%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU662^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 52 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 151 ( 16 ~; 7 |; 19 &; 92 @)
% ( 1 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 48 ( 0 ^; 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,
kfst: $i > $i ).
thf(func_def_3,type,
kfstpairEq: $o ).
thf(func_def_5,type,
cartprodmempaircEq: $o ).
thf(f1,axiom,
! [X1: $i,X0: $i] :
( ( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 )
= kfstpairEq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(f3,conjecture,
( kfstpairEq
=> ( cartprodmempaircEq
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(f4,negated_conjecture,
~ ( kfstpairEq
=> ( cartprodmempaircEq
=> ! [X2: $i,X0: $i,X1: $i] :
( ( in @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
~ ( kfstpairEq
=> ( cartprodmempaircEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ! [X3: $i] :
( ( in @ X3 @ X2 )
=> ( ( kfst @ ( kpair @ X0 @ X3 ) )
= X0 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
~ ( ( kfstpairEq = $true )
=> ( ( cartprodmempaircEq = $true )
=> ! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ! [X3: $i] :
( ( ( in @ X3 @ X2 )
= $true )
=> ( ( kfst @ ( kpair @ X0 @ X3 ) )
= X0 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f9,plain,
! [X0: $i,X1: $i] :
( ( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
= kfstpairEq ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
( ( kfstpairEq = $true )
<=> ! [X1: $i,X0: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 ) ),
inference(fool_elimination,[],[f9]) ).
thf(f12,plain,
( ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( kfst @ ( kpair @ X0 @ X3 ) )
!= X0 )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( cartprodmempaircEq = $true )
& ( kfstpairEq = $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f13,plain,
( ( cartprodmempaircEq = $true )
& ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ X1 )
= $true )
& ? [X3: $i] :
( ( ( kfst @ ( kpair @ X0 @ X3 ) )
!= X0 )
& ( ( in @ X3 @ X2 )
= $true ) ) )
& ( kfstpairEq = $true ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
( ( cartprodmempaircEq = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
= $true )
& ? [X3: $i] :
( ( ( kfst @ ( kpair @ X0 @ X3 ) )
!= X0 )
& ( ( in @ X3 @ X1 )
= $true ) ) )
& ( kfstpairEq = $true ) ),
inference(rectify,[],[f13]) ).
thf(f15,plain,
( ( cartprodmempaircEq = $true )
& ( ( in @ sK0 @ sK2 )
= $true )
& ( ( kfst @ ( kpair @ sK0 @ sK3 ) )
!= sK0 )
& ( ( in @ sK3 @ sK1 )
= $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)],[f14]) ).
thf(f16,plain,
( ( ( kfstpairEq = $true )
| ? [X1: $i,X0: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
!= X1 ) )
& ( ! [X1: $i,X0: $i] :
( ( kfst @ ( kpair @ X1 @ X0 ) )
= X1 )
| ( kfstpairEq != $true ) ) ),
inference(nnf_transformation,[],[f10]) ).
thf(f17,plain,
( ( ( kfstpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 ) )
& ( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( kfstpairEq = $true )
| ( ( kfst @ ( kpair @ sK4 @ sK5 ) )
!= sK4 ) )
& ( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f17]) ).
thf(f22,plain,
kfstpairEq = $true,
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
( ( kfst @ ( kpair @ sK0 @ sK3 ) )
!= sK0 ),
inference(cnf_transformation,[],[f15]) ).
thf(f27,plain,
! [X2: $i,X3: $i] :
( ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f37,plain,
! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ),
inference(forward_subsumption_resolution,[],[f27,f22]) ).
thf(f38,plain,
sK0 != sK0,
inference(superposition,[],[f24,f37]) ).
thf(f39,plain,
$false,
inference(trivial_inequality_removal,[],[f38]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.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 14:08:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (127507)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (127516)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3913683042:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (127516) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-127507-127516"...
% 0.21/0.29 % (127516)...printing done.
% 0.21/0.29 % (127516)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (127516)------------------------------
% 0.21/0.29 % (127516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (127516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (127516)CaDiCaL version: 2.1.3
% 0.21/0.29 % (127516)Termination reason: Refutation
% 0.21/0.29 % (127516)Time elapsed: 0.001 s
% 0.21/0.29 % (127516)Peak memory usage: 12 MB
% 0.21/0.29 % (127516)Instructions burned: 2 (million)
% 0.21/0.29 % (127507)Success in time 0.037 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------