%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET628^5 : 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 : 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 08:23:45 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 7 unt; 0 typ; 3 def)
% Number of atoms : 184 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 150 ( 46 ~; 43 |; 11 &; 42 @)
% ( 7 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 46 ( 21 sgn 15 !; 10 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
sK0: a > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(f1,conjecture,
! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( X0
!= ( ^ [X1: a] : $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_110_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( X0
!= ( ^ [X1: a] : $false ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o] :
( ? [X1: a] :
( ( X0 @ X1 )
& ( X0 @ X1 ) )
<=> ( X0
!= ( ^ [X2: a] : $false ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o] :
( ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
<=> ( ( ^ [Y0: a] : $false )
!= X0 ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: a > $o] :
( ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
<~> ( ( ^ [Y0: a] : $false )
!= X0 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
= X0 )
| ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X1 )
!= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
!= X0 )
| ? [X1: a] :
( ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o] :
( ( ( ( ^ [Y0: a] : $false )
= X0 )
| ! [X1: a] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ X1 )
!= $true ) ) )
& ( ( ( ^ [Y0: a] : $false )
!= X0 )
| ? [X2: a] :
( ( $true
= ( X0 @ X2 ) )
& ( $true
= ( X0 @ X2 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( ( ^ [Y0: a] : $false )
= sK0 )
| ! [X1: a] :
( ( $true
!= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X1 ) ) ) )
& ( ( ( ^ [Y0: a] : $false )
!= sK0 )
| ( ( $true
= ( sK0 @ sK1 ) )
& ( $true
= ( sK0 @ sK1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1)],[f7]) ).
thf(f9,plain,
( ( ( ^ [Y0: a] : $false )
!= sK0 )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X1: a] :
( ( ( ^ [Y0: a] : $false )
= sK0 )
| ( $true
!= ( sK0 @ X1 ) )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
! [X1: a] :
( ( ( ^ [Y0: a] : $false )
= sK0 )
| ( $true
!= ( sK0 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f11]) ).
thf(f16,definition,
( spl2_1
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f18,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f20,definition,
( spl2_2
<=> ( ( ^ [Y0: a] : $false )
= sK0 ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( ^ [Y0: a] : $false )
= sK0 )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( ( ( ^ [Y0: a] : $false )
!= sK0 )
| spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f23,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f9,f20,f16]) ).
thf(f26,definition,
( spl2_3
<=> ! [X1: a] :
( $true
!= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f27,plain,
( ! [X1: a] :
( $true
!= ( sK0 @ X1 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f26]) ).
thf(f28,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f14,f20,f26]) ).
thf(f29,plain,
( ( ( ^ [Y0: a] : $false
@ sK3 )
!= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(negative_extensionality,[],[f22]) ).
thf(f30,plain,
( ( $true
= ( ^ [Y0: a] : $false
@ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(xor_proxy_clausification,[],[f29]) ).
thf(f33,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f34,plain,
( ( $true
= ( sK0 @ sK3 ) )
| spl2_2 ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f35,plain,
( $false
| spl2_2
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f34,f27]) ).
thf(f36,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f35]) ).
thf(f39,plain,
( ! [X1: a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a] : $false
@ X1 ) )
| ~ spl2_2 ),
inference(argument_congruence,[],[f21]) ).
thf(f41,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: a] : $false
@ X1 ) ) )
| ~ spl2_2 ),
inference(iff_proxy_clausification,[],[f39]) ).
thf(f42,plain,
( ! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true = $false ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
( ! [X1: a] :
( $false
= ( sK0 @ X1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f42]) ).
thf(f45,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_2 ),
inference(constrained_superposition,[],[f43,f18]) ).
thf(f49,plain,
( $false
| ~ spl2_1
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f45]) ).
thf(f50,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f49]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s3,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f28]) ).
cnf(s4,plain,
( spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f36]) ).
cnf(s7,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f50]) ).
cnf(s8,plain,
spl2_2,
inference(rat,[],[s3,s4]) ).
cnf(s9,plain,
~ spl2_1,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9]) ).
thf(f51,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET628^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.17 % Computer : n017.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 13:35:22 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 Running first-order model finding
% 0.10/0.20 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
% 0.10/0.25 % (344818)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (344827)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1972228159:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.25 % (344827)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.25 % (344827) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-344818-344827"...
% 0.10/0.25 % (344824)% WARNING: option uhcvi not known.
% 0.10/0.25 % (344827)...printing done.
% 0.10/0.25 % (344827)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Theorem for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (344827)------------------------------
% 0.10/0.25 % (344827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (344827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (344827)CaDiCaL version: 2.1.3
% 0.10/0.25 % (344827)Termination reason: Refutation
% 0.10/0.25 % (344827)Time elapsed: 0.002 s
% 0.10/0.25 % (344827)Peak memory usage: 13 MB
% 0.10/0.25 % (344827)Instructions burned: 2 (million)
% 0.10/0.25 % (344818)Success in time 0.04 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------