%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL153-1 : 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 : n012.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 11:51:21 AM UTC 2026
% Result : Unsatisfiable 2.78s 1.16s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 64 unt; 1 def)
% Number of atoms : 64 ( 46 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 : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 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,axiom,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition) ).
fof(f9,axiom,
! [X0,X1] : or(X0,X1) = or(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_commutativity) ).
fof(f10,axiom,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_definition) ).
fof(f13,axiom,
! [X0,X1] : xor(X0,X1) = or(and(X0,not(X1)),and(not(X0),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_definition) ).
fof(f19,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_definition) ).
fof(f20,negated_conjecture,
not(x) != xor(x,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f21,plain,
! [X0,X1] : and(X0,X1) = not(implies(not(not(X0)),not(X1))),
inference(definition_unfolding,[],[f10,f7]) ).
fof(f22,plain,
! [X0,X1] : xor(X0,X1) = implies(not(not(implies(not(not(X0)),not(not(X1))))),not(implies(not(not(not(X0))),not(X1)))),
inference(definition_unfolding,[],[f13,f7,f21,f21]) ).
fof(f25,plain,
! [X0,X1] : implies(not(X0),X1) = implies(not(X1),X0),
inference(definition_unfolding,[],[f9,f7,f7]) ).
fof(f31,plain,
not(x) != implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth)))),
inference(definition_unfolding,[],[f20,f22]) ).
fof(f32,definition,
~ sP0(not(x)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f33,plain,
sP0(implies(not(not(implies(not(not(x)),not(not(truth))))),not(implies(not(not(not(x))),not(truth))))),
inference(inequality_splitting,[],[f31,f32]) ).
fof(f34,plain,
sP0(implies(not(not(implies(not(not(x)),not(falsehood)))),not(implies(not(not(not(x))),falsehood)))),
inference(backward_demodulation,[],[f33,f19]) ).
fof(f36,plain,
! [X0] : implies(not(X0),truth) = implies(falsehood,X0),
inference(superposition,[],[f25,f19]) ).
fof(f39,plain,
sP0(implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(not(not(x))),falsehood)))),
inference(superposition,[],[f34,f25]) ).
fof(f46,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f52,plain,
sP0(implies(not(not(implies(not(not(falsehood)),not(x)))),not(implies(not(falsehood),not(not(x)))))),
inference(superposition,[],[f39,f25]) ).
fof(f57,plain,
! [X0] : truth = implies(implies(not(X0),not(truth)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f67,plain,
! [X0] : truth = implies(implies(not(X0),falsehood),X0),
inference(forward_demodulation,[],[f57,f19]) ).
fof(f94,plain,
! [X0] : truth = implies(implies(X0,not(not(X0))),truth),
inference(superposition,[],[f3,f6]) ).
fof(f343,plain,
truth = implies(implies(falsehood,falsehood),truth),
inference(superposition,[],[f67,f19]) ).
fof(f354,plain,
truth = implies(implies(falsehood,not(falsehood)),not(falsehood)),
inference(superposition,[],[f4,f67]) ).
fof(f402,plain,
! [X0] : truth = implies(implies(implies(falsehood,falsehood),X0),implies(implies(X0,truth),truth)),
inference(superposition,[],[f3,f343]) ).
fof(f404,plain,
! [X0] : truth = implies(truth,implies(implies(truth,X0),implies(implies(falsehood,falsehood),X0))),
inference(superposition,[],[f3,f343]) ).
fof(f411,plain,
! [X0] : truth = implies(implies(truth,X0),implies(implies(falsehood,falsehood),X0)),
inference(forward_demodulation,[],[f404,f1]) ).
fof(f413,plain,
! [X0] : truth = implies(implies(implies(falsehood,falsehood),X0),implies(X0,X0)),
inference(forward_demodulation,[],[f402,f46]) ).
fof(f417,plain,
! [X0] : truth = implies(X0,implies(implies(falsehood,falsehood),X0)),
inference(forward_demodulation,[],[f411,f1]) ).
fof(f423,plain,
truth = implies(not(not(truth)),truth),
inference(superposition,[],[f94,f1]) ).
fof(f439,plain,
truth = implies(falsehood,not(truth)),
inference(forward_demodulation,[],[f423,f36]) ).
fof(f444,plain,
truth = implies(falsehood,falsehood),
inference(forward_demodulation,[],[f439,f19]) ).
fof(f446,plain,
! [X0] : truth = implies(X0,implies(truth,X0)),
inference(backward_demodulation,[],[f417,f444]) ).
fof(f447,plain,
! [X0] : truth = implies(implies(truth,X0),implies(X0,X0)),
inference(backward_demodulation,[],[f413,f444]) ).
fof(f452,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(forward_demodulation,[],[f447,f1]) ).
fof(f453,plain,
! [X0] : truth = implies(X0,X0),
inference(forward_demodulation,[],[f446,f1]) ).
fof(f461,plain,
! [X0] : truth = implies(X0,truth),
inference(backward_demodulation,[],[f452,f453]) ).
