%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU864^5 : 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 : n005.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 08:34:19 AM UTC 2026
% Result : Theorem 0.26s 0.37s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 60 equ; 2 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 115 ( 18 ~; 22 |; 10 &; 53 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 54 ( 31 ^; 21 !; 2 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
t: a ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_5,type,
vOR: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_8,type,
sK0: ( a > $o ) > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X0
@ ^ [X4: a] :
( ( X3 = X4 )
| ( X2 @ X4 ) ) ) ) )
& ( X0
@ ^ [X1: a] : $false ) )
=> ( X0
@ ^ [X1: a] : ( t = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cDOMLEMMA1_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X2: a > $o] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X0
@ ^ [X4: a] :
( ( X3 = X4 )
| ( X2 @ X4 ) ) ) ) )
& ( X0
@ ^ [X1: a] : $false ) )
=> ( X0
@ ^ [X1: a] : ( t = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ! [X2: a] :
( ( t = X2 )
=> ( X0
@ ^ [X3: a] :
( ( X2 = X3 )
| ( X1 @ X3 ) ) ) ) )
& ( X0
@ ^ [X4: a] : $false ) )
=> ( X0
@ ^ [X5: a] : ( t = X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
=> ! [X2: a] :
( ( t = X2 )
=> ( $true
= ( X0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) ) ) )
& ( ( X0
@ ^ [Y0: a] : $false )
= $true ) )
=> ( $true
= ( X0
@ ^ [Y0: a] : ( t = Y0 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: ( a > $o ) > $o] :
( ( $true
!= ( X0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( X0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) )
| ( t != X2 ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( X0
@ ^ [Y0: a] : $false )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: ( a > $o ) > $o] :
( ( $true
!= ( X0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( X0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) )
| ( t != X2 ) )
| ( ( X0 @ X1 )
!= $true ) )
& ( ( X0
@ ^ [Y0: a] : $false )
= $true ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ( $true
!= ( sK0
@ ^ [Y0: a] : ( t = Y0 ) ) )
& ! [X1: a > $o] :
( ! [X2: a] :
( ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) )
| ( t != X2 ) )
| ( $true
!= ( sK0 @ X1 ) ) )
& ( $true
= ( sK0
@ ^ [Y0: a] : $false ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
( $true
= ( sK0
@ ^ [Y0: a] : $false ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: a,X1: a > $o] :
( ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( X2 = Y0 ) ) ) )
| ( t != X2 )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( $true
!= ( sK0
@ ^ [Y0: a] : ( t = Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X1: a > $o] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( X1 @ Y0 )
| ( t = Y0 ) ) ) ) ),
inference(equality_resolution,[],[f9]) ).
thf(f14,plain,
( $true
!= ( sK0 @ ( (=) @ t ) ) ),
inference(beta-eta_normalization,[],[f10]) ).
thf(f21,plain,
( ( $true != $true )
| ( $true
= ( sK0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( t = Y0 ) ) ) ) ),
inference(constrained_superposition,[],[f13,f8]) ).
thf(f22,plain,
( $true
= ( sK0
@ ^ [Y0: a] :
( ( ^ [Y1: a] : $false
@ Y0 )
| ( t = Y0 ) ) ) ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f23,plain,
( $true
= ( sK0
@ ^ [Y0: a] :
( $false
| ( t = Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( $true
= ( sK0
@ ^ [Y0: a] : ( t = Y0 ) ) ),
inference(boolean_simplification,[],[f23]) ).
thf(f25,plain,
( $true
= ( sK0 @ ( (=) @ t ) ) ),
inference(beta-eta_normalization,[],[f24]) ).
thf(f26,plain,
$false,
inference(forward_subsumption_resolution,[],[f25,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU864^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.26 % Computer : n005.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 14:40:59 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.32 Running first-order model finding
% 0.26/0.32 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
% 0.26/0.37 % (1754793)Will run a generic schedule for satisfiability detection.
% 0.26/0.37 % (1754800)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3980374632:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.26/0.37 % (1754800) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1754793-1754800"...
% 0.26/0.37 % (1754800)...printing done.
% 0.26/0.37 % (1754800)Refutation found. Thanks to Tanya!
% 0.26/0.37 % SZS status Theorem for theBenchmark
% 0.26/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.37 % (1754800)------------------------------
% 0.26/0.37 % (1754800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.37 % (1754800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.37 % (1754800)CaDiCaL version: 2.1.3
% 0.26/0.37 % (1754800)Termination reason: Refutation
% 0.26/0.37 % (1754800)Time elapsed: 0.002 s
% 0.26/0.37 % (1754800)Peak memory usage: 12 MB
% 0.26/0.37 % (1754800)Instructions burned: 2 (million)
% 0.26/0.37 % (1754793)Success in time 0.041 s
% 0.26/0.37 % Vampire exiting
%------------------------------------------------------------------------------