%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN036+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 : Tue Sep 29 02:06:28 PM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of formulae : 196 ( 16 unt; 19 def)
% Number of atoms : 568 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 641 ( 269 ~; 332 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 27 ( 26 usr; 24 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 93 ( 0 sgn 81 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_p(X3) ) )
<=> ( ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_q(X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel34) ).
fof(f2,negated_conjecture,
~ ( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_p(X3) ) )
<=> ( ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_q(X7) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) )
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_p(X3) ) )
<~> ( ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) )
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_q(X7) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f4,plain,
! [X4] :
( big_q(sK10(X4))
| big_q(X4)
| sP1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f5,plain,
! [X4] :
( ~ big_q(sK10(X4))
| ~ big_q(X4)
| sP1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f6,plain,
! [X5] :
( ~ big_q(X5)
| big_q(sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f7,plain,
! [X5] :
( big_q(X5)
| ~ big_q(sK6)
| ~ sP1 ),
inference(cnf_transformation,[],[f3]) ).
fof(f8,plain,
! [X0] :
( big_p(sK7(X0))
| big_p(X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f9,plain,
! [X0] :
( ~ big_p(sK7(X0))
| ~ big_p(X0)
| sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f10,plain,
! [X0,X1] :
( ~ big_p(X1)
| big_p(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f11,plain,
! [X0,X1] :
( big_p(X1)
| ~ big_p(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f12,plain,
! [X7] :
( big_q(X7)
| big_p(sK11)
| sP2 ),
inference(cnf_transformation,[],[f3]) ).
fof(f13,plain,
! [X6] :
( ~ big_q(sK12)
| ~ big_p(X6)
| sP2 ),
inference(cnf_transformation,[],[f3]) ).
fof(f14,plain,
( ~ big_q(sK12)
| big_p(sK11)
| ~ sP2 ),
inference(cnf_transformation,[],[f3]) ).
fof(f15,plain,
! [X6,X7] :
( big_q(X7)
| ~ big_p(X6)
| ~ sP2 ),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X3] :
( big_p(X3)
| ~ sP5 ),
inference(cnf_transformation,[],[f3]) ).
fof(f17,plain,
( ~ big_p(sK9)
| sP5 ),
inference(cnf_transformation,[],[f3]) ).
fof(f18,plain,
( big_q(sK8)
| ~ sP4 ),
inference(cnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X2] :
( ~ big_q(X2)
| sP4 ),
inference(cnf_transformation,[],[f3]) ).
fof(f21,plain,
( ~ sP2
| ~ sP1
| sP5
| ~ sP4
| sP3(sK0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f23,plain,
( sP2
| sP1
| sP5
| ~ sP4
| sP3(sK0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f24,plain,
! [X0] :
( ~ sP2
| ~ sP1
| sP5
| sP4
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f25,plain,
! [X0] :
( ~ sP2
| ~ sP1
| ~ sP5
| ~ sP4
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0] :
( sP2
| sP1
| ~ sP5
| ~ sP4
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f28,plain,
( sP2
| ~ sP1
| sP5
| sP4
| sP3(sK0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X0] :
( sP2
| ~ sP1
| ~ sP5
| sP4
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( sP2
| ~ sP1
| sP5
| ~ sP4
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ sP2
| sP1
| sP5
| ~ sP4
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f3]) ).
fof(f36,plain,
! [X0] :
( sP2
| sP1
| sP5
| sP4
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f35]) ).
fof(f38,plain,
! [X0] :
( ~ sP2
| ~ sP1
| sP5
| sP4
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f33]) ).
fof(f39,plain,
! [X0] :
( ~ sP2
| ~ sP1
| ~ sP5
| ~ sP4
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f32]) ).
fof(f43,plain,
( ~ sP2
| ~ sP1
| sP5
| ~ sP4
| sP3(sK0) ),
inference(consistent_polarity_flipping,[],[f28]) ).
fof(f44,plain,
! [X0] :
( ~ sP2
| sP1
| ~ sP5
| sP4
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f27]) ).
fof(f46,plain,
! [X0] :
( sP2
| ~ sP1
| ~ sP5
| sP4
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f25]) ).
