%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 11:51:28 AM UTC 2026
% Result : Unsatisfiable 4.10s 1.63s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 23 unt; 1 def)
% Number of atoms : 29 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 2 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 33 ( 0 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f3,axiom,
! [X0,X1] : axiom(or(not(X0),or(X1,X0))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f4,plain,
! [X0,X1] : true = axiom(or(not(X0),or(X1,X0))),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] : axiom(or(not(or(X0,X1)),or(X1,X0))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f6,plain,
! [X0,X1] : true = axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(reorient_equations,[],[f5]) ).
fof(f11,axiom,
! [X0] : ifeq(axiom(X0),true,theorem(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f12,plain,
! [X0] : true = ifeq(axiom(X0),true,theorem(X0),true),
inference(reorient_equations,[],[f11]) ).
fof(f15,axiom,
! [X2,X0,X1] : ifeq(theorem(or(not(X0),X1)),true,ifeq(axiom(or(not(X2),X0)),true,theorem(or(not(X2),X1)),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).
fof(f16,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(not(X0),X1)),true,ifeq(axiom(or(not(X2),X0)),true,theorem(or(not(X2),X1)),true),true),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
theorem(or(not(not(p)),or(not(p),q))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f18,plain,
true != theorem(or(not(not(p)),or(not(p),q))),
inference(reorient_equations,[],[f17]) ).
fof(f20,definition,
( spl0_1
<=> true = theorem(or(not(not(p)),or(not(p),q))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( true != theorem(or(not(not(p)),or(not(p),q)))
| spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f23,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f18,f20]) ).
fof(f30,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(or(X0,X1)),or(X1,X0))),true),
inference(superposition,[],[f12,f6]) ).
fof(f31,plain,
! [X0,X1] : true = theorem(or(not(or(X0,X1)),or(X1,X0))),
inference(forward_demodulation,[],[f30,f1]) ).
fof(f84,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(not(or(X0,X1)),X2)),true,ifeq(true,true,theorem(or(not(X1),X2)),true),true),
inference(superposition,[],[f16,f4]) ).
fof(f90,plain,
! [X2,X0,X1] : true = ifeq(theorem(or(not(or(X0,X1)),X2)),true,theorem(or(not(X1),X2)),true),
inference(forward_demodulation,[],[f84,f1]) ).
fof(f333,plain,
! [X0,X1] : true = ifeq(true,true,theorem(or(not(X1),or(X1,X0))),true),
inference(superposition,[],[f90,f31]) ).
fof(f363,plain,
! [X0,X1] : true = theorem(or(not(X1),or(X1,X0))),
inference(forward_demodulation,[],[f333,f1]) ).
fof(f365,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[],[f22,f363]) ).
fof(f366,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f365]) ).
cnf(s1,plain,
~ spl0_1,
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f366]) ).
cnf(s3,plain,
$false,
inference(rat,[],[s1,s2]) ).
fof(f367,plain,
$false,
inference(avatar_sat_refutation,[],[s3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 % Computer : n005.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 15:25:17 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 Running first-order theorem proving
% 0.14/0.45 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
% 4.10/1.63 % (4133260)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.10/1.63 % (4133270)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=40428232:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 4.10/1.63 % (4133270)First to succeed.
% 4.10/1.63 % (4133270)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4133260"
% 4.10/1.63 % (4133269)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2165849123:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 4.10/1.63 % (4133265)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=52903156:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 4.10/1.63 % (4133268)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=826663568:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 4.10/1.63 % (4133271)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3152009881:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 4.10/1.63 % (4133266)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=377573742:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 4.10/1.63 % (4133267)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1793367042:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 4.10/1.63 % (4133268)Also succeeded, but the first one will report.
% 4.10/1.63 % (4133271)Also succeeded, but the first one will report.
% 4.10/1.63 % (4133269)Also succeeded, but the first one will report.
% 4.10/1.63 % (4133270)Refutation found. Thanks to Tanya!
% 4.10/1.63 % SZS status Unsatisfiable for theBenchmark
% 4.10/1.63 % SZS output start Proof for theBenchmark
% See solution above
% 4.10/1.63 % (4133270)------------------------------
% 4.10/1.63 % (4133270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.10/1.63 % (4133270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.10/1.63 % (4133270)CaDiCaL version: 2.1.3
% 4.10/1.63 % (4133270)Termination reason: Refutation
% 4.10/1.63 % (4133270)Time elapsed: 0.014 s
% 4.10/1.63 % (4133270)Peak memory usage: 89 MB
% 4.10/1.63 % (4133270)Instructions burned: 24 (million)
% 4.10/1.63 % (4133270)------------------------------
% 4.10/1.63 % (4133270)------------------------------
% 4.10/1.63 % (4133260)Success in time 0.472 s
% 4.10/1.63 % Vampire exiting
%------------------------------------------------------------------------------