%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL158-1 : 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 : n008.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 11:51:22 AM UTC 2026
% Result : Unsatisfiable 0.92s 1.21s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 92 ( 92 unt; 0 def)
% Number of atoms : 92 ( 91 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 110 !; 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(f11,axiom,
! [X2,X0,X1] : and(and(X0,X1),X2) = and(X0,and(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_associativity) ).
fof(f12,axiom,
! [X0,X1] : and(X0,X1) = and(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).
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(f15,axiom,
! [X0,X1] : and_star(X0,X1) = not(or(not(X0),not(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_definition) ).
fof(f16,plain,
! [X0,X1] : not(or(not(X0),not(X1))) = and_star(X0,X1),
inference(reorient_equations,[],[f15]) ).
fof(f19,axiom,
not(truth) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',false_definition) ).
fof(f20,negated_conjecture,
and_star(xor(truth,x),x) != falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f21,plain,
falsehood != and_star(xor(truth,x),x),
inference(reorient_equations,[],[f20]) ).
fof(f24,plain,
! [X0] : or(truth,X0) = implies(falsehood,X0),
inference(superposition,[],[f7,f19]) ).
fof(f25,plain,
! [X0] : implies(falsehood,X0) = or(X0,truth),
inference(superposition,[],[f24,f9]) ).
fof(f33,plain,
! [X0] : and(truth,X0) = not(or(falsehood,not(X0))),
inference(superposition,[],[f10,f19]) ).
fof(f35,plain,
! [X0] : and(X0,truth) = not(or(not(X0),falsehood)),
inference(superposition,[],[f10,f19]) ).
fof(f37,plain,
! [X0,X1] : not(or(not(X0),not(X1))) = and(X1,X0),
inference(superposition,[],[f10,f9]) ).
fof(f40,plain,
! [X0] : not(or(falsehood,not(X0))) = and(X0,truth),
inference(forward_demodulation,[],[f35,f9]) ).
fof(f41,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(superposition,[],[f33,f19]) ).
fof(f47,plain,
! [X0,X1] : and(X0,X1) = and_star(X0,X1),
inference(forward_demodulation,[],[f16,f10]) ).
fof(f50,plain,
falsehood != and(xor(truth,x),x),
inference(superposition,[],[f21,f47]) ).
fof(f54,plain,
falsehood != and(x,xor(truth,x)),
inference(forward_demodulation,[],[f50,f12]) ).
fof(f64,plain,
! [X0] : implies(implies(X0,truth),truth) = implies(X0,X0),
inference(superposition,[],[f4,f1]) ).
fof(f98,plain,
! [X0] : implies(implies(not(X0),truth),truth) = or(X0,not(X0)),
inference(superposition,[],[f7,f64]) ).
fof(f99,plain,
! [X0] : implies(or(X0,truth),truth) = or(X0,not(X0)),
inference(forward_demodulation,[],[f98,f7]) ).
fof(f104,plain,
! [X0] : or(X0,not(X0)) = implies(implies(falsehood,X0),truth),
inference(forward_demodulation,[],[f99,f25]) ).
fof(f159,plain,
! [X0,X1] : truth = implies(or(X0,not(X1)),implies(X1,X0)),
inference(forward_demodulation,[],[f6,f7]) ).
fof(f167,plain,
! [X0,X1] : truth = implies(or(not(X0),X1),implies(X0,X1)),
inference(superposition,[],[f159,f9]) ).
fof(f171,plain,
! [X0] : truth = implies(or(X0,not(truth)),X0),
inference(superposition,[],[f159,f1]) ).
fof(f180,plain,
! [X0] : truth = implies(or(X0,falsehood),X0),
inference(forward_demodulation,[],[f171,f19]) ).
fof(f182,plain,
! [X0] : truth = implies(or(falsehood,X0),X0),
inference(superposition,[],[f180,f9]) ).
fof(f184,plain,
truth = implies(implies(falsehood,falsehood),truth),
inference(superposition,[],[f180,f24]) ).
fof(f188,plain,
truth = or(falsehood,not(falsehood)),
inference(forward_demodulation,[],[f184,f104]) ).
fof(f225,plain,
truth = implies(truth,not(falsehood)),
inference(superposition,[],[f182,f188]) ).
fof(f233,plain,
truth = not(falsehood),
inference(forward_demodulation,[],[f225,f1]) ).
fof(f236,plain,
! [X0] : implies(truth,X0) = or(falsehood,X0),
inference(superposition,[],[f7,f233]) ).
fof(f240,plain,
! [X0] : not(or(truth,not(X0))) = and(X0,falsehood),
inference(superposition,[],[f37,f233]) ).
