%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL116-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:51:16 AM UTC 2026
% Result : Unsatisfiable 7.26s 2.27s
% Output : Refutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of formulae : 63 ( 63 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 100 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : implies(truth,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_1) ).
fof(f2,axiom,
! [X2,X0,X1] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_2) ).
fof(f3,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f5,axiom,
! [X0,X1] : implies(implies(not(X0),not(X1)),implies(X1,X0)) = truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_4) ).
fof(f6,plain,
! [X0,X1] : truth = implies(implies(not(X0),not(X1)),implies(X1,X0)),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
implies(not(a),implies(b,not(implies(b,a)))) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mv_50) ).
fof(f8,plain,
truth != implies(not(a),implies(b,not(implies(b,a)))),
inference(reorient_equations,[],[f7]) ).
fof(f9,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f23,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f44,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(X1,X0),X2),implies(implies(not(X0),not(X1)),X2))),
inference(superposition,[],[f3,f6]) ).
fof(f49,plain,
! [X2,X0,X1] : truth = implies(implies(X2,implies(X1,X0)),implies(implies(implies(X0,X1),X1),implies(X2,X0))),
inference(superposition,[],[f3,f4]) ).
fof(f53,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(truth,implies(X0,implies(X2,X1)))),
inference(superposition,[],[f3,f6]) ).
fof(f57,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f77,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f57,f1]) ).
fof(f80,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f53,f1]) ).
fof(f84,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(implies(not(X0),not(X1)),X2)),
inference(forward_demodulation,[],[f44,f1]) ).
fof(f137,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f77,f9]) ).
fof(f146,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f1,f77]) ).
fof(f148,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f146,f1]) ).
fof(f180,plain,
! [X0] : truth = implies(X0,truth),
inference(forward_demodulation,[],[f137,f148]) ).
fof(f187,plain,
! [X0,X1] : truth = implies(truth,implies(implies(truth,X1),implies(X0,X1))),
inference(superposition,[],[f3,f180]) ).
fof(f209,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(X0,X1)),
inference(forward_demodulation,[],[f187,f1]) ).
fof(f216,plain,
! [X0,X1] : truth = implies(X1,implies(X0,X1)),
inference(forward_demodulation,[],[f209,f1]) ).
fof(f234,plain,
! [X2,X0,X1] : truth = implies(truth,implies(implies(implies(X1,X0),X2),implies(X0,X2))),
inference(superposition,[],[f3,f216]) ).
fof(f247,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(X0,X2)),
inference(forward_demodulation,[],[f234,f1]) ).
fof(f632,plain,
! [X0,X1] : truth = implies(truth,implies(not(X1),implies(X1,X0))),
inference(superposition,[],[f247,f6]) ).
fof(f634,plain,
! [X0] : truth = implies(truth,implies(not(truth),X0)),
inference(superposition,[],[f247,f23]) ).
fof(f702,plain,
! [X0] : truth = implies(not(truth),X0),
inference(forward_demodulation,[],[f634,f1]) ).
fof(f704,plain,
! [X0,X1] : truth = implies(not(X1),implies(X1,X0)),
inference(forward_demodulation,[],[f632,f1]) ).
fof(f739,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,not(truth)),not(truth)),
inference(superposition,[],[f4,f702]) ).
fof(f762,plain,
! [X0] : implies(implies(X0,not(truth)),not(truth)) = X0,
inference(forward_demodulation,[],[f739,f1]) ).
fof(f855,plain,
! [X0] : truth = implies(not(implies(X0,not(truth))),X0),
inference(superposition,[],[f704,f762]) ).
fof(f907,plain,
! [X0,X1] : truth = implies(truth,implies(not(not(X0)),implies(X1,X0))),
inference(superposition,[],[f80,f704]) ).
fof(f1009,plain,
! [X0,X1] : truth = implies(not(not(X0)),implies(X1,X0)),
inference(forward_demodulation,[],[f907,f1]) ).
fof(f1039,plain,
! [X0] : truth = implies(not(not(X0)),X0),
inference(superposition,[],[f1009,f1]) ).
