%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU663^2 : 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 : n013.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 08:30:35 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 174 ( 54 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 180 ( 26 ~; 17 |; 19 &; 98 @)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 32 !; 16 ?; 48 :)
% 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,
ksnd: $i > $i ).
thf(func_def_3,type,
ksndpairEq: $o ).
thf(func_def_5,type,
cartprodmempaircEq: $o ).
thf(f1,axiom,
! [X0: $i,X1: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
= ksndpairEq ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(f3,conjecture,
( ksndpairEq
=> ( cartprodmempaircEq
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(f4,negated_conjecture,
~ ( ksndpairEq
=> ( cartprodmempaircEq
=> ! [X2: $i,X1: $i,X0: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( ksndpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( ksnd @ ( kpair @ X0 @ X3 ) )
= X3 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( ksndpairEq = $true )
=> ( ( cartprodmempaircEq = $true )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
=> ( ( ksnd @ ( kpair @ X0 @ X3 ) )
= X3 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
( ( ksndpairEq = $true )
<=> ! [X1: $i,X0: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ),
inference(fool_elimination,[],[f1]) ).
thf(f11,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ? [X3: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X3 ) )
!= X3 )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( cartprodmempaircEq = $true )
& ( ksndpairEq = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
( ( ksndpairEq = $true )
& ( cartprodmempaircEq = $true )
& ? [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ? [X3: $i] :
( ( ( ksnd @ ( kpair @ X0 @ X3 ) )
!= X3 )
& ( ( in @ X3 @ X1 )
= $true ) ) ) ),
inference(flattening,[],[f11]) ).
thf(f16,plain,
( ( ksndpairEq = $true )
& ( cartprodmempaircEq = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
& ? [X3: $i] :
( ( ( ksnd @ ( kpair @ X1 @ X3 ) )
!= X3 )
& ( $true
= ( in @ X3 @ X2 ) ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f17,plain,
( ( ksndpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( $true
= ( in @ sK5 @ sK4 ) )
& ( ( ksnd @ ( kpair @ sK5 @ sK7 ) )
!= sK7 )
& ( $true
= ( in @ sK7 @ sK6 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f16]) ).
thf(f18,plain,
( ( ( ksndpairEq = $true )
| ? [X1: $i,X0: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 ) )
& ( ! [X1: $i,X0: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( ksndpairEq != $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f19,plain,
( ( ( ksndpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X1 @ X0 ) )
!= X0 ) )
& ( ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
= X2 )
| ( ksndpairEq != $true ) ) ),
inference(rectify,[],[f18]) ).
thf(f20,plain,
( ( ( ksndpairEq = $true )
| ( sK8
!= ( ksnd @ ( kpair @ sK9 @ sK8 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
= X2 )
| ( ksndpairEq != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f19]) ).
thf(f26,plain,
( ( ksnd @ ( kpair @ sK5 @ sK7 ) )
!= sK7 ),
inference(cnf_transformation,[],[f17]) ).
thf(f29,plain,
ksndpairEq = $true,
inference(cnf_transformation,[],[f17]) ).
thf(f30,plain,
! [X2: $i,X3: $i] :
( ( ksndpairEq != $true )
| ( ( ksnd @ ( kpair @ X3 @ X2 ) )
= X2 ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f40,definition,
( spl10_2
<=> ( ( ksnd @ ( kpair @ sK5 @ sK7 ) )
= sK7 ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f42,plain,
( ( ( ksnd @ ( kpair @ sK5 @ sK7 ) )
!= sK7 )
| spl10_2 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
~ spl10_2,
inference(avatar_split_clause,[],[f26,f40]) ).
thf(f45,definition,
( spl10_3
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
= X2 ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f46,plain,
( ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X3 @ X2 ) )
= X2 )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,definition,
( spl10_4
<=> ( ksndpairEq = $true ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f51,plain,
( spl10_3
| ~ spl10_4 ),
inference(avatar_split_clause,[],[f30,f48,f45]) ).
thf(f52,plain,
spl10_4,
inference(avatar_split_clause,[],[f29,f48]) ).
thf(f80,plain,
( ( sK7 != sK7 )
| spl10_2
| ~ spl10_3 ),
inference(superposition,[],[f42,f46]) ).
thf(f81,plain,
( $false
| spl10_2
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f82,plain,
( spl10_2
| ~ spl10_3 ),
inference(avatar_contradiction_clause,[],[f81]) ).
cnf(s2,plain,
~ spl10_2,
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl10_3
| ~ spl10_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
spl10_4,
inference(sat_conversion,[],[f52]) ).
cnf(s11,plain,
( spl10_2
| ~ spl10_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s12,plain,
spl10_3,
inference(rat,[],[s3,s4]) ).
cnf(s13,plain,
spl10_2,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s13]) ).
thf(f83,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU663^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.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 14:03:36 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.22/0.27 % (2169109)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (2169117)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=3940079163: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)
% 0.22/0.27 % (2169117) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2169109-2169117"...
% 0.22/0.27 % (2169117)...printing done.
% 0.22/0.27 % (2169117)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (2169117)------------------------------
% 0.22/0.27 % (2169117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (2169117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (2169117)CaDiCaL version: 2.1.3
% 0.22/0.27 % (2169117)Termination reason: Refutation
% 0.22/0.27 % (2169117)Time elapsed: 0.002 s
% 0.22/0.27 % (2169117)Peak memory usage: 13 MB
% 0.22/0.27 % (2169117)Instructions burned: 3 (million)
% 0.22/0.27 % (2169109)Success in time 0.026 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------