%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV043^5 : 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 : 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 08:37:32 AM UTC 2026
% Result : Theorem 0.29s 0.28s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 53 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 226 ( 28 ~; 20 |; 20 &; 142 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 59 !; 9 ?; 68 :)
% 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(func_def_5,type,
sK2: a ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X1: a,X3: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM510_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X1: a,X3: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
=> ! [X2: a,X1: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X1 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > $o] :
( ( ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) )
& ! [X3: a,X4: a,X5: a] :
( ( ( X0 @ X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X0 @ X3 @ X4 ) ) )
=> ! [X6: a,X7: a] :
( ( X0 @ X7 @ X6 )
=> ( X0 @ X7 @ X7 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > a > $o] :
( ( ! [X2: a,X1: a] :
( ( ( X0 @ X1 @ X2 )
= $true )
=> ( ( X0 @ X2 @ X1 )
= $true ) )
& ! [X3: a,X4: a,X5: a] :
( ( ( $true
= ( X0 @ X5 @ X4 ) )
& ( $true
= ( X0 @ X3 @ X5 ) ) )
=> ( $true
= ( X0 @ X3 @ X4 ) ) ) )
=> ! [X7: a,X6: a] :
( ( $true
= ( X0 @ X7 @ X6 ) )
=> ( $true
= ( X0 @ X7 @ X7 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > a > $o] :
( ? [X7: a,X6: a] :
( ( $true
= ( X0 @ X7 @ X6 ) )
& ( $true
!= ( X0 @ X7 @ X7 ) ) )
& ! [X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
!= $true )
| ( ( X0 @ X2 @ X1 )
= $true ) )
& ! [X3: a,X4: a,X5: a] :
( ( $true
= ( X0 @ X3 @ X4 ) )
| ( $true
!= ( X0 @ X5 @ X4 ) )
| ( $true
!= ( X0 @ X3 @ X5 ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > a > $o] :
( ! [X3: a,X4: a,X5: a] :
( ( $true
= ( X0 @ X3 @ X4 ) )
| ( $true
!= ( X0 @ X5 @ X4 ) )
| ( $true
!= ( X0 @ X3 @ X5 ) ) )
& ! [X1: a,X2: a] :
( ( ( X0 @ X1 @ X2 )
!= $true )
| ( ( X0 @ X2 @ X1 )
= $true ) )
& ? [X7: a,X6: a] :
( ( $true
= ( X0 @ X7 @ X6 ) )
& ( $true
!= ( X0 @ X7 @ X7 ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( ( X0 @ X1 @ X2 )
= $true )
| ( ( X0 @ X3 @ X2 )
!= $true )
| ( ( X0 @ X1 @ X3 )
!= $true ) )
& ! [X4: a,X5: a] :
( ( $true
!= ( X0 @ X4 @ X5 ) )
| ( $true
= ( X0 @ X5 @ X4 ) ) )
& ? [X6: a,X7: a] :
( ( ( X0 @ X6 @ X7 )
= $true )
& ( $true
!= ( X0 @ X6 @ X6 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X1: a,X2: a,X3: a] :
( ( ( sK0 @ X1 @ X2 )
= $true )
| ( $true
!= ( sK0 @ X3 @ X2 ) )
| ( ( sK0 @ X1 @ X3 )
!= $true ) )
& ! [X4: a,X5: a] :
( ( ( sK0 @ X4 @ X5 )
!= $true )
| ( $true
= ( sK0 @ X5 @ X4 ) ) )
& ( $true
= ( sK0 @ sK1 @ sK2 ) )
& ( $true
!= ( sK0 @ sK1 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X6,sK1),skolemize(X7,sK2)],[f7]) ).
thf(f9,plain,
( $true
!= ( sK0 @ sK1 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X4: a,X5: a] :
( ( ( sK0 @ X4 @ X5 )
!= $true )
| ( $true
= ( sK0 @ X5 @ X4 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
! [X2: a,X3: a,X1: a] :
( ( $true
!= ( sK0 @ X3 @ X2 ) )
| ( ( sK0 @ X1 @ X3 )
!= $true )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f11,f10]) ).
thf(f16,plain,
( $true
= ( sK0 @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f15]) ).
thf(f20,plain,
! [X0: a] :
( ( ( sK0 @ X0 @ sK2 )
!= $true )
| ( $true != $true )
| ( $true
= ( sK0 @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f12,f16]) ).
thf(f21,plain,
! [X0: a] :
( ( ( sK0 @ X0 @ sK2 )
!= $true )
| ( $true
= ( sK0 @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f26,plain,
( ( $true
= ( sK0 @ sK1 @ sK1 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f21,f10]) ).
thf(f29,plain,
( $true
= ( sK0 @ sK1 @ sK1 ) ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f30,plain,
$false,
inference(forward_subsumption_resolution,[],[f29,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV043^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.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 15:04:45 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 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
% 0.29/0.28 % (2780465)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.29/0.28 % (2780470)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4149818628:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.29/0.28 % (2780470) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2780465-2780470"...
% 0.29/0.28 % (2780470)...printing done.
% 0.29/0.28 % (2780470)Refutation found. Thanks to Tanya!
% 0.29/0.28 % SZS status Theorem for theBenchmark
% 0.29/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/0.28 % (2780470)------------------------------
% 0.29/0.28 % (2780470)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.29/0.28 % (2780470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/0.28 % (2780470)CaDiCaL version: 2.1.3
% 0.29/0.28 % (2780470)Termination reason: Refutation
% 0.29/0.28 % (2780470)Time elapsed: 0.002 s
% 0.29/0.28 % (2780470)Peak memory usage: 12 MB
% 0.29/0.28 % (2780470)Instructions burned: 3 (million)
% 0.29/0.28 % (2780465)Success in time 0.028 s
% 0.29/0.28 % Vampire exiting
%------------------------------------------------------------------------------