%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU667^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:30:37 AM UTC 2026
% Result : Theorem 0.14s 0.28s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 193 ( 51 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 418 ( 18 ~; 8 |; 33 &; 340 @)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 50 ( 50 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 8 con; 0-4 aty)
% ( 0 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 156 ( 98 ^; 42 !; 16 ?; 156 :)
% 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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_17,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
sK1: $i > $i > $o ).
thf(func_def_24,type,
sK4: $i > $i > $o ).
thf(func_def_26,type,
vNOT: $o > $o ).
thf(f1,axiom,
( breln
= ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(f2,axiom,
( dpsetconstr
= ( ^ [X0: $i,X1: $i,X2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ X0 @ X1 )
@ ^ [X3: $i] :
? [X4: $i] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( in @ X5 @ X1 )
& ( X3
= ( kpair @ X4 @ X5 ) )
& ( X2 @ X4 @ X5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstr) ).
thf(f3,axiom,
( dpsetconstrSub
= ( ! [X0: $i,X2: $i > $i > $o,X1: $i] :
( subset
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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] :
( ( in @ X4 @ X0 )
& ? [X5: $i] :
( ( in @ X5 @ X1 )
& ( X3
= ( kpair @ X4 @ X5 ) )
& ( X2 @ X4 @ X5 ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( dpsetconstrSub
= ( ! [X0: $i,X1: $i > $i > $o,X2: $i] :
( subset
@ ( dpsetconstr @ X0 @ X2
@ ^ [X3: $i,X4: $i] : ( X1 @ X3 @ X4 ) )
@ ( cartprod @ X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f10,plain,
( ( dpsetconstrSub = $true )
<=> ! [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) )
@ ( cartprod @ X0 @ X2 ) )
= $true ) ),
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 )
=> ! [X1: $i,X0: $i,X2: $i > $i > $o] :
( ( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
( ( dpsetconstrSub = $true )
& ? [X1: $i,X2: $i > $i > $o,X0: $i] :
( ( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [Y0: $i,Y1: $i] : ( X2 @ Y0 @ Y1 ) ) )
!= $true ) ),
inference(ennf_transformation,[],[f12]) ).
thf(f14,plain,
( ( ( dpsetconstrSub = $true )
| ? [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) )
@ ( cartprod @ X0 @ X2 ) )
!= $true ) )
& ( ! [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) )
@ ( cartprod @ X0 @ X2 ) )
= $true )
| ( dpsetconstrSub != $true ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f15,plain,
( ( ( dpsetconstrSub = $true )
| ? [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( subset
@ ( dpsetconstr @ X0 @ X2
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) )
@ ( cartprod @ X0 @ X2 ) )
!= $true ) )
& ( ! [X3: $i,X4: $i > $i > $o,X5: $i] :
( ( subset
@ ( dpsetconstr @ X3 @ X5
@ ^ [Y0: $i,Y1: $i] : ( X4 @ Y0 @ Y1 ) )
@ ( cartprod @ X3 @ X5 ) )
= $true )
| ( dpsetconstrSub != $true ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ( dpsetconstrSub = $true )
| ( ( subset
@ ( dpsetconstr @ sK0 @ sK2
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) )
@ ( cartprod @ sK0 @ sK2 ) )
!= $true ) )
& ( ! [X3: $i,X4: $i > $i > $o,X5: $i] :
( ( subset
@ ( dpsetconstr @ X3 @ X5
@ ^ [Y0: $i,Y1: $i] : ( X4 @ Y0 @ Y1 ) )
@ ( cartprod @ X3 @ X5 ) )
= $true )
| ( dpsetconstrSub != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
thf(f17,plain,
( ( dpsetconstrSub = $true )
& ? [X0: $i,X1: $i > $i > $o,X2: $i] :
( ( breln @ X2 @ X0
@ ( dpsetconstr @ X2 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) )
!= $true ) ),
inference(rectify,[],[f13]) ).
thf(f18,plain,
( ( dpsetconstrSub = $true )
& ( $true
!= ( breln @ sK5 @ sK3
@ ( dpsetconstr @ sK5 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ Y1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f17]) ).
