%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU620^2 : 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 08:30:22 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 38 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 259 ( 15 ~; 7 |; 6 &; 226 @)
% ( 1 <=>; 4 =>; 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 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 50 ( 10 ^; 32 !; 8 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
setadjoin: $i > $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
iskpair: $i > $o ).
thf(func_def_6,type,
kpairiskpair: $o ).
thf(func_def_7,type,
kpair: $i > $i > $i ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db0:
!>[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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f2,axiom,
! [X1: $i,X0: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpairiskpair ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(f3,axiom,
( ( ^ [X0: $i,X1: $i] : ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= kpair ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(f4,conjecture,
( kpairiskpair
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(f5,negated_conjecture,
~ ( kpairiskpair
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ( kpairiskpair
=> ! [X0: $i,X1: $i] : ( iskpair @ ( kpair @ X0 @ X1 ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ( ( kpairiskpair = $true )
=> ! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
= kpairiskpair ),
inference(rectify,[],[f2]) ).
thf(f10,plain,
( ! [X1: $i,X0: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
<=> ( kpairiskpair = $true ) ),
inference(fool_elimination,[],[f9]) ).
thf(f13,plain,
( ( kpairiskpair = $true )
& ? [X1: $i,X0: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
!= $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f14,plain,
( ( ! [X1: $i,X0: $i] :
( $true
= ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
| ( kpairiskpair != $true ) )
& ( ( kpairiskpair = $true )
| ? [X1: $i,X0: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f15,plain,
( ( ! [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( kpairiskpair != $true ) )
& ( ( kpairiskpair = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( iskpair @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[],[f14]) ).
thf(f16,plain,
( ( ! [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( kpairiskpair != $true ) )
& ( ( kpairiskpair = $true )
| ( ( iskpair @ ( setadjoin @ ( setadjoin @ sK0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) @ emptyset ) ) )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0),skolemize(X3,sK1)],[f15]) ).
thf(f17,plain,
( ( kpairiskpair = $true )
& ? [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X1 @ X0 ) )
!= $true ) ),
inference(rectify,[],[f13]) ).
thf(f18,plain,
( ( kpairiskpair = $true )
& ( ( iskpair @ ( kpair @ sK3 @ sK2 ) )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f17]) ).
thf(f19,plain,
( kpair
= ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( kpairiskpair != $true ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f22,plain,
( ( iskpair @ ( kpair @ sK3 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f23,plain,
kpairiskpair = $true,
inference(cnf_transformation,[],[f18]) ).
thf(f27,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(forward_subsumption_resolution,[],[f21,f23]) ).
thf(f28,plain,
! [X1: $i] :
( ( ^ [Y0: $i,Y1: $i] : ( setadjoin @ ( setadjoin @ Y0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) @ emptyset ) )
@ X1 )
= ( kpair @ X1 ) ),
inference(argument_congruence,[],[f19]) ).
thf(f29,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) ) )
= ( kpair @ X1 ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] : ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ Y0 @ emptyset ) ) @ emptyset ) )
@ X2 )
= ( kpair @ X1 @ X2 ) ),
inference(argument_congruence,[],[f29]) ).
thf(f31,plain,
! [X2: $i,X1: $i] :
( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( kpair @ X1 @ X2 ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
= $true ),
inference(superposition,[],[f27,f31]) ).
thf(f35,plain,
$true != $true,
inference(superposition,[],[f22,f33]) ).
thf(f36,plain,
$false,
inference(trivial_inequality_removal,[],[f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU620^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:58:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.19/0.28 % (2705291)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (2705297)lrs+10_16_si=on:nwc=1.5:random_seed=943242755:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (2705302)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (2705302)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
% 0.19/0.28 % (2705297)Instruction limit reached!
% 0.19/0.28 % (2705297)------------------------------
% 0.19/0.28 % (2705297)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2705297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2705297)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2705297)Termination reason: Instruction limit
% 0.19/0.28 % (2705297)Termination phase: Saturation
% 0.19/0.28 % (2705297)Time elapsed: 0.006 s
% 0.19/0.28 % (2705297)Peak memory usage: 12 MB
% 0.19/0.28 % (2705297)Instructions burned: 19 (million)
% 0.19/0.28 % (2705296)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1355538391:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (2705301)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3996878800:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (2705300)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3634912630:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (2705299)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3260551334:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.19/0.28 % (2705298)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4256322472:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (2705302)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1318367421:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (2705298)Instruction limit reached!
% 0.19/0.28 % (2705298)------------------------------
% 0.19/0.28 % (2705298)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2705298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2705298)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2705298)Termination reason: Instruction limit
% 0.19/0.28 % (2705298)Time elapsed: 0.002 s
% 0.19/0.28 % (2705298)Peak memory usage: 12 MB
% 0.19/0.28 % (2705298)Instructions burned: 3 (million)
% 0.19/0.28 % (2705300) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2705291-2705300"...
% 0.19/0.28 % (2705299) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2705291-2705299"...
% 0.19/0.28 % (2705300)...printing done.
% 0.19/0.28 % (2705300)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (2705300)------------------------------
% 0.19/0.28 % (2705300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (2705300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (2705300)CaDiCaL version: 2.1.3
% 0.19/0.28 % (2705300)Termination reason: Refutation
% 0.19/0.28 % (2705300)Time elapsed: 0.003 s
% 0.19/0.28 % (2705300)Peak memory usage: 12 MB
% 0.19/0.28 % (2705300)Instructions burned: 5 (million)
% 0.19/0.28 % (2705291)Success in time 0.037 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------