%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP209_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 11:30:05 AM UTC 2026
% Result : Theorem 0.17s 1.50s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 14 ( 8 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 : 5 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 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,
bool: $tType ).
tff(type_def_8,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,
fFalse: bool ).
tff(func_def_3,type,
fTrue: bool ).
tff(func_def_4,type,
a2: a ).
tff(func_def_5,type,
b: a ).
tff(func_def_6,type,
c: a ).
tff(func_def_7,type,
f: fun_a_fun_a_a ).
tff(pred_def_1,type,
syntax_ac_operator_a: fun_a_fun_a_a > $o ).
tff(pred_def_2,type,
pp: bool > $o ).
tff(pred_def_3,type,
sP0: 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/sandbox2/benchmark/theBenchmark.p',fact_1_commute) ).
tff(f4,axiom,
! [X0: a,X1: a,X2: a] : ( aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X0),X1)),X2) = aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_right__assoc) ).
tff(f13,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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f14,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)],[f13]) ).
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,[],[f14]) ).
tff(f17,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(f18,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,aa_a_a(aa_a_fun_a_a(f,X0),X1)),X2) ),
inference(cnf_transformation,[],[f4]) ).
tff(f20,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(f21,definition,
~ sP0(aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
tff(f22,plain,
sP0(aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b)),
inference(inequality_splitting,[],[f17,f21]) ).
tff(f23,plain,
~ sP0(aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c))),
inference(forward_demodulation,[],[f21,f18]) ).
tff(f24,plain,
sP0(aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,c),b))),
inference(forward_demodulation,[],[f22,f18]) ).
tff(f25,plain,
sP0(aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c))),
inference(forward_demodulation,[],[f24,f20]) ).
tff(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f25,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP209_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 12:29:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.17/1.50 % (3491936)Detected formulas, will run a generic FOF schedule.
% 0.17/1.50 % (3492017)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=535988678:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.50 % (3492018)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=284314441:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.50 % (3492023)dis-21_1_sil=8000:lcm=predicate:random_seed=2979871890:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.17/1.50 % (3492021)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3730757473:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.50 % (3492020)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2479839746:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.50 % (3492020)First to succeed.
% 0.17/1.50 % (3492020)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3491936"
% 0.17/1.50 % (3492023)Refutation not found, incomplete strategy
% 0.17/1.50 % (3492023)------------------------------
% 0.17/1.50 % (3492023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3492023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3492023)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3492023)Termination reason: Refutation not found, incomplete strategy
% 0.17/1.50 % (3492023)Time elapsed: 0.002 s
% 0.17/1.50 % (3492023)Peak memory usage: 88 MB
% 0.17/1.50 % (3492023)Instructions burned: 2 (million)
% 0.17/1.50 % (3492021)Also succeeded, but the first one will report.
% 0.17/1.50 % (3492019)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3680853227:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.50 % (3492022)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=949756824:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.50 % (3492022)Also succeeded, but the first one will report.
% 0.17/1.50 % (3492023)------------------------------
% 0.17/1.50 % (3492023)------------------------------
% 0.17/1.50 % (3492020)Refutation found. Thanks to Tanya!
% 0.17/1.50 % SZS status Theorem for theBenchmark
% 0.17/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (3492020)------------------------------
% 0.17/1.50 % (3492020)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (3492020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (3492020)CaDiCaL version: 2.1.3
% 0.17/1.50 % (3492020)Termination reason: Refutation
% 0.17/1.50 % (3492020)Time elapsed: 0.002 s
% 0.17/1.50 % (3492020)Peak memory usage: 88 MB
% 0.17/1.50 % (3492020)Instructions burned: 1 (million)
% 0.17/1.50 % (3492020)------------------------------
% 0.17/1.50 % (3492020)------------------------------
% 0.17/1.50 % (3491936)Success in time 0.435 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------