%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU667^2 : 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 : n009.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 08:32:54 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 186 ( 44 equ; 0 cnn)
% Maximal formula atoms : 2 ( 6 avg)
% Number of connectives : 485 ( 11 ~; 1 |; 41 &; 391 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 7 con; 0-4 aty)
% ( 15 !!; 22 ??; 0 @@+; 0 @@-)
% Number of variables : 161 ( 122 ^; 32 !; 7 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_2,type,
subset: $i > $i > $o ).
thf(func_def_3,type,
kpair: $i > $i > $i ).
thf(func_def_4,type,
cartprod: $i > $i > $i ).
thf(func_def_5,type,
breln: $i > $i > $i > $o ).
thf(func_def_7,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_8,type,
dpsetconstrSub: $o ).
thf(func_def_9,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_14,type,
vAND: $o > $o > $o ).
thf(func_def_15,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_18,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_23,type,
sK2: $i > $i > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_26,type,
sK3: ( $i > $i > $i ) > $i ).
thf(f1,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f2,axiom,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X3
= ( kpair @ X4 @ X5 ) )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) )
& ( in @ X4 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstr) ).
thf(f3,axiom,
( dpsetconstrSub
= ( ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(f4,conjecture,
( dpsetconstrSub
=> ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(f5,negated_conjecture,
~ ( dpsetconstrSub
=> ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f7,plain,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ? [X5: $i] :
( ( X3
= ( kpair @ X4 @ X5 ) )
& ( X2 @ X4 @ X5 )
& ( in @ X5 @ X1 ) )
& ( in @ X4 @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( dpsetconstrSub
= ( ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f10,plain,
( dpsetconstrSub
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
~ ( dpsetconstrSub
=> ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f12,plain,
~ ( ( dpsetconstrSub = $true )
=> ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( $true
= ( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ? [X0: $i,X1: $i,X2: $i > $i > $o] :
( $true
!= ( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) ) )
& ( dpsetconstrSub = $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ( $true
!= ( breln @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) )
& ( dpsetconstrSub = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13]) ).
thf(f15,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f16,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
( dpsetconstrSub
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
dpsetconstrSub = $true,
inference(cnf_transformation,[],[f14]) ).
thf(f19,plain,
( $true
!= ( breln @ sK0 @ sK1
@ ( dpsetconstr @ sK0 @ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y3 @ Y4 )
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y3 )
& ( ?? @ $i
@ ^ [Y8: $i] :
( ( in @ Y8 @ Y4 )
& ( Y5 @ Y7 @ Y8 )
& ( ( kpair @ Y7 @ Y8 )
= Y6 ) ) ) ) ) )
@ Y2
@ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f17,f18,f16]) ).
thf(f23,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK0
@ sK1
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ Y5 @ Y1 )
& ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 ) ) ) ) ) )
@ sK0
@ sK1
@ ^ [Y0: $i,Y1: $i] : ( sK2 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f19,f15,f16]) ).
thf(f24,plain,
( $true
!= ( subset
@ ( dsetconstr @ ( cartprod @ sK0 @ sK1 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ sK0 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ sK1 )
& ( sK2 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) ) )
@ ( cartprod @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( subset
@ ( ^ [Y3: $i,Y4: $i,Y5: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y3 @ Y4 )
@ ^ [Y6: $i] :
( ?? @ $i
@ ^ [Y7: $i] :
( ( in @ Y7 @ Y3 )
& ( ?? @ $i
@ ^ [Y8: $i] :
( ( in @ Y8 @ Y4 )
& ( Y5 @ Y7 @ Y8 )
& ( ( kpair @ Y7 @ Y8 )
= Y6 ) ) ) ) ) )
@ Y2
@ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) )
@ ( cartprod @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f26,plain,
! [X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y1 @ Y0 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( X1 @ Y3 @ Y4 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) )
@ ( cartprod @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y1 @ Y0 )
@ ^ [Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ Y1 )
& ( ?? @ $i
@ ^ [Y4: $i] :
( ( in @ Y4 @ Y0 )
& ( X1 @ Y3 @ Y4 )
& ( ( kpair @ Y3 @ Y4 )
= Y2 ) ) ) ) ) )
@ ( cartprod @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y0 @ X2 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
& ( X1 @ Y2 @ Y3 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) ) ) ) )
@ ( cartprod @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( subset
@ ( dsetconstr @ ( cartprod @ Y0 @ X2 )
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( ?? @ $i
@ ^ [Y3: $i] :
( ( in @ Y3 @ X2 )
& ( X1 @ Y2 @ Y3 )
& ( ( kpair @ Y2 @ Y3 )
= Y1 ) ) ) ) ) )
@ ( cartprod @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( subset
@ ( dsetconstr @ ( cartprod @ X3 @ X2 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X3 )
& ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ X2 )
& ( X1 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 ) ) ) ) ) )
@ ( cartprod @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f40,plain,
! [X0: $i > $i > $i] :
( ( $true != $true )
| ( ( ^ [Y0: $i,Y1: $i,Y2: $i] : Y1 )
!= ( ^ [Y0: $i] : X0 ) ) ),
inference(constrained_superposition,[],[f24,f30]) ).
thf(f41,plain,
! [X0: $i > $i > $i] :
( ( ^ [Y0: $i,Y1: $i,Y2: $i] : Y1 )
!= ( ^ [Y0: $i] : X0 ) ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f43,plain,
$false,
inference(equality_resolution,[],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU667^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n009.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 14:06:45 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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
% 0.21/0.27 % (4052918)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (4052927)dis+10_1_sil=32000:sp=arity:random_seed=772605592:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.27 % (4052925)% WARNING: option uhcvi not known.
% 0.21/0.27 % (4052927) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4052918-4052927"...
% 0.21/0.27 % (4052927)...printing done.
% 0.21/0.27 % (4052927)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (4052927)------------------------------
% 0.21/0.27 % (4052927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (4052927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (4052927)CaDiCaL version: 2.1.3
% 0.21/0.27 % (4052927)Termination reason: Refutation
% 0.21/0.27 % (4052927)Time elapsed: 0.003 s
% 0.21/0.27 % (4052927)Peak memory usage: 12 MB
% 0.21/0.27 % (4052927)Instructions burned: 8 (million)
% 0.21/0.27 % (4052918)Success in time 0.036 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------