%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL134-1 : 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 : n007.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 11:51:18 AM UTC 2026
% Result : Unsatisfiable 4.21s 1.84s
% Output : Refutation 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 37 unt; 5 def)
% Number of atoms : 37 ( 36 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [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,negated_conjecture,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wajsberg_3) ).
fof(f7,negated_conjecture,
implies(x,truth) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_lemma) ).
fof(f8,plain,
truth != implies(x,truth),
inference(reorient_equations,[],[f7]) ).
fof(f9,definition,
! [X0] : sF0(X0) = implies(truth,X0),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f10,plain,
! [X0] : implies(truth,X0) = sF0(X0),
inference(reorient_equations,[],[f9]) ).
fof(f11,plain,
! [X0] : sF0(X0) = X0,
inference(definition_folding,[],[f1,f10]) ).
fof(f12,definition,
! [X2,X0,X1] : sF1(X1,X2,X0) = implies(implies(X1,X2),implies(X0,X2)),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f13,plain,
! [X2,X0,X1] : implies(implies(X1,X2),implies(X0,X2)) = sF1(X1,X2,X0),
inference(reorient_equations,[],[f12]) ).
fof(f14,definition,
! [X2,X0,X1] : sF2(X0,X1,X2) = implies(implies(X0,X1),sF1(X1,X2,X0)),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f15,plain,
! [X2,X0,X1] : implies(implies(X0,X1),sF1(X1,X2,X0)) = sF2(X0,X1,X2),
inference(reorient_equations,[],[f14]) ).
fof(f16,plain,
! [X2,X0,X1] : truth = sF2(X0,X1,X2),
inference(definition_folding,[],[f3,f15,f13]) ).
fof(f17,definition,
! [X0,X1] : sF3(X0,X1) = implies(implies(X0,X1),X1),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f18,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = sF3(X0,X1),
inference(reorient_equations,[],[f17]) ).
fof(f19,plain,
! [X0,X1] : sF3(X0,X1) = sF3(X1,X0),
inference(definition_folding,[],[f4,f18,f18]) ).
fof(f25,definition,
sF6 = implies(x,truth),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
fof(f26,plain,
implies(x,truth) = sF6,
inference(reorient_equations,[],[f25]) ).
fof(f27,plain,
truth != sF6,
inference(definition_folding,[],[f8,f26]) ).
fof(f29,plain,
! [X0,X1] : implies(implies(X1,X0),X0) = sF3(X0,X1),
inference(forward_demodulation,[],[f19,f18]) ).
fof(f30,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),sF1(X1,X2,X0)),
inference(forward_demodulation,[],[f16,f15]) ).
fof(f31,plain,
! [X0] : implies(truth,X0) = X0,
inference(forward_demodulation,[],[f11,f10]) ).
fof(f33,plain,
! [X0,X1] : implies(implies(X0,X1),X1) = implies(implies(X1,X0),X0),
inference(forward_demodulation,[],[f29,f18]) ).
fof(f34,plain,
! [X2,X0,X1] : truth = implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))),
inference(forward_demodulation,[],[f30,f13]) ).
fof(f48,plain,
implies(implies(truth,x),x) = implies(sF6,truth),
inference(superposition,[],[f33,f26]) ).
fof(f63,plain,
implies(sF6,truth) = implies(x,x),
inference(forward_demodulation,[],[f48,f31]) ).
fof(f123,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f34,f31]) ).
fof(f141,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f123,f31]) ).
fof(f203,plain,
truth = implies(x,implies(sF6,truth)),
inference(superposition,[],[f141,f26]) ).
fof(f215,plain,
! [X0] : truth = implies(implies(truth,X0),X0),
inference(superposition,[],[f31,f141]) ).
fof(f217,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f215,f31]) ).
fof(f230,plain,
truth = implies(sF6,truth),
inference(superposition,[],[f217,f63]) ).
fof(f289,plain,
truth = implies(x,truth),
inference(forward_demodulation,[],[f203,f230]) ).
fof(f290,plain,
truth = sF6,
inference(forward_demodulation,[],[f289,f26]) ).
fof(f294,plain,
truth != truth,
inference(superposition,[],[f27,f290]) ).
fof(f295,plain,
$false,
inference(trivial_inequality_removal,[],[f294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL134-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n007.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 27 15:20:55 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.49 Running first-order theorem proving
% 0.25/0.49 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
% 4.21/1.84 % (1577709)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.21/1.84 % (1577718)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=534389428:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.21/1.84 % (1577718)First to succeed.
% 4.21/1.84 % (1577718)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1577709"
% 4.21/1.84 % (1577716)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1292749617:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.21/1.84 % (1577714)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=184971755:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.21/1.84 % (1577717)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4168212617:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.21/1.84 % (1577715)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=2858840221:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.21/1.84 % (1577717)Also succeeded, but the first one will report.
% 4.21/1.84 % (1577720)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=428433507:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.21/1.84 % (1577719)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4007017413:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.21/1.84 % (1577720)Also succeeded, but the first one will report.
% 4.21/1.84 % (1577719)Also succeeded, but the first one will report.
% 4.21/1.84 % (1577718)Refutation found. Thanks to Tanya!
% 4.21/1.84 % SZS status Unsatisfiable for theBenchmark
% 4.21/1.84 % SZS output start Proof for theBenchmark
% See solution above
% 4.21/1.84 % (1577718)------------------------------
% 4.21/1.84 % (1577718)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.21/1.84 % (1577718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.21/1.84 % (1577718)CaDiCaL version: 2.1.3
% 4.21/1.84 % (1577718)Termination reason: Refutation
% 4.21/1.84 % (1577718)Time elapsed: 0.007 s
% 4.21/1.84 % (1577718)Peak memory usage: 88 MB
% 4.21/1.84 % (1577718)Instructions burned: 11 (million)
% 4.21/1.84 % (1577718)------------------------------
% 4.21/1.84 % (1577718)------------------------------
% 4.21/1.84 % (1577709)Success in time 0.481 s
% 4.21/1.84 % Vampire exiting
%------------------------------------------------------------------------------