%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM812^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 08:19:35 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 30 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 152 ( 61 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 210 ( 17 ~; 20 |; 12 &; 120 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 6 con; 0-4 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 56 ( 22 ^; 29 !; 5 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_2,type,
cIND: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $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,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vNOT: $o > $o ).
thf(func_def_14,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( cIND
= ( ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) )
& ( X0 @ c0 ) )
=> ! [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cIND_def) ).
thf(f2,conjecture,
( cIND
=> ! [X0: $i] :
( ? [X1: $i] :
( X0
= ( cS @ X1 ) )
| ( X0 = c0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM578) ).
thf(f3,negated_conjecture,
~ ( cIND
=> ! [X0: $i] :
( ? [X1: $i] :
( X0
= ( cS @ X1 ) )
| ( X0 = c0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( cIND
= ( ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) )
& ( X0 @ c0 ) )
=> ! [X2: $i] : ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( cIND
=> ! [X0: $i] :
( ? [X1: $i] :
( X0
= ( cS @ X1 ) )
| ( X0 = c0 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( cIND = $true )
=> ! [X0: $i] :
( ? [X1: $i] :
( ( cS @ X1 )
= X0 )
| ( c0 = X0 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( cS @ X1 )
!= X0 )
& ( c0 != X0 ) )
& ( cIND = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ! [X1: $i] :
( ( cS @ X1 )
!= sK0 )
& ( c0 != sK0 )
& ( cIND = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f8]) ).
thf(f10,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
cIND = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
c0 != sK0,
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X1: $i] :
( ( cS @ X1 )
!= sK0 ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f17,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: $i > $o] :
( $true
= ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) )
=> ( !! @ $i @ X1 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i @ X1 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f21,plain,
! [X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i @ X1 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(sigma_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) )
@ ( sK1 @ X1 ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ( X1 @ ( sK1 @ X1 ) )
=> ( X1 @ ( cS @ ( sK1 @ X1 ) ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( sK1 @ X1 ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f86,plain,
! [X0: $i] :
( ( ( cS
@ ( sK1
@ ^ [Y0: $i] : ( Y0 != X0 ) ) )
= X0 )
| ( $false
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ c0 ) ) ),
inference(leibniz_equality_elimination,[],[f24]) ).
thf(f169,plain,
! [X0: $i] :
( ( ( cS
@ ( sK1
@ ^ [Y0: $i] : ( Y0 != X0 ) ) )
= X0 )
| ( $false
= ( c0 != X0 ) ) ),
inference(beta-eta_normalization,[],[f86]) ).
thf(f170,plain,
! [X0: $i] :
( ( ( cS
@ ( sK1
@ ^ [Y0: $i] : ( Y0 != X0 ) ) )
= X0 )
| ( $true
= ( c0 = X0 ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X0: $i] :
( ( ( cS
@ ( sK1
@ ^ [Y0: $i] : ( Y0 != X0 ) ) )
= X0 )
| ( c0 = X0 ) ),
inference(equality_proxy_clausification,[],[f170]) ).
thf(f293,plain,
! [X0: $i] :
( ( sK0 != X0 )
| ( c0 = X0 ) ),
inference(constrained_superposition,[],[f13,f171]) ).
thf(f303,plain,
c0 = sK0,
inference(equality_resolution,[],[f293]) ).
thf(f305,plain,
c0 != c0,
inference(constrained_superposition,[],[f12,f303]) ).
thf(f306,plain,
$false,
inference(trivial_inequality_removal,[],[f305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM812^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n019.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:01:33 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (723188)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (723199)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2879004296:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (723194)% WARNING: option uhcvi not known.
% 0.09/0.25 % (723199) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-723188-723199"...
% 0.09/0.25 % (723199)...printing done.
% 0.09/0.25 % (723199)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (723199)------------------------------
% 0.09/0.25 % (723199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (723199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (723199)CaDiCaL version: 2.1.3
% 0.09/0.25 % (723199)Termination reason: Refutation
% 0.09/0.25 % (723199)Time elapsed: 0.004 s
% 0.09/0.25 % (723199)Peak memory usage: 12 MB
% 0.09/0.25 % (723199)Instructions burned: 12 (million)
% 0.09/0.25 % (723188)Success in time 0.032 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------