%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO112^5 : 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 : n015.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 08:46:38 AM UTC 2026
% Result : Theorem 0.23s 0.28s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 81 ( 7 unt; 0 typ; 10 def)
% Number of atoms : 500 ( 118 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 359 ( 101 ~; 114 |; 19 &; 97 @)
% ( 26 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 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 : 22 ( 19 usr; 19 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 44 !; 26 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_4,type,
sP0: $o ).
thf(func_def_5,type,
sP1: $o ).
thf(f1,conjecture,
( ( ? [X1: $i] : ( cP @ X1 )
<=> ! [X0: $i] : ( cP @ X0 ) )
<=> ! [X0: $i] :
( ? [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM53) ).
thf(f2,negated_conjecture,
~ ( ( ? [X1: $i] : ( cP @ X1 )
<=> ! [X0: $i] : ( cP @ X0 ) )
<=> ! [X0: $i] :
( ? [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) )
<=> ! [X2: $i] :
( ? [X3: $i] : ( cP @ X3 )
<=> ( cP @ X2 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) )
<=> ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
<=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) )
<~> ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
<=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,definition,
( ( $true = sP0 )
<=> ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f7,definition,
( ( $true = sP1 )
<=> ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
<=> ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
( ( $true = sP0 )
<~> ( $true = sP1 ) ),
inference(definition_folding,[],[f5,f7,f6]) ).
thf(f9,plain,
( ( ( $true = sP1 )
| ? [X2: $i] :
( ( ! [X3: $i] :
( ( cP @ X3 )
!= $true )
| ( $true
!= ( cP @ X2 ) ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ( $true
= ( cP @ X2 ) ) ) ) )
& ( ! [X2: $i] :
( ( ( $true
= ( cP @ X2 ) )
| ! [X3: $i] :
( ( cP @ X3 )
!= $true ) )
& ( ? [X3: $i] :
( ( cP @ X3 )
= $true )
| ( $true
!= ( cP @ X2 ) ) ) )
| ( $true != sP1 ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ( $true = sP1 )
| ? [X0: $i] :
( ( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ( ( cP @ X0 )
!= $true ) )
& ( ? [X2: $i] :
( $true
= ( cP @ X2 ) )
| ( ( cP @ X0 )
= $true ) ) ) )
& ( ! [X3: $i] :
( ( ( ( cP @ X3 )
= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) )
& ( ? [X5: $i] :
( ( cP @ X5 )
= $true )
| ( ( cP @ X3 )
!= $true ) ) )
| ( $true != sP1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ( $true = sP1 )
| ( ( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ( ( cP @ sK2 )
!= $true ) )
& ( ( ( cP @ sK3 )
= $true )
| ( ( cP @ sK2 )
= $true ) ) ) )
& ( ! [X3: $i] :
( ( ( ( cP @ X3 )
= $true )
| ! [X4: $i] :
( ( cP @ X4 )
!= $true ) )
& ( ( ( cP @ sK4 )
= $true )
| ( ( cP @ X3 )
!= $true ) ) )
| ( $true != sP1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X2,sK3),skolemize(X5,sK4)],[f10]) ).
thf(f12,plain,
( ( ( $true = sP0 )
| ( ( ? [X1: $i] :
( ( cP @ X1 )
!= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ? [X0: $i] :
( ( cP @ X0 )
= $true ) ) ) )
& ( ( ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
| ? [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ! [X0: $i] :
( ( cP @ X0 )
!= $true ) ) )
| ( $true != sP0 ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f13,plain,
( ( ( $true = sP0 )
| ( ( ? [X0: $i] :
( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cP @ X2 ) )
| ? [X3: $i] :
( ( cP @ X3 )
= $true ) ) ) )
& ( ( ( ? [X4: $i] :
( ( cP @ X4 )
= $true )
| ? [X5: $i] :
( ( cP @ X5 )
!= $true ) )
& ( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ! [X7: $i] :
( ( cP @ X7 )
!= $true ) ) )
| ( $true != sP0 ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ( $true = sP0 )
| ( ( ( ( cP @ sK5 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cP @ X2 ) )
| ( ( cP @ sK6 )
= $true ) ) ) )
& ( ( ( ( $true
= ( cP @ sK7 ) )
| ( ( cP @ sK8 )
!= $true ) )
& ( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ! [X7: $i] :
( ( cP @ X7 )
!= $true ) ) )
| ( $true != sP0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8)],[f13]) ).