fof(f47,plain,
! [X0] :
( sP2
| ~ sP1
| sP5
| ~ sP4
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f24]) ).
fof(f48,plain,
( ~ sP2
| sP1
| sP5
| sP4
| sP3(sK0) ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f50,plain,
( sP2
| ~ sP1
| sP5
| sP4
| sP3(sK0) ),
inference(consistent_polarity_flipping,[],[f21]) ).
fof(f52,plain,
! [X2] :
( big_q(X2)
| ~ sP4 ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f53,plain,
( ~ big_q(sK8)
| sP4 ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f54,plain,
( big_p(sK9)
| sP5 ),
inference(consistent_polarity_flipping,[],[f17]) ).
fof(f55,plain,
! [X3] :
( ~ big_p(X3)
| ~ sP5 ),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f56,plain,
! [X6,X7] :
( ~ big_q(X7)
| big_p(X6)
| sP2 ),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f57,plain,
( big_q(sK12)
| ~ big_p(sK11)
| sP2 ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f58,plain,
! [X6] :
( big_q(sK12)
| big_p(X6)
| ~ sP2 ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f59,plain,
! [X7] :
( ~ big_q(X7)
| ~ big_p(sK11)
| ~ sP2 ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f60,plain,
! [X0,X1] :
( ~ big_p(X1)
| big_p(X0)
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f11]) ).
fof(f61,plain,
! [X0,X1] :
( big_p(X1)
| ~ big_p(X0)
| ~ sP3(X0) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f62,plain,
! [X0] :
( big_p(sK7(X0))
| big_p(X0)
| sP3(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f63,plain,
! [X0] :
( ~ big_p(sK7(X0))
| ~ big_p(X0)
| sP3(X0) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f64,plain,
! [X5] :
( ~ big_q(X5)
| big_q(sK6)
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f65,plain,
! [X5] :
( big_q(X5)
| ~ big_q(sK6)
| ~ sP1 ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f66,plain,
! [X4] :
( big_q(sK10(X4))
| big_q(X4)
| sP1 ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f67,plain,
! [X4] :
( ~ big_q(sK10(X4))
| ~ big_q(X4)
| sP1 ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f69,definition,
( spl13_1
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f73,definition,
( spl13_2
<=> ! [X4] :
( ~ big_q(sK10(X4))
| ~ big_q(X4) ) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f74,plain,
( ! [X4] :
( ~ big_q(sK10(X4))
| ~ big_q(X4) )
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f67,f73,f69]) ).
fof(f77,definition,
( spl13_3
<=> ! [X4] :
( big_q(sK10(X4))
| big_q(X4) ) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f78,plain,
( ! [X4] :
( big_q(sK10(X4))
| big_q(X4) )
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f79,plain,
( spl13_1
| spl13_3 ),
inference(avatar_split_clause,[],[f66,f77,f69]) ).
fof(f81,definition,
( spl13_4
<=> big_q(sK6) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f85,definition,
( spl13_5
<=> ! [X5] : big_q(X5) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f86,plain,
( ! [X5] : big_q(X5)
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f87,plain,
( ~ spl13_1
| ~ spl13_4
| spl13_5 ),
inference(avatar_split_clause,[],[f65,f85,f81,f69]) ).
fof(f89,definition,
( spl13_6
<=> ! [X5] : ~ big_q(X5) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f90,plain,
( ! [X5] : ~ big_q(X5)
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f91,plain,
( ~ spl13_1
| spl13_4
| spl13_6 ),
inference(avatar_split_clause,[],[f64,f89,f81,f69]) ).
fof(f93,definition,
( spl13_7
<=> ! [X0] :
( ~ big_p(X0)
| ~ sP3(X0) ) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f94,plain,
( ! [X0] :
( ~ sP3(X0)
| ~ big_p(X0) )
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f93]) ).
fof(f96,definition,
( spl13_8
<=> ! [X1] : big_p(X1) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f97,plain,
( ! [X1] : big_p(X1)
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f98,plain,
( spl13_7
| spl13_8 ),
inference(avatar_split_clause,[],[f61,f96,f93]) ).
