%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP209_2 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 0.22s 0.52s
% Output : Refutation 0.22s
% 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 : 6 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-4 aty)
% Number of variables : 10 ( 10 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
a: $tType ).
tff(func_def_0,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
fFalse: bool ).
tff(func_def_2,type,
fTrue: bool ).
tff(func_def_3,type,
a2: a ).
tff(func_def_4,type,
b: a ).
tff(func_def_5,type,
c: a ).
tff(func_def_6,type,
f: fun(a,fun(a,a)) ).
tff(func_def_7,type,
sK0:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_8,type,
sK1:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_9,type,
sK2:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_10,type,
sK3:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_11,type,
sK4:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_12,type,
sK5:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_13,type,
sK6:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_14,type,
sK7:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_15,type,
sK8:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(func_def_16,type,
sK9:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > X0 ) ).
tff(pred_def_1,type,
syntax_ac_operator:
!>[X0: $tType] : ( fun(X0,fun(X0,X0)) > $o ) ).
tff(pred_def_2,type,
syntax7388354845996824322omatch:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > $o ) ).
tff(pred_def_3,type,
syntax2379306206330768139omatch:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $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(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/sandbox2/benchmark/theBenchmark.p',fact_2_left__commute) ).
tff(f15,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(f16,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)],[f15]) ).
tff(f19,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,[],[f16]) ).
tff(f35,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(f36,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(f48,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,[],[f19]) ).
tff(f50,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,[],[f48,f35]) ).
tff(f51,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,[],[f50,f35]) ).
tff(f71,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,[],[f51,f36]) ).
tff(f72,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,[],[f71,f35]) ).
tff(f74,plain,
$false,
inference(forward_subsumption_resolution,[],[f72,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP209_2 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43 % Computer : n005.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sun Sep 27 12:23:03 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.22/0.48 Running first-order model finding
% 0.22/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.52 % (3914303)Will run a generic schedule for satisfiability detection.
% 0.22/0.52 % (3914311)dis+10_1_sil=32000:sp=arity:random_seed=4054513506:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.52 % (3914311) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3914303-3914311"...
% 0.22/0.52 % (3914313)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3182315673:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.52 % (3914311)...printing done.
% 0.22/0.52 % (3914313) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3914303-3914313"...
% 0.22/0.52 % (3914311)Refutation found. Thanks to Tanya!
% 0.22/0.52 % SZS status Theorem for theBenchmark
% 0.22/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.52 % (3914311)------------------------------
% 0.22/0.52 % (3914311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.52 % (3914311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.52 % (3914311)CaDiCaL version: 2.1.3
% 0.22/0.52 % (3914311)Termination reason: Refutation
% 0.22/0.52 % (3914311)Time elapsed: 0.004 s
% 0.22/0.52 % (3914311)Peak memory usage: 11 MB
% 0.22/0.52 % (3914311)Instructions burned: 5 (million)
% 0.22/0.52 % (3914303)Success in time 0.03 s
% 0.22/0.52 % Vampire exiting
%------------------------------------------------------------------------------