%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN377^5 : 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 : n002.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 08:41:41 AM UTC 2026
% Result : Theorem 0.14s 0.27s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of formulae : 78 ( 8 unt; 0 typ; 10 def)
% Number of atoms : 489 ( 117 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 344 ( 92 ~; 108 |; 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 50 !; 20 ?; 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,
( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) )
<=> ! [X0: $i] :
( ! [X1: $i] : ( cP @ X1 )
<=> ( cP @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2128) ).
thf(f2,negated_conjecture,
~ ( ( ? [X0: $i] : ( cP @ X0 )
<=> ! [X1: $i] : ( cP @ X1 ) )
<=> ! [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,
~ ( ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
<=> ! [X3: $i] :
( ( cP @ X3 )
= $true ) )
<=> ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
<=> ! [X1: $i] :
( ( cP @ X1 )
= $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,
( ( sP0 = $true )
<=> ( ? [X0: $i] :
( ( cP @ X0 )
= $true )
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f7,definition,
( ( sP1 = $true )
<=> ! [X2: $i] :
( ( $true
= ( cP @ X2 ) )
<=> ! [X3: $i] :
( ( cP @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
( ( sP0 = $true )
<~> ( sP1 = $true ) ),
inference(definition_folding,[],[f5,f7,f6]) ).
thf(f9,plain,
( ( ( sP1 = $true )
| ? [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 ) ) ) )
| ( sP1 != $true ) ) ),
inference(nnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ( sP1 = $true )
| ? [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 ) ) )
| ( sP1 != $true ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( ( sP1 = $true )
| ( ( ( $true
!= ( cP @ sK3 ) )
| ( ( cP @ sK2 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cP @ X2 ) )
| ( ( cP @ sK2 )
= $true ) ) ) )
& ( ! [X3: $i] :
( ( ( ( cP @ X3 )
= $true )
| ( $true
!= ( cP @ sK4 ) ) )
& ( ! [X5: $i] :
( ( cP @ X5 )
= $true )
| ( ( cP @ X3 )
!= $true ) ) )
| ( sP1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X4,sK4)],[f10]) ).
thf(f12,plain,
( ( ( sP0 = $true )
| ( ( ? [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 ) ) )
| ( sP0 != $true ) ) ),
inference(nnf_transformation,[],[f6]) ).
thf(f13,plain,
( ( ( sP0 = $true )
| ( ( ? [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 ) ) )
| ( sP0 != $true ) ) ),
inference(rectify,[],[f12]) ).
thf(f14,plain,
( ( ( sP0 = $true )
| ( ( ( ( cP @ sK5 )
!= $true )
| ! [X1: $i] :
( ( cP @ X1 )
!= $true ) )
& ( ! [X2: $i] :
( $true
= ( cP @ X2 ) )
| ( ( cP @ sK6 )
= $true ) ) ) )
& ( ( ( ( ( cP @ sK7 )
= $true )
| ( $true
!= ( cP @ sK8 ) ) )
& ( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ! [X7: $i] :
( ( cP @ X7 )
!= $true ) ) )
| ( sP0 != $true ) ) ),
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,
( ( ( sP1 != $true )
| ( sP0 != $true ) )
& ( ( sP1 = $true )
| ( sP0 = $true ) ) ),
inference(nnf_transformation,[],[f8]) ).
thf(f16,plain,
! [X3: $i,X5: $i] :
( ( sP1 != $true )
| ( ( cP @ X5 )
= $true )
| ( ( cP @ X3 )
!= $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f18,plain,
! [X2: $i] :
( ( ( cP @ sK2 )
= $true )
| ( $true
= ( cP @ X2 ) )
| ( sP1 = $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( ( $true
!= ( cP @ sK3 ) )
| ( ( cP @ sK2 )
!= $true )
| ( sP1 = $true ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
! [X6: $i,X7: $i] :
( ( ( cP @ X6 )
= $true )
| ( ( cP @ X7 )
!= $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f22,plain,
! [X2: $i] :
( ( ( cP @ sK6 )
= $true )
| ( $true
= ( cP @ X2 ) )
| ( sP0 = $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f23,plain,
! [X1: $i] :
( ( ( cP @ sK5 )
!= $true )
| ( sP0 = $true )
| ( ( cP @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
( ( sP1 = $true )
| ( sP0 = $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f25,plain,
( ( sP1 != $true )
| ( sP0 != $true ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f29,definition,
( spl9_1
<=> ! [X7: $i] :
( ( cP @ X7 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f30,plain,
( ! [X7: $i] :
( ( cP @ X7 )
!= $true )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f29]) ).