thf(f15,plain,
( ( ( $true != sP1 )
| ( $true != sP0 ) )
& ( ( $true = sP1 )
| ( $true = sP0 ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f17,plain,
! [X3: $i,X4: $i] :
( ( ( cP @ X3 )
= $true )
| ( $true != sP1 )
| ( ( cP @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,plain,
( ( ( cP @ sK3 )
= $true )
| ( ( cP @ sK2 )
= $true )
| ( $true = sP1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
! [X1: $i] :
( ( ( cP @ sK2 )
!= $true )
| ( $true = sP1 )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
! [X6: $i,X7: $i] :
( ( ( cP @ X7 )
!= $true )
| ( ( cP @ X6 )
= $true )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
| ( ( cP @ sK6 )
= $true )
| ( $true = sP0 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
! [X1: $i] :
( ( $true = sP0 )
| ( ( cP @ sK5 )
!= $true )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
( ( $true = sP1 )
| ( $true = sP0 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
( ( $true != sP1 )
| ( $true != sP0 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f29,definition,
( spl9_1
<=> ( $true = sP1 ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f33,definition,
( spl9_2
<=> ! [X1: $i] :
( ( cP @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f34,plain,
( ! [X1: $i] :
( ( cP @ X1 )
!= $true )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f36,definition,
( spl9_3
<=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f37,plain,
( ( ( cP @ sK2 )
= $true )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f38,plain,
( ( ( cP @ sK2 )
!= $true )
| spl9_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f39,plain,
( spl9_1
| spl9_2
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f19,f36,f33,f29]) ).
thf(f41,definition,
( spl9_4
<=> ( $true = sP0 ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f53,plain,
( ~ spl9_1
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f25,f41,f29]) ).
thf(f60,definition,
( spl9_8
<=> ! [X6: $i] :
( ( cP @ X6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f61,plain,
( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f60]) ).
thf(f62,plain,
( spl9_8
| ~ spl9_4
| spl9_2 ),
inference(avatar_split_clause,[],[f20,f33,f41,f60]) ).
thf(f63,plain,
( spl9_4
| spl9_1 ),
inference(avatar_split_clause,[],[f24,f29,f41]) ).
thf(f64,plain,
( ~ spl9_1
| spl9_2
| spl9_8 ),
inference(avatar_split_clause,[],[f17,f60,f33,f29]) ).
thf(f66,definition,
( spl9_9
<=> ( ( cP @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
thf(f68,plain,
( ( ( cP @ sK5 )
!= $true )
| spl9_9 ),
inference(avatar_component_clause,[],[f66]) ).
thf(f69,plain,
( spl9_4
| ~ spl9_9
| spl9_2 ),
inference(avatar_split_clause,[],[f23,f33,f66,f41]) ).
thf(f71,definition,
( spl9_10
<=> ( ( cP @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f73,plain,
( ( ( cP @ sK3 )
= $true )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f71]) ).
thf(f74,plain,
( spl9_10
| spl9_1
| spl9_3 ),
inference(avatar_split_clause,[],[f18,f36,f29,f71]) ).
thf(f76,definition,
( spl9_11
<=> ( ( cP @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f78,plain,
( ( ( cP @ sK6 )
= $true )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f79,plain,
( spl9_11
| spl9_8
| spl9_4 ),
inference(avatar_split_clause,[],[f22,f41,f60,f76]) ).
thf(f94,plain,
( $false
| ~ spl9_2
| ~ spl9_3 ),
inference(forward_subsumption_resolution,[],[f37,f34]) ).
thf(f95,plain,
( ~ spl9_2
| ~ spl9_3 ),
inference(avatar_contradiction_clause,[],[f94]) ).
thf(f96,plain,
( $false
| ~ spl9_2
| ~ spl9_10 ),
inference(forward_subsumption_resolution,[],[f73,f34]) ).
thf(f97,plain,
( ~ spl9_2
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f96]) ).
thf(f98,plain,
( $false
| ~ spl9_2
| ~ spl9_11 ),
inference(forward_subsumption_resolution,[],[f78,f34]) ).
thf(f99,plain,
( ~ spl9_2
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f98]) ).
