82 inference(unit_resolution,[status(thm)],[115, 112, 109])).
% 4.02/2.82 tff(117,plain,
% 4.02/2.82 (p12(f4(f6(c15, c13)), c16)),
% 4.02/2.82 inference(unit_resolution,[status(thm)],[116, 99])).
% 4.02/2.82 tff(118,plain,
% 4.02/2.82 (^[X14: $i, X17: $i, X16: $i, X15: $i] : refl(((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)) <=> ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)))),
% 4.02/2.82 inference(bind,[status(th)],[])).
% 4.02/2.82 tff(119,plain,
% 4.02/2.82 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 4.02/2.82 inference(quant_intro,[status(thm)],[118])).
% 4.02/2.82 tff(120,plain,
% 4.02/2.82 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15)) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 4.02/2.82 inference(rewrite,[status(thm)],[])).
% 4.02/2.82 tff(121,plain,
% 4.02/2.82 (^[X14: $i, X17: $i, X16: $i, X15: $i] : trans(monotonicity(trans(monotonicity(rewrite((p12(X14, X15) | (~p2(X16, X14))) <=> ((~p2(X16, X14)) | p12(X14, X15))), (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) <=> (((~p2(X16, X14)) | p12(X14, X15)) | (~p2(X17, X15))))), rewrite((((~p2(X16, X14)) | p12(X14, X15)) | (~p2(X17, X15))) <=> ((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15))), (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) <=> ((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15)))), ((((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17))) <=> (((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15)) | (~p12(X16, X17))))), rewrite((((~p2(X17, X15)) | (~p2(X16, X14)) | p12(X14, X15)) | (~p12(X16, X17))) <=> ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))), ((((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17))) <=> ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))))),
% 4.02/2.82 inference(bind,[status(th)],[])).
% 4.02/2.82 tff(122,plain,
% 4.02/2.82 (![X14: $i, X17: $i, X16: $i, X15: $i] : (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17))) <=> ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 4.02/2.82 inference(quant_intro,[status(thm)],[121])).
% 4.02/2.82 tff(123,axiom,(![X14: $i, X17: $i, X16: $i, X15: $i] : (((p12(X14, X15) | (~p2(X16, X14))) | (~p2(X17, X15))) | (~p12(X16, X17)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','p12_22')).
% 4.02/2.82 tff(124,plain,
% 4.02/2.82 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[123, 122])).
% 4.02/2.82 tff(125,plain,
% 4.02/2.82 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[124, 120])).
% 4.02/2.82 tff(126,plain,(
% 4.02/2.82 ![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 4.02/2.82 inference(skolemize,[status(sab)],[125])).
% 4.02/2.82 tff(127,plain,
% 4.02/2.82 (![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[126, 119])).
% 4.02/2.82 tff(128,plain,
% 4.02/2.82 (((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | ((~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16))) <=> ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | (~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16))),
% 4.02/2.82 inference(rewrite,[status(thm)],[])).
% 4.02/2.82 tff(129,plain,
% 4.02/2.82 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | ((~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16))),
% 4.02/2.82 inference(quant_inst,[status(thm)],[])).
% 4.02/2.82 tff(130,plain,
% 4.02/2.82 ((~![X14: $i, X17: $i, X16: $i, X15: $i] : ((~p2(X17, X15)) | (~p12(X16, X17)) | (~p2(X16, X14)) | p12(X14, X15))) | (~p2(c16, c16)) | (~p12(f4(f6(c15, c13)), c16)) | (~p2(f4(f6(c15, c13)), f4(f6(c15, c18)))) | p12(f4(f6(c15, c18)), c16)),
% 4.02/2.82 inference(modus_ponens,[status(thm)],[129, 128])).
% 4.02/2.82 tff(131,plain,
% 4.02/2.82 ($false),
% 4.02/2.82 inference(unit_resolution,[status(thm)],[130, 127, 117, 72, 55, 9])).
% 4.02/2.82 % SZS output end Proof
%------------------------------------------------------------------------------