%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU654^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:30:32 AM UTC 2026
% Result : Theorem 0.35s 0.42s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 77 equ; 0 cnn)
% Maximal formula atoms : 3 ( 8 avg)
% Number of connectives : 563 ( 10 ~; 4 |; 6 &; 498 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 9 con; 0-4 aty)
% ( 24 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 104 ( 38 ^; 58 !; 8 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
setadjoin: $i > $i > $i ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_4,type,
setukpairinjR2: $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpair) ).
thf(f2,axiom,
( setukpairinjR2
= ( ! [X2: $i,X0: $i,X1: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) )
=> ( X1 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(f3,conjecture,
( setukpairinjR2
=> ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(f4,negated_conjecture,
~ ( setukpairinjR2
=> ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( setukpairinjR2
= ( ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f6,plain,
( setukpairinjR2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
~ ( setukpairinjR2
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
~ ( ( setukpairinjR2 = $true )
=> ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) )
=> ( X1 = X3 ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ? [X1: $i,X2: $i,X0: $i,X3: $i] :
( ( X1 != X3 )
& ( ( kpair @ X0 @ X1 )
= ( kpair @ X2 @ X3 ) ) )
& ( setukpairinjR2 = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X3 )
& ( ( kpair @ X2 @ X0 )
= ( kpair @ X1 @ X3 ) ) )
& ( setukpairinjR2 = $true ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
( ( sK3 != sK0 )
& ( ( kpair @ sK1 @ sK3 )
= ( kpair @ sK2 @ sK0 ) )
& ( setukpairinjR2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f11]) ).
thf(f13,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
setukpairinjR2 = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f15,plain,
( ( kpair @ sK1 @ sK3 )
= ( kpair @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f16,plain,
sK3 != sK0,
inference(cnf_transformation,[],[f12]) ).
thf(f17,plain,
( setukpairinjR2
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f20,plain,
( ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK1
@ sK3 )
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ sK2
@ sK0 ) ),
inference(definition_unfolding,[],[f15,f13,f13]) ).
thf(f21,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f17,f14]) ).
thf(f22,plain,
( ( setadjoin @ ( setadjoin @ sK2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK2 @ ( setadjoin @ sK0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f23,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( setadjoin @ ( setadjoin @ Y3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y3 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) )
=> ( Y1 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f24,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( setadjoin @ ( setadjoin @ Y2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y2 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
=> ( Y0 = X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( setadjoin @ ( setadjoin @ Y1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ^ [Y0: $i] :
( ( ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) )
@ X4 )
= $true ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( $true
= ( ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X4 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f32]) ).
thf(f35,plain,
! [X0: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1 @ ( setadjoin @ sK3 @ emptyset ) ) @ emptyset ) ) )
| ( sK0 = X1 ) ),
inference(constrained_superposition,[],[f33,f22]) ).
thf(f40,plain,
sK3 = sK0,
inference(equality_resolution,[],[f35]) ).
thf(f50,plain,
$false,
inference(forward_subsumption_resolution,[],[f40,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU654^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.29 % Computer : n004.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
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Sep 29 14:03:07 UTC 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.30/0.34 Running higher-order theorem proving
% 0.30/0.36 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.35/0.42 % (1335633)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.42 % (1335639)lrs+10_16_si=on:nwc=1.5:random_seed=500388513:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.35/0.42 % (1335639) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1335633-1335639"...
% 0.35/0.42 % (1335639)...printing done.
% 0.35/0.42 % (1335639)Refutation found. Thanks to Tanya!
% 0.35/0.42 % SZS status Theorem for theBenchmark
% 0.35/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.43 % (1335639)------------------------------
% 0.35/0.43 % (1335639)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.43 % (1335639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.43 % (1335639)CaDiCaL version: 2.1.3
% 0.35/0.43 % (1335639)Termination reason: Refutation
% 0.35/0.43 % (1335639)Time elapsed: 0.005 s
% 0.35/0.43 % (1335639)Peak memory usage: 12 MB
% 0.35/0.43 % (1335639)Instructions burned: 7 (million)
% 0.35/0.43 % (1335633)Success in time 0.051 s
% 0.35/0.43 % Vampire exiting
%------------------------------------------------------------------------------