%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU633^2 : 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 08:32:46 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 2
% Syntax : Number of formulae : 38 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 295 ( 73 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 424 ( 18 ~; 32 |; 8 &; 279 @)
% ( 0 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 6 con; 0-4 aty)
% ( 27 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 97 ( 31 ^; 60 !; 6 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
setunion: $i > $i ).
thf(func_def_2,type,
setunionE: $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK2: $o > $i > $i > $i ).
thf(f1,axiom,
( setunionE
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> X2 ) )
=> X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(f2,conjecture,
( setunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ? [X2: $i] :
( ( in @ X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(f3,negated_conjecture,
~ ( setunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ? [X2: $i] :
( ( in @ X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( setunionE
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ! [X2: $o] :
( ! [X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X3 @ X0 )
=> X2 ) )
=> X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( setunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( setunionE
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
=> ? [X2: $i] :
( ( in @ X1 @ X2 )
& ( in @ X2 @ X0 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( setunionE = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
= $true )
=> ? [X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X0: $i,X1: $i] :
( ! [X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ( ( in @ X1 @ ( setunion @ X0 ) )
= $true ) )
& ( setunionE = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ! [X2: $i] :
( ( $true
!= ( in @ sK1 @ X2 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) )
& ( $true
= ( in @ sK1 @ ( setunion @ sK0 ) ) )
& ( setunionE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f8]) ).
thf(f10,plain,
( setunionE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f11,plain,
setunionE = $true,
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( $true
= ( in @ sK1 @ ( setunion @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X2: $i] :
( ( $true
!= ( in @ sK1 @ X2 ) )
| ( $true
!= ( in @ X2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f10,f11]) ).
thf(f17,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
=> ( !! @ $o
@ ^ [Y2: $o] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( in @ Y0 @ Y3 )
=> ( ( in @ Y3 @ Y1 )
=> Y2 ) ) )
=> Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f16]) ).
thf(f18,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> Y1 ) ) )
=> Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
=> ( !! @ $o
@ ^ [Y1: $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( in @ X1 @ Y2 )
=> ( ( in @ Y2 @ Y0 )
=> Y1 ) ) )
=> Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setunion @ X2 ) )
=> ( !! @ $o
@ ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f21,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
= ( ^ [Y0: $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( in @ Y1 @ X2 )
=> Y0 ) ) )
=> Y0 )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f21]) ).
thf(f23,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) ) )
=> X3 ) ) ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) ) ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( in @ Y0 @ X2 )
=> X3 ) )
@ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $true = X3 ) ),
inference(sigma_proxy_clausification,[],[f24]) ).
thf(f26,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ( in @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) )
=> ( ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 )
=> X3 ) ) )
| ( $true = X3 ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 )
=> X3 ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f26]) ).
thf(f28,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( in @ X1 @ ( sK2 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f26]) ).
thf(f30,plain,
! [X2: $i,X3: $o,X1: $i] :
( ( $true
= ( in @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 ) )
| ( $false
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $true = X3 ) ),
inference(imp_proxy_clausification,[],[f27]) ).
thf(f46,plain,
( ( $true != $true )
| ( $true
!= ( in @ ( setunion @ sK0 ) @ sK0 ) ) ),
inference(constrained_superposition,[],[f13,f12]) ).
thf(f47,plain,
( $true
!= ( in @ ( setunion @ sK0 ) @ sK0 ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f52,plain,
! [X0: $o,X1: $i] :
( ( $true != $true )
| ( $true
!= ( in @ ( sK2 @ X0 @ sK1 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ sK1 @ ( setunion @ X1 ) ) )
| ( $true = X0 ) ),
inference(constrained_superposition,[],[f13,f28]) ).
thf(f53,plain,
! [X0: $o,X1: $i] :
( ( $true
!= ( in @ ( sK2 @ X0 @ sK1 @ X1 ) @ sK0 ) )
| ( $false
= ( in @ sK1 @ ( setunion @ X1 ) ) )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f63,plain,
! [X0: $o] :
( ( $true != $true )
| ( ( in @ sK1 @ ( setunion @ sK0 ) )
= $false )
| ( $true = X0 )
| ( ( in @ sK1 @ ( setunion @ sK0 ) )
= $false )
| ( $true = X0 ) ),
inference(constrained_superposition,[],[f53,f30]) ).
thf(f64,plain,
! [X0: $o] :
( ( $true != $true )
| ( ( in @ sK1 @ ( setunion @ sK0 ) )
= $false )
| ( $true = X0 ) ),
inference(duplicate_literal_removal,[],[f63]) ).
thf(f65,plain,
! [X0: $o] :
( ( ( in @ sK1 @ ( setunion @ sK0 ) )
= $false )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f67,plain,
! [X0: $o] :
( ( $true = $false )
| ( $true = X0 ) ),
inference(forward_demodulation,[],[f65,f12]) ).
thf(f68,plain,
! [X0: $o] : ( $true = X0 ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f75,plain,
$true != $true,
inference(constrained_superposition,[],[f47,f68]) ).
thf(f80,plain,
$false,
inference(trivial_inequality_removal,[],[f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU633^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:00:30 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.28 % (4046264)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (4046270)% WARNING: option uhcvi not known.
% 0.20/0.28 % (4046273)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=303818991:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (4046272)dis+10_1_sil=32000:sp=arity:random_seed=4016167326:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (4046269)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3268066831_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (4046271)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1016467704:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (4046270)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2669213231:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (4046273)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (4046270)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (4046274)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2974310023:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (4046270)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (4046275)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3904808983:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (4046274) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4046264-4046274"...
% 0.20/0.28 % (4046272) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4046264-4046272"...
% 0.20/0.28 % (4046273) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4046264-4046273"...
% 0.20/0.28 % (4046274)...printing done.
% 0.20/0.28 % (4046274)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (4046274)------------------------------
% 0.20/0.28 % (4046274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4046274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4046274)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4046274)Termination reason: Refutation
% 0.20/0.28 % (4046274)Time elapsed: 0.003 s
% 0.20/0.28 % (4046274)Peak memory usage: 12 MB
% 0.20/0.28 % (4046274)Instructions burned: 6 (million)
% 0.20/0.28 % (4046264)Success in time 0.041 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------