%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO262^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:49:37 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 89 ( 18 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 294 ( 50 ~; 4 |; 6 &; 234 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 78 ( 55 ^; 23 !; 0 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(func_def_1,type,
cE: ( $i > $o ) > $i ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
sK0: ( $i > $i > $i ) > ( $i > $i > $i ) > $i ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
sK1: ( $i > $i > $i ) > $i ).
thf(f1,conjecture,
~ ( ! [X2: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) )
@ ( X2
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) ) ) )
& ! [X0: $i] :
( cP @ X0
@ ( cE
@ ^ [X1: $i] : ( cP @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM19SK1) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X2: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) )
@ ( X2
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) ) ) )
& ! [X0: $i] :
( cP @ X0
@ ( cE
@ ^ [X1: $i] : ( cP @ X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ! [X0: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X1: $i] :
~ ( cP @ X1 @ ( X0 @ X1 ) ) )
@ ( X0
@ ( cE
@ ^ [X2: $i] :
~ ( cP @ X2 @ ( X0 @ X2 ) ) ) ) )
& ! [X3: $i] :
( cP @ X3
@ ( cE
@ ^ [X4: $i] : ( cP @ X3 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) ) ) ) )
& ! [X3: $i] :
( ( cP @ X3
@ ( cE
@ ^ [Y0: $i] : ( cP @ X3 @ Y0 ) ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) ) ) ) )
& ! [X1: $i] :
( $true
= ( cP @ X1
@ ( cE
@ ^ [Y0: $i] : ( cP @ X1 @ Y0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) ) ) ) )
& ! [X1: $i] :
( $true
= ( cP @ X1
@ ( cE
@ ^ [Y0: $i] : ( cP @ X1 @ Y0 ) ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
! [X1: $i] :
( $true
= ( cP @ X1
@ ( cE
@ ^ [Y0: $i] : ( cP @ X1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
! [X0: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X0 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
! [X1: $i] :
( $true
= ( cP @ X1 @ ( cE @ ( cP @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f7]) ).
thf(f19,plain,
! [X0: $i > $i > $i,X1: $i > $i > $i] :
( ( $true != $true )
| ( ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] : ( cP @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( cE
@ ^ [Y1: $i] :
~ ( cP @ Y1
@ ( cE
@ ( ^ [Y2: $i,Y3: $i] : ( cP @ ( X0 @ Y2 @ Y3 ) @ ( X1 @ Y2 @ Y3 ) )
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i] : Y0 )
!= ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] : ( cP @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f8,f11]) ).
thf(f22,plain,
! [X0: $i > $i > $i,X1: $i > $i > $i] :
( ( ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] : ( cP @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( cE
@ ^ [Y1: $i] :
~ ( cP @ Y1
@ ( cE
@ ( ^ [Y2: $i,Y3: $i] : ( cP @ ( X0 @ Y2 @ Y3 ) @ ( X1 @ Y2 @ Y3 ) )
@ Y1 ) ) ) ) ) )
| ( ( ^ [Y0: $i] : Y0 )
!= ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] : ( cP @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f19]) ).
thf(f23,plain,
! [X0: $i > $i > $i,X1: $i > $i > $i] :
( ( ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] : ( cP @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) )
!= ( ^ [Y0: $i] :
( cE
@ ^ [Y1: $i] :
~ ( cP @ Y1
@ ( cE
@ ^ [Y2: $i] : ( cP @ ( X0 @ Y1 @ Y2 ) @ ( X1 @ Y1 @ Y2 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] : Y0 )
!= ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] : ( cP @ ( X0 @ Y0 @ Y1 ) @ ( X1 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f34,plain,
! [X0: $i > $i > $i] :
( ( ^ [Y0: $i] : Y0 )
!= ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] :
( cP
@ ( ^ [Y2: $i,Y3: $i] : Y2
@ Y0
@ Y1 )
@ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(equality_resolution,[],[f23]) ).
thf(f37,plain,
! [X0: $i > $i > $i] :
( ( ^ [Y0: $i] : Y0 )
!= ( X0
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0
@ ( cE
@ ^ [Y1: $i] : ( cP @ Y0 @ ( X0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f40,plain,
$false,
inference(equality_resolution,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO262^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n017.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:37:23 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.21 Running first-order model finding
% 0.10/0.21 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
% 0.10/0.25 % (572177)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (572185)dis+10_1_sil=32000:sp=arity:random_seed=2708501408:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.25 % (572185) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-572177-572185"...
% 0.10/0.25 % (572183)% WARNING: option uhcvi not known.
% 0.10/0.25 % (572185)...printing done.
% 0.10/0.25 % (572185)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (572185)------------------------------
% 0.10/0.25 % (572185)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (572185)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (572185)CaDiCaL version: 2.1.3
% 0.10/0.25 % (572185)Termination reason: Refutation
% 0.10/0.25 % (572185)Time elapsed: 0.003 s
% 0.10/0.25 % (572185)Peak memory usage: 12 MB
% 0.10/0.25 % (572185)Instructions burned: 8 (million)
% 0.10/0.25 % (572177)Success in time 0.028 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------