fof(f1104,plain,
! [X0] : truth = implies(truth,implies(X0,not(not(X0)))),
inference(superposition,[],[f6,f1039]) ).
fof(f1144,plain,
! [X0] : truth = implies(X0,not(not(X0))),
inference(forward_demodulation,[],[f1104,f1]) ).
fof(f1157,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(superposition,[],[f4,f1144]) ).
fof(f1188,plain,
! [X0] : not(not(X0)) = implies(implies(not(not(X0)),X0),X0),
inference(forward_demodulation,[],[f1157,f1]) ).
fof(f1195,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(forward_demodulation,[],[f1188,f1039]) ).
fof(f1197,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f1195,f1]) ).
fof(f1351,plain,
! [X0] : truth = implies(implies(implies(truth,X0),not(truth)),not(X0)),
inference(superposition,[],[f84,f762]) ).
fof(f1399,plain,
! [X0] : truth = implies(implies(X0,not(truth)),not(X0)),
inference(forward_demodulation,[],[f1351,f1]) ).
fof(f1553,plain,
! [X0] : truth = implies(X0,not(implies(X0,not(truth)))),
inference(superposition,[],[f1399,f762]) ).
fof(f1645,plain,
! [X0] : implies(truth,not(implies(X0,not(truth)))) = implies(implies(not(implies(X0,not(truth))),X0),X0),
inference(superposition,[],[f4,f1553]) ).
fof(f1687,plain,
! [X0] : implies(truth,X0) = implies(truth,not(implies(X0,not(truth)))),
inference(forward_demodulation,[],[f1645,f855]) ).
fof(f1700,plain,
! [X0] : implies(truth,X0) = not(implies(X0,not(truth))),
inference(forward_demodulation,[],[f1687,f1]) ).
fof(f1706,plain,
! [X0] : not(implies(X0,not(truth))) = X0,
inference(forward_demodulation,[],[f1700,f1]) ).
fof(f1710,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(superposition,[],[f1706,f762]) ).
fof(f2619,plain,
! [X0,X1] : truth = implies(implies(X0,implies(X1,not(truth))),implies(implies(truth,X1),implies(X0,not(truth)))),
inference(superposition,[],[f49,f702]) ).
fof(f2792,plain,
! [X0,X1] : truth = implies(implies(X0,implies(X1,not(truth))),implies(implies(truth,X1),not(X0))),
inference(forward_demodulation,[],[f2619,f1710]) ).
fof(f2891,plain,
! [X0,X1] : truth = implies(implies(X0,implies(X1,not(truth))),implies(X1,not(X0))),
inference(forward_demodulation,[],[f2792,f1]) ).
fof(f2955,plain,
! [X0,X1] : truth = implies(implies(X0,not(X1)),implies(X1,not(X0))),
inference(forward_demodulation,[],[f2891,f1710]) ).
fof(f5390,plain,
! [X0,X1] : implies(truth,implies(X0,not(X1))) = implies(implies(implies(X0,not(X1)),implies(X1,not(X0))),implies(X1,not(X0))),
inference(superposition,[],[f4,f2955]) ).
fof(f5450,plain,
! [X0,X1] : implies(truth,implies(X0,not(X1))) = implies(truth,implies(X1,not(X0))),
inference(forward_demodulation,[],[f5390,f2955]) ).
fof(f5492,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(truth,implies(X0,not(X1))),
inference(forward_demodulation,[],[f5450,f1]) ).
fof(f5511,plain,
! [X0,X1] : implies(X1,not(X0)) = implies(X0,not(X1)),
inference(forward_demodulation,[],[f5492,f1]) ).
fof(f5677,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X0,not(X1)),not(X0))),
inference(superposition,[],[f77,f5511]) ).
fof(f5760,plain,
! [X0,X1] : truth = implies(X1,implies(X0,not(implies(X0,not(X1))))),
inference(forward_demodulation,[],[f5677,f5511]) ).
fof(f8895,plain,
! [X0,X1] : truth = implies(not(X0),implies(X1,not(implies(X1,X0)))),
inference(superposition,[],[f5760,f1197]) ).
fof(f9812,plain,
truth != truth,
inference(superposition,[],[f8,f8895]) ).
fof(f9879,plain,
$false,
inference(trivial_inequality_removal,[],[f9812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL116-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.47 % Computer : n020.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sun Sep 27 15:23:49 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.47 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.26/2.27 % (3527679)Detected a unit-equality problem, will run specialized UEQ schedule.