thf(f19,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f20,plain,
! [X3: $i,X4: $i > $i > $o,X5: $i] :
( ( ( subset
@ ( dpsetconstr @ X3 @ X5
@ ^ [Y0: $i,Y1: $i] : ( X4 @ Y0 @ Y1 ) )
@ ( cartprod @ X3 @ X5 ) )
= $true )
| ( dpsetconstrSub != $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( $true
!= ( breln @ sK5 @ sK3
@ ( dpsetconstr @ sK5 @ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f23,plain,
dpsetconstrSub = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f24,plain,
( dpsetconstr
= ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 ) ) )
& ( in @ Y4 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f28,plain,
! [X3: $i,X4: $i > $i > $o,X5: $i] :
( ( $true != $true )
| ( ( subset
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ X3
@ X5
@ ^ [Y0: $i,Y1: $i] : ( X4 @ Y0 @ Y1 ) )
@ ( cartprod @ X3 @ X5 ) )
= $true ) ),
inference(definition_unfolding,[],[f20,f24,f23]) ).
thf(f29,plain,
( ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) )
@ sK5
@ sK3
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ sK5
@ sK3
@ ^ [Y0: $i,Y1: $i] : ( sK4 @ Y0 @ Y1 ) ) )
!= $true ),
inference(definition_unfolding,[],[f22,f19,f24]) ).
thf(f30,plain,
( ( subset
@ ( dsetconstr @ ( cartprod @ sK5 @ sK3 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK4 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 )
& ( in @ Y2 @ sK3 ) ) )
& ( in @ Y1 @ sK5 ) ) ) )
@ ( cartprod @ sK5 @ sK3 ) )
!= $true ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
! [X3: $i,X4: $i > $i > $o,X5: $i] :
( ( subset
@ ( ^ [Y0: $i,Y1: $i,Y2: $i > $i > $o] :
( dsetconstr @ ( cartprod @ Y0 @ Y1 )
@ ^ [Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( ?? @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
& ( ( kpair @ Y4 @ Y5 )
= Y3 )
& ( in @ Y5 @ Y1 ) ) )
& ( in @ Y4 @ Y0 ) ) ) )
@ X3
@ X5
@ ^ [Y0: $i,Y1: $i] : ( X4 @ Y0 @ Y1 ) )
@ ( cartprod @ X3 @ X5 ) )
= $true ),
inference(trivial_inequality_removal,[],[f28]) ).
thf(f32,plain,
! [X3: $i,X4: $i > $i > $o,X5: $i] :
( ( subset
@ ( dsetconstr @ ( cartprod @ X3 @ X5 )
@ ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ $i
@ ^ [Y2: $i] :
( ( X4 @ Y1 @ Y2 )
& ( ( kpair @ Y1 @ Y2 )
= Y0 )
& ( in @ Y2 @ X5 ) ) )
& ( in @ Y1 @ X3 ) ) ) )
@ ( cartprod @ X3 @ X5 ) )
= $true ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
$true != $true,
inference(backward_demodulation,[],[f30,f32]) ).
thf(f34,plain,
$false,
inference(trivial_inequality_removal,[],[f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU667^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.18 % Computer : n014.cluster.edu
% 0.14/0.18 % Model : x86_64 x86_64
% 0.14/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.18 % Memory : 8046.5625MB
% 0.14/0.18 % OS : Linux 6.8.0-71-generic
% 0.14/0.18 % CPULimit : 300
% 0.14/0.18 % WCLimit : 300
% 0.14/0.18 % DateTime : Tue Sep 29 14:06:30 UTC 2026
% 0.14/0.19 % CPUTime :
% 0.14/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.22 Running higher-order theorem proving
% 0.14/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.28 % (2713034)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.14/0.28 % (2713044)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1239321878:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.14/0.28 % (2713044) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2713034-2713044"...
% 0.14/0.28 % (2713044)...printing done.
% 0.14/0.28 % (2713045)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.14/0.28 % (2713045)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.14/0.28 % (2713044)Refutation found. Thanks to Tanya!
% 0.14/0.28 % SZS status Theorem for theBenchmark
% 0.14/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.28 % (2713044)------------------------------
% 0.14/0.28 % (2713044)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.28 % (2713044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.28 % (2713044)CaDiCaL version: 2.1.3
% 0.14/0.28 % (2713044)Termination reason: Refutation
% 0.14/0.28 % (2713044)Time elapsed: 0.002 s
% 0.14/0.28 % (2713044)Peak memory usage: 12 MB
% 0.14/0.28 % (2713044)Instructions burned: 6 (million)
% 0.14/0.28 % (2713034)Success in time 0.04 s
% 0.14/0.28 % Vampire exiting
%------------------------------------------------------------------------------