fof(f100,definition,
( spl13_9
<=> ! [X0] :
( big_p(X0)
| ~ sP3(X0) ) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f101,plain,
( ! [X0] :
( big_p(X0)
| ~ sP3(X0) )
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f103,definition,
( spl13_10
<=> ! [X1] : ~ big_p(X1) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f104,plain,
( ! [X1] : ~ big_p(X1)
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f105,plain,
( spl13_9
| spl13_10 ),
inference(avatar_split_clause,[],[f60,f103,f100]) ).
fof(f107,definition,
( spl13_11
<=> sP2 ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f111,definition,
( spl13_12
<=> big_p(sK11) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f113,plain,
( ~ big_p(sK11)
| spl13_12 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f114,plain,
( ~ spl13_11
| ~ spl13_12
| spl13_6 ),
inference(avatar_split_clause,[],[f59,f89,f111,f107]) ).
fof(f116,definition,
( spl13_13
<=> big_q(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
fof(f118,plain,
( big_q(sK12)
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,plain,
( ~ spl13_11
| spl13_8
| spl13_13 ),
inference(avatar_split_clause,[],[f58,f116,f96,f107]) ).
fof(f120,plain,
( spl13_11
| ~ spl13_12
| spl13_13 ),
inference(avatar_split_clause,[],[f57,f116,f111,f107]) ).
fof(f121,plain,
( spl13_11
| spl13_8
| spl13_6 ),
inference(avatar_split_clause,[],[f56,f89,f96,f107]) ).
fof(f123,definition,
( spl13_14
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
fof(f126,plain,
( ~ spl13_14
| spl13_10 ),
inference(avatar_split_clause,[],[f55,f103,f123]) ).
fof(f128,definition,
( spl13_15
<=> big_p(sK9) ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
fof(f130,plain,
( big_p(sK9)
| ~ spl13_15 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f131,plain,
( spl13_14
| spl13_15 ),
inference(avatar_split_clause,[],[f54,f128,f123]) ).
fof(f133,definition,
( spl13_16
<=> sP4 ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
fof(f137,definition,
( spl13_17
<=> big_q(sK8) ),
introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition]) ).
fof(f139,plain,
( ~ big_q(sK8)
| spl13_17 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f140,plain,
( spl13_16
| ~ spl13_17 ),
inference(avatar_split_clause,[],[f53,f137,f133]) ).
fof(f141,plain,
( ~ spl13_16
| spl13_5 ),
inference(avatar_split_clause,[],[f52,f85,f133]) ).
fof(f143,definition,
( spl13_18
<=> sP3(sK0) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
fof(f145,plain,
( sP3(sK0)
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f147,plain,
( spl13_18
| spl13_16
| spl13_14
| ~ spl13_1
| spl13_11 ),
inference(avatar_split_clause,[],[f50,f107,f69,f123,f133,f143]) ).
fof(f149,plain,
( spl13_18
| spl13_16
| spl13_14
| spl13_1
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f48,f107,f69,f123,f133,f143]) ).
fof(f151,definition,
( spl13_19
<=> ! [X0] : ~ sP3(X0) ),
introduced(definition,[new_symbols(definition,[spl13_19])],[avatar_definition]) ).
fof(f152,plain,
( ! [X0] : ~ sP3(X0)
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f153,plain,
( spl13_19
| ~ spl13_16
| spl13_14
| ~ spl13_1
| spl13_11 ),
inference(avatar_split_clause,[],[f47,f107,f69,f123,f133,f151]) ).
fof(f154,plain,
( spl13_19
| spl13_16
| ~ spl13_14
| ~ spl13_1
| spl13_11 ),
inference(avatar_split_clause,[],[f46,f107,f69,f123,f133,f151]) ).
fof(f156,plain,
( spl13_19
| spl13_16
| ~ spl13_14
| spl13_1
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f44,f107,f69,f123,f133,f151]) ).
fof(f157,plain,
( spl13_18
| ~ spl13_16
| spl13_14
| ~ spl13_1
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f43,f107,f69,f123,f133,f143]) ).
fof(f161,plain,
( spl13_19
| ~ spl13_16
| ~ spl13_14
| ~ spl13_1
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f39,f107,f69,f123,f133,f151]) ).
