%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU693^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 : Wed Sep 30 08:33:00 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 53 ( 13 equ; 0 cnn)
% Maximal formula atoms : 3 ( 6 avg)
% Number of connectives : 110 ( 6 ~; 0 |; 4 &; 92 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 20 ( 0 ^; 16 !; 4 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
funcSet: $i > $i > $i ).
thf(func_def_2,type,
ap: $i > $i > $i > $i > $i ).
thf(f1,conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap2apEq1) ).
thf(f2,negated_conjecture,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ap @ X0 @ X1 @ X2 @ X3 )
= ( ap @ X0 @ X1 @ X2 @ X3 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( ap @ X0 @ X1 @ X2 @ X3 )
!= ( ap @ X0 @ X1 @ X2 @ X3 ) )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( ( in @ X2 @ ( funcSet @ X0 @ X1 ) )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ap @ sK0 @ sK1 @ sK2 @ sK3 )
!= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) )
& ( $true
= ( in @ sK3 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( funcSet @ sK0 @ sK1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f5]) ).
thf(f9,plain,
( ( ap @ sK0 @ sK1 @ sK2 @ sK3 )
!= ( ap @ sK0 @ sK1 @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
$false,
inference(trivial_inequality_removal,[],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU693^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n020.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 14:12:22 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.07/0.25 % (1112723)Will run a generic schedule for satisfiability detection.
% 0.07/0.25 % (1112732)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1235500296_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.25 % Exception at run slice level
% 0.07/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.25 % (1112735)dis+10_1_sil=32000:sp=arity:random_seed=382099280:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.25 % (1112734)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1506937417:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.25 % (1112738)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=323154003:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.25 % (1112737)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2902910487:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.25 % (1112739)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2777640304:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.25 % (1112737)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.07/0.25 % (1112735) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1112723-1112735"...
% 0.07/0.25 % (1112738) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1112723-1112738"...
% 0.07/0.25 % (1112734) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1112723-1112734"...
% 0.07/0.25 % (1112737) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1112723-1112737"...
% 0.07/0.25 % (1112739) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1112723-1112739"...
% 0.07/0.25 % (1112743)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2134147192:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.07/0.25 % Exception at run slice level
% 0.07/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.07/0.25 % (1112738)...printing done.
% 0.07/0.25 % (1112734)...printing done.
% 0.07/0.25 % (1112735)...printing done.
% 0.07/0.25 % (1112737)...printing done.
% 0.07/0.25 % (1112739)...printing done.
% 0.07/0.25 % (1112734)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.25 % (1112734)------------------------------
% 0.07/0.25 % (1112734)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (1112734)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (1112734)CaDiCaL version: 2.1.3
% 0.07/0.25 % (1112734)Termination reason: Refutation
% 0.07/0.25 % (1112734)Time elapsed: 0.001 s
% 0.07/0.25 % (1112734)Peak memory usage: 11 MB
% 0.07/0.25 % (1112734)Instructions burned: 1 (million)
% 0.07/0.25 % (1112723)Success in time 0.038 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------