fof(f247,plain,
! [X0] : and(X0,falsehood) = not(implies(falsehood,not(X0))),
inference(forward_demodulation,[],[f240,f24]) ).
fof(f251,plain,
! [X0] : or(falsehood,X0) = X0,
inference(forward_demodulation,[],[f236,f1]) ).
fof(f264,plain,
! [X0] : or(X0,falsehood) = X0,
inference(superposition,[],[f251,f9]) ).
fof(f267,plain,
! [X0] : and(X0,truth) = not(not(X0)),
inference(superposition,[],[f40,f251]) ).
fof(f268,plain,
! [X0] : and(truth,X0) = not(not(X0)),
inference(superposition,[],[f33,f251]) ).
fof(f271,plain,
! [X0] : truth = implies(X0,X0),
inference(superposition,[],[f182,f251]) ).
fof(f294,plain,
! [X0] : truth = or(X0,not(X0)),
inference(superposition,[],[f271,f7]) ).
fof(f319,plain,
! [X0] : truth = implies(implies(falsehood,X0),truth),
inference(superposition,[],[f294,f104]) ).
fof(f328,plain,
! [X0] : not(truth) = and(X0,not(X0)),
inference(superposition,[],[f10,f294]) ).
fof(f337,plain,
! [X0] : falsehood = and(X0,not(X0)),
inference(forward_demodulation,[],[f328,f19]) ).
fof(f509,plain,
! [X0,X1] : truth = implies(implies(truth,X1),implies(implies(X1,X0),X0)),
inference(superposition,[],[f3,f1]) ).
fof(f538,plain,
! [X0,X1] : truth = implies(X1,implies(implies(X1,X0),X0)),
inference(forward_demodulation,[],[f509,f1]) ).
fof(f618,plain,
! [X0,X1] : xor(or(falsehood,not(X0)),X1) = or(and(or(falsehood,not(X0)),not(X1)),and(and(X0,truth),X1)),
inference(superposition,[],[f13,f40]) ).
fof(f632,plain,
! [X0,X1] : xor(or(falsehood,not(X0)),X1) = or(and(and(X0,truth),X1),and(or(falsehood,not(X0)),not(X1))),
inference(forward_demodulation,[],[f618,f9]) ).
fof(f648,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(and(X0,truth),X1),and(not(X0),not(X1))),
inference(forward_demodulation,[],[f632,f251]) ).
fof(f662,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(not(X0),not(X1)),and(and(X0,truth),X1)),
inference(forward_demodulation,[],[f648,f9]) ).
fof(f667,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(not(X0),not(X1)),and(X0,and(truth,X1))),
inference(forward_demodulation,[],[f662,f11]) ).
fof(f671,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(X0,and(truth,X1)),and(not(X0),not(X1))),
inference(forward_demodulation,[],[f667,f9]) ).
fof(f675,plain,
! [X0,X1] : xor(not(X0),X1) = or(and(X0,not(not(X1))),and(not(X0),not(X1))),
inference(forward_demodulation,[],[f671,f268]) ).
fof(f676,plain,
! [X0,X1] : xor(not(X0),X1) = xor(X0,not(X1)),
inference(forward_demodulation,[],[f675,f13]) ).
fof(f768,plain,
! [X0] : truth = implies(X0,implies(X0,X0)),
inference(superposition,[],[f538,f64]) ).
fof(f793,plain,
! [X0] : truth = implies(X0,truth),
inference(forward_demodulation,[],[f768,f271]) ).
fof(f815,plain,
! [X0] : truth = or(X0,truth),
inference(superposition,[],[f793,f7]) ).
fof(f850,plain,
! [X0] : truth = implies(falsehood,X0),
inference(superposition,[],[f815,f25]) ).
fof(f952,plain,
! [X0] : truth = implies(implies(implies(falsehood,not(X0)),truth),implies(X0,not(not(X0)))),
inference(superposition,[],[f167,f104]) ).
fof(f991,plain,
! [X0] : truth = implies(truth,implies(X0,not(not(X0)))),
inference(forward_demodulation,[],[f952,f319]) ).
fof(f1000,plain,
! [X0] : truth = implies(X0,not(not(X0))),
inference(forward_demodulation,[],[f991,f1]) ).
fof(f1021,plain,
! [X0] : implies(implies(not(not(X0)),X0),X0) = implies(truth,not(not(X0))),
inference(superposition,[],[f4,f1000]) ).
fof(f1031,plain,
! [X0] : not(not(X0)) = implies(implies(not(not(X0)),X0),X0),
inference(forward_demodulation,[],[f1021,f1]) ).
fof(f1041,plain,
! [X0] : not(not(X0)) = implies(or(not(X0),X0),X0),
inference(forward_demodulation,[],[f1031,f7]) ).
