%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL111-2 : 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 : n016.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 11:51:14 AM UTC 2026
% Result : Unsatisfiable 1.08s 1.55s
% Output : Refutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 64 unt; 1 def)
% Number of atoms : 64 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 91 !; 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(implies(x,y),implies(implies(z,x),implies(z,y))) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_mv_25) ).
fof(f8,plain,
truth != implies(implies(x,y),implies(implies(z,x),implies(z,y))),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
~ sP0(implies(implies(x,y),implies(implies(z,x),implies(z,y)))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f10,plain,
sP0(truth),
inference(inequality_splitting,[],[f8,f9]) ).
fof(f14,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f16,plain,
! [X0,X1] : implies(implies(X0,implies(X1,X0)),implies(X1,X0)) = implies(implies(implies(X0,X1),X1),X0),
inference(superposition,[],[f4,f4]) ).
fof(f31,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f37,plain,
! [X0,X1] : implies(implies(implies(X1,X0),implies(not(X0),not(X1))),implies(not(X0),not(X1))) = implies(truth,implies(X1,X0)),
inference(superposition,[],[f4,f6]) ).
fof(f38,plain,
! [X0,X1] : implies(X1,X0) = implies(implies(implies(X1,X0),implies(not(X0),not(X1))),implies(not(X0),not(X1))),
inference(forward_demodulation,[],[f37,f1]) ).
fof(f46,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,implies(not(X0),not(truth))),implies(not(X0),not(truth))),
inference(superposition,[],[f4,f31]) ).
fof(f49,plain,
! [X0] : implies(implies(X0,implies(not(X0),not(truth))),implies(not(X0),not(truth))) = X0,
inference(forward_demodulation,[],[f46,f1]) ).
fof(f56,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(f58,plain,
! [X0,X1] : truth = implies(implies(X1,truth),implies(X0,implies(X1,X0))),
inference(superposition,[],[f3,f1]) ).
fof(f63,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(f65,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f67,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(implies(X2,X0),implies(implies(X0,X1),X1))),
inference(superposition,[],[f3,f4]) ).
fof(f81,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f65,f1]) ).
fof(f83,plain,
! [X2,X0,X1] : truth = implies(implies(X0,implies(not(X1),not(X2))),implies(X0,implies(X2,X1))),
inference(forward_demodulation,[],[f63,f1]) ).
fof(f86,plain,
! [X2,X0,X1] : truth = implies(implies(implies(X1,X0),X2),implies(implies(not(X0),not(X1)),X2)),
inference(forward_demodulation,[],[f56,f1]) ).
fof(f118,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f81,f14]) ).
fof(f125,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f1,f81]) ).
fof(f128,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f125,f1]) ).
fof(f147,plain,
! [X0] : truth = implies(X0,truth),
inference(backward_demodulation,[],[f118,f128]) ).
fof(f148,plain,
! [X0,X1] : truth = implies(truth,implies(X0,implies(X1,X0))),
inference(backward_demodulation,[],[f58,f147]) ).
fof(f159,plain,
! [X0,X1] : truth = implies(X0,implies(X1,X0)),
inference(forward_demodulation,[],[f148,f1]) ).
fof(f162,plain,
! [X0,X1] : implies(implies(implies(X0,X1),X1),X0) = implies(truth,implies(X1,X0)),
inference(backward_demodulation,[],[f16,f159]) ).
fof(f163,plain,
! [X0,X1] : implies(X1,X0) = implies(implies(implies(X0,X1),X1),X0),
inference(forward_demodulation,[],[f162,f1]) ).
fof(f235,plain,
implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))),
inference(superposition,[],[f163,f31]) ).
fof(f261,plain,
not(not(truth)) = implies(not(truth),not(not(truth))),
inference(forward_demodulation,[],[f235,f1]) ).
fof(f381,plain,
! [X0,X1] : truth = implies(truth,implies(not(X0),implies(X0,X1))),
inference(superposition,[],[f83,f159]) ).
fof(f448,plain,
! [X0,X1] : truth = implies(not(X0),implies(X0,X1)),
inference(forward_demodulation,[],[f381,f1]) ).
fof(f457,plain,
! [X0] : truth = implies(not(truth),X0),
inference(superposition,[],[f448,f1]) ).
fof(f488,plain,
truth = not(not(truth)),
inference(backward_demodulation,[],[f261,f457]) ).
fof(f526,plain,
! [X0] : truth = implies(truth,implies(implies(not(not(truth)),not(not(X0))),X0)),
inference(superposition,[],[f86,f31]) ).
fof(f572,plain,
! [X0] : truth = implies(implies(not(not(truth)),not(not(X0))),X0),
inference(forward_demodulation,[],[f526,f1]) ).
fof(f590,plain,
! [X0] : truth = implies(implies(truth,not(not(X0))),X0),
inference(forward_demodulation,[],[f572,f488]) ).
fof(f592,plain,
! [X0] : truth = implies(not(not(X0)),X0),
inference(forward_demodulation,[],[f590,f1]) ).
fof(f1073,plain,
! [X0] : truth = implies(truth,implies(X0,not(not(X0)))),
inference(superposition,[],[f6,f592]) ).
fof(f1079,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,not(not(X0))),not(not(X0))),
inference(superposition,[],[f4,f592]) ).
fof(f1109,plain,
! [X0] : implies(implies(X0,not(not(X0))),not(not(X0))) = X0,
inference(forward_demodulation,[],[f1079,f1]) ).
