%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO315^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:47:25 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 10 unt; 0 typ; 2 def)
% Number of atoms : 177 ( 60 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 202 ( 51 ~; 25 |; 42 &; 77 @)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 72 ( 0 sgn 24 !; 48 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_4,type,
sK0: $i > $o ).
thf(func_def_7,type,
sK3: $i > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(f1,conjecture,
( ? [X2: $i,X3: $i,X0: $i > $o,X1: $i > $o] :
( ~ ( X1 @ z )
& ( X0 @ X2 )
& ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 )
& ~ ( X0 @ X3 )
& ( X1 @ X3 )
& ~ ( X1 @ z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSILLYWFF) ).
thf(f2,negated_conjecture,
~ ( ? [X2: $i,X3: $i,X0: $i > $o,X1: $i > $o] :
( ~ ( X1 @ z )
& ( X0 @ X2 )
& ~ ( X0 @ X3 )
& ( X1 @ X3 ) )
=> ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( X0 @ X2 )
& ~ ( X0 @ X3 )
& ( X1 @ X3 )
& ~ ( X1 @ z ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ? [X0: $i,X1: $i,X2: $i > $o,X3: $i > $o] :
( ~ ( X3 @ z )
& ( X2 @ X0 )
& ~ ( X2 @ X1 )
& ( X3 @ X1 ) )
=> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( X4 @ X6 )
& ~ ( X4 @ X7 )
& ( X5 @ X7 )
& ~ ( X5 @ z ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ? [X0: $i,X1: $i,X2: $i > $o,X3: $i > $o] :
( ( ( X3 @ z )
!= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( X2 @ X1 )
!= $true )
& ( ( X3 @ X1 )
= $true ) )
=> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( ( X4 @ X6 )
= $true )
& ( ( X4 @ X7 )
!= $true )
& ( ( X5 @ X7 )
= $true )
& ( ( X5 @ z )
!= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
~ ( ? [X2: $i > $o,X1: $i,X0: $i,X3: $i > $o] :
( ( ( X3 @ z )
!= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( X2 @ X1 )
!= $true )
& ( ( X3 @ X1 )
= $true ) )
=> ? [X5: $i > $o,X7: $i,X6: $i,X4: $i > $o] :
( ( ( X5 @ X7 )
= $true )
& ( ( X4 @ X6 )
= $true )
& ( ( X5 @ z )
!= $true )
& ( ( X4 @ X7 )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ? [X2: $i > $o,X1: $i,X0: $i,X3: $i > $o] :
( ( ( X3 @ z )
!= $true )
& ( ( X2 @ X0 )
= $true )
& ( ( X2 @ X1 )
!= $true )
& ( ( X3 @ X1 )
= $true ) )
& ! [X7: $i,X5: $i > $o,X4: $i > $o,X6: $i] :
( ( ( X5 @ z )
= $true )
| ( ( X4 @ X6 )
!= $true )
| ( ( X4 @ X7 )
= $true )
| ( ( X5 @ X7 )
!= $true ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f7,plain,
( ? [X0: $i > $o,X1: $i,X2: $i,X3: $i > $o] :
( ( ( X3 @ z )
!= $true )
& ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X1 )
!= $true )
& ( ( X3 @ X1 )
= $true ) )
& ! [X4: $i,X5: $i > $o,X6: $i > $o,X7: $i] :
( ( ( X5 @ z )
= $true )
| ( ( X6 @ X7 )
!= $true )
| ( $true
= ( X6 @ X4 ) )
| ( ( X5 @ X4 )
!= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( sK3 @ z )
!= $true )
& ( $true
= ( sK0 @ sK2 ) )
& ( ( sK0 @ sK1 )
!= $true )
& ( ( sK3 @ sK1 )
= $true )
& ! [X4: $i,X5: $i > $o,X6: $i > $o,X7: $i] :
( ( ( X5 @ z )
= $true )
| ( ( X6 @ X7 )
!= $true )
| ( $true
= ( X6 @ X4 ) )
| ( ( X5 @ X4 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7]) ).
thf(f9,plain,
! [X6: $i > $o,X7: $i,X4: $i,X5: $i > $o] :
( ( $true
= ( X6 @ X4 ) )
| ( ( X6 @ X7 )
!= $true )
| ( ( X5 @ X4 )
!= $true )
| ( ( X5 @ z )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
( ( sK3 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( sK3 @ z )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,definition,
( spl4_1
<=> ( ( sK3 @ z )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f18,plain,
( ( ( sK3 @ z )
!= $true )
| spl4_1 ),
inference(avatar_component_clause,[],[f16]) ).
thf(f19,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f13,f16]) ).
thf(f31,definition,
( spl4_4
<=> ( ( sK3 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f33,plain,
( ( ( sK3 @ sK1 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
spl4_4,
inference(avatar_split_clause,[],[f10,f31]) ).
thf(f35,plain,
! [X2: $i > $o,X0: $i,X1: $i] :
( ( ( X2 @ z )
= $true )
| ( ( X2 @ X0 )
!= $true )
| ( X0 = X1 ) ),
inference(leibniz_equality_elimination,[],[f9]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( z = X0 )
| ( X0 = X1 ) ),
inference(leibniz_equality_elimination,[],[f35]) ).
thf(f62,plain,
! [X0: $i] :
( ( z = X0 )
| ( X0 != X0 ) ),
inference(equality_factoring,[],[f47]) ).
thf(f64,plain,
! [X0: $i] : ( z = X0 ),
inference(trivial_inequality_removal,[],[f62]) ).
thf(f79,plain,
( ! [X0: $i] :
( ( sK3 @ X0 )
!= $true )
| spl4_1 ),
inference(superposition,[],[f18,f64]) ).
thf(f93,plain,
( ( $true != $true )
| spl4_1
| ~ spl4_4 ),
inference(superposition,[],[f79,f33]) ).
thf(f96,plain,
( $false
| spl4_1
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f97,plain,
( spl4_1
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f96]) ).
cnf(s1,plain,
~ spl4_1,
inference(sat_conversion,[],[f19]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f34]) ).
cnf(s7,plain,
( spl4_1
| ~ spl4_4 ),
inference(sat_conversion,[],[f97]) ).
cnf(s8,plain,
spl4_1,
inference(rat,[],[s7,s4]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s8]) ).
thf(f100,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO315^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n016.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:50:05 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.26 % (601697)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.26 % (601705)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3041008844:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.18/0.26 % (601705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-601697-601705"...
% 0.18/0.26 % (601705)...printing done.
% 0.18/0.26 % (601708)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.26 % (601708)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.18/0.26 % (601705)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (601705)------------------------------
% 0.18/0.26 % (601705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (601705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (601705)CaDiCaL version: 2.1.3
% 0.18/0.26 % (601705)Termination reason: Refutation
% 0.18/0.26 % (601705)Time elapsed: 0.002 s
% 0.18/0.26 % (601705)Peak memory usage: 13 MB
% 0.18/0.26 % (601705)Instructions burned: 5 (million)
% 0.18/0.26 % (601697)Success in time 0.039 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------