%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO161^5 : 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 : n006.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 08:49:04 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 236 ( 49 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 202 ( 47 ~; 37 |; 20 &; 73 @)
% ( 5 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 13 ( 10 usr; 10 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 29 !; 18 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $o ).
thf(f1,conjecture,
( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X1 )
=> ( cP @ X0 ) )
& ( ( cP @ X0 )
=> ( cP @ X1 ) ) )
=> ( ( ! [X1: $i] : ( cP @ X1 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ! [X1: $i] : ( cP @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2125_HALF) ).
thf(f2,negated_conjecture,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X1 )
=> ( cP @ X0 ) )
& ( ( cP @ X0 )
=> ( cP @ X1 ) ) )
=> ( ( ! [X1: $i] : ( cP @ X1 )
=> ? [X0: $i] : ( cP @ X0 ) )
& ( ? [X0: $i] : ( cP @ X0 )
=> ! [X1: $i] : ( cP @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( cP @ X1 )
=> ( cP @ X0 ) )
& ( ( cP @ X0 )
=> ( cP @ X1 ) ) )
=> ( ( ! [X2: $i] : ( cP @ X2 )
=> ? [X3: $i] : ( cP @ X3 ) )
& ( ? [X4: $i] : ( cP @ X4 )
=> ! [X5: $i] : ( cP @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP @ X1 )
= $true )
=> ( ( cP @ X0 )
= $true ) )
& ( ( ( cP @ X0 )
= $true )
=> ( ( cP @ X1 )
= $true ) ) )
=> ( ( ! [X2: $i] :
( ( cP @ X2 )
= $true )
=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) )
& ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
=> ! [X5: $i] :
( ( cP @ X5 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( ! [X3: $i] :
( ( cP @ X3 )
!= $true )
& ! [X2: $i] :
( ( cP @ X2 )
= $true ) )
| ( ? [X5: $i] :
( ( cP @ X5 )
!= $true )
& ? [X4: $i] :
( ( cP @ X4 )
= $true ) ) )
& ? [X0: $i] :
! [X1: $i] :
( ( ( ( cP @ X0 )
= $true )
| ( ( cP @ X1 )
!= $true ) )
& ( ( ( cP @ X1 )
= $true )
| ( ( cP @ X0 )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( ! [X0: $i] :
( ( cP @ X0 )
!= $true )
& ! [X1: $i] :
( ( cP @ X1 )
= $true ) )
| ( ? [X2: $i] :
( ( cP @ X2 )
!= $true )
& ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) )
& ? [X4: $i] :
! [X5: $i] :
( ( ( ( cP @ X4 )
= $true )
| ( ( cP @ X5 )
!= $true ) )
& ( ( ( cP @ X5 )
= $true )
| ( ( cP @ X4 )
!= $true ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ( ! [X0: $i] :
( ( cP @ X0 )
!= $true )
& ! [X1: $i] :
( ( cP @ X1 )
= $true ) )
| ( ( $true
!= ( cP @ sK0 ) )
& ( $true
= ( cP @ sK1 ) ) ) )
& ! [X5: $i] :
( ( ( $true
= ( cP @ sK2 ) )
| ( ( cP @ X5 )
!= $true ) )
& ( ( ( cP @ X5 )
= $true )
| ( $true
!= ( cP @ sK2 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0),skolemize(X3,sK1),skolemize(X4,sK2)],[f6]) ).
thf(f8,plain,
! [X5: $i] :
( ( ( cP @ X5 )
= $true )
| ( $true
!= ( cP @ sK2 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X5: $i] :
( ( $true
= ( cP @ sK2 ) )
| ( ( cP @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X1: $i] :
( ( ( cP @ X1 )
= $true )
| ( $true
= ( cP @ sK1 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ( $true
!= ( cP @ sK0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f17,definition,
( spl3_1
<=> ( $true
= ( cP @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f21,definition,
( spl3_2
<=> ! [X5: $i] :
( ( cP @ X5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f22,plain,
( ! [X5: $i] :
( ( cP @ X5 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f21]) ).
