%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU778^2 : 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 : n017.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 08:31:18 AM UTC 2026
% Result : Theorem 0.19s 0.29s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 31 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 166 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 334 ( 8 ~; 0 |; 18 &; 284 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 24 usr; 8 con; 0-4 aty)
% ( 8 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 115 ( 88 ^; 22 !; 5 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
subset: $i > $i > $o ).
thf(func_def_2,type,
kpair: $i > $i > $i ).
thf(func_def_3,type,
cartprod: $i > $i > $i ).
thf(func_def_4,type,
breln: $i > $i > $i > $o ).
thf(func_def_6,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_7,type,
breln1: $i > $i > $o ).
thf(func_def_8,type,
setOfPairsIsBReln1: $o ).
thf(func_def_9,type,
breln1compset: $i > $i > $i > $i ).
thf(func_def_10,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_11,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_18,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vNOT: $o > $o ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] : ( subset @ X2 @ ( cartprod @ X0 @ X1 ) ) )
= breln ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(f2,axiom,
( ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) )
= breln1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).
thf(f3,axiom,
( setOfPairsIsBReln1
= ( ! [X1: $i > $i > $o,X0: $i] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( X1 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(f4,axiom,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ X5 @ X0 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 ) ) ) )
= breln1compset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compset) ).
thf(f5,conjecture,
( setOfPairsIsBReln1
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compprop) ).
thf(f6,negated_conjecture,
~ ( setOfPairsIsBReln1
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( setOfPairsIsBReln1
= ( ! [X0: $i > $i > $o,X1: $i] :
( breln1 @ X1
@ ( dpsetconstr @ X1 @ X1
@ ^ [X2: $i,X3: $i] : ( X0 @ X2 @ X3 ) ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f8,plain,
( setOfPairsIsBReln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( breln1 @ Y0
@ ( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f10,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f11,plain,
( ( ^ [X0: $i,X1: $i,X2: $i] :
( dpsetconstr @ X0 @ X0
@ ^ [X3: $i,X4: $i] :
? [X5: $i] :
( ( in @ ( kpair @ X5 @ X4 ) @ X2 )
& ( in @ X5 @ X0 )
& ( in @ ( kpair @ X3 @ X5 ) @ X1 ) ) ) )
= breln1compset ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
~ ( setOfPairsIsBReln1
=> ! [X0: $i,X1: $i] :
( ( breln1 @ X0 @ X1 )
=> ! [X2: $i] :
( ( breln1 @ X0 @ X2 )
=> ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f14,plain,
~ ( ( setOfPairsIsBReln1 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
=> ! [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
=> ( ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
= $true ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
( ? [X0: $i,X1: $i] :
( ( ( breln1 @ X0 @ X1 )
= $true )
& ? [X2: $i] :
( ( ( breln1 @ X0 @ X2 )
= $true )
& ( ( breln1 @ X0 @ ( breln1compset @ X0 @ X1 @ X2 ) )
!= $true ) ) )
& ( setOfPairsIsBReln1 = $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f16,plain,
( ( $true
= ( breln1 @ sK0 @ sK1 ) )
& ( ( breln1 @ sK0 @ sK2 )
= $true )
& ( ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK2 ) )
!= $true )
& ( setOfPairsIsBReln1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f15]) ).
thf(f17,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f10]) ).
thf(f18,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
setOfPairsIsBReln1 = $true,
inference(cnf_transformation,[],[f16]) ).
thf(f20,plain,
( ( breln1 @ sK0 @ ( breln1compset @ sK0 @ sK1 @ sK2 ) )
!= $true ),
inference(cnf_transformation,[],[f16]) ).
thf(f23,plain,
( breln1compset
= ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f24,plain,
( setOfPairsIsBReln1
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( breln1 @ Y0
@ ( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f27,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f18,f17]) ).
