%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:01:25 PM UTC 2026
% Result : Unsatisfiable 4.17s 1.53s
% Output : Refutation 4.17s
% 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/sandbox2/benchmark/theBenchmark.p',a1) ).
fof(f11,axiom,
tt = f(t,t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
fof(f13,axiom,
ts = f(t,s),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
fof(f14,axiom,
tt_ts = f(tt,ts),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
fof(f17,axiom,
tk = f(t,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
fof(f19,axiom,
tsk = f(ts,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
fof(f21,negated_conjecture,
f(t,tsk) != f(tt_ts,tk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f59,plain,
! [X0] : f(t,f(t,X0)) = f(tt,f(t,X0)),
inference(superposition,[],[f1,f11]) ).
fof(f74,plain,
! [X0] : f(t,f(X0,k)) = f(f(t,X0),tk),
inference(superposition,[],[f1,f17]) ).
fof(f318,plain,
f(tt,ts) = f(t,ts),
inference(superposition,[],[f59,f13]) ).
fof(f325,plain,
tt_ts = f(t,ts),
inference(forward_demodulation,[],[f318,f14]) ).
fof(f493,plain,
f(tt_ts,tk) = f(t,f(ts,k)),
inference(superposition,[],[f74,f325]) ).
fof(f500,plain,
f(t,tsk) = f(tt_ts,tk),
inference(forward_demodulation,[],[f493,f19]) ).
fof(f504,plain,
$false,
inference(forward_subsumption_resolution,[],[f500,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LDA007-2 : TPTP v9.3.1. Bugfixed v2.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n008.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 17:10:39 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.17/1.53 % (1466230)Input is clausal, will run a generic CNF schedule.
% 4.17/1.53 % (1466242)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2805038832:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.17/1.53 % (1466242)First to succeed.
% 4.17/1.53 % (1466242)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1466230"
% 4.17/1.53 % (1466237)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1710069286:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.17/1.53 % (1466243)dis-21_1_sil=8000:lcm=predicate:random_seed=1448265961:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 4.17/1.53 % (1466240)lrs+10_1_sil=8000:sp=occurrence:random_seed=3886844533:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.17/1.53 % (1466238)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=75100947:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.17/1.53 % (1466239)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=234186190:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.17/1.53 % (1466241)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1877661706:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.17/1.53 % (1466243)Refutation not found, incomplete strategy
% 4.17/1.53 % (1466243)------------------------------
% 4.17/1.53 % (1466243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.53 % (1466243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.53 % (1466243)CaDiCaL version: 2.1.3
% 4.17/1.53 % (1466243)Termination reason: Refutation not found, incomplete strategy
% 4.17/1.53 % (1466243)Time elapsed: 0.002 s
% 4.17/1.53 % (1466243)Peak memory usage: 88 MB
% 4.17/1.53 % (1466243)Instructions burned: 1 (million)
% 4.17/1.53 % (1466241)Also succeeded, but the first one will report.
% 4.17/1.53 % (1466240)Also succeeded, but the first one will report.
% 4.17/1.53 % (1466242)Refutation found. Thanks to Tanya!
% 4.17/1.53 % SZS status Unsatisfiable for theBenchmark
% 4.17/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 4.17/1.53 % (1466242)------------------------------
% 4.17/1.53 % (1466242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.17/1.53 % (1466242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.17/1.53 % (1466242)CaDiCaL version: 2.1.3
% 4.17/1.53 % (1466242)Termination reason: Refutation
% 4.17/1.53 % (1466242)Time elapsed: 0.012 s
% 4.17/1.53 % (1466242)Peak memory usage: 88 MB
% 4.17/1.53 % (1466242)Instructions burned: 17 (million)
% 4.17/1.53 % (1466242)------------------------------
% 4.17/1.53 % (1466242)------------------------------
% 4.17/1.53 % (1466230)Success in time 0.507 s
% 4.17/1.53 % Vampire exiting
%------------------------------------------------------------------------------