thf(f32,definition,
( spl9_2
<=> ( sP0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f36,definition,
( spl9_3
<=> ! [X6: $i] :
( ( cP @ X6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f37,plain,
( ! [X6: $i] :
( ( cP @ X6 )
= $true )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f36]) ).
thf(f38,plain,
( spl9_1
| ~ spl9_2
| spl9_3 ),
inference(avatar_split_clause,[],[f20,f36,f32,f29]) ).
thf(f40,definition,
( spl9_4
<=> ( sP1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f43,plain,
( spl9_4
| spl9_2 ),
inference(avatar_split_clause,[],[f24,f32,f40]) ).
thf(f45,definition,
( spl9_5
<=> ( ( cP @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f47,plain,
( ( ( cP @ sK6 )
= $true )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f45]) ).
thf(f48,plain,
( spl9_3
| spl9_5
| spl9_2 ),
inference(avatar_split_clause,[],[f22,f32,f45,f36]) ).
thf(f50,definition,
( spl9_6
<=> ( ( cP @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f52,plain,
( ( ( cP @ sK5 )
!= $true )
| spl9_6 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
( ~ spl9_6
| spl9_2
| spl9_1 ),
inference(avatar_split_clause,[],[f23,f29,f32,f50]) ).
thf(f54,plain,
( ~ spl9_4
| spl9_1
| spl9_3 ),
inference(avatar_split_clause,[],[f16,f36,f29,f40]) ).
thf(f70,definition,
( spl9_10
<=> ( ( cP @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f71,plain,
( ( ( cP @ sK2 )
= $true )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f72,plain,
( ( ( cP @ sK2 )
!= $true )
| spl9_10 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f74,definition,
( spl9_11
<=> ( $true
= ( cP @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f76,plain,
( ( $true
!= ( cP @ sK3 ) )
| spl9_11 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f77,plain,
( spl9_4
| ~ spl9_10
| ~ spl9_11 ),
inference(avatar_split_clause,[],[f19,f74,f70,f40]) ).
thf(f78,plain,
( spl9_4
| spl9_10
| spl9_3 ),
inference(avatar_split_clause,[],[f18,f36,f70,f40]) ).
thf(f79,plain,
( ~ spl9_4
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f25,f32,f40]) ).
thf(f94,plain,
( $false
| ~ spl9_3
| spl9_6 ),
inference(forward_subsumption_resolution,[],[f52,f37]) ).
thf(f95,plain,
( ~ spl9_3
| spl9_6 ),
inference(avatar_contradiction_clause,[],[f94]) ).
thf(f101,plain,
( $false
| ~ spl9_3
| spl9_10 ),
inference(forward_subsumption_resolution,[],[f72,f37]) ).
thf(f102,plain,
( ~ spl9_3
| spl9_10 ),
inference(avatar_contradiction_clause,[],[f101]) ).
thf(f103,plain,
( $false
| ~ spl9_3
| spl9_11 ),
inference(forward_subsumption_resolution,[],[f76,f37]) ).
thf(f104,plain,
( ~ spl9_3
| spl9_11 ),
inference(avatar_contradiction_clause,[],[f103]) ).
thf(f113,plain,
( $false
| ~ spl9_1
| ~ spl9_10 ),
inference(forward_subsumption_resolution,[],[f71,f30]) ).
thf(f114,plain,
( ~ spl9_1
| ~ spl9_10 ),
inference(avatar_contradiction_clause,[],[f113]) ).
thf(f115,plain,
( $false
| ~ spl9_1
| ~ spl9_5 ),
inference(forward_subsumption_resolution,[],[f47,f30]) ).
thf(f116,plain,
( ~ spl9_1
| ~ spl9_5 ),
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( spl9_1
| ~ spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f38]) ).
