%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET594^5 : 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 08:23:39 AM UTC 2026
% Result : Theorem 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 14 unt; 0 typ; 2 def)
% Number of atoms : 168 ( 52 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 208 ( 24 ~; 36 |; 36 &; 100 @)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 45 ( 0 sgn 26 !; 8 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vOR: $o > $o > $o ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
sK0: a > $o ).
thf(func_def_8,type,
sK1: a > $o ).
thf(func_def_9,type,
sK2: a > $o ).
thf(func_def_10,type,
sK3: a ).
thf(f1,conjecture,
! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
= X0 )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_53_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
= X0 )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [X3: a] :
( ( ( X2 @ X3 )
& ( X0 @ X3 ) )
| ( ( X1 @ X3 )
& ( X0 @ X3 ) ) ) )
= X0 )
=> ! [X4: a] :
( ( X0 @ X4 )
=> ( ( X2 @ X4 )
| ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X0 )
=> ! [X4: a] :
( ( ( X0 @ X4 )
= $true )
=> ( ( ( X2 @ X4 )
= $true )
| ( ( X1 @ X4 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: a > $o,X2: a > $o] :
( ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X0 )
=> ! [X3: a] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( X2 @ X3 )
= $true )
| ( ( X1 @ X3 )
= $true ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f6,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X0 ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > $o,X1: a > $o,X2: a > $o] :
( ? [X3: a] :
( ( ( X2 @ X3 )
!= $true )
& ( ( X1 @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ( ( ^ [Y0: a] :
( ( ( X0 @ Y0 )
& ( X1 @ Y0 ) )
| ( ( X0 @ Y0 )
& ( X2 @ Y0 ) ) ) )
= X0 ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( sK2 @ sK3 ) )
& ( $true
!= ( sK1 @ sK3 ) )
& ( $true
= ( sK0 @ sK3 ) )
& ( sK0
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
( sK0
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
!= ( sK1 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
!= ( sK2 @ sK3 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X1: a] :
( ( sK0 @ X1 )
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ X1 ) ),
inference(argument_congruence,[],[f9]) ).
thf(f17,plain,
! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 )
& ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ X1 ) ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f18,plain,
! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( ( sK0 @ X1 )
& ( sK1 @ X1 ) )
| ( ( sK0 @ X1 )
& ( sK2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f19,plain,
! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( sK0 @ X1 )
& ( sK2 @ X1 ) ) )
| ( $true
= ( ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f18]) ).
thf(f20,plain,
! [X1: a] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( ( sK0 @ X1 )
& ( sK1 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f25,plain,
! [X1: a] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f20]) ).
thf(f32,plain,
( ( $true != $true )
| ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(constrained_superposition,[],[f12,f25]) ).
thf(f33,plain,
( ( ( sK0 @ sK3 )
= $false )
| ( $true
= ( sK1 @ sK3 ) ) ),
inference(trivial_inequality_removal,[],[f32]) ).
thf(f35,definition,
( spl4_1
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f39,definition,
( spl4_2
<=> ( ( sK0 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f41,plain,
( ( ( sK0 @ sK3 )
= $false )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
thf(f42,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f33,f39,f35]) ).
thf(f43,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f41,f10]) ).
thf(f47,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f43]) ).
thf(f48,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f47]) ).
thf(f49,plain,
( ( $true != $true )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f11,f37]) ).
thf(f50,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f50]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
~ spl4_1,
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
thf(f52,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET594^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n020.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:39:20 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 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 % (1061026)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (1061034)% WARNING: option uhcvi not known.
% 0.10/0.25 % (1061039)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1556097740:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.10/0.25 % (1061037)dis+10_1_sil=32000:sp=arity:random_seed=2217899573:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.10/0.25 % (1061035)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=853214179:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.10/0.25 % (1061038)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3788922728:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.10/0.25 % (1061034)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=653474181:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.10/0.25 % (1061040)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=955404415:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.10/0.25 % (1061038)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.25 % (1061034)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.10/0.25 % (1061034)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.10/0.25 % (1061039) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1061026-1061039"...
% 0.10/0.25 % (1061038) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1061026-1061038"...
% 0.10/0.25 % (1061040) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1061026-1061040"...
% 0.10/0.25 % (1061037) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1061026-1061037"...
% 0.10/0.25 % (1061034) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1061026-1061034"...
% 0.10/0.25 % (1061035) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1061026-1061035"...
% 0.10/0.25 % (1061039)...printing done.
% 0.10/0.25 % (1061038)...printing done.
% 0.10/0.25 % (1061040)...printing done.
% 0.10/0.25 % (1061037)...printing done.
% 0.10/0.25 % (1061034)...printing done.
% 0.10/0.25 % (1061033)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2642557302_3000 on theBenchmark for (3000ds/0Mi)
% 0.10/0.25 % (1061035)...printing done.
% 0.10/0.25 % (1061040)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 % (1061040)------------------------------
% 0.10/0.25 % (1061040)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (1061040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (1061040)CaDiCaL version: 2.1.3
% 0.10/0.25 % (1061040)Termination reason: Refutation
% 0.10/0.25 % (1061040)Time elapsed: 0.003 s
% 0.10/0.25 % (1061040)Peak memory usage: 12 MB
% 0.10/0.25 % (1061040)Instructions burned: 3 (million)
% 0.10/0.25 % (1061026)Success in time 0.025 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------