%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LDA007-3 : 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 : n014.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 12:01:25 PM UTC 2026
% Result : Unsatisfiable 4.08s 1.66s
% Output : Refutation 4.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 5 ( 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : f(X0,f(X1,X2)) = f(f(X0,X1),f(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
fof(f2,axiom,
tt = f(t,t),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f3,axiom,
ts = f(t,s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f4,axiom,
tt_ts = f(tt,ts),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f5,axiom,
tk = f(t,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f6,axiom,
tsk = f(ts,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f7,negated_conjecture,
f(t,tsk) != f(tt_ts,tk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f10,plain,
! [X0] : f(t,f(t,X0)) = f(tt,f(t,X0)),
inference(superposition,[],[f1,f2]) ).
fof(f18,plain,
! [X0] : f(t,f(X0,k)) = f(f(t,X0),tk),
inference(superposition,[],[f1,f5]) ).
fof(f27,plain,
f(tt,ts) = f(t,ts),
inference(superposition,[],[f10,f3]) ).
fof(f32,plain,
tt_ts = f(t,ts),
inference(forward_demodulation,[],[f27,f4]) ).
fof(f180,plain,
f(tt_ts,tk) = f(t,f(ts,k)),
inference(superposition,[],[f18,f32]) ).
fof(f185,plain,
f(t,tsk) = f(tt_ts,tk),
inference(forward_demodulation,[],[f180,f6]) ).
fof(f187,plain,
$false,
inference(forward_subsumption_resolution,[],[f185,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n014.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 27 17:09:46 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 4.08/1.66 % (1026663)Detected a unit-equality problem, will run specialized UEQ schedule.
% 4.08/1.66 % (1026674)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2764386445:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 4.08/1.66 % (1026674)First to succeed.
% 4.08/1.66 % (1026674)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1026663"
% 4.08/1.66 % (1026668)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=2689775031:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 4.08/1.66 % (1026671)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3656858276:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 4.08/1.66 % (1026669)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=1057742841:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 4.08/1.66 % (1026670)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1525882159:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 4.08/1.66 % (1026673)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=212520378:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 4.08/1.66 % (1026672)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=4017624347:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 4.08/1.66 % (1026672)Refutation not found, incomplete strategy
% 4.08/1.66 % (1026672)------------------------------
% 4.08/1.66 % (1026672)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.66 % (1026672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.66 % (1026672)CaDiCaL version: 2.1.3
% 4.08/1.66 % (1026672)Termination reason: Refutation not found, incomplete strategy
% 4.08/1.66 % (1026672)Time elapsed: 0.002 s
% 4.08/1.66 % (1026672)Peak memory usage: 87 MB
% 4.08/1.66 % (1026672)Instructions burned: 1 (million)
% 4.08/1.66 % (1026671)Also succeeded, but the first one will report.
% 4.08/1.66 % (1026674)Refutation found. Thanks to Tanya!
% 4.08/1.66 % SZS status Unsatisfiable for theBenchmark
% 4.08/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 4.08/1.66 % (1026674)------------------------------
% 4.08/1.66 % (1026674)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.08/1.66 % (1026674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.08/1.66 % (1026674)CaDiCaL version: 2.1.3
% 4.08/1.66 % (1026674)Termination reason: Refutation
% 4.08/1.66 % (1026674)Time elapsed: 0.006 s
% 4.08/1.66 % (1026674)Peak memory usage: 88 MB
% 4.08/1.66 % (1026674)Instructions burned: 11 (million)
% 4.08/1.66 % (1026674)------------------------------
% 4.08/1.66 % (1026674)------------------------------
% 4.08/1.66 % (1026663)Success in time 0.467 s
% 4.08/1.66 % Vampire exiting
%------------------------------------------------------------------------------