%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV053^5 : 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 : 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 08:37:33 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 39 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 240 ( 23 ~; 14 |; 16 &; 179 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 0 ^; 46 !; 3 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(type_def_6,type,
a: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cF: b > b ).
thf(func_def_1,type,
cA: b > a ).
thf(func_def_2,type,
cL: a > a > $o ).
thf(func_def_6,type,
sK0: b ).
thf(f1,conjecture,
( ( ! [X3: b] : ( cL @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ! [X1: a,X0: a,X2: a] :
( ( ( cL @ X1 @ X2 )
& ( cL @ X0 @ X1 ) )
=> ( cL @ X0 @ X2 ) ) )
=> ! [X4: b] : ( cL @ ( cA @ X4 ) @ ( cA @ ( cF @ ( cF @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM89B_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X3: b] : ( cL @ ( cA @ X3 ) @ ( cA @ ( cF @ X3 ) ) )
& ! [X1: a,X0: a,X2: a] :
( ( ( cL @ X1 @ X2 )
& ( cL @ X0 @ X1 ) )
=> ( cL @ X0 @ X2 ) ) )
=> ! [X4: b] : ( cL @ ( cA @ X4 ) @ ( cA @ ( cF @ ( cF @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: b] : ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
& ! [X1: a,X2: a,X3: a] :
( ( ( cL @ X1 @ X3 )
& ( cL @ X2 @ X1 ) )
=> ( cL @ X2 @ X3 ) ) )
=> ! [X4: b] : ( cL @ ( cA @ X4 ) @ ( cA @ ( cF @ ( cF @ X4 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X2: a,X3: a,X1: a] :
( ( ( $true
= ( cL @ X2 @ X1 ) )
& ( ( cL @ X1 @ X3 )
= $true ) )
=> ( ( cL @ X2 @ X3 )
= $true ) )
& ! [X0: b] :
( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true ) )
=> ! [X4: b] :
( ( cL @ ( cA @ X4 ) @ ( cA @ ( cF @ ( cF @ X4 ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X4: b] :
( ( cL @ ( cA @ X4 ) @ ( cA @ ( cF @ ( cF @ X4 ) ) ) )
!= $true )
& ! [X2: a,X3: a,X1: a] :
( ( ( cL @ X2 @ X3 )
= $true )
| ( $true
!= ( cL @ X2 @ X1 ) )
| ( ( cL @ X1 @ X3 )
!= $true ) )
& ! [X0: b] :
( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: b] :
( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ? [X4: b] :
( ( cL @ ( cA @ X4 ) @ ( cA @ ( cF @ ( cF @ X4 ) ) ) )
!= $true )
& ! [X2: a,X1: a,X3: a] :
( ( $true
!= ( cL @ X2 @ X1 ) )
| ( ( cL @ X2 @ X3 )
= $true )
| ( ( cL @ X1 @ X3 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: b] :
( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ? [X1: b] :
( ( cL @ ( cA @ X1 ) @ ( cA @ ( cF @ ( cF @ X1 ) ) ) )
!= $true )
& ! [X2: a,X3: a,X4: a] :
( ( ( cL @ X2 @ X3 )
!= $true )
| ( ( cL @ X2 @ X4 )
= $true )
| ( ( cL @ X3 @ X4 )
!= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X0: b] :
( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true )
& ( $true
!= ( cL @ ( cA @ sK0 ) @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( ( cL @ X2 @ X3 )
!= $true )
| ( ( cL @ X2 @ X4 )
= $true )
| ( ( cL @ X3 @ X4 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[f7]) ).
thf(f9,plain,
! [X2: a,X3: a,X4: a] :
( ( ( cL @ X3 @ X4 )
!= $true )
| ( ( cL @ X2 @ X3 )
!= $true )
| ( ( cL @ X2 @ X4 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
!= ( cL @ ( cA @ sK0 ) @ ( cA @ ( cF @ ( cF @ sK0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X0: b] :
( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ X0 ) ) )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: b,X1: a] :
( ( ( cL @ X1 @ ( cA @ X0 ) )
!= $true )
| ( ( cL @ X1 @ ( cA @ ( cF @ X0 ) ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f9,f11]) ).
thf(f15,plain,
! [X0: b,X1: a] :
( ( ( cL @ X1 @ ( cA @ X0 ) )
!= $true )
| ( ( cL @ X1 @ ( cA @ ( cF @ X0 ) ) )
= $true ) ),
inference(trivial_inequality_removal,[],[f14]) ).
thf(f16,plain,
! [X0: b] :
( ( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ ( cF @ X0 ) ) ) )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f15,f11]) ).
thf(f17,plain,
! [X0: b] :
( ( cL @ ( cA @ X0 ) @ ( cA @ ( cF @ ( cF @ X0 ) ) ) )
= $true ),
inference(trivial_inequality_removal,[],[f16]) ).
thf(f18,plain,
$true != $true,
inference(constrained_superposition,[],[f10,f17]) ).
thf(f21,plain,
$false,
inference(trivial_inequality_removal,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV053^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n017.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Sep 29 15:01:07 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running higher-order theorem proving
% 0.06/0.22 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
% 0.18/0.27 % (437689)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.27 % (437716)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1592682739:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.27 % (437716) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-437689-437716"...
% 0.18/0.27 % (437716)...printing done.
% 0.18/0.27 % (437716)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (437716)------------------------------
% 0.18/0.27 % (437716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (437716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (437716)CaDiCaL version: 2.1.3
% 0.18/0.27 % (437716)Termination reason: Refutation
% 0.18/0.27 % (437716)Time elapsed: 0.001 s
% 0.18/0.27 % (437716)Peak memory usage: 12 MB
% 0.18/0.27 % (437716)Instructions burned: 3 (million)
% 0.18/0.27 % (437689)Success in time 0.039 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------