%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO557^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:50:25 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 14 unt; 0 typ; 5 def)
% Number of atoms : 194 ( 46 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 205 ( 45 ~; 43 |; 0 &; 99 @)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 14 usr; 9 con; 0-4 aty)
% ( 0 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 45 ( 0 sgn 16 !; 3 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
eps: ( $i > $o ) > $i ).
thf(func_def_2,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(func_def_8,type,
sK0: $i > $o ).
thf(func_def_11,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choiceax) ).
thf(f2,conjecture,
( ( ^ [X0: $i > $o] : ( X0 @ ( eps @ X0 ) ) )
= ( ^ [X0: $i > $o] : ( ?? @ $i @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f3,negated_conjecture,
( ( ^ [X0: $i > $o] : ( X0 @ ( eps @ X0 ) ) )
!= ( ^ [X0: $i > $o] : ( ?? @ $i @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( X0 @ ( eps @ X0 ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i > $o] : ( X0 @ ( eps @ X0 ) ) )
!= ( ^ [X1: $i > $o] : ( ?? @ $i @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
( ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) )
!= ( ^ [Y0: $i > $o] : ( ?? @ $i @ Y0 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) )
!= ( ^ [Y0: $i > $o] : ( ?? @ $i @ Y0 ) ) ),
inference(flattening,[],[f7]) ).
thf(f9,plain,
! [X0: $i > $o] :
( ( ( X0 @ ( eps @ X0 ) )
= $true )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f10,plain,
! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
| ( ( X0 @ ( eps @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f11,plain,
( ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) )
!= ( ^ [Y0: $i > $o] : ( ?? @ $i @ Y0 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f14,plain,
( ??
@ ( $i
!= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f15,plain,
( ( ?? @ $i @ sK0 )
!= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f16,plain,
( ( $true
= ( ?? @ $i @ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f17,plain,
( ( $false
= ( ?? @ $i @ sK0 ) )
| ( $false
= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f15]) ).
thf(f18,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) )
@ sK0 ) ) ),
inference(pi_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ ( eps @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( ^ [Y0: $i > $o] : ( Y0 @ ( eps @ Y0 ) )
@ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f21,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
= ( sK0 @ ( eps @ sK0 ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f23,definition,
( spl2_1
<=> ( $false
= ( sK0 @ ( eps @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f24,plain,
( ( $false
!= ( sK0 @ ( eps @ sK0 ) ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f25,plain,
( ( $false
= ( sK0 @ ( eps @ sK0 ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f27,definition,
( spl2_2
<=> ! [X1: $i] :
( $false
= ( sK0 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f28,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ X1 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f19,f27,f23]) ).
thf(f31,definition,
( spl2_3
<=> ( $true
= ( sK0 @ ( eps @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f33,plain,
( ( $true
= ( sK0 @ ( eps @ sK0 ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f35,definition,
( spl2_4
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f37,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f21,f35,f31]) ).
thf(f40,plain,
( ( $false != $false )
| spl2_1
| ~ spl2_2 ),
inference(constrained_superposition,[],[f24,f28]) ).
thf(f41,plain,
( $false
| spl2_1
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f42,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f41]) ).
thf(f71,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( eps
@ ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ( sK1 != X0 ) )
| ~ spl2_4 ),
inference(constrained_superposition,[],[f10,f37]) ).
thf(f85,plain,
( ! [X0: $i] :
( ( $true
= ( ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( eps
@ ^ [Y0: $i] :
( sK0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ( sK1 != X0 ) )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f86,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ ( eps @ sK0 ) ) )
| ( sK1 != X0 ) )
| ~ spl2_4 ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f93,definition,
( spl2_5
<=> ! [X0: $i] : ( sK1 != X0 ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
thf(f94,plain,
( ! [X0: $i] : ( sK1 != X0 )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f95,plain,
( spl2_5
| spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f86,f35,f31,f93]) ).
thf(f96,plain,
( $false
| ~ spl2_5 ),
inference(equality_resolution,[],[f94]) ).
thf(f97,plain,
~ spl2_5,
inference(avatar_contradiction_clause,[],[f96]) ).
thf(f98,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_3 ),
inference(constrained_superposition,[],[f33,f25]) ).
thf(f108,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f109,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f108]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s8,plain,
( spl2_3
| ~ spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f95]) ).
cnf(s9,plain,
~ spl2_5,
inference(sat_conversion,[],[f97]) ).
cnf(s11,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f109]) ).
cnf(s12,plain,
( spl2_3
| ~ spl2_4 ),
inference(rat,[],[s8,s9]) ).
cnf(s13,plain,
spl2_1,
inference(rat,[],[s1,s3]) ).
cnf(s14,plain,
~ spl2_3,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
~ spl2_4,
inference(rat,[],[s12,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s15,s14]) ).
thf(f110,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO557^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:14:21 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.20/0.27 % (2399690)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (2399701)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2432073128:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (2399701) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2399690-2399701"...
% 0.20/0.27 % (2399695)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1313395989_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % Exception at run slice level
% 0.20/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.27 % (2399697)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2880936653:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (2399698)dis+10_1_sil=32000:sp=arity:random_seed=758486836:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (2399699)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1323829531:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (2399701)...printing done.
% 0.20/0.27 % (2399699)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (2399701)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (2399701)------------------------------
% 0.20/0.27 % (2399701)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (2399701)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (2399701)CaDiCaL version: 2.1.3
% 0.20/0.27 % (2399701)Termination reason: Refutation
% 0.20/0.27 % (2399701)Time elapsed: 0.003 s
% 0.20/0.27 % (2399701)Peak memory usage: 13 MB
% 0.20/0.27 % (2399701)Instructions burned: 4 (million)
% 0.20/0.27 % (2399690)Success in time 0.037 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------