%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL157-1 : 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 : n001.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 2.67s 1.33s
% Output : Refutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 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(f12,axiom,
! [X0,X1] : and(X0,X1) = and(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_commutativity) ).
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(x,falsehood) != falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_alternative_wajsberg_axiom) ).
fof(f21,plain,
falsehood != and_star(x,falsehood),
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(f37,plain,
! [X0,X1] : not(or(not(X0),not(X1))) = and(X1,X0),
inference(superposition,[],[f10,f9]) ).
fof(f47,plain,
! [X0,X1] : and(X0,X1) = and_star(X0,X1),
inference(forward_demodulation,[],[f16,f10]) ).
fof(f50,plain,
falsehood != and(x,falsehood),
inference(superposition,[],[f21,f47]) ).
fof(f54,plain,
falsehood != and(falsehood,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(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(f271,plain,
! [X0] : truth = implies(X0,X0),
inference(superposition,[],[f182,f251]) ).
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(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(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(f2576,plain,
falsehood != falsehood,
inference(superposition,[],[f54,f2556]) ).
fof(f2582,plain,
$false,
inference(trivial_inequality_removal,[],[f2576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL157-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 15:30:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 2.67/1.33 % (3712996)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.67/1.33 % (3713007)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3409075807:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.67/1.33 % (3713007)First to succeed.
% 2.67/1.33 % (3713007)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3712996"
% 2.67/1.33 % (3713002)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=3270416470:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.67/1.33 % (3713005)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=741704892:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.67/1.33 % (3713004)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1492557834:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.67/1.33 % (3713001)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=1684296363:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.67/1.33 % (3713003)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1252336018:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.67/1.33 % (3713006)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1220675738:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.67/1.33 % (3713005)Also succeeded, but the first one will report.
% 2.67/1.33 % (3713004)Also succeeded, but the first one will report.
% 2.67/1.33 % (3713006)Also succeeded, but the first one will report.
% 2.67/1.33 % (3713007)Refutation found. Thanks to Tanya!
% 2.67/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.67/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.67/1.33 % (3713007)------------------------------
% 2.67/1.33 % (3713007)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.33 % (3713007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.33 % (3713007)CaDiCaL version: 2.1.3
% 2.67/1.33 % (3713007)Termination reason: Refutation
% 2.67/1.33 % (3713007)Time elapsed: 0.023 s
% 2.67/1.33 % (3713007)Peak memory usage: 88 MB
% 2.67/1.33 % (3713007)Instructions burned: 71 (million)
% 2.67/1.33 % (3713007)------------------------------
% 2.67/1.33 % (3713007)------------------------------
% 2.67/1.33 % (3712996)Success in time 0.293 s
% 2.67/1.33 % Vampire exiting
%------------------------------------------------------------------------------