%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP001^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:09:58 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 39 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 16 ( 9 ~; 3 |; 1 &; 0 @)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 3 con; 0-4 aty)
% Number of variables : 12 ( 12 ^; 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
thf(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
c_2Ebool_2E_21:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
c_2Ebool_2E_2F_5C: $o > $o > $o ).
thf(func_def_2,type,
c_2Emin_2E_3D:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_3,type,
c_2Emin_2E_3D_3D_3E: $o > $o > $o ).
thf(func_def_4,type,
c_2Ebool_2E_3F:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
c_2Ebool_2ET: $o ).
thf(func_def_6,type,
c_2Ebool_2E_5C_2F: $o > $o > $o ).
thf(func_def_7,type,
c_2Ebool_2E_7E: $o > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(func_def_12,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_15,type,
sK1:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(f8,axiom,
( c_2Ebool_2ET
<=> ( ( ^ [X0: $o] : X0 )
= ( ^ [X1: $o] : X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ET__DEF) ).
thf(f9,conjecture,
c_2Ebool_2ET,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH) ).
thf(f10,negated_conjecture,
~ c_2Ebool_2ET,
inference(negated_conjecture,[status(cth)],[f9]) ).
thf(f25,plain,
( c_2Ebool_2ET
<=> ( ( ^ [X0: $o] : X0 )
= ( ^ [X1: $o] : X1 ) ) ),
inference(rectify,[],[f8]) ).
thf(f26,plain,
( ( c_2Ebool_2ET = $true )
<=> ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
~ c_2Ebool_2ET,
inference(rectify,[],[f10]) ).
thf(f28,plain,
c_2Ebool_2ET != $true,
inference(fool_elimination,[],[f27]) ).
thf(f29,plain,
c_2Ebool_2ET != $true,
inference(flattening,[],[f28]) ).
thf(f44,plain,
( ( ( c_2Ebool_2ET = $true )
| ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) ) )
& ( ( ( ^ [Y0: $o] : Y0 )
= ( ^ [Y0: $o] : Y0 ) )
| ( c_2Ebool_2ET != $true ) ) ),
inference(nnf_transformation,[],[f26]) ).
thf(f62,plain,
( ( c_2Ebool_2ET = $true )
| ( ( ^ [Y0: $o] : Y0 )
!= ( ^ [Y0: $o] : Y0 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f63,plain,
c_2Ebool_2ET != $true,
inference(cnf_transformation,[],[f29]) ).
thf(f73,plain,
c_2Ebool_2ET = $true,
inference(trivial_inequality_removal,[],[f62]) ).
thf(f78,plain,
$true != $true,
inference(constrained_superposition,[],[f63,f73]) ).
thf(f79,plain,
$false,
inference(trivial_inequality_removal,[],[f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP001^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n011.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 19:17:32 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 0.07/0.24 % (524866)Will run a generic schedule for satisfiability detection.
% 0.07/0.24 % (524877)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3382417025:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.24 % (524877) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-524866-524877"...
% 0.07/0.24 % (524877)...printing done.
% 0.07/0.24 % (524877)Refutation found. Thanks to Tanya!
% 0.07/0.24 % SZS status Theorem for theBenchmark
% 0.07/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.24 % (524877)------------------------------
% 0.07/0.24 % (524877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.24 % (524877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.24 % (524877)CaDiCaL version: 2.1.3
% 0.07/0.24 % (524877)Termination reason: Refutation
% 0.07/0.24 % (524877)Time elapsed: 0.001 s
% 0.07/0.24 % (524877)Peak memory usage: 12 MB
% 0.07/0.24 % (524877)Instructions burned: 2 (million)
% 0.07/0.24 % (524866)Success in time 0.03 s
% 0.07/0.24 % Vampire exiting
%------------------------------------------------------------------------------