%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV175^5 : 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 : n018.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 08:39:06 AM UTC 2026
% Result : Theorem 0.29s 0.40s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 44 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 204 ( 32 ~; 4 |; 23 &; 132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 12 usr; 3 con; 0-4 aty)
% ( 0 !!; 13 ??; 0 @@+; 0 @@-)
% Number of variables : 47 ( 29 ^; 9 !; 9 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_4,type,
vAND: $o > $o > $o ).
thf(func_def_5,type,
vNOT: $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_12,type,
sK2: $i > $o ).
thf(func_def_13,type,
sK3: $i > $o ).
thf(func_def_14,type,
sK4: $i > $o ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) )
= ( X0 @ X1 ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM144A_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) )
= ( X0 @ X1 ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0
@ ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) )
= ( X0 @ X1 ) )
& ~ ( X1 @ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] :
? [X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
& ( ( X1 @ ( X0 @ X1 ) )
!= $true ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: ( $i > $o ) > $i] :
! [X1: $i > $o] :
( ( ( X0 @ X1 )
!= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) ) )
| ( ( X1 @ ( X0 @ X1 ) )
= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
! [X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( X1 @ ( sK0 @ X1 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
! [X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( X1 @ ( sK0 @ X1 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f44,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(equality_resolution,[],[f8]) ).
thf(f45,plain,
( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f45]) ).
thf(f47,plain,
( $true
= ( ~ ( sK2 @ ( sK0 @ sK2 ) )
& ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
( $true
= ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f49,plain,
( $true
= ( ~ ( sK2 @ ( sK0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f47]) ).
thf(f50,plain,
( $false
= ( sK2 @ ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f49]) ).
thf(f51,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= ( sK0 @ sK2 ) ),
inference(equality_proxy_clausification,[],[f48]) ).
thf(f75,plain,
! [X0: $i > $o] :
( ( ( sK0 @ X0 )
!= ( sK0 @ sK2 ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f8,f51]) ).
thf(f94,plain,
( $true
= ( sK2 @ ( sK0 @ sK2 ) ) ),
inference(equality_resolution,[],[f75]) ).
thf(f104,plain,
$true = $false,
inference(forward_demodulation,[],[f94,f50]) ).
thf(f105,plain,
$false,
inference(trivial_inequality_removal,[],[f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV175^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.29 % Computer : n018.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8046.5625MB
% 0.12/0.29 % OS : Linux 6.8.0-71-generic
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Sep 29 15:20:42 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.29/0.35 Running first-order model finding
% 0.29/0.35 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
% 0.29/0.40 % (212161)Will run a generic schedule for satisfiability detection.
% 0.29/0.40 % (212168)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1761771774:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.29/0.40 % (212168) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-212161-212168"...
% 0.29/0.40 % (212168)...printing done.
% 0.29/0.40 % (212167)% WARNING: option uhcvi not known.
% 0.29/0.40 % (212168)Refutation found. Thanks to Tanya!
% 0.29/0.40 % SZS status Theorem for theBenchmark
% 0.29/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.40 % (212168)------------------------------
% 0.29/0.40 % (212168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.40 % (212168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.40 % (212168)CaDiCaL version: 2.1.3
% 0.29/0.40 % (212168)Termination reason: Refutation
% 0.29/0.40 % (212168)Time elapsed: 0.004 s
% 0.29/0.40 % (212168)Peak memory usage: 12 MB
% 0.29/0.40 % (212168)Instructions burned: 5 (million)
% 0.29/0.40 % (212161)Success in time 0.041 s
% 0.29/0.40 % Vampire exiting
%------------------------------------------------------------------------------