%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV230^5 : 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 : 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 08:38:04 AM UTC 2026
% Result : Theorem 0.26s 0.37s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 130 ( 51 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 153 ( 24 ~; 17 |; 12 &; 72 @)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 ^; 46 !; 10 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: ( a > $o ) > $o ).
thf(func_def_6,type,
sK3: a > $o ).
thf(func_def_7,type,
sK4: a ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: ( a > $o ) > $o] :
( ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X0 @ X4 ) ) )
=> ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM88_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) )
=> ! [X2: ( a > $o ) > $o] :
( ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X0 @ X4 ) ) )
=> ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X3 @ X4 )
=> ( X1 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o] :
( ! [X2: a] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) )
=> ! [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X4 @ X5 )
=> ( X1 @ X5 ) ) )
=> ! [X6: a > $o] :
( ( X3 @ X6 )
=> ! [X7: a] :
( ( X6 @ X7 )
=> ( X0 @ X7 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X1: a > $o,X0: a > $o] :
( ! [X2: a] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) )
=> ! [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ( $true
= ( X3 @ X4 ) )
=> ! [X5: a] :
( ( $true
= ( X4 @ X5 ) )
=> ( ( X1 @ X5 )
= $true ) ) )
=> ! [X6: a > $o] :
( ( ( X3 @ X6 )
= $true )
=> ! [X7: a] :
( ( $true
= ( X6 @ X7 ) )
=> ( $true
= ( X0 @ X7 ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o,X1: a > $o] :
( ? [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ! [X5: a] :
( ( ( X1 @ X5 )
= $true )
| ( $true
!= ( X4 @ X5 ) ) )
| ( $true
!= ( X3 @ X4 ) ) )
& ? [X6: a > $o] :
( ? [X7: a] :
( ( $true
= ( X6 @ X7 ) )
& ( $true
!= ( X0 @ X7 ) ) )
& ( ( X3 @ X6 )
= $true ) ) )
& ! [X2: a] :
( ( ( X0 @ X2 )
= $true )
| ( ( X1 @ X2 )
!= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o] :
( ? [X2: ( a > $o ) > $o] :
( ! [X3: a > $o] :
( ! [X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( ( X3 @ X4 )
!= $true ) )
| ( ( X2 @ X3 )
!= $true ) )
& ? [X5: a > $o] :
( ? [X6: a] :
( ( ( X5 @ X6 )
= $true )
& ( $true
!= ( X0 @ X6 ) ) )
& ( $true
= ( X2 @ X5 ) ) ) )
& ! [X7: a] :
( ( $true
= ( X0 @ X7 ) )
| ( $true
!= ( X1 @ X7 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X3: a > $o] :
( ! [X4: a] :
( ( $true
= ( sK1 @ X4 ) )
| ( ( X3 @ X4 )
!= $true ) )
| ( $true
!= ( sK2 @ X3 ) ) )
& ( ( sK3 @ sK4 )
= $true )
& ( $true
!= ( sK0 @ sK4 ) )
& ( $true
= ( sK2 @ sK3 ) )
& ! [X7: a] :
( ( ( sK0 @ X7 )
= $true )
| ( $true
!= ( sK1 @ X7 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3),skolemize(X6,sK4)],[f6]) ).
thf(f8,plain,
! [X7: a] :
( ( $true
!= ( sK1 @ X7 ) )
| ( ( sK0 @ X7 )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( $true
= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( $true
!= ( sK0 @ sK4 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( sK3 @ sK4 )
= $true ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
! [X3: a > $o,X4: a] :
( ( $true
!= ( sK2 @ X3 ) )
| ( ( X3 @ X4 )
!= $true )
| ( $true
= ( sK1 @ X4 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
! [X0: a] :
( ( ( sK3 @ X0 )
!= $true )
| ( ( sK1 @ X0 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f12,f9]) ).
thf(f16,plain,
! [X0: a] :
( ( ( sK3 @ X0 )
!= $true )
| ( ( sK1 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f15]) ).
thf(f17,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK4 ) ) ),
inference(constrained_superposition,[],[f16,f11]) ).
thf(f18,plain,
( $true
= ( sK1 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f17]) ).
thf(f19,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f8,f18]) ).
thf(f20,plain,
( $true
= ( sK0 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f19]) ).
thf(f21,plain,
$false,
inference(forward_subsumption_resolution,[],[f20,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEV230^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n018.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 15:25:26 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running higher-order theorem proving
% 0.26/0.33 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
% 0.26/0.37 % (221923)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.37 % (221928)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=659252653:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.37 % (221928) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-221923-221928"...
% 0.26/0.37 % (221928)...printing done.
% 0.26/0.37 % (221928)Refutation found. Thanks to Tanya!
% 0.26/0.37 % SZS status Theorem for theBenchmark
% 0.26/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.37 % (221928)------------------------------
% 0.26/0.37 % (221928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.37 % (221928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.37 % (221928)CaDiCaL version: 2.1.3
% 0.26/0.37 % (221928)Termination reason: Refutation
% 0.26/0.37 % (221928)Time elapsed: 0.002 s
% 0.26/0.37 % (221928)Peak memory usage: 12 MB
% 0.26/0.37 % (221928)Instructions burned: 2 (million)
% 0.26/0.37 % (221923)Success in time 0.026 s
% 0.26/0.37 % Vampire exiting
%------------------------------------------------------------------------------