%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU661^2 : 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 : 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 08:30:35 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 9 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 16 equ; 0 cnn)
% Maximal formula atoms : 3 ( 5 avg)
% Number of connectives : 81 ( 7 ~; 0 |; 6 &; 60 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 16 !; 8 ?; 24 :)
% 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(f1,conjecture,
! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(f2,negated_conjecture,
~ ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kpair @ X2 @ X3 )
= ( kpair @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( kpair @ X0 @ X3 )
= ( kpair @ X0 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X2 ) )
=> ( ( kpair @ X0 @ X3 )
= ( kpair @ X0 @ X3 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: $i,X2: $i,X0: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ? [X3: $i] :
( ( ( kpair @ X0 @ X3 )
!= ( kpair @ X0 @ X3 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ? [X3: $i] :
( ( ( kpair @ X2 @ X3 )
!= ( kpair @ X2 @ X3 ) )
& ( ( in @ X3 @ X1 )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( $true
= ( in @ sK2 @ sK0 ) )
& ( ( kpair @ sK2 @ sK3 )
!= ( kpair @ sK2 @ sK3 ) )
& ( $true
= ( in @ sK3 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f6]) ).
thf(f9,plain,
( ( kpair @ sK2 @ sK3 )
!= ( kpair @ sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
$false,
inference(trivial_inequality_removal,[],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU661^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % 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 13:59:54 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.28 % (389024)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (389029)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=77198012:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (389029) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-389024-389029"...
% 0.21/0.28 % (389029)...printing done.
% 0.21/0.28 % (389029)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (389029)------------------------------
% 0.21/0.28 % (389029)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (389029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (389029)CaDiCaL version: 2.1.3
% 0.21/0.28 % (389029)Termination reason: Refutation
% 0.21/0.28 % (389029)Time elapsed: 0.001 s
% 0.21/0.28 % (389029)Peak memory usage: 12 MB
% 0.21/0.28 % (389029)Instructions burned: 1 (million)
% 0.21/0.28 % (389024)Success in time 0.031 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------