%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV220^5 : 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 08:39:10 AM UTC 2026
% Result : Theorem 0.29s 0.39s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 24 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 64 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 163 ( 16 ~; 8 |; 32 &; 88 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 5 con; 0-4 aty)
% ( 0 !!; 7 ??; 0 @@+; 0 @@-)
% Number of variables : 56 ( 17 ^; 20 !; 19 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
f: b > a ).
thf(func_def_1,type,
w: ( b > $o ) > $o ).
thf(func_def_5,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
sK0: a ).
thf(func_def_12,type,
sK1: a > $o ).
thf(func_def_13,type,
sK2: b > $o ).
thf(func_def_14,type,
sK3: b ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X3: a] :
? [X4: b] :
( ( X3
= ( f @ X4 ) )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
=> ( X2 @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5205_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) ) )
=> ! [X2: a > $o] :
( ? [X1: b > $o] :
( ( X2
= ( ^ [X3: a] :
? [X4: b] :
( ( X3
= ( f @ X4 ) )
& ( X1 @ X4 ) ) ) )
& ( w @ X1 ) )
=> ( X2 @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ! [X2: b > $o] :
( ( w @ X2 )
=> ( X2 @ X1 ) ) )
=> ! [X3: a > $o] :
( ? [X4: b > $o] :
( ( X3
= ( ^ [X5: a] :
? [X6: b] :
( ( ( f @ X6 )
= X5 )
& ( X4 @ X6 ) ) ) )
& ( w @ X4 ) )
=> ( X3 @ X0 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ! [X2: b > $o] :
( ( ( w @ X2 )
= $true )
=> ( ( X2 @ X1 )
= $true ) ) )
=> ! [X3: a > $o] :
( ? [X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X3 )
& ( ( w @ X4 )
= $true ) )
=> ( ( X3 @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ? [X3: a > $o] :
( ( ( X3 @ X0 )
!= $true )
& ? [X4: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X4 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X3 )
& ( ( w @ X4 )
= $true ) ) )
& ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ! [X2: b > $o] :
( ( ( X2 @ X1 )
= $true )
| ( ( w @ X2 )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a] :
( ? [X1: a > $o] :
( ( $true
!= ( X1 @ X0 ) )
& ? [X2: b > $o] :
( ( ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( X2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) )
= X1 )
& ( ( w @ X2 )
= $true ) ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ! [X4: b > $o] :
( ( $true
= ( X4 @ X3 ) )
| ( ( w @ X4 )
!= $true ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( $true
!= ( sK1 @ sK0 ) )
& ( sK1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) )
& ( $true
= ( w @ sK2 ) )
& ( sK0
= ( f @ sK3 ) )
& ! [X4: b > $o] :
( ( $true
= ( X4 @ sK3 ) )
| ( ( w @ X4 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f6]) ).
thf(f8,plain,
! [X4: b > $o] :
( ( ( w @ X4 )
!= $true )
| ( $true
= ( X4 @ sK3 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( sK0
= ( f @ sK3 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( $true
= ( w @ sK2 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( sK1
= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( $true
!= ( sK1 @ sK0 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
( $true
!= ( ^ [Y0: a] :
( ?? @ b
@ ^ [Y1: b] :
( ( sK2 @ Y1 )
& ( ( f @ Y1 )
= Y0 ) ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f12,f11]) ).
thf(f16,plain,
( $true
!= ( ?? @ b
@ ^ [Y0: b] :
( ( sK2 @ Y0 )
& ( ( f @ Y0 )
= sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
! [X1: b] :
( $false
= ( ^ [Y0: b] :
( ( sK2 @ Y0 )
& ( ( f @ Y0 )
= sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: b] :
( $false
= ( ( sK2 @ X1 )
& ( ( f @ X1 )
= sK0 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X1: b] :
( ( $false
= ( ( f @ X1 )
= sK0 ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( sK0 != sK0 )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f20,f9]) ).
thf(f22,plain,
( $false
= ( sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f23,plain,
( ( $true != $true )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(constrained_superposition,[],[f8,f10]) ).
thf(f24,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(trivial_inequality_removal,[],[f23]) ).
thf(f25,plain,
$true = $false,
inference(forward_demodulation,[],[f24,f22]) ).
thf(f26,plain,
$false,
inference(trivial_inequality_removal,[],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV220^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.28 % Computer : n002.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8046.5625MB
% 0.11/0.28 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 15:25:22 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.29/0.34 Running first-order model finding
% 0.29/0.34 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
% 0.29/0.39 % (1425292)Will run a generic schedule for satisfiability detection.
% 0.29/0.39 % (1425301)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=943195016:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.29/0.39 % (1425301)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.29/0.39 % (1425301) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1425292-1425301"...
% 0.29/0.39 % (1425301)...printing done.
% 0.29/0.39 % (1425301)Refutation found. Thanks to Tanya!
% 0.29/0.39 % SZS status Theorem for theBenchmark
% 0.29/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.39 % (1425301)------------------------------
% 0.29/0.39 % (1425301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.39 % (1425301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.39 % (1425301)CaDiCaL version: 2.1.3
% 0.29/0.39 % (1425301)Termination reason: Refutation
% 0.29/0.39 % (1425301)Time elapsed: 0.002 s
% 0.29/0.39 % (1425301)Peak memory usage: 12 MB
% 0.29/0.39 % (1425301)Instructions burned: 2 (million)
% 0.29/0.39 % (1425292)Success in time 0.033 s
% 0.29/0.39 % Vampire exiting
%------------------------------------------------------------------------------