%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET633^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:23:46 AM UTC 2026
% Result : Theorem 0.09s 0.24s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 40 ( 5 unt; 0 typ; 2 def)
% Number of atoms : 264 ( 95 equ; 0 cnn)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 319 ( 71 ~; 55 |; 45 &; 126 @)
% ( 2 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 40 !; 12 ?; 52 :)
% 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 ).
thf(func_def_6,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
=> ( X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_115_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X3: a] :
( ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) )
=> ( X2 @ X3 ) ) )
=> ! [X3: a] :
( ( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
| ( ~ ( X1 @ X3 )
& ( X0 @ X3 ) ) )
=> ( X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ( X2 @ X3 ) )
& ! [X4: a] :
( ( ~ ( X1 @ X4 )
& ( X0 @ X4 ) )
=> ( X2 @ X4 ) ) )
=> ! [X5: a] :
( ( ( ~ ( X0 @ X5 )
& ( X1 @ X5 ) )
| ( ~ ( X1 @ X5 )
& ( X0 @ X5 ) ) )
=> ( X2 @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
=> ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( ( X1 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ! [X5: a] :
( ( ( ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true ) )
| ( ( ( X1 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) ) )
=> ( ( X2 @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ! [X3: a] :
( ( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
=> ( ( X2 @ X3 )
= $true ) )
& ! [X4: a] :
( ( ( ( X1 @ X4 )
!= $true )
& ( ( X0 @ X4 )
= $true ) )
=> ( ( X2 @ X4 )
= $true ) ) )
=> ! [X5: a] :
( ( ( ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true ) )
| ( ( ( X1 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) ) )
=> ( ( X2 @ X5 )
= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( ( X2 @ X5 )
!= $true )
& ( ( ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true ) )
| ( ( ( X1 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X1 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X5: a] :
( ( ( X2 @ X5 )
!= $true )
& ( ( ( ( X0 @ X5 )
!= $true )
& ( ( X1 @ X5 )
= $true ) )
| ( ( ( X1 @ X5 )
!= $true )
& ( ( X0 @ X5 )
= $true ) ) ) )
& ! [X3: a] :
( ( ( X2 @ X3 )
= $true )
| ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X1 @ X4 )
= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( ( ( X0 @ X3 )
!= $true )
& ( ( X1 @ X3 )
= $true ) )
| ( ( ( X1 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) ) ) )
& ! [X4: a] :
( ( ( X2 @ X4 )
= $true )
| ( ( X0 @ X4 )
= $true )
| ( ( X1 @ X4 )
!= $true ) )
& ! [X5: a] :
( ( ( X2 @ X5 )
= $true )
| ( ( X1 @ X5 )
= $true )
| ( ( X0 @ X5 )
!= $true ) ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( $true
!= ( sK2 @ sK3 ) )
& ( ( ( $true
!= ( sK0 @ sK3 ) )
& ( $true
= ( sK1 @ sK3 ) ) )
| ( ( $true
!= ( sK1 @ sK3 ) )
& ( $true
= ( sK0 @ sK3 ) ) ) )
& ! [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
| ( $true
= ( sK0 @ X4 ) )
| ( $true
!= ( sK1 @ X4 ) ) )
& ! [X5: a] :
( ( $true
= ( sK2 @ X5 ) )
| ( $true
= ( sK1 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f8]) ).
thf(f10,plain,
! [X5: a] :
( ( $true
= ( sK2 @ X5 ) )
| ( $true
= ( sK1 @ X5 ) )
| ( $true
!= ( sK0 @ X5 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
! [X4: a] :
( ( $true
= ( sK2 @ X4 ) )
| ( $true
= ( sK0 @ X4 ) )
| ( $true
!= ( sK1 @ X4 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f15,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f16,plain,
( $true
!= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f20,definition,
( spl4_1
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f21,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| spl4_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f24,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| spl4_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f26,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f12,f24,f20]) ).
thf(f28,plain,
( ~ spl4_2
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f15,f20,f24]) ).
thf(f29,plain,
( ( $true != $true )
| ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(constrained_superposition,[],[f16,f10]) ).
thf(f30,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
!= ( sK0 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f29]) ).
thf(f31,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f16,f11]) ).
thf(f32,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
!= ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f31]) ).
thf(f33,plain,
( ( $true
!= ( sK1 @ sK3 ) )
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f32,f21]) ).
thf(f34,plain,
( $false
| spl4_1
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f33,f26]) ).
thf(f35,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_contradiction_clause,[],[f34]) ).
thf(f36,plain,
( ( $true
!= ( sK0 @ sK3 ) )
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f30,f25]) ).
thf(f37,plain,
( $false
| ~ spl4_1
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f36,f22]) ).
thf(f38,plain,
( ~ spl4_1
| spl4_2 ),
inference(avatar_contradiction_clause,[],[f37]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s4,plain,
( ~ spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f38]) ).
cnf(s5,plain,
spl4_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl4_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
thf(f39,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET633^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:46:06 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.24 % (1259421)Will run a generic schedule for satisfiability detection.
% 0.09/0.24 % (1259430)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1998587850:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.09/0.24 % (1259430)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.24 % (1259430) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1259421-1259430"...
% 0.09/0.24 % (1259430)...printing done.
% 0.09/0.24 % (1259427)% WARNING: option uhcvi not known.
% 0.09/0.24 % (1259430)Refutation found. Thanks to Tanya!
% 0.09/0.24 % SZS status Theorem for theBenchmark
% 0.09/0.24 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.24 % (1259430)------------------------------
% 0.09/0.24 % (1259430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.24 % (1259430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.24 % (1259430)CaDiCaL version: 2.1.3
% 0.09/0.24 % (1259430)Termination reason: Refutation
% 0.09/0.24 % (1259430)Time elapsed: 0.002 s
% 0.09/0.24 % (1259430)Peak memory usage: 12 MB
% 0.09/0.24 % (1259430)Instructions burned: 3 (million)
% 0.09/0.24 % (1259421)Success in time 0.02 s
% 0.09/0.24 % Vampire exiting
%------------------------------------------------------------------------------