%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET580^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:23:17 AM UTC 2026
% Result : Theorem 0.24s 0.34s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 3 unt; 0 typ; 1 def)
% Number of atoms : 355 ( 152 equ; 0 cnn)
% Maximal formula atoms : 22 ( 10 avg)
% Number of connectives : 446 ( 90 ~; 79 |; 44 &; 218 @)
% ( 13 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 46 ( 46 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 69 ( 0 ^; 57 !; 12 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sP0: ( a > $o ) > ( a > $o ) > a > $o ).
thf(func_def_4,type,
sK1: a > $o ).
thf(func_def_5,type,
sK2: a ).
thf(func_def_6,type,
sK3: a > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,conjecture,
! [X0: a,X2: a > $o,X1: a > $o] :
( ~ ( X2 @ X0 )
<=> ( ( X1 @ X0 )
<=> ( ( ( X1 @ X0 )
& ~ ( X2 @ X0 ) )
| ( ( X2 @ X0 )
& ~ ( X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_23_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a,X2: a > $o,X1: a > $o] :
( ~ ( X2 @ X0 )
<=> ( ( X1 @ X0 )
<=> ( ( ( X1 @ X0 )
& ~ ( X2 @ X0 ) )
| ( ( X2 @ X0 )
& ~ ( X1 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a,X1: a > $o,X2: a > $o] :
( ~ ( X1 @ X0 )
<=> ( ( X2 @ X0 )
<=> ( ( ( X2 @ X0 )
& ~ ( X1 @ X0 ) )
| ( ( X1 @ X0 )
& ~ ( X2 @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a,X1: a > $o,X2: a > $o] :
( ( ( X1 @ X0 )
!= $true )
<=> ( ( ( X2 @ X0 )
= $true )
<=> ( ( ( ( X2 @ X0 )
= $true )
& ( ( X1 @ X0 )
!= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X2: a > $o,X1: a > $o,X0: a] :
( ( ( ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) ) )
<=> ( ( X2 @ X0 )
= $true ) )
<=> ( ( X1 @ X0 )
!= $true ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X1: a > $o,X0: a,X2: a > $o] :
( ( ( ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) ) )
<=> ( ( X2 @ X0 )
= $true ) )
<~> ( ( X1 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,definition,
! [X0: a,X2: a > $o,X1: a > $o] :
( ( ( sP0 @ X1 @ X2 @ X0 )
= $true )
<=> ( ( ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) ) )
<=> ( ( X2 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
? [X1: a > $o,X0: a,X2: a > $o] :
( ( ( sP0 @ X1 @ X2 @ X0 )
= $true )
<~> ( ( X1 @ X0 )
!= $true ) ),
inference(definition_folding,[],[f6,f7]) ).
thf(f9,plain,
! [X0: a,X2: a > $o,X1: a > $o] :
( ( ( ( sP0 @ X1 @ X2 @ X0 )
= $true )
| ( ( ( ( X2 @ X0 )
!= $true )
| ( ( ( ( X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
!= $true ) )
& ( ( ( X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
= $true ) ) ) )
& ( ( ( X2 @ X0 )
= $true )
| ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) ) ) ) )
& ( ( ( ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) )
| ( ( X2 @ X0 )
!= $true ) )
& ( ( ( X2 @ X0 )
= $true )
| ( ( ( ( X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
!= $true ) )
& ( ( ( X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
= $true ) ) ) ) )
| ( ( sP0 @ X1 @ X2 @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X0: a,X2: a > $o,X1: a > $o] :
( ( ( ( sP0 @ X1 @ X2 @ X0 )
= $true )
| ( ( ( ( X2 @ X0 )
!= $true )
| ( ( ( ( X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
!= $true ) )
& ( ( ( X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
= $true ) ) ) )
& ( ( ( X2 @ X0 )
= $true )
| ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) ) ) ) )
& ( ( ( ( ( ( X1 @ X0 )
!= $true )
& ( ( X2 @ X0 )
= $true ) )
| ( ( ( X1 @ X0 )
= $true )
& ( ( X2 @ X0 )
!= $true ) )
| ( ( X2 @ X0 )
!= $true ) )
& ( ( ( X2 @ X0 )
= $true )
| ( ( ( ( X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
!= $true ) )
& ( ( ( X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
= $true ) ) ) ) )
| ( ( sP0 @ X1 @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[],[f9]) ).