thf(f100,plain,
( $false
| ~ spl9_2
| ~ spl9_8 ),
inference(forward_subsumption_resolution,[],[f61,f34]) ).
thf(f101,plain,
( ~ spl9_2
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f100]) ).
thf(f111,plain,
( ( $true != $true )
| spl9_3
| ~ spl9_8 ),
inference(constrained_superposition,[],[f38,f61]) ).
thf(f115,plain,
( $false
| spl9_3
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f111]) ).
thf(f116,plain,
( spl9_3
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f115]) ).
thf(f117,plain,
( $false
| ~ spl9_8
| spl9_9 ),
inference(forward_subsumption_resolution,[],[f68,f61]) ).
thf(f118,plain,
( ~ spl9_8
| spl9_9 ),
inference(avatar_contradiction_clause,[],[f117]) ).
cnf(s1,plain,
( spl9_1
| spl9_2
| ~ spl9_3 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( ~ spl9_1
| ~ spl9_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s5,plain,
( spl9_2
| ~ spl9_4
| spl9_8 ),
inference(sat_conversion,[],[f62]) ).
cnf(s6,plain,
( spl9_1
| spl9_4 ),
inference(sat_conversion,[],[f63]) ).
cnf(s7,plain,
( ~ spl9_1
| spl9_2
| spl9_8 ),
inference(sat_conversion,[],[f64]) ).
cnf(s8,plain,
( spl9_2
| spl9_4
| ~ spl9_9 ),
inference(sat_conversion,[],[f69]) ).
cnf(s9,plain,
( spl9_1
| spl9_3
| spl9_10 ),
inference(sat_conversion,[],[f74]) ).
cnf(s10,plain,
( spl9_4
| spl9_8
| spl9_11 ),
inference(sat_conversion,[],[f79]) ).
cnf(s11,plain,
( ~ spl9_2
| ~ spl9_3 ),
inference(sat_conversion,[],[f95]) ).
cnf(s12,plain,
( ~ spl9_2
| ~ spl9_10 ),
inference(sat_conversion,[],[f97]) ).
cnf(s13,plain,
( ~ spl9_2
| ~ spl9_11 ),
inference(sat_conversion,[],[f99]) ).
cnf(s14,plain,
( ~ spl9_2
| ~ spl9_8 ),
inference(sat_conversion,[],[f101]) ).
cnf(s16,plain,
( spl9_3
| ~ spl9_8 ),
inference(sat_conversion,[],[f116]) ).
cnf(s17,plain,
( ~ spl9_8
| spl9_9 ),
inference(sat_conversion,[],[f118]) ).
cnf(s18,plain,
( spl9_2
| spl9_1 ),
inference(rat,[],[s16,s1,s5,s6]) ).
cnf(s19,plain,
spl9_1,
inference(rat,[],[s9,s11,s12,s18]) ).
cnf(s20,plain,
~ spl9_4,
inference(rat,[],[s3,s19]) ).
cnf(s21,plain,
spl9_2,
inference(rat,[],[s17,s8,s7,s20,s19]) ).
cnf(s22,plain,
~ spl9_8,
inference(rat,[],[s14,s21]) ).
cnf(s23,plain,
~ spl9_11,
inference(rat,[],[s13,s21]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s10,s20,s22,s23]) ).
thf(f119,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO112^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n015.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:37:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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
% 0.23/0.28 % (3754504)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.28 % (3754515)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.28 % (3754515)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
% 0.23/0.28 % (3754515)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2775380184:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.28 % (3754515) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3754504-3754515"...
% 0.23/0.28 % (3754515)...printing done.
% 0.23/0.28 % (3754515)Refutation found. Thanks to Tanya!
% 0.23/0.28 % SZS status Theorem for theBenchmark
% 0.23/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.28 % (3754515)------------------------------
% 0.23/0.28 % (3754515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.28 % (3754515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.28 % (3754515)CaDiCaL version: 2.1.3
% 0.23/0.28 % (3754515)Termination reason: Refutation
% 0.23/0.28 % (3754515)Time elapsed: 0.002 s
% 0.23/0.28 % (3754515)Peak memory usage: 13 MB
% 0.23/0.28 % (3754515)Instructions burned: 4 (million)
% 0.23/0.28 % (3754504)Success in time 0.038 s
% 0.23/0.28 % Vampire exiting
%------------------------------------------------------------------------------