%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU650^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:32:50 AM UTC 2026
% Result : Theorem 0.10s 0.23s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 188 ( 57 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 267 ( 14 ~; 5 |; 4 &; 220 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 13 usr; 7 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 34 ( 10 ^; 22 !; 2 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
setukpairinjR11: $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,
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_14,type,
vNOT: $o > $o ).
thf(f1,axiom,
( setukpairinjR11
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X0 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(f2,conjecture,
( setukpairinjR11
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(f3,negated_conjecture,
~ ( setukpairinjR11
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setukpairinjR11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f5,plain,
~ ( setukpairinjR11
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f6,plain,
~ ( ( setukpairinjR11 = $true )
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) )
& ( X0 = X1 ) )
& ( setukpairinjR11 = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f8,plain,
( ( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) )
& ( sK0 = sK1 )
& ( setukpairinjR11 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f9,plain,
( setukpairinjR11
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f10,plain,
setukpairinjR11 = $true,
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
sK0 = sK1,
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ emptyset ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f9,f10]) ).
thf(f16,plain,
( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset ) ),
inference(definition_unfolding,[],[f12,f11,f11,f11]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( Y1 = Y0 )
=> ( ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
= ( setadjoin @ Y1 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f15]) ).
thf(f18,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ Y0 @ emptyset ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( Y0 = X1 )
=> ( ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ Y0 @ emptyset ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( X2 = X1 )
=> ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( X2 = X1 ) )
| ( $true
= ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X1: $i] :
( ( X1 != X2 )
| ( $true
= ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) ) ) ),
inference(equality_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X1: $i] :
( ( ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= ( setadjoin @ X2 @ emptyset ) )
| ( X1 != X2 ) ),
inference(equality_proxy_clausification,[],[f22]) ).
thf(f32,plain,
( ( ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ emptyset ) )
| ( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ ( setadjoin @ sK1 @ emptyset ) ) ) ),
inference(constrained_superposition,[],[f16,f23]) ).
thf(f33,plain,
( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ ( setadjoin @ sK1 @ emptyset ) ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f35,plain,
( ( ( setadjoin @ sK1 @ emptyset )
!= ( setadjoin @ sK1 @ emptyset ) )
| ( sK1 != sK1 ) ),
inference(constrained_superposition,[],[f33,f23]) ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU650^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.16 % Computer : n019.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 14:02:48 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 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
% 0.10/0.23 % (820266)Will run a generic schedule for satisfiability detection.
% 0.10/0.23 % (820276)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3525291039:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.23 % (820276) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-820266-820276"...
% 0.10/0.23 % (820276)...printing done.
% 0.10/0.23 % (820276)Refutation found. Thanks to Tanya!
% 0.10/0.23 % SZS status Theorem for theBenchmark
% 0.10/0.23 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.23 % (820276)------------------------------
% 0.10/0.23 % (820276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.23 % (820276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.23 % (820276)CaDiCaL version: 2.1.3
% 0.10/0.23 % (820276)Termination reason: Refutation
% 0.10/0.23 % (820276)Time elapsed: 0.002 s
% 0.10/0.23 % (820276)Peak memory usage: 12 MB
% 0.10/0.23 % (820276)Instructions burned: 3 (million)
% 0.10/0.23 % (820266)Success in time 0.024 s
% 0.10/0.23 % Vampire exiting
%------------------------------------------------------------------------------