thf(f23,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f8,f21,f17]) ).
thf(f25,definition,
( spl3_3
<=> ! [X5: $i] :
( ( cP @ X5 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f26,plain,
( ! [X5: $i] :
( ( cP @ X5 )
!= $true )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f25]) ).
thf(f27,plain,
( spl3_3
| spl3_1 ),
inference(avatar_split_clause,[],[f9,f17,f25]) ).
thf(f29,definition,
( spl3_4
<=> ( $true
= ( cP @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f31,plain,
( ( $true
= ( cP @ sK1 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f10,f21,f29]) ).
thf(f34,definition,
( spl3_5
<=> ( $true
= ( cP @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f36,plain,
( ( $true
!= ( cP @ sK0 ) )
| spl3_5 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f39,plain,
( ~ spl3_5
| spl3_3 ),
inference(avatar_split_clause,[],[f13,f25,f34]) ).
thf(f40,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f26,f22]) ).
thf(f41,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f40]) ).
thf(f42,plain,
( $false
| ~ spl3_2
| spl3_5 ),
inference(forward_subsumption_resolution,[],[f36,f22]) ).
thf(f43,plain,
( ~ spl3_2
| spl3_5 ),
inference(avatar_contradiction_clause,[],[f42]) ).
thf(f44,plain,
( $false
| ~ spl3_3
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f31,f26]) ).
thf(f45,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f44]) ).
cnf(s1,plain,
( ~ spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f23]) ).
cnf(s2,plain,
( spl3_1
| spl3_3 ),
inference(sat_conversion,[],[f27]) ).
cnf(s3,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f32]) ).
cnf(s6,plain,
( spl3_3
| ~ spl3_5 ),
inference(sat_conversion,[],[f39]) ).
cnf(s7,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f41]) ).
cnf(s8,plain,
( ~ spl3_2
| spl3_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s9,plain,
( ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s10,plain,
~ spl3_3,
inference(rat,[],[s3,s7,s9]) ).
cnf(s11,plain,
~ spl3_5,
inference(rat,[],[s6,s10]) ).
cnf(s13,plain,
spl3_1,
inference(rat,[],[s2,s10]) ).
cnf(s14,plain,
~ spl3_2,
inference(rat,[],[s8,s11]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s14,s13]) ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO161^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:35:54 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.28 % (955313)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (955326)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2010636227_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (955327)% WARNING: option uhcvi not known.
% 0.20/0.28 % (955328)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=715136956:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (955327)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=891337886:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (955329)dis+10_1_sil=32000:sp=arity:random_seed=3242137325:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (955330)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=283742837:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (955331)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3031658421:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (955332)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1562042271:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (955327)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (955330)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (955327)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % (955330) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-955313-955330"...
% 0.20/0.28 % (955331) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-955313-955331"...
% 0.20/0.28 % (955329) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-955313-955329"...
% 0.20/0.28 % (955327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-955313-955327"...
% 0.20/0.28 % (955328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-955313-955328"...
% 0.20/0.28 % (955332) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-955313-955332"...
% 0.20/0.28 % (955330)...printing done.
% 0.20/0.28 % (955331)...printing done.
% 0.20/0.28 % (955329)...printing done.
% 0.20/0.28 % (955327)...printing done.
% 0.20/0.28 % (955334)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2943762978:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.28 % (955328)...printing done.
% 0.20/0.28 % (955332)...printing done.
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (955330)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (955330)------------------------------
% 0.20/0.28 % (955330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (955330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (955330)CaDiCaL version: 2.1.3
% 0.20/0.28 % (955330)Termination reason: Refutation
% 0.20/0.28 % (955330)Time elapsed: 0.002 s
% 0.20/0.28 % (955330)Peak memory usage: 12 MB
% 0.20/0.28 % (955330)Instructions burned: 2 (million)
% 0.20/0.28 % (955313)Success in time 0.041 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------