%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO098^5 : 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 : n007.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 08:48:57 AM UTC 2026
% Result : Theorem 0.21s 0.26s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 145 ( 33 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 156 ( 32 ~; 15 |; 11 &; 86 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 28 !; 12 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ: $i > $i > $o ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(f1,conjecture,
( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X1: $i,X2: $i] :
( ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) )
& ~ ( cR @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM65) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X1: $i,X2: $i] :
( ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) )
& ~ ( cR @ X1 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i] :
~ ( cR @ X0 @ X0 )
=> ? [X1: $i,X2: $i] :
( ( ( cQ @ X2 @ X1 )
=> ! [X3: $i] : ( cQ @ X3 @ X3 ) )
& ~ ( cR @ X1 @ X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
=> ? [X1: $i,X2: $i] :
( ( ( ( cQ @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( cQ @ X3 @ X3 )
= $true ) )
& ( ( cR @ X1 @ X2 )
!= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
=> ? [X1: $i,X2: $i] :
( ( ( ( cQ @ X2 @ X1 )
= $true )
=> ! [X3: $i] :
( ( cQ @ X3 @ X3 )
= $true ) )
& ( ( cR @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ! [X1: $i,X2: $i] :
( ( ? [X3: $i] :
( ( cQ @ X3 @ X3 )
!= $true )
& ( ( cQ @ X2 @ X1 )
= $true ) )
| ( ( cR @ X1 @ X2 )
= $true ) )
& ! [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i] :
( ( ? [X2: $i] :
( $true
!= ( cQ @ X2 @ X2 ) )
& ( $true
= ( cQ @ X1 @ X0 ) ) )
| ( $true
= ( cR @ X0 @ X1 ) ) )
& ! [X3: $i] :
( $true
!= ( cR @ X3 @ X3 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( ( $true
!= ( cQ @ sK0 @ sK0 ) )
& ( $true
= ( cQ @ X1 @ X0 ) ) )
| ( $true
= ( cR @ X0 @ X1 ) ) )
& ! [X3: $i] :
( $true
!= ( cR @ X3 @ X3 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0)],[f7]) ).
thf(f9,plain,
! [X3: $i] :
( $true
!= ( cR @ X3 @ X3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cQ @ X1 @ X0 ) )
| ( $true
= ( cR @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cQ @ sK0 @ sK0 ) )
| ( $true
= ( cR @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,definition,
( spl1_2
<=> ! [X0: $i,X1: $i] :
( $true
= ( cR @ X0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f19,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( cR @ X0 @ X1 ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f20,plain,
( ( $true != $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f9,f19]) ).
thf(f21,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f20]) ).
thf(f22,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f21]) ).
thf(f26,definition,
( spl1_3
<=> ( $true
= ( cQ @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f28,plain,
( ( $true
!= ( cQ @ sK0 @ sK0 ) )
| spl1_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f29,plain,
( spl1_2
| ~ spl1_3 ),
inference(avatar_split_clause,[],[f11,f26,f18]) ).
thf(f30,plain,
( ( $true != $true )
| ( $true
= ( cR @ sK0 @ sK0 ) )
| spl1_3 ),
inference(constrained_superposition,[],[f28,f10]) ).
thf(f31,plain,
( ( $true
= ( cR @ sK0 @ sK0 ) )
| spl1_3 ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( $false
| spl1_3 ),
inference(forward_subsumption_resolution,[],[f31,f9]) ).
thf(f33,plain,
spl1_3,
inference(avatar_contradiction_clause,[],[f32]) ).
cnf(s13,plain,
~ spl1_2,
inference(sat_conversion,[],[f22]) ).
cnf(s19,plain,
( spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f29]) ).
cnf(s22,plain,
spl1_3,
inference(sat_conversion,[],[f33]) ).
cnf(s23,plain,
spl1_2,
inference(rat,[],[s19,s22]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s13,s23]) ).
thf(f34,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO098^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n007.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:31:41 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.21/0.26 % (3595180)Will run a generic schedule for satisfiability detection.
% 0.21/0.26 % (3595187)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3885253703:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.26 % (3595187) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3595180-3595187"...
% 0.21/0.26 % (3595187)...printing done.
% 0.21/0.26 % (3595186)% WARNING: option uhcvi not known.
% 0.21/0.26 % (3595187)Refutation found. Thanks to Tanya!
% 0.21/0.26 % SZS status Theorem for theBenchmark
% 0.21/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.26 % (3595187)------------------------------
% 0.21/0.26 % (3595187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.26 % (3595187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.26 % (3595187)CaDiCaL version: 2.1.3
% 0.21/0.26 % (3595187)Termination reason: Refutation
% 0.21/0.26 % (3595187)Time elapsed: 0.002 s
% 0.21/0.26 % (3595187)Peak memory usage: 12 MB
% 0.21/0.26 % (3595187)Instructions burned: 2 (million)
% 0.21/0.26 % (3595180)Success in time 0.041 s
% 0.21/0.26 % Vampire exiting
%------------------------------------------------------------------------------