%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n026.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 12:01:29 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 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 : 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(f8,plain,
f(tt_ts,tk) != f(t,f(ts,k)),
inference(superposition,[],[f7,f6]) ).
fof(f9,plain,
f(t,f(ts,k)) != f(f(tt,ts),tk),
inference(forward_demodulation,[],[f8,f4]) ).
fof(f10,plain,
! [X0] : f(t,f(t,X0)) = f(tt,f(t,X0)),
inference(superposition,[],[f1,f2]) ).
fof(f16,plain,
! [X0] : f(t,f(X0,k)) = f(f(t,X0),tk),
inference(superposition,[],[f1,f5]) ).
fof(f20,plain,
f(tt,ts) = f(t,ts),
inference(superposition,[],[f10,f3]) ).
fof(f98,plain,
f(f(tt,ts),tk) != f(f(t,ts),tk),
inference(superposition,[],[f9,f16]) ).
fof(f110,plain,
f(f(tt,ts),tk) != f(f(tt,ts),tk),
inference(forward_demodulation,[],[f98,f20]) ).
fof(f111,plain,
$false,
inference(trivial_inequality_removal,[],[f110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LDA007-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 17:12:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44 % (3075191)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (3075201)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2105268552:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.44 % (3075201) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3075191-3075201"...
% 0.10/0.44 % (3075197)% WARNING: option uhcvi not known.
% 0.10/0.44 % (3075201)...printing done.
% 0.10/0.44 % (3075201)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (3075201)------------------------------
% 0.10/0.44 % (3075201)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (3075201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (3075201)CaDiCaL version: 2.1.3
% 0.10/0.44 % (3075201)Termination reason: Refutation
% 0.10/0.44 % (3075201)Time elapsed: 0.002 s
% 0.10/0.44 % (3075201)Peak memory usage: 11 MB
% 0.10/0.44 % (3075201)Instructions burned: 6 (million)
% 0.10/0.44 % (3075191)Success in time 0.033 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------