%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO308^5 : 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 : n012.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 08:49:42 AM UTC 2026
% Result : Theorem 0.06s 0.20s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 200 ( 56 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 189 ( 45 ~; 39 |; 12 &; 75 @)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 30 !; 6 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cB: $i > $o ).
thf(func_def_1,type,
cA: $i > $o ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(f1,conjecture,
! [X0: $i > $o] :
( ( ! [X2: $i] :
( ( X0 @ X2 )
=> ( cB @ X2 ) )
| ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
=> ( ( cB @ X3 )
| ( cA @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSET81_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
( ( ! [X2: $i] :
( ( X0 @ X2 )
=> ( cB @ X2 ) )
| ! [X1: $i] :
( ( X0 @ X1 )
=> ( cA @ X1 ) ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
=> ( ( cB @ X3 )
| ( cA @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cB @ X1 ) )
| ! [X2: $i] :
( ( X0 @ X2 )
=> ( cA @ X2 ) ) )
=> ! [X3: $i] :
( ( X0 @ X3 )
=> ( ( cB @ X3 )
| ( cA @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( cB @ X1 )
= $true ) )
| ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( cA @ X2 )
= $true ) ) )
=> ! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( cB @ X3 )
= $true )
| ( ( cA @ X3 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: $i > $o] :
( ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( cA @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ( ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
| ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: $i > $o] :
( ? [X3: $i] :
( ( ( cB @ X3 )
!= $true )
& ( ( cA @ X3 )
!= $true )
& ( ( X0 @ X3 )
= $true ) )
& ( ! [X1: $i] :
( ( ( cB @ X1 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
| ! [X2: $i] :
( ( ( cA @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: $i > $o] :
( ? [X1: $i] :
( ( ( cB @ X1 )
!= $true )
& ( ( cA @ X1 )
!= $true )
& ( ( X0 @ X1 )
= $true ) )
& ( ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( ( X0 @ X2 )
!= $true ) )
| ! [X3: $i] :
( ( ( cA @ X3 )
= $true )
| ( ( X0 @ X3 )
!= $true ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( $true
!= ( cB @ sK1 ) )
& ( $true
!= ( cA @ sK1 ) )
& ( $true
= ( sK0 @ sK1 ) )
& ( ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( $true
!= ( sK0 @ X2 ) ) )
| ! [X3: $i] :
( ( ( cA @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f7]) ).
thf(f9,plain,
! [X2: $i,X3: $i] :
( ( ( cB @ X2 )
= $true )
| ( $true
!= ( sK0 @ X2 ) )
| ( ( cA @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
( $true
!= ( cA @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
!= ( cB @ sK1 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,definition,
( spl2_1
<=> ! [X3: $i] :
( ( ( cA @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f17,plain,
( ! [X3: $i] :
( ( ( cA @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,definition,
( spl2_2
<=> ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( $true
!= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f20,plain,
( ! [X2: $i] :
( ( ( cB @ X2 )
= $true )
| ( $true
!= ( sK0 @ X2 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f21,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f9,f19,f16]) ).
thf(f22,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f12,f20]) ).
thf(f23,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f22]) ).
thf(f24,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f23,f10]) ).
thf(f25,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f24]) ).
thf(f26,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK1 ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f11,f17]) ).
thf(f27,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f28,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f27,f10]) ).
thf(f29,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f28]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
~ spl2_2,
inference(sat_conversion,[],[f25]) ).
cnf(s3,plain,
~ spl2_1,
inference(sat_conversion,[],[f29]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
thf(f30,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO308^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.14 % Computer : n012.cluster.edu
% 0.06/0.14 % Model : x86_64 x86_64
% 0.06/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.14 % Memory : 8046.5625MB
% 0.06/0.14 % OS : Linux 6.8.0-71-generic
% 0.06/0.14 % CPULimit : 300
% 0.06/0.14 % WCLimit : 300
% 0.06/0.14 % DateTime : Tue Sep 29 16:44:19 UTC 2026
% 0.06/0.15 % CPUTime :
% 0.06/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.17 Running first-order model finding
% 0.06/0.17 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
% 0.06/0.20 % (359362)Will run a generic schedule for satisfiability detection.
% 0.06/0.20 % (359367)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3149880066_3000 on theBenchmark for (3000ds/0Mi)
% 0.06/0.20 % Exception at run slice level
% 0.06/0.20 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.06/0.20 % (359371)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=156759238:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.06/0.20 % (359370)dis+10_1_sil=32000:sp=arity:random_seed=1103699814:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.06/0.20 % (359372)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4143894357:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.06/0.20 % (359373)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1420820693:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.06/0.20 % (359371)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.06/0.20 % (359371) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-359362-359371"...
% 0.06/0.20 % (359372) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-359362-359372"...
% 0.06/0.20 % (359370) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-359362-359370"...
% 0.06/0.20 % (359373) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-359362-359373"...
% 0.06/0.20 % (359368)% WARNING: option uhcvi not known.
% 0.06/0.20 % (359369)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3371052141:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.06/0.20 % (359371)...printing done.
% 0.06/0.20 % (359370)...printing done.
% 0.06/0.20 % (359372)...printing done.
% 0.06/0.20 % (359373)...printing done.
% 0.06/0.20 % (359371)Refutation found. Thanks to Tanya!
% 0.06/0.20 % SZS status Theorem for theBenchmark
% 0.06/0.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.20 % (359371)------------------------------
% 0.06/0.20 % (359371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.20 % (359371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.20 % (359371)CaDiCaL version: 2.1.3
% 0.06/0.20 % (359371)Termination reason: Refutation
% 0.06/0.20 % (359371)Time elapsed: 0.002 s
% 0.06/0.20 % (359371)Peak memory usage: 12 MB
% 0.06/0.20 % (359371)Instructions burned: 2 (million)
% 0.06/0.20 % (359362)Success in time 0.022 s
% 0.06/0.20 % Vampire exiting
%------------------------------------------------------------------------------