%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP209_3 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 11:36:50 AM UTC 2026
% Result : Theorem 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
fun_a_fun_a_a: $tType ).
tff(type_def_6,type,
fun_a_a: $tType ).
tff(type_def_7,type,
a: $tType ).
tff(func_def_0,type,
aa_a_fun_a_a: ( fun_a_fun_a_a * a ) > fun_a_a ).
tff(func_def_1,type,
aa_a_a: ( fun_a_a * a ) > a ).
tff(func_def_2,type,
a2: a ).
tff(func_def_3,type,
b: a ).
tff(func_def_4,type,
c: a ).
tff(func_def_5,type,
f: fun_a_fun_a_a ).
tff(func_def_6,type,
sK0: fun_a_fun_a_a > a ).
tff(func_def_7,type,
sK1: fun_a_fun_a_a > a ).
tff(func_def_8,type,
sK2: fun_a_fun_a_a > a ).
tff(func_def_9,type,
sK3: fun_a_fun_a_a > a ).
tff(func_def_10,type,
sK4: fun_a_fun_a_a > a ).
tff(func_def_11,type,
sK5: fun_a_fun_a_a > a ).
tff(func_def_12,type,
sK6: fun_a_fun_a_a > a ).
tff(func_def_13,type,
sK7: fun_a_fun_a_a > a ).
tff(func_def_14,type,
sK8: fun_a_fun_a_a > a ).
tff(func_def_15,type,
sK9: fun_a_fun_a_a > a ).
tff(pred_def_1,type,
syntax_ac_operator_a: fun_a_fun_a_a > $o ).
tff(f2,axiom,
! [X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),X1) = aa_a_a(aa_a_fun_a_a(f,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_commute) ).
tff(f3,axiom,
! [X0: a,X1: a,X2: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) = aa_a_a(aa_a_fun_a_a(f,X1),aa_a_a(aa_a_fun_a_a(f,X0),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_left__commute) ).
tff(f11,conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f12,negated_conjecture,
( ( ~ aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) ) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
tff(f15,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(flattening,[],[f12]) ).
tff(f29,plain,
! [X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),X1) = aa_a_a(aa_a_fun_a_a(f,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tff(f30,plain,
! [X2: a,X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) = aa_a_a(aa_a_fun_a_a(f,X1),aa_a_a(aa_a_fun_a_a(f,X0),X2)) ),
inference(cnf_transformation,[],[f3]) ).
tff(f40,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(cnf_transformation,[],[f15]) ).
tff(f42,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)),
inference(superposition,[],[f40,f29]) ).
tff(f43,plain,
aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) != aa_a_a(aa_a_fun_a_a(f,c),aa_a_a(aa_a_fun_a_a(f,a2),b)),
inference(forward_demodulation,[],[f42,f29]) ).
tff(f85,plain,
aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) != aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,c),b)),
inference(superposition,[],[f43,f30]) ).
tff(f88,plain,
aa_a_a(aa_a_fun_a_a(f,b),aa_a_a(aa_a_fun_a_a(f,a2),c)) != aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)),
inference(forward_demodulation,[],[f85,f29]) ).
tff(f90,plain,
$false,
inference(forward_subsumption_resolution,[],[f88,f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP209_3 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 27 12:23:49 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.21/0.49 Running first-order model finding
% 0.21/0.50 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
% 0.21/0.54 % (3014257)Will run a generic schedule for satisfiability detection.
% 0.21/0.54 % (3014264)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3594766533:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.54 % (3014264) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3014257-3014264"...
% 0.21/0.54 % (3014262)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1418940799_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.54 % (3014264)...printing done.
% 0.21/0.54 % (3014264)Refutation found. Thanks to Tanya!
% 0.21/0.54 % SZS status Theorem for theBenchmark
% 0.21/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54 % (3014264)------------------------------
% 0.21/0.54 % (3014264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.54 % (3014264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.54 % (3014264)CaDiCaL version: 2.1.3
% 0.21/0.54 % (3014264)Termination reason: Refutation
% 0.21/0.54 % (3014264)Time elapsed: 0.004 s
% 0.21/0.54 % (3014264)Peak memory usage: 12 MB
% 0.21/0.54 % (3014264)Instructions burned: 5 (million)
% 0.21/0.54 % (3014257)Success in time 0.031 s
% 0.21/0.54 % Vampire exiting
%------------------------------------------------------------------------------