thf(f30,plain,
( ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ ( ^ [Y0: $i,Y1: $i,Y2: $i] :
( dpsetconstr @ Y0 @ Y0
@ ^ [Y3: $i,Y4: $i] :
( ?? @ $i
@ ^ [Y5: $i] :
( ( in @ ( kpair @ Y3 @ Y5 ) @ Y1 )
& ( in @ Y5 @ Y0 )
& ( in @ ( kpair @ Y5 @ Y4 ) @ Y2 ) ) ) )
@ sK0
@ sK1
@ sK2 ) )
!= $true ),
inference(definition_unfolding,[],[f20,f27,f23]) ).
thf(f31,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y0
@ ( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f24,f19,f27]) ).
thf(f33,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i,Y3: $i] :
( ^ [Y4: $i,Y5: $i,Y6: $i] : ( subset @ Y6 @ ( cartprod @ Y4 @ Y5 ) )
@ Y2
@ Y2
@ Y3 )
@ Y0
@ ( dpsetconstr @ Y0 @ Y0
@ ^ [Y2: $i,Y3: $i] : ( Y1 @ Y2 @ Y3 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f34,plain,
! [X1: $i] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1 @ X1 @ Y0 ) @ ( cartprod @ X1 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( ^ [Y0: $i > $i > $o] : ( subset @ ( dpsetconstr @ X1 @ X1 @ Y0 ) @ ( cartprod @ X1 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: $i > $i > $o,X1: $i] :
( ( subset @ ( dpsetconstr @ X1 @ X1 @ X2 ) @ ( cartprod @ X1 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
( ( subset
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ ( kpair @ Y0 @ Y2 ) @ sK1 )
& ( in @ Y2 @ sK0 )
& ( in @ ( kpair @ Y2 @ Y1 ) @ sK2 ) ) ) )
@ ( cartprod @ sK0 @ sK0 ) )
!= $true ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f39,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU778^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:23:22 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.19/0.29 % (409597)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.29 % (409616)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=483961417:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.29 % (409616)Refutation not found, incomplete strategy
% 0.19/0.29 % (409616)------------------------------
% 0.19/0.29 % (409616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (409616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (409616)CaDiCaL version: 2.1.3
% 0.19/0.29 % (409616)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.29 % (409616)Time elapsed: 0.001 s
% 0.19/0.29 % (409616)Peak memory usage: 12 MB
% 0.19/0.29 % (409616)Instructions burned: 3 (million)
% 0.19/0.29 % (409616)------------------------------
% 0.19/0.29 % (409616)------------------------------
% 0.19/0.29 % (409620)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.29 % (409620)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
% 0.19/0.29 % (409614)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3498796655:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.29 % (409615)lrs+10_16_si=on:nwc=1.5:random_seed=1097207010:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.29 % (409619)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3110940582:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.29 % (409617)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=1169049383: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)
% 0.19/0.29 % (409620)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=614095796:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.29 % (409618)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3523107567:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.29 % (409615) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-409597-409615"...
% 0.19/0.29 % (409614) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-409597-409614"...
% 0.19/0.29 % (409619) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-409597-409619"...
% 0.19/0.29 % (409615)...printing done.
% 0.19/0.29 % (409614)...printing done.
% 0.19/0.29 % (409619)...printing done.
% 0.19/0.29 % (409627)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2823068905:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.19/0.29 % (409620) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-409597-409620"...
% 0.19/0.29 % (409618) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-409597-409618"...
% 0.19/0.29 % (409615)Refutation found. Thanks to Tanya!
% 0.19/0.29 % SZS status Theorem for theBenchmark
% 0.19/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.29 % (409615)------------------------------
% 0.19/0.29 % (409615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (409615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (409615)CaDiCaL version: 2.1.3
% 0.19/0.29 % (409615)Termination reason: Refutation
% 0.19/0.29 % (409615)Time elapsed: 0.004 s
% 0.19/0.29 % (409615)Peak memory usage: 12 MB
% 0.19/0.29 % (409615)Instructions burned: 5 (million)
% 0.19/0.29 % (409597)Success in time 0.047 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------