fof(f1047,plain,
! [X0] : not(not(X0)) = implies(or(X0,not(X0)),X0),
inference(forward_demodulation,[],[f1041,f9]) ).
fof(f1050,plain,
! [X0] : implies(truth,X0) = not(not(X0)),
inference(forward_demodulation,[],[f1047,f294]) ).
fof(f1053,plain,
! [X0] : not(not(X0)) = X0,
inference(forward_demodulation,[],[f1050,f1]) ).
fof(f1905,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(and(truth,truth),X0),
inference(superposition,[],[f676,f41]) ).
fof(f1917,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(not(not(truth)),X0),
inference(forward_demodulation,[],[f1905,f267]) ).
fof(f1923,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(not(truth),not(X0)),
inference(forward_demodulation,[],[f1917,f676]) ).
fof(f1926,plain,
! [X0] : xor(or(falsehood,falsehood),not(X0)) = xor(truth,not(not(X0))),
inference(forward_demodulation,[],[f1923,f676]) ).
fof(f1929,plain,
! [X0] : xor(truth,X0) = xor(or(falsehood,falsehood),not(X0)),
inference(forward_demodulation,[],[f1926,f1053]) ).
fof(f1930,plain,
! [X0] : xor(truth,X0) = xor(falsehood,not(X0)),
inference(forward_demodulation,[],[f1929,f264]) ).
fof(f2554,plain,
! [X0] : not(truth) = and(X0,falsehood),
inference(forward_demodulation,[],[f247,f850]) ).
fof(f2555,plain,
! [X0] : falsehood = and(X0,falsehood),
inference(forward_demodulation,[],[f2554,f19]) ).
fof(f2556,plain,
! [X0] : falsehood = and(falsehood,X0),
inference(superposition,[],[f2555,f12]) ).
fof(f2580,plain,
! [X0] : xor(falsehood,X0) = or(falsehood,and(not(falsehood),X0)),
inference(superposition,[],[f13,f2556]) ).
fof(f2581,plain,
! [X0] : xor(falsehood,X0) = and(not(falsehood),X0),
inference(forward_demodulation,[],[f2580,f251]) ).
fof(f2583,plain,
! [X0] : and(truth,X0) = xor(falsehood,X0),
inference(forward_demodulation,[],[f2581,f233]) ).
fof(f2584,plain,
! [X0] : not(not(X0)) = xor(falsehood,X0),
inference(forward_demodulation,[],[f2583,f268]) ).
fof(f2585,plain,
! [X0] : xor(falsehood,X0) = X0,
inference(forward_demodulation,[],[f2584,f1053]) ).
fof(f2595,plain,
! [X0] : not(X0) = xor(truth,X0),
inference(superposition,[],[f2585,f1930]) ).
fof(f2693,plain,
falsehood != and(x,not(x)),
inference(superposition,[],[f54,f2595]) ).
fof(f2712,plain,
$false,
inference(forward_subsumption_resolution,[],[f2693,f337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL158-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 15:25:24 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 0.92/1.21 % (1375819)Detected a unit-equality problem, will run specialized UEQ schedule.
% 0.92/1.21 % (1375931)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2878042057:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 0.92/1.21 % (1375931)First to succeed.
% 0.92/1.21 % (1375931)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1375819"
% 0.92/1.21 % (1375927)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2738834962:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 0.92/1.21 % (1375929)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1618462005:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 0.92/1.21 % (1375930)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=4192847735:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 0.92/1.21 % (1375928)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2654187393:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 0.92/1.21 % (1375925)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=3161448993:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 0.92/1.21 % (1375926)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=312749958:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 0.92/1.21 % (1375929)Also succeeded, but the first one will report.
% 0.92/1.21 % (1375928)Also succeeded, but the first one will report.
% 0.92/1.21 % (1375931)Refutation found. Thanks to Tanya!
% 0.92/1.21 % SZS status Unsatisfiable for theBenchmark
% 0.92/1.21 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.41 % (1375931)------------------------------
% 0.17/1.41 % (1375931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.41 % (1375931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.41 % (1375931)CaDiCaL version: 2.1.3
% 0.17/1.41 % (1375931)Termination reason: Refutation
% 0.17/1.41 % (1375931)Time elapsed: 0.024 s
% 0.17/1.41 % (1375931)Peak memory usage: 88 MB
% 0.17/1.41 % (1375931)Instructions burned: 75 (million)
% 0.17/1.41 % (1375931)------------------------------
% 0.17/1.41 % (1375931)------------------------------
% 0.17/1.41 % (1375819)Success in time 0.343 s
% 0.17/1.41 % Vampire exiting
%------------------------------------------------------------------------------