fof(f1115,plain,
! [X0] : truth = implies(X0,not(not(X0))),
inference(forward_demodulation,[],[f1073,f1]) ).
fof(f1121,plain,
! [X0] : implies(truth,not(not(X0))) = X0,
inference(backward_demodulation,[],[f1109,f1115]) ).
fof(f1130,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f1121,f1]) ).
fof(f1393,plain,
! [X0,X1] : truth = implies(X0,implies(not(X0),X1)),
inference(superposition,[],[f448,f1130]) ).
fof(f1398,plain,
! [X0] : implies(truth,implies(not(X0),not(truth))) = X0,
inference(backward_demodulation,[],[f49,f1393]) ).
fof(f1399,plain,
! [X0] : implies(not(X0),not(truth)) = X0,
inference(forward_demodulation,[],[f1398,f1]) ).
fof(f1667,plain,
! [X0] : not(X0) = implies(X0,not(truth)),
inference(superposition,[],[f1399,f1130]) ).
fof(f1686,plain,
! [X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,not(truth)),implies(implies(not(truth),not(X0)),not(X0)))),
inference(superposition,[],[f67,f1399]) ).
fof(f1703,plain,
! [X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,not(truth)),implies(truth,not(X0)))),
inference(forward_demodulation,[],[f1686,f457]) ).
fof(f1735,plain,
! [X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,not(truth)),not(X0))),
inference(forward_demodulation,[],[f1703,f1]) ).
fof(f1755,plain,
! [X0,X1] : truth = implies(implies(X0,X1),implies(not(X1),not(X0))),
inference(forward_demodulation,[],[f1735,f1667]) ).
fof(f1768,plain,
! [X0,X1] : implies(X1,X0) = implies(truth,implies(not(X0),not(X1))),
inference(backward_demodulation,[],[f38,f1755]) ).
fof(f1772,plain,
! [X0,X1] : implies(X1,X0) = implies(not(X0),not(X1)),
inference(forward_demodulation,[],[f1768,f1]) ).
fof(f1860,plain,
~ sP0(implies(implies(x,y),implies(implies(not(x),not(z)),implies(z,y)))),
inference(superposition,[],[f9,f1772]) ).
fof(f1867,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(not(X0),X2),implies(not(X1),X2))),
inference(superposition,[],[f3,f1772]) ).
fof(f2173,plain,
~ sP0(implies(implies(x,y),implies(implies(not(x),not(z)),implies(not(y),not(z))))),
inference(superposition,[],[f1860,f1772]) ).
fof(f2174,plain,
~ sP0(truth),
inference(forward_demodulation,[],[f2173,f1867]) ).
fof(f2175,plain,
$false,
inference(forward_subsumption_resolution,[],[f2174,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL111-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.38 % Computer : n016.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 15:27:17 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.45 Running first-order theorem proving
% 0.09/0.45 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
% 1.08/1.55 % (2778503)Detected a unit-equality problem, will run specialized UEQ schedule.
% 1.08/1.55 % (2778518)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=3225724854:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 1.08/1.55 % (2778517)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=661656780:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 1.08/1.55 % (2778521)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=508777111:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 1.08/1.55 % (2778523)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2203064359:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 1.08/1.55 % (2778519)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=3818946044:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 1.08/1.55 % (2778520)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1984344004:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 1.08/1.55 % (2778522)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3794323567:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 1.08/1.55 % (2778520)First to succeed.
% 1.08/1.55 % (2778520)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2778503"
% 1.08/1.55 % (2778521)Also succeeded, but the first one will report.
% 1.08/1.55 % (2778522)Instruction limit reached!
% 1.08/1.55 % (2778522)------------------------------
% 1.08/1.55 % (2778522)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.08/1.55 % (2778522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/1.55 % (2778522)CaDiCaL version: 2.1.3
% 1.08/1.55 % (2778522)Termination reason: Instruction limit
% 1.08/1.55 % (2778522)Termination phase: Saturation
% 1.08/1.55 % (2778522)Time elapsed: 0.163 s
% 1.08/1.55 % (2778522)Peak memory usage: 90 MB
% 1.08/1.55 % (2778522)Instructions burned: 258 (million)
% 1.08/1.55 % (2778531)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3561643402:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 1.08/1.55 % (2778518)Also succeeded, but the first one will report.
% 1.08/1.55 % (2778520)Refutation found. Thanks to Tanya!
% 1.08/1.55 % SZS status Unsatisfiable for theBenchmark
% 1.08/1.55 % SZS output start Proof for theBenchmark
% See solution above
% 4.32/1.74 % (2778520)------------------------------
% 4.32/1.74 % (2778520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.32/1.74 % (2778520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.32/1.74 % (2778520)CaDiCaL version: 2.1.3
% 4.32/1.74 % (2778520)Termination reason: Refutation
% 4.32/1.74 % (2778520)Time elapsed: 0.087 s
% 4.32/1.74 % (2778520)Peak memory usage: 89 MB
% 4.32/1.74 % (2778520)Instructions burned: 138 (million)
% 4.32/1.74 % (2778520)------------------------------
% 4.32/1.74 % (2778520)------------------------------
% 4.32/1.74 % (2778503)Success in time 0.506 s
% 4.32/1.74 % Vampire exiting
%------------------------------------------------------------------------------