cnf(s2,plain,
( spl9_2
| spl9_4 ),
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( spl9_2
| spl9_3
| spl9_5 ),
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
( spl9_1
| spl9_2
| ~ spl9_6 ),
inference(sat_conversion,[],[f53]) ).
cnf(s5,plain,
( spl9_1
| spl9_3
| ~ spl9_4 ),
inference(sat_conversion,[],[f54]) ).
cnf(s8,plain,
( spl9_4
| ~ spl9_10
| ~ spl9_11 ),
inference(sat_conversion,[],[f77]) ).
cnf(s9,plain,
( spl9_3
| spl9_4
| spl9_10 ),
inference(sat_conversion,[],[f78]) ).
cnf(s10,plain,
( ~ spl9_2
| ~ spl9_4 ),
inference(sat_conversion,[],[f79]) ).
cnf(s12,plain,
( ~ spl9_3
| spl9_6 ),
inference(sat_conversion,[],[f95]) ).
cnf(s13,plain,
( ~ spl9_3
| spl9_10 ),
inference(sat_conversion,[],[f102]) ).
cnf(s14,plain,
( ~ spl9_3
| spl9_11 ),
inference(sat_conversion,[],[f104]) ).
cnf(s18,plain,
( ~ spl9_1
| ~ spl9_10 ),
inference(sat_conversion,[],[f114]) ).
cnf(s19,plain,
( ~ spl9_1
| ~ spl9_5 ),
inference(sat_conversion,[],[f116]) ).
cnf(s20,plain,
( spl9_2
| spl9_1 ),
inference(rat,[],[s5,s12,s2,s4]) ).
cnf(s21,plain,
spl9_1,
inference(rat,[],[s8,s13,s14,s1,s10,s20]) ).
cnf(s22,plain,
~ spl9_5,
inference(rat,[],[s19,s21]) ).
cnf(s23,plain,
~ spl9_10,
inference(rat,[],[s18,s21]) ).
cnf(s27,plain,
~ spl9_3,
inference(rat,[],[s13,s23]) ).
cnf(s28,plain,
spl9_4,
inference(rat,[],[s9,s27,s23]) ).
cnf(s30,plain,
spl9_2,
inference(rat,[],[s3,s22,s27]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s10,s28,s30]) ).
thf(f117,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN377^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.17 % Computer : n002.cluster.edu
% 0.14/0.17 % Model : x86_64 x86_64
% 0.14/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.17 % Memory : 8046.5625MB
% 0.14/0.17 % OS : Linux 6.8.0-71-generic
% 0.14/0.17 % CPULimit : 300
% 0.14/0.17 % WCLimit : 300
% 0.14/0.17 % DateTime : Tue Sep 29 16:18:07 UTC 2026
% 0.14/0.18 % CPUTime :
% 0.14/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.22 Running higher-order theorem proving
% 0.14/0.23 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
% 0.14/0.27 % (1487276)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.14/0.27 % (1487287)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.14/0.27 % (1487287)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
% 0.14/0.27 % (1487287)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=1865636834:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.14/0.27 % (1487287) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1487276-1487287"...
% 0.14/0.27 % (1487287)...printing done.
% 0.14/0.27 % (1487281)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4262521656:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.14/0.27 % (1487282)lrs+10_16_si=on:nwc=1.5:random_seed=4116972690:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.14/0.27 % (1487287)Refutation found. Thanks to Tanya!
% 0.14/0.27 % SZS status Theorem for theBenchmark
% 0.14/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.27 % (1487287)------------------------------
% 0.14/0.27 % (1487287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.27 % (1487287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.27 % (1487287)CaDiCaL version: 2.1.3
% 0.14/0.27 % (1487287)Termination reason: Refutation
% 0.14/0.27 % (1487287)Time elapsed: 0.002 s
% 0.14/0.27 % (1487287)Peak memory usage: 13 MB
% 0.14/0.27 % (1487287)Instructions burned: 4 (million)
% 0.14/0.27 % (1487276)Success in time 0.035 s
% 0.14/0.27 % Vampire exiting
%------------------------------------------------------------------------------