%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET027^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 08:23:32 AM UTC 2026
% Result : Theorem 0.09s 0.28s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 106 ( 43 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 123 ( 21 ~; 12 |; 16 &; 58 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 ^; 34 !; 12 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a > $o ).
thf(func_def_6,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_29_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( X0 @ X3 )
=> ( X1 @ X3 ) ) )
=> ! [X3: a] :
( ( X0 @ X3 )
=> ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) )
& ! [X4: a] :
( ( X0 @ X4 )
=> ( X1 @ X4 ) ) )
=> ! [X5: a] :
( ( X0 @ X5 )
=> ( X2 @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( X1 @ X3 )
= $true )
=> ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( X1 @ X4 )
= $true ) ) )
=> ! [X5: a] :
( ( ( X0 @ X5 )
= $true )
=> ( ( X2 @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( ( X2 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( ( X2 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ! [X4: a] :
( ( $true
= ( X2 @ X4 ) )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X5: a] :
( ( $true
= ( X1 @ X5 ) )
| ( ( X0 @ X5 )
!= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( sK2 @ sK3 ) )
& ( $true
= ( sK0 @ sK3 ) )
& ! [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
| ( $true
!= ( sK1 @ X4 ) ) )
& ! [X5: a] :
( ( $true
= ( sK1 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
! [X5: a] :
( ( $true
!= ( sK0 @ X5 ) )
| ( $true
= ( sK1 @ X5 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X4: a] :
( ( $true
!= ( sK1 @ X4 ) )
| ( $true
= ( sK2 @ X4 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
!= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f9,f11]) ).
thf(f16,plain,
( $true
= ( sK1 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f15]) ).
thf(f17,plain,
( ( $true != $true )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f10,f16]) ).
thf(f18,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f17]) ).
thf(f19,plain,
$true != $true,
inference(constrained_superposition,[],[f12,f18]) ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:38:38 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.09/0.28 % (1286093)Will run a generic schedule for satisfiability detection.
% 0.09/0.28 % (1286104)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=393080840:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.09/0.28 % (1286104) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1286093-1286104"...
% 0.09/0.28 % (1286104)...printing done.
% 0.09/0.28 % (1286104)Refutation found. Thanks to Tanya!
% 0.09/0.28 % SZS status Theorem for theBenchmark
% 0.09/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.28 % (1286104)------------------------------
% 0.09/0.28 % (1286104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.28 % (1286104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.28 % (1286104)CaDiCaL version: 2.1.3
% 0.09/0.28 % (1286104)Termination reason: Refutation
% 0.09/0.28 % (1286104)Time elapsed: 0.002 s
% 0.09/0.28 % (1286104)Peak memory usage: 12 MB
% 0.09/0.28 % (1286104)Instructions burned: 1 (million)
% 0.09/0.28 % (1286093)Success in time 0.026 s
% 0.09/0.28 % Vampire exiting
%------------------------------------------------------------------------------