%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYP119^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 08:50:42 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 12 unt; 0 typ; 2 def)
% Number of atoms : 52 ( 27 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 177 ( 20 ~; 16 |; 2 &; 137 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 5 con; 0-6 aty)
% Number of variables : 37 ( 0 sgn 27 !; 3 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(func_def_0,type,
i:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_1,type,
o:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X2 ) > ( X1 > X0 ) > X1 > X2 ) ).
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_5,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_6,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_7,type,
sK2: sK0 > sK1 ).
thf(func_def_10,type,
sK3:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_12,type,
sK5: sK0 ).
thf(func_def_13,type,
sK6: sK0 ).
thf(f1,axiom,
! [X0: $tType,X3: X0] :
( ( i @ X0 @ X3 )
= X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','trivia/I_THM_') ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [X5: X2] : ( X3 @ ( X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','trivia/o_DEF_') ).
thf(f5,conjecture,
! [X0: $tType,X1: $tType,X2: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
= X2 )
& ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','trivia/I_O_ID_') ).
thf(f6,negated_conjecture,
~ ! [X0: $tType,X1: $tType,X2: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
= X2 )
& ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
= X2 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f9,plain,
! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
inference(rectify,[],[f1]) ).
thf(f10,plain,
? [X0: $tType,X1: $tType,X2: X0 > X1] :
( ( ( o @ X0 @ X0 @ X1 @ X2 @ i @ X0 )
!= X2 )
| ( ( o @ X1 @ X0 @ X1 @ i @ X1 @ X2 )
!= X2 ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f11,plain,
( ( sK2
!= ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 ) )
| ( sK2
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
thf(f12,plain,
! [X0: $tType,X1: X0] :
( ( i @ X0 @ X1 )
= X1 ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( ( sK2
!= ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 ) )
| ( sK2
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f30,definition,
( spl4_1
<=> ( sK2
= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f32,plain,
( ( sK2
!= ( o @ sK1 @ sK0 @ sK1 @ i @ sK1 @ sK2 ) )
| spl4_1 ),
inference(avatar_component_clause,[],[f30]) ).
thf(f34,definition,
( spl4_2
<=> ( sK2
= ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f36,plain,
( ( sK2
!= ( o @ sK0 @ sK0 @ sK1 @ sK2 @ i @ sK0 ) )
| spl4_2 ),
inference(avatar_component_clause,[],[f34]) ).
thf(f37,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f16,f34,f30]) ).
thf(f38,plain,
( ( sK2
!= ( ^ [Y0: sK0] : ( i @ sK1 @ ( sK2 @ Y0 ) ) ) )
| spl4_1 ),
inference(forward_demodulation,[],[f32,f13]) ).
thf(f39,plain,
( ( ( sK2 @ sK5 )
!= ( ^ [Y0: sK0] : ( i @ sK1 @ ( sK2 @ Y0 ) )
@ sK5 ) )
| spl4_1 ),
inference(negative_extensionality,[],[f38]) ).
thf(f40,plain,
( ( ( sK2 @ sK5 )
!= ( i @ sK1 @ ( sK2 @ sK5 ) ) )
| spl4_1 ),
inference(beta-eta_normalization,[],[f39]) ).
thf(f41,plain,
( $false
| spl4_1 ),
inference(forward_subsumption_resolution,[],[f40,f12]) ).
thf(f42,plain,
spl4_1,
inference(avatar_contradiction_clause,[],[f41]) ).
thf(f44,plain,
( ( sK2
!= ( ^ [Y0: sK0] : ( sK2 @ ( i @ sK0 @ Y0 ) ) ) )
| spl4_2 ),
inference(forward_demodulation,[],[f36,f13]) ).
thf(f47,plain,
( ( ( sK2 @ sK6 )
!= ( ^ [Y0: sK0] : ( sK2 @ ( i @ sK0 @ Y0 ) )
@ sK6 ) )
| spl4_2 ),
inference(negative_extensionality,[],[f44]) ).
thf(f48,plain,
( ( ( sK2 @ sK6 )
!= ( sK2 @ ( i @ sK0 @ sK6 ) ) )
| spl4_2 ),
inference(beta-eta_normalization,[],[f47]) ).
thf(f49,plain,
( ( ( sK2 @ sK6 )
!= ( sK2 @ sK6 ) )
| spl4_2 ),
inference(forward_demodulation,[],[f48,f12]) ).
thf(f50,plain,
( $false
| spl4_2 ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f51,plain,
spl4_2,
inference(avatar_contradiction_clause,[],[f50]) ).
cnf(s1,plain,
( ~ spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
spl4_2,
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
thf(f52,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYP119^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:29:16 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25 % (401942)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (401953)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1842015455:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.08/0.25 % (401947)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=112878095_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % (401949)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1147391918:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.25 % (401951)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3812032591:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.25 % (401952)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3654118236:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (401950)dis+10_1_sil=32000:sp=arity:random_seed=2634176373:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.08/0.25 % (401951)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % Exception at run slice level
% 0.08/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.08/0.25 % (401951) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-401942-401951"...
% 0.08/0.25 % (401950) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-401942-401950"...
% 0.08/0.25 % (401951)...printing done.
% 0.08/0.25 % (401950)...printing done.
% 0.08/0.25 % (401951)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (401951)------------------------------
% 0.08/0.25 % (401951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (401951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (401951)CaDiCaL version: 2.1.3
% 0.08/0.25 % (401951)Termination reason: Refutation
% 0.08/0.25 % (401951)Time elapsed: 0.003 s
% 0.08/0.25 % (401951)Peak memory usage: 12 MB
% 0.08/0.25 % (401951)Instructions burned: 3 (million)
% 0.08/0.25 % (401942)Success in time 0.037 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------