%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL164-1 : 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 11:51:23 AM UTC 2026
% Result : Unsatisfiable 10.06s 2.64s
% Output : Refutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 26 ( 26 unt; 1 def)
% Number of atoms : 26 ( 17 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 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; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : not(X0) = xor(X0,truth),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f2,axiom,
! [X0] : xor(X0,falsehood) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f3,axiom,
! [X0] : xor(X0,X0) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f4,plain,
! [X0] : falsehood = xor(X0,X0),
inference(reorient_equations,[],[f3]) ).
fof(f8,axiom,
! [X0] : and_star(xor(truth,X0),X0) = falsehood,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
fof(f9,plain,
! [X0] : falsehood = and_star(xor(truth,X0),X0),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] : xor(X0,xor(truth,X1)) = xor(xor(X0,truth),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
fof(f12,axiom,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutativity) ).
fof(f14,axiom,
! [X0,X1] : and_star(X0,X1) = and_star(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_star_commutativity) ).
fof(f17,axiom,
! [X0,X1] : implies(X0,X1) = xor(truth,and_star(X0,xor(truth,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
fof(f18,negated_conjecture,
implies(implies(not(x),not(y)),implies(y,x)) != truth,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_wajsberg_axiom) ).
fof(f19,plain,
truth != implies(implies(not(x),not(y)),implies(y,x)),
inference(reorient_equations,[],[f18]) ).
fof(f21,plain,
truth != xor(truth,and_star(xor(truth,and_star(xor(x,truth),xor(truth,xor(y,truth)))),xor(truth,xor(truth,and_star(y,xor(truth,x)))))),
inference(definition_unfolding,[],[f19,f17,f17,f1,f1,f17]) ).
fof(f22,definition,
~ sP0(xor(truth,and_star(xor(truth,and_star(xor(x,truth),xor(truth,xor(y,truth)))),xor(truth,xor(truth,and_star(y,xor(truth,x))))))),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f23,plain,
sP0(truth),
inference(inequality_splitting,[],[f21,f22]) ).
fof(f34,plain,
! [X0] : xor(falsehood,X0) = X0,
inference(superposition,[],[f2,f12]) ).
fof(f35,plain,
~ sP0(xor(truth,and_star(xor(truth,and_star(xor(x,truth),xor(truth,xor(y,truth)))),xor(truth,xor(truth,and_star(y,xor(x,truth))))))),
inference(superposition,[],[f22,f12]) ).
fof(f50,plain,
! [X0] : xor(falsehood,X0) = xor(truth,xor(truth,X0)),
inference(superposition,[],[f10,f4]) ).
fof(f63,plain,
! [X0] : xor(truth,xor(truth,X0)) = X0,
inference(forward_demodulation,[],[f50,f34]) ).
fof(f67,plain,
~ sP0(xor(truth,and_star(xor(truth,and_star(xor(x,truth),xor(truth,xor(y,truth)))),and_star(y,xor(x,truth))))),
inference(backward_demodulation,[],[f35,f63]) ).
fof(f295,plain,
! [X0] : xor(truth,xor(X0,truth)) = X0,
inference(superposition,[],[f63,f12]) ).
fof(f303,plain,
~ sP0(xor(truth,and_star(xor(truth,and_star(xor(x,truth),y)),and_star(y,xor(x,truth))))),
inference(backward_demodulation,[],[f67,f295]) ).
fof(f317,plain,
~ sP0(xor(truth,and_star(xor(truth,and_star(y,xor(x,truth))),and_star(y,xor(x,truth))))),
inference(superposition,[],[f303,f14]) ).
fof(f322,plain,
~ sP0(xor(truth,falsehood)),
inference(forward_demodulation,[],[f317,f9]) ).
fof(f324,plain,
~ sP0(truth),
inference(forward_demodulation,[],[f322,f2]) ).
fof(f326,plain,
$false,
inference(forward_subsumption_resolution,[],[f324,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL164-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n001.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 15:30:15 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.22/0.48 Running first-order theorem proving
% 0.22/0.48 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
% 10.06/2.64 % (3712409)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.06/2.64 % (3712414)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=2672067193:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 10.06/2.64 % (3712419)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2638324676:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 10.06/2.64 % (3712417)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=156642612:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 10.06/2.64 % (3712418)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2719756638:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 10.06/2.64 % (3712416)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4028732235:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 10.06/2.64 % (3712415)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=3949170642:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 10.06/2.64 % (3712420)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2436417932:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 10.06/2.64 % (3712417)First to succeed.
% 10.06/2.64 % (3712418)Also succeeded, but the first one will report.
% 10.06/2.64 % (3712420)Also succeeded, but the first one will report.
% 10.06/2.64 % (3712417)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3712409"
% 10.06/2.64 % (3712419)Instruction limit reached!
% 10.06/2.64 % (3712419)------------------------------
% 10.06/2.64 % (3712419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.64 % (3712419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.64 % (3712419)CaDiCaL version: 2.1.3
% 10.06/2.64 % (3712419)Termination reason: Instruction limit
% 10.06/2.64 % (3712419)Termination phase: Saturation
% 10.06/2.64 % (3712419)Time elapsed: 0.252 s
% 10.06/2.64 % (3712419)Peak memory usage: 90 MB
% 10.06/2.64 % (3712419)Instructions burned: 257 (million)
% 10.06/2.64 % (3712428)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1831238329:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2995 on theBenchmark for (2995ds/2051Mi)
% 10.06/2.64 % (3712429)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2377076406:i=4948:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/4948Mi)
% 10.06/2.64 % (3712430)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=2911359801:i=215:ep=RSTC_2992 on theBenchmark for (2992ds/215Mi)
% 10.06/2.64 % (3712414)Also succeeded, but the first one will report.
% 10.06/2.64 % (3712430)Instruction limit reached!
% 10.06/2.64 % (3712430)------------------------------
% 10.06/2.64 % (3712430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.64 % (3712430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.64 % (3712430)CaDiCaL version: 2.1.3
% 10.06/2.64 % (3712430)Termination reason: Instruction limit
% 10.06/2.64 % (3712430)Termination phase: Saturation
% 10.06/2.64 % (3712430)Time elapsed: 0.189 s
% 10.06/2.64 % (3712430)Peak memory usage: 89 MB
% 10.06/2.64 % (3712430)Instructions burned: 215 (million)
% 10.06/2.64 % (3712415)Also succeeded, but the first one will report.
% 10.06/2.64 % (3712417)Refutation found. Thanks to Tanya!
% 10.06/2.64 % SZS status Unsatisfiable for theBenchmark
% 10.06/2.64 % SZS output start Proof for theBenchmark
% See solution above
% 10.06/2.64 % (3712417)------------------------------
% 10.06/2.64 % (3712417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.06/2.64 % (3712417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.06/2.64 % (3712417)CaDiCaL version: 2.1.3
% 10.06/2.64 % (3712417)Termination reason: Refutation
% 10.06/2.64 % (3712417)Time elapsed: 0.037 s
% 10.06/2.64 % (3712417)Peak memory usage: 88 MB
% 10.06/2.64 % (3712417)Instructions burned: 15 (million)
% 10.06/2.64 % (3712417)------------------------------
% 10.06/2.64 % (3712417)------------------------------
% 10.06/2.64 % (3712409)Success in time 1.426 s
% 10.06/2.64 % Vampire exiting
%------------------------------------------------------------------------------