fof(f471,plain,
! [X0] : truth = implies(falsehood,X0),
inference(backward_demodulation,[],[f36,f461]) ).
fof(f481,plain,
truth = implies(truth,not(falsehood)),
inference(backward_demodulation,[],[f354,f471]) ).
fof(f487,plain,
truth = not(falsehood),
inference(forward_demodulation,[],[f481,f1]) ).
fof(f493,plain,
sP0(implies(not(not(implies(not(truth),not(x)))),not(implies(truth,not(not(x)))))),
inference(backward_demodulation,[],[f52,f487]) ).
fof(f512,plain,
sP0(implies(not(not(implies(not(truth),not(x)))),not(not(not(x))))),
inference(forward_demodulation,[],[f493,f1]) ).
fof(f519,plain,
sP0(implies(not(not(implies(falsehood,not(x)))),not(not(not(x))))),
inference(forward_demodulation,[],[f512,f19]) ).
fof(f546,plain,
sP0(implies(not(not(truth)),not(not(not(x))))),
inference(forward_demodulation,[],[f519,f471]) ).
fof(f570,plain,
sP0(implies(not(falsehood),not(not(not(x))))),
inference(forward_demodulation,[],[f546,f19]) ).
fof(f588,plain,
sP0(implies(truth,not(not(not(x))))),
inference(forward_demodulation,[],[f570,f487]) ).
fof(f604,plain,
sP0(not(not(not(x)))),
inference(forward_demodulation,[],[f588,f1]) ).
fof(f713,plain,
! [X0] : implies(truth,X0) = implies(not(X0),falsehood),
inference(superposition,[],[f25,f487]) ).
fof(f730,plain,
! [X0] : implies(not(X0),falsehood) = X0,
inference(forward_demodulation,[],[f713,f1]) ).
fof(f780,plain,
! [X0] : implies(truth,X0) = implies(implies(X0,falsehood),falsehood),
inference(superposition,[],[f4,f471]) ).
fof(f781,plain,
! [X0] : implies(implies(X0,falsehood),falsehood) = X0,
inference(forward_demodulation,[],[f780,f1]) ).
fof(f939,plain,
! [X0] : implies(X0,falsehood) = implies(implies(falsehood,not(X0)),not(X0)),
inference(superposition,[],[f4,f730]) ).
fof(f944,plain,
! [X0] : implies(truth,not(X0)) = implies(X0,falsehood),
inference(forward_demodulation,[],[f939,f471]) ).
fof(f956,plain,
! [X0] : not(X0) = implies(X0,falsehood),
inference(forward_demodulation,[],[f944,f1]) ).
fof(f1040,plain,
sP0(implies(not(not(x)),falsehood)),
inference(backward_demodulation,[],[f604,f956]) ).
fof(f1042,plain,
~ sP0(implies(x,falsehood)),
inference(backward_demodulation,[],[f32,f956]) ).
fof(f1048,plain,
sP0(implies(implies(not(x),falsehood),falsehood)),
inference(forward_demodulation,[],[f1040,f956]) ).
fof(f1124,plain,
sP0(not(x)),
inference(forward_demodulation,[],[f1048,f781]) ).
fof(f1183,plain,
sP0(implies(x,falsehood)),
inference(forward_demodulation,[],[f1124,f956]) ).
fof(f1232,plain,
$false,
inference(forward_subsumption_resolution,[],[f1183,f1042]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL153-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 % Computer : n012.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 27 15:23:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 Running first-order theorem proving
% 0.08/0.36 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
% 2.78/1.16 % (2506498)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.78/1.16 % (2506506)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=668902282:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 2.78/1.16 % (2506506)First to succeed.
% 2.78/1.16 % (2506506)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2506498"
% 2.78/1.16 % (2506504)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=2165676528:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 2.78/1.16 % (2506507)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=955653816:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 2.78/1.16 % (2506503)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=3294616617:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 2.78/1.16 % (2506505)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=841189440:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 2.78/1.16 % (2506509)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2683020238:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 2.78/1.16 % (2506508)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=982336607:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 2.78/1.16 % (2506507)Also succeeded, but the first one will report.
% 2.78/1.16 % (2506509)Also succeeded, but the first one will report.
% 2.78/1.16 % (2506506)Refutation found. Thanks to Tanya!
% 2.78/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.16 % (2506506)------------------------------
% 2.78/1.16 % (2506506)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.16 % (2506506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.16 % (2506506)CaDiCaL version: 2.1.3
% 2.78/1.16 % (2506506)Termination reason: Refutation
% 2.78/1.16 % (2506506)Time elapsed: 0.026 s
% 2.78/1.16 % (2506506)Peak memory usage: 88 MB
% 2.78/1.16 % (2506506)Instructions burned: 82 (million)
% 2.78/1.16 % (2506506)------------------------------
% 2.78/1.16 % (2506506)------------------------------
% 2.78/1.16 % (2506498)Success in time 0.329 s
% 2.78/1.16 % Vampire exiting
%------------------------------------------------------------------------------