%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV014^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:37:28 AM UTC 2026
% Result : Theorem 0.26s 0.34s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 87 ( 38 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 185 ( 21 ~; 12 |; 24 &; 116 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 ^; 57 !; 6 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > a > $o ).
thf(func_def_4,type,
sK1: a ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: a] : ( X0 @ X1 @ X1 ) )
=> ! [X1: a] : ( X0 @ X1 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM513_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ( ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X3: a,X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) )
& ! [X1: a] : ( X0 @ X1 @ X1 ) )
=> ! [X1: a] : ( X0 @ X1 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a,X2: a] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) )
& ! [X3: a,X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
& ( X0 @ X5 @ X3 ) )
=> ( X0 @ X4 @ X3 ) )
& ! [X6: a] : ( X0 @ X6 @ X6 ) )
=> ! [X7: a] : ( X0 @ X7 @ X7 ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ( ! [X4: a,X5: a,X3: a] :
( ( ( $true
= ( X0 @ X5 @ X3 ) )
& ( $true
= ( X0 @ X4 @ X5 ) ) )
=> ( ( X0 @ X4 @ X3 )
= $true ) )
& ! [X6: a] :
( $true
= ( X0 @ X6 @ X6 ) )
& ! [X2: a,X1: a] :
( ( ( X0 @ X2 @ X1 )
= $true )
=> ( ( X0 @ X1 @ X2 )
= $true ) ) )
=> ! [X7: a] :
( $true
= ( X0 @ X7 @ X7 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > a > $o] :
( ? [X7: a] :
( $true
!= ( X0 @ X7 @ X7 ) )
& ! [X4: a,X5: a,X3: a] :
( ( ( X0 @ X4 @ X3 )
= $true )
| ( $true
!= ( X0 @ X5 @ X3 ) )
| ( $true
!= ( X0 @ X4 @ X5 ) ) )
& ! [X6: a] :
( $true
= ( X0 @ X6 @ X6 ) )
& ! [X2: a,X1: a] :
( ( ( X0 @ X1 @ X2 )
= $true )
| ( ( X0 @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > a > $o] :
( ! [X4: a,X3: a,X5: a] :
( ( ( X0 @ X4 @ X3 )
= $true )
| ( $true
!= ( X0 @ X4 @ X5 ) )
| ( $true
!= ( X0 @ X5 @ X3 ) ) )
& ! [X2: a,X1: a] :
( ( ( X0 @ X1 @ X2 )
= $true )
| ( ( X0 @ X2 @ X1 )
!= $true ) )
& ? [X7: a] :
( $true
!= ( X0 @ X7 @ X7 ) )
& ! [X6: a] :
( $true
= ( X0 @ X6 @ X6 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( ( X0 @ X1 @ X2 )
= $true )
| ( ( X0 @ X1 @ X3 )
!= $true )
| ( $true
!= ( X0 @ X3 @ X2 ) ) )
& ! [X4: a,X5: a] :
( ( $true
= ( X0 @ X5 @ X4 ) )
| ( $true
!= ( X0 @ X4 @ X5 ) ) )
& ? [X6: a] :
( $true
!= ( X0 @ X6 @ X6 ) )
& ! [X7: a] :
( $true
= ( X0 @ X7 @ X7 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X1: a,X2: a,X3: a] :
( ( $true
= ( sK0 @ X1 @ X2 ) )
| ( $true
!= ( sK0 @ X1 @ X3 ) )
| ( $true
!= ( sK0 @ X3 @ X2 ) ) )
& ! [X4: a,X5: a] :
( ( $true
= ( sK0 @ X5 @ X4 ) )
| ( $true
!= ( sK0 @ X4 @ X5 ) ) )
& ( $true
!= ( sK0 @ sK1 @ sK1 ) )
& ! [X7: a] :
( $true
= ( sK0 @ X7 @ X7 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X6,sK1)],[f7]) ).
thf(f9,plain,
! [X7: a] :
( $true
= ( sK0 @ X7 @ X7 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
!= ( sK0 @ sK1 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
$true != $true,
inference(constrained_superposition,[],[f10,f9]) ).
thf(f16,plain,
$false,
inference(trivial_inequality_removal,[],[f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV014^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n003.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 15:02:14 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running higher-order theorem proving
% 0.26/0.31 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
% 0.26/0.34 % (2617559)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.34 % (2617566)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3295628795:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.34 % (2617566) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2617559-2617566"...
% 0.26/0.34 % (2617566)...printing done.
% 0.26/0.34 % (2617565)lrs+10_16_si=on:nwc=1.5:random_seed=624359971:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.34 % (2617566)Refutation found. Thanks to Tanya!
% 0.26/0.34 % SZS status Theorem for theBenchmark
% 0.26/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.34 % (2617566)------------------------------
% 0.26/0.34 % (2617566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.34 % (2617566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.34 % (2617566)CaDiCaL version: 2.1.3
% 0.26/0.34 % (2617566)Termination reason: Refutation
% 0.26/0.34 % (2617566)Time elapsed: 0.002 s
% 0.26/0.34 % (2617566)Peak memory usage: 12 MB
% 0.26/0.34 % (2617566)Instructions burned: 2 (million)
% 0.26/0.34 % (2617559)Success in time 0.026 s
% 0.26/0.34 % Vampire exiting
%------------------------------------------------------------------------------