%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU662^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 08:32:53 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 43 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 141 ( 8 ~; 0 |; 12 &; 97 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 19 usr; 9 con; 0-4 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 44 ( 10 ^; 26 !; 8 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
kpair: $i > $i > $i ).
thf(func_def_2,type,
kfst: $i > $i ).
thf(func_def_3,type,
kfstpairEq: $o ).
thf(func_def_5,type,
cartprodmempaircEq: $o ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vIMP: $o > $o > $o ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(f1,axiom,
( kfstpairEq
= ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(f3,conjecture,
( kfstpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(f4,negated_conjecture,
~ ( kfstpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
~ ( kfstpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f9,plain,
~ ( ( kfstpairEq = $true )
=> ( ( cartprodmempaircEq = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( kfst @ ( kpair @ X2 @ X3 ) )
!= X2 )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( cartprodmempaircEq = $true )
& ( kfstpairEq = $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f11,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( ( kfst @ ( kpair @ X2 @ X3 ) )
!= X2 )
& ( ( in @ X3 @ X1 )
= $true ) )
& ( ( in @ X2 @ X0 )
= $true ) )
& ( cartprodmempaircEq = $true )
& ( kfstpairEq = $true ) ),
inference(flattening,[],[f10]) ).
thf(f12,plain,
( ( sK2
!= ( kfst @ ( kpair @ sK2 @ sK3 ) ) )
& ( $true
= ( in @ sK3 @ sK1 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( cartprodmempaircEq = $true )
& ( kfstpairEq = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f11]) ).
thf(f13,plain,
( kfstpairEq
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f15,plain,
kfstpairEq = $true,
inference(cnf_transformation,[],[f12]) ).
thf(f19,plain,
( sK2
!= ( kfst @ ( kpair @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f22,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) ) )
= $true ),
inference(definition_unfolding,[],[f13,f15]) ).
thf(f35,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( kfst @ ( kpair @ Y1 @ Y0 ) )
= Y1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f36,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( kfst @ ( kpair @ Y0 @ X1 ) )
= Y0 ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( kfst @ ( kpair @ Y0 @ X1 ) )
= Y0 )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( kfst @ ( kpair @ X2 @ X1 ) )
= X2 ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f39,plain,
! [X2: $i,X1: $i] :
( ( kfst @ ( kpair @ X2 @ X1 ) )
= X2 ),
inference(equality_proxy_clausification,[],[f38]) ).
thf(f40,plain,
sK2 != sK2,
inference(constrained_superposition,[],[f19,f39]) ).
thf(f41,plain,
$false,
inference(trivial_inequality_removal,[],[f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU662^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n014.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 14:06:26 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.27 % (2712341)Will run a generic schedule for satisfiability detection.
% 0.21/0.27 % (2712346)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1773189035_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.27 % Exception at run slice level
% 0.21/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.27 % (2712347)% WARNING: option uhcvi not known.
% 0.21/0.27 % (2712349)dis+10_1_sil=32000:sp=arity:random_seed=3100233070:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.27 % (2712347)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1862091950:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.27 % (2712348)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3110205887:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.27 % (2712350)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3638339974:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.27 % (2712352)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1169191884:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.27 % (2712351)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1784085020:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.27 % (2712347)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.27 % (2712350)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.27 % (2712347)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.27 % (2712349) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2712341-2712349"...
% 0.21/0.27 % (2712347) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2712341-2712347"...
% 0.21/0.27 % (2712350) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2712341-2712350"...
% 0.21/0.27 % (2712348) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2712341-2712348"...
% 0.21/0.27 % (2712352) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2712341-2712352"...
% 0.21/0.27 % (2712351) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2712341-2712351"...
% 0.21/0.27 % (2712349)...printing done.
% 0.21/0.27 % (2712347)...printing done.
% 0.21/0.27 % (2712354)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=471383676:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.27 % (2712350)...printing done.
% 0.21/0.27 % (2712348)...printing done.
% 0.21/0.27 % (2712352)...printing done.
% 0.21/0.27 % (2712351)...printing done.
% 0.21/0.27 % (2712349)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (2712349)------------------------------
% 0.21/0.27 % (2712349)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (2712349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (2712349)CaDiCaL version: 2.1.3
% 0.21/0.27 % (2712349)Termination reason: Refutation
% 0.21/0.27 % (2712349)Time elapsed: 0.003 s
% 0.21/0.27 % (2712349)Peak memory usage: 12 MB
% 0.21/0.27 % (2712349)Instructions burned: 3 (million)
% 0.21/0.27 % (2712341)Success in time 0.034 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------