% 7.26/2.27 % (3527687)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1235256071:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 7.26/2.27 % (3527684)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=3239939890:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 7.26/2.27 % (3527686)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=88913836:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 7.26/2.27 % (3527685)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=435746458:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 7.26/2.27 % (3527687)Instruction limit reached!
% 7.26/2.27 % (3527687)------------------------------
% 7.26/2.27 % (3527687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.26/2.27 % (3527687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.26/2.27 % (3527687)CaDiCaL version: 2.1.3
% 7.26/2.27 % (3527687)Termination reason: Instruction limit
% 7.26/2.27 % (3527687)Termination phase: Saturation
% 7.26/2.27 % (3527687)Time elapsed: 0.067 s
% 7.26/2.27 % (3527687)Peak memory usage: 88 MB
% 7.26/2.27 % (3527687)Instructions burned: 137 (million)
% 7.26/2.27 % (3527689)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3795483346:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 7.26/2.27 % (3527690)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2257501667:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 7.26/2.27 % (3527688)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2885488059:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 7.26/2.27 % (3527688)Instruction limit reached!
% 7.26/2.27 % (3527688)------------------------------
% 7.26/2.27 % (3527688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.26/2.27 % (3527688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.26/2.27 % (3527688)CaDiCaL version: 2.1.3
% 7.26/2.27 % (3527688)Termination reason: Instruction limit
% 7.26/2.27 % (3527688)Termination phase: Saturation
% 7.26/2.27 % (3527688)Time elapsed: 0.170 s
% 7.26/2.27 % (3527688)Peak memory usage: 89 MB
% 7.26/2.27 % (3527688)Instructions burned: 181 (million)
% 7.26/2.27 % (3527695)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1265255465:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 7.26/2.27 % (3527689)Instruction limit reached!
% 7.26/2.27 % (3527689)------------------------------
% 7.26/2.27 % (3527689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.26/2.27 % (3527689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.26/2.27 % (3527689)CaDiCaL version: 2.1.3
% 7.26/2.27 % (3527689)Termination reason: Instruction limit
% 7.26/2.27 % (3527689)Termination phase: Saturation
% 7.26/2.27 % (3527689)Time elapsed: 0.258 s
% 7.26/2.27 % (3527689)Peak memory usage: 90 MB
% 7.26/2.27 % (3527689)Instructions burned: 257 (million)
% 7.26/2.27 % (3527690)First to succeed.
% 7.26/2.27 % (3527690)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3527679"
% 7.26/2.27 % (3527699)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2990294126:i=4948:ss=axioms:sgt=16_2995 on theBenchmark for (2995ds/4948Mi)
% 7.26/2.27 % (3527701)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2092878612:i=215:ep=RSTC_2994 on theBenchmark for (2994ds/215Mi)
% 7.26/2.27 % (3527690)Refutation found. Thanks to Tanya!
% 7.26/2.27 % SZS status Unsatisfiable for theBenchmark
% 7.26/2.27 % SZS output start Proof for theBenchmark
% See solution above
% 8.04/2.65 % (3527690)------------------------------
% 8.04/2.65 % (3527690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.65 % (3527690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.65 % (3527690)CaDiCaL version: 2.1.3
% 8.04/2.65 % (3527690)Termination reason: Refutation
% 8.04/2.65 % (3527690)Time elapsed: 0.272 s
% 8.04/2.65 % (3527690)Peak memory usage: 91 MB
% 8.04/2.65 % (3527690)Instructions burned: 313 (million)
% 8.04/2.65 % (3527690)------------------------------
% 8.04/2.65 % (3527690)------------------------------
% 8.04/2.65 % (3527679)Success in time 0.988 s
% 8.04/2.65 % Vampire exiting
%------------------------------------------------------------------------------