fof(f162,plain,
( spl13_19
| spl13_16
| spl13_14
| ~ spl13_1
| ~ spl13_11 ),
inference(avatar_split_clause,[],[f38,f107,f69,f123,f133,f151]) ).
fof(f164,plain,
( spl13_19
| spl13_16
| spl13_14
| spl13_1
| spl13_11 ),
inference(avatar_split_clause,[],[f36,f107,f69,f123,f133,f151]) ).
fof(f165,plain,
( $false
| ~ spl13_8
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f104,f97]) ).
fof(f166,plain,
( ~ spl13_8
| ~ spl13_10 ),
inference(avatar_contradiction_clause,[],[f165]) ).
fof(f167,plain,
( $false
| ~ spl13_10
| ~ spl13_15 ),
inference(forward_subsumption_resolution,[],[f130,f104]) ).
fof(f168,plain,
( ~ spl13_10
| ~ spl13_15 ),
inference(avatar_contradiction_clause,[],[f167]) ).
fof(f170,plain,
( ! [X0] : ~ sP3(X0)
| ~ spl13_7
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f101,f94]) ).
fof(f171,plain,
( spl13_19
| ~ spl13_7
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f170,f100,f93,f151]) ).
fof(f172,plain,
( $false
| ~ spl13_8
| spl13_12 ),
inference(backward_subsumption_resolution,[],[f113,f97]) ).
fof(f173,plain,
( ~ spl13_8
| spl13_12 ),
inference(avatar_contradiction_clause,[],[f172]) ).
fof(f174,plain,
( $false
| ~ spl13_6
| ~ spl13_13 ),
inference(backward_subsumption_resolution,[],[f118,f90]) ).
fof(f175,plain,
( ~ spl13_6
| ~ spl13_13 ),
inference(avatar_contradiction_clause,[],[f174]) ).
fof(f176,plain,
( ! [X4] : big_q(X4)
| ~ spl13_3
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f78,f90]) ).
fof(f177,plain,
( $false
| ~ spl13_3
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f176,f90]) ).
fof(f178,plain,
( ~ spl13_3
| ~ spl13_6 ),
inference(avatar_contradiction_clause,[],[f177]) ).
fof(f179,plain,
( $false
| ~ spl13_5
| spl13_17 ),
inference(backward_subsumption_resolution,[],[f139,f86]) ).
fof(f180,plain,
( ~ spl13_5
| spl13_17 ),
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f181,plain,
( ! [X4] : ~ big_q(X4)
| ~ spl13_2
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f74,f86]) ).
fof(f182,plain,
( $false
| ~ spl13_2
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f181,f86]) ).
fof(f183,plain,
( ~ spl13_2
| ~ spl13_5 ),
inference(avatar_contradiction_clause,[],[f182]) ).
fof(f184,plain,
( $false
| ~ spl13_18
| ~ spl13_19 ),
inference(backward_subsumption_resolution,[],[f145,f152]) ).
fof(f185,plain,
( ~ spl13_18
| ~ spl13_19 ),
inference(avatar_contradiction_clause,[],[f184]) ).
fof(f187,plain,
( ! [X0] :
( ~ big_p(X0)
| sP3(X0) )
| ~ spl13_8 ),
inference(forward_subsumption_resolution,[],[f63,f97]) ).
fof(f188,plain,
( ! [X0] : sP3(X0)
| ~ spl13_8 ),
inference(forward_subsumption_resolution,[],[f187,f97]) ).
fof(f189,plain,
( $false
| ~ spl13_8
| ~ spl13_19 ),
inference(forward_subsumption_resolution,[],[f188,f152]) ).
fof(f190,plain,
( ~ spl13_8
| ~ spl13_19 ),
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f191,plain,
( ! [X0] :
( big_p(sK7(X0))
| big_p(X0) )
| ~ spl13_19 ),
inference(forward_subsumption_resolution,[],[f62,f152]) ).
fof(f193,plain,
( $false
| ~ spl13_5
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f90,f86]) ).
fof(f194,plain,
( ~ spl13_5
| ~ spl13_6 ),
inference(avