%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU886^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:34:20 AM UTC 2026
% Result : Theorem 0.24s 0.31s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 146 ( 58 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 176 ( 45 ~; 28 |; 29 &; 68 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 16 !; 16 ?; 32 :)
% 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,
f: b > a ).
thf(func_def_1,type,
y: b > $o ).
thf(func_def_2,type,
x: b > $o ).
thf(func_def_6,type,
sK0: a ).
thf(func_def_7,type,
sK1: b ).
thf(f1,conjecture,
! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 ) )
& ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( x @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX5203_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 ) )
& ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( x @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( X0
= ( f @ X1 ) )
& ( y @ X1 )
& ( x @ X1 ) )
=> ( ? [X2: b] :
( ( ( f @ X2 )
= X0 )
& ( y @ X2 ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ( x @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a] :
( ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( ( y @ X1 )
= $true )
& ( ( x @ X1 )
= $true ) )
=> ( ? [X2: b] :
( ( ( f @ X2 )
= X0 )
& ( ( y @ X2 )
= $true ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ( ( x @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a] :
( ( ! [X2: b] :
( ( ( f @ X2 )
!= X0 )
| ( ( y @ X2 )
!= $true ) )
| ! [X3: b] :
( ( ( f @ X3 )
!= X0 )
| ( ( x @ X3 )
!= $true ) ) )
& ? [X1: b] :
( ( ( f @ X1 )
= X0 )
& ( ( y @ X1 )
= $true )
& ( ( x @ X1 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a] :
( ( ! [X1: b] :
( ( ( f @ X1 )
!= X0 )
| ( ( y @ X1 )
!= $true ) )
| ! [X2: b] :
( ( ( f @ X2 )
!= X0 )
| ( $true
!= ( x @ X2 ) ) ) )
& ? [X3: b] :
( ( ( f @ X3 )
= X0 )
& ( $true
= ( y @ X3 ) )
& ( ( x @ X3 )
= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( y @ X1 )
!= $true ) )
| ! [X2: b] :
( ( ( f @ X2 )
!= sK0 )
| ( $true
!= ( x @ X2 ) ) ) )
& ( sK0
= ( f @ sK1 ) )
& ( $true
= ( y @ sK1 ) )
& ( $true
= ( x @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X3,sK1)],[f6]) ).
thf(f8,plain,
( $true
= ( x @ sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( $true
= ( y @ sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( sK0
= ( f @ sK1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X2: b,X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( y @ X1 )
!= $true )
| ( ( f @ X2 )
!= sK0 )
| ( $true
!= ( x @ X2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,definition,
( spl2_1
<=> ! [X2: b] :
( ( ( f @ X2 )
!= sK0 )
| ( $true
!= ( x @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f16,plain,
( ! [X2: b] :
( ( $true
!= ( x @ X2 ) )
| ( ( f @ X2 )
!= sK0 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f18,definition,
( spl2_2
<=> ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( y @ X1 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f19,plain,
( ! [X1: b] :
( ( ( f @ X1 )
!= sK0 )
| ( ( y @ X1 )
!= $true ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f20,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f11,f18,f15]) ).
thf(f21,plain,
( ( sK0 != sK0 )
| ( $true
!= ( y @ sK1 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f19,f10]) ).
thf(f22,plain,
( ( $true
!= ( y @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f23,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f22,f9]) ).
thf(f24,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f23]) ).
thf(f25,plain,
( ( $true != $true )
| ( sK0
!= ( f @ sK1 ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f16,f8]) ).
thf(f26,plain,
( ( sK0
!= ( f @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f25]) ).
thf(f27,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f26,f10]) ).
thf(f28,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f27]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f20]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f24]) ).
cnf(s3,plain,
~ spl2_1,
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f29,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU886^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n020.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:44:04 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 Running first-order model finding
% 0.10/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.31 % (1144601)Will run a generic schedule for satisfiability detection.
% 0.24/0.31 % (1144607)% WARNING: option uhcvi not known.
% 0.24/0.31 % (1144607)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1174216278:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.31 % (1144607)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.31 % (1144607)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.24/0.31 % (1144607) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1144601-1144607"...
% 0.24/0.31 % (1144607)...printing done.
% 0.24/0.31 % (1144607)Refutation found. Thanks to Tanya!
% 0.24/0.31 % SZS status Theorem for theBenchmark
% 0.24/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.31 % (1144607)------------------------------
% 0.24/0.31 % (1144607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.31 % (1144607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.31 % (1144607)CaDiCaL version: 2.1.3
% 0.24/0.31 % (1144607)Termination reason: Refutation
% 0.24/0.31 % (1144607)Time elapsed: 0.003 s
% 0.24/0.31 % (1144607)Peak memory usage: 12 MB
% 0.24/0.31 % (1144607)Instructions burned: 2 (million)
% 0.24/0.31 % (1144601)Success in time 0.039 s
% 0.24/0.31 % Vampire exiting
%------------------------------------------------------------------------------