%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO095^5 : 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 : 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 08:48:57 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 14 unt; 0 typ; 1 def)
% Number of atoms : 182 ( 47 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 200 ( 14 ~; 11 |; 16 &; 144 @)
% ( 7 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 58 !; 10 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cR: $i > $i > $o ).
thf(f1,conjecture,
( ( ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
<=> ( cR @ X3 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X0 )
<=> ( cR @ X0 @ X1 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM81) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
<=> ( cR @ X3 @ X2 ) )
& ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X0 )
<=> ( cR @ X0 @ X1 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X0 )
<=> ( cR @ X1 @ X0 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
<=> ( cR @ X2 @ X3 ) ) )
=> ( ? [X4: $i] : ( cR @ X4 @ X4 )
=> ! [X5: $i] : ( cR @ X5 @ X5 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X0 )
= ( cR @ X1 @ X0 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X2 @ X3 ) ) )
=> ( ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
=> ! [X5: $i] :
( ( cR @ X5 @ X5 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ? [X5: $i] :
( ( cR @ X5 @ X5 )
!= $true )
& ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
& ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X0 )
= ( cR @ X1 @ X0 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X2 @ X3 ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ? [X5: $i] :
( ( cR @ X5 @ X5 )
!= $true )
& ? [X4: $i] :
( ( cR @ X4 @ X4 )
= $true )
& ! [X0: $i,X1: $i] :
( ( cR @ X0 @ X0 )
= ( cR @ X1 @ X0 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X2 @ X3 ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i] :
( ( cR @ X0 @ X0 )
!= $true )
& ? [X1: $i] :
( $true
= ( cR @ X1 @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X3 @ X2 ) )
& ! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( cR @ sK0 @ sK0 ) )
& ( $true
= ( cR @ sK1 @ sK1 ) )
& ! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X3 @ X2 ) )
& ! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f9,plain,
! [X4: $i,X5: $i] :
( ( cR @ X4 @ X4 )
= ( cR @ X4 @ X5 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X2: $i,X3: $i] :
( ( cR @ X2 @ X2 )
= ( cR @ X3 @ X2 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
= ( cR @ sK1 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
!= ( cR @ sK0 @ sK0 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X4: $i,X5: $i] :
( ( ( cR @ X4 @ X4 )
= $true )
| ( ( cR @ X4 @ X5 )
= $false ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f16,plain,
! [X4: $i,X5: $i] :
( ( ( cR @ X4 @ X4 )
= $false )
| ( $true
= ( cR @ X4 @ X5 ) ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f17,plain,
! [X2: $i,X3: $i] :
( ( ( cR @ X2 @ X2 )
= $true )
| ( ( cR @ X3 @ X2 )
= $false ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f18,plain,
! [X2: $i,X3: $i] :
( ( ( cR @ X2 @ X2 )
= $false )
| ( ( cR @ X3 @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f10]) ).
thf(f19,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( cR @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f12,f15]) ).
thf(f21,plain,
! [X0: $i] :
( $false
= ( cR @ sK0 @ X0 ) ),
inference(trivial_inequality_removal,[],[f19]) ).
thf(f46,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( cR @ sK1 @ X0 ) ) ),
inference(constrained_superposition,[],[f11,f16]) ).
thf(f57,plain,
! [X0: $i] :
( $true
= ( cR @ sK1 @ X0 ) ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f85,definition,
( spl2_2
<=> ! [X0: $i] :
( ( cR @ X0 @ X0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f86,plain,
( ! [X0: $i] :
( ( cR @ X0 @ X0 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f85]) ).
thf(f90,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( cR @ X0 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f57,f17]) ).
thf(f99,plain,
! [X0: $i] :
( ( cR @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f104,plain,
( ( $true = $false )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f99,f86]) ).
thf(f105,plain,
( $false
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f106,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f105]) ).
thf(f123,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( cR @ X0 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f21,f18]) ).
thf(f131,plain,
! [X0: $i] :
( ( cR @ X0 @ X0 )
= $false ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f147,plain,
spl2_2,
inference(avatar_split_clause,[],[f131,f85]) ).
cnf(s4,plain,
~ spl2_2,
inference(sat_conversion,[],[f106]) ).
cnf(s5,plain,
spl2_2,
inference(sat_conversion,[],[f147]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s4,s5]) ).
thf(f148,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO095^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n001.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:39:36 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.25 Running first-order model finding
% 0.09/0.25 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
% 0.20/0.30 % (1463617)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (1463624)% WARNING: option uhcvi not known.
% 0.20/0.30 % (1463628)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3273070761:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (1463623)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=455690123_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (1463625)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=234865751:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (1463626)dis+10_1_sil=32000:sp=arity:random_seed=2042033267:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1463628) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1463617-1463628"...
% 0.20/0.30 % (1463624)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=680793236:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (1463624)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (1463625) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1463617-1463625"...
% 0.20/0.30 % (1463624)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 % (1463626) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1463617-1463626"...
% 0.20/0.30 % (1463628)...printing done.
% 0.20/0.30 % (1463628)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (1463628)------------------------------
% 0.20/0.30 % (1463628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1463628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1463628)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1463628)Termination reason: Refutation
% 0.20/0.30 % (1463628)Time elapsed: 0.005 s
% 0.20/0.30 % (1463628)Peak memory usage: 12 MB
% 0.20/0.30 % (1463628)Instructions burned: 7 (million)
% 0.20/0.30 % (1463617)Success in time 0.041 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------