%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU771^2 : 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 : 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 08:33:21 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 126 ( 29 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 252 ( 9 ~; 0 |; 2 &; 222 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 16 usr; 5 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 105 ( 77 ^; 26 !; 2 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subset: $i > $i > $o ).
thf(func_def_1,type,
cartprod: $i > $i > $i ).
thf(func_def_2,type,
breln: $i > $i > $i > $o ).
thf(func_def_4,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_5,type,
setOfPairsIsBReln: $o ).
thf(func_def_6,type,
breln1: $i > $i > $o ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_12,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK1: $i > $i > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
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,
( setOfPairsIsBReln
= ( ! [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(f3,axiom,
( breln1
= ( ^ [X0: $i,X1: $i] : ( breln @ X0 @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).
thf(f4,conjecture,
( setOfPairsIsBReln
=> ! [X0: $i,X1: $i > $i > $o] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( X1 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
thf(f5,negated_conjecture,
~ ( setOfPairsIsBReln
=> ! [X0: $i,X1: $i > $i > $o] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( X1 @ X2 @ X3 ) ) ) ),
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,
( setOfPairsIsBReln
= ( ! [X0: $i,X1: $i,X2: $i > $i > $o] :
( breln @ X0 @ X1
@ ( dpsetconstr @ X0 @ X1
@ ^ [X3: $i,X4: $i] : ( X2 @ X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
( setOfPairsIsBReln
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( breln @ Y2 @ Y1
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f10,plain,
~ ( setOfPairsIsBReln
=> ! [X0: $i,X1: $i > $i > $o] :
( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [X2: $i,X3: $i] : ( X1 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f11,plain,
~ ( ( setOfPairsIsBReln = $true )
=> ! [X0: $i,X1: $i > $i > $o] :
( $true
= ( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
( ? [X0: $i,X1: $i > $i > $o] :
( $true
!= ( breln1 @ X0
@ ( dpsetconstr @ X0 @ X0
@ ^ [Y0: $i,Y1: $i] : ( X1 @ Y0 @ Y1 ) ) ) )
& ( setOfPairsIsBReln = $true ) ),
inference(ennf_transformation,[],[f11]) ).
thf(f13,plain,
( ( $true
!= ( breln1 @ sK0
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) )
& ( setOfPairsIsBReln = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f14,plain,
( breln
= ( ^ [Y0: $i,Y1: $i,Y2: $i] : ( subset @ Y2 @ ( cartprod @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
( setOfPairsIsBReln
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( breln @ Y2 @ Y1
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] : ( breln @ Y0 @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
setOfPairsIsBReln = $true,
inference(cnf_transformation,[],[f13]) ).
thf(f18,plain,
( $true
!= ( breln1 @ sK0
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f21,plain,
( breln1
= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f16,f14]) ).
thf(f22,plain,
( $true
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y2
@ Y1
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f15,f17,f14]) ).
thf(f23,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( ^ [Y2: $i,Y3: $i,Y4: $i] : ( subset @ Y4 @ ( cartprod @ Y2 @ Y3 ) )
@ Y0
@ Y0
@ Y1 )
@ sK0
@ ( dpsetconstr @ sK0 @ sK0
@ ^ [Y0: $i,Y1: $i] : ( sK1 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f18,f21]) ).
thf(f24,plain,
( $true
!= ( subset @ ( dpsetconstr @ sK0 @ sK0 @ sK1 ) @ ( cartprod @ sK0 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ^ [Y3: $i,Y4: $i,Y5: $i] : ( subset @ Y5 @ ( cartprod @ Y3 @ Y4 ) )
@ Y2
@ Y1
@ ( dpsetconstr @ Y2 @ Y1
@ ^ [Y3: $i,Y4: $i] : ( Y0 @ Y3 @ Y4 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f26,plain,
! [X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ Y0 @ X1 ) @ ( cartprod @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( subset @ ( dpsetconstr @ Y1 @ Y0 @ X1 ) @ ( cartprod @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ X2 @ X1 ) @ ( cartprod @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i] : ( subset @ ( dpsetconstr @ Y0 @ X2 @ X1 ) @ ( cartprod @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f28]) ).
thf(f30,plain,
! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( subset @ ( dpsetconstr @ X3 @ X2 @ X1 ) @ ( cartprod @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
$true != $true,
inference(constrained_superposition,[],[f24,f30]) ).
thf(f32,plain,
$false,
inference(trivial_inequality_removal,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU771^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n004.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:24:07 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.22/0.28 % (1360923)Will run a generic schedule for satisfiability detection.
% 0.22/0.28 % (1360930)% WARNING: option uhcvi not known.
% 0.22/0.28 % (1360932)dis+10_1_sil=32000:sp=arity:random_seed=3574488158:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.28 % (1360931)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2262988903:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.28 % (1360930)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=786129632:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.28 % (1360929)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3959783492_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.28 % (1360930)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.28 % (1360932) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1360923-1360932"...
% 0.22/0.28 % (1360930)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.28 % Exception at run slice level
% 0.22/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.28 % (1360931) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1360923-1360931"...
% 0.22/0.28 % (1360930) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1360923-1360930"...
% 0.22/0.28 % (1360932)...printing done.
% 0.22/0.28 % (1360932)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (1360932)------------------------------
% 0.22/0.28 % (1360932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (1360932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (1360932)CaDiCaL version: 2.1.3
% 0.22/0.28 % (1360932)Termination reason: Refutation
% 0.22/0.28 % (1360932)Time elapsed: 0.003 s
% 0.22/0.28 % (1360932)Peak memory usage: 12 MB
% 0.22/0.28 % (1360932)Instructions burned: 4 (million)
% 0.22/0.28 % (1360923)Success in time 0.033 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------