thf(f11,plain,
! [X0: a,X1: a > $o,X2: a > $o] :
( ( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( ( ( ( X1 @ X0 )
!= $true )
| ( ( ( ( X2 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true ) ) ) )
& ( ( ( X1 @ X0 )
= $true )
| ( ( ( X2 @ X0 )
!= $true )
& ( ( X1 @ X0 )
= $true ) )
| ( ( ( X2 @ X0 )
= $true )
& ( ( X1 @ X0 )
!= $true ) ) ) ) )
& ( ( ( ( ( ( X2 @ X0 )
!= $true )
& ( ( X1 @ X0 )
= $true ) )
| ( ( ( X2 @ X0 )
= $true )
& ( ( X1 @ X0 )
!= $true ) )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( ( X1 @ X0 )
= $true )
| ( ( ( ( X2 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true ) )
& ( ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true ) ) ) ) )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) ) ),
inference(rectify,[],[f10]) ).
thf(f12,plain,
? [X1: a > $o,X0: a,X2: a > $o] :
( ( ( ( X1 @ X0 )
= $true )
| ( ( sP0 @ X1 @ X2 @ X0 )
!= $true ) )
& ( ( ( X1 @ X0 )
!= $true )
| ( ( sP0 @ X1 @ X2 @ X0 )
= $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f13,plain,
? [X0: a > $o,X1: a,X2: a > $o] :
( ( ( ( X0 @ X1 )
= $true )
| ( ( sP0 @ X0 @ X2 @ X1 )
!= $true ) )
& ( ( ( X0 @ X1 )
!= $true )
| ( ( sP0 @ X0 @ X2 @ X1 )
= $true ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ( ( sK1 @ sK2 )
= $true )
| ( ( sP0 @ sK1 @ sK3 @ sK2 )
!= $true ) )
& ( ( ( sK1 @ sK2 )
!= $true )
| ( ( sP0 @ sK1 @ sK3 @ sK2 )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f13]) ).
thf(f15,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( sP0 @ X2 @ X1 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
!= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f22,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
| ( ( X1 @ X0 )
= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f26,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true )
| ( ( X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f27,plain,
( ( ( sP0 @ sK1 @ sK3 @ sK2 )
= $true )
| ( ( sK1 @ sK2 )
!= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f28,plain,
( ( ( sP0 @ sK1 @ sK3 @ sK2 )
!= $true )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f31,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( ( X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f22]) ).
thf(f33,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( ( X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f26]) ).
thf(f34,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( sP0 @ X2 @ X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
!= $true )
| ( ( X1 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f15]) ).
thf(f35,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( X1 @ X0 )
!= $true )
| ( ( sP0 @ X2 @ X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f19]) ).
thf(f40,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( sP0 @ X2 @ X1 @ X0 )
= $true )
| ( ( X2 @ X0 )
= $true ) ),
inference(forward_subsumption_resolution,[],[f33,f31]) ).
thf(f41,plain,
( ( $true != $true )
| ( ( sK1 @ sK2 )
= $true )
| ( ( sK1 @ sK2 )
= $true ) ),
inference(superposition,[],[f28,f40]) ).
thf(f42,plain,
( ( ( sK1 @ sK2 )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[],[f41]) ).
thf(f43,plain,
( ( sK1 @ sK2 )
= $true ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f51,plain,
! [X2: a > $o,X0: a,X1: a > $o] :
( ( ( sP0 @ X2 @ X1 @ X0 )
!= $true )
| ( ( X2 @ X0 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f35,f34]) ).
thf(f52,plain,
( ( ( sK1 @ sK2 )
!= $true )
| ( $true != $true )
| ( ( sK1 @ sK2 )
!= $true ) ),
inference(superposition,[],[f51,f27]) ).
thf(f55,plain,
( ( $true != $true )
| ( ( sK1 @ sK2 )
!= $true ) ),
inference(duplicate_literal_removal,[],[f52]) ).
thf(f56,plain,
( ( sK1 @ sK2 )
!= $true ),
inference(trivial_inequality_removal,[],[f55]) ).
thf(f57,plain,
$false,
inference(forward_subsumption_resolution,[],[f56,f43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET580^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n011.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Tue Sep 29 13:38:01 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.34 % (100826)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.34 % (100835)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3067737173:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.34 % (100835) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-100826-100835"...
% 0.24/0.34 % (100835)...printing done.
% 0.24/0.34 % (100835)Refutation found. Thanks to Tanya!
% 0.24/0.34 % SZS status Theorem for theBenchmark
% 0.24/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.34 % (100835)------------------------------
% 0.24/0.34 % (100835)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.34 % (100835)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.34 % (100835)CaDiCaL version: 2.1.3
% 0.24/0.34 % (100835)Termination reason: Refutation
% 0.24/0.34 % (100835)Time elapsed: 0.003 s
% 0.24/0.34 % (100835)Peak memory usage: 12 MB
% 0.24/0.34 % (100835)Instructions burned: 5 (million)
% 0.24/0.34 % (100826)Success in time 0.028 s
% 0.24/0.35 % Vampire exiting
%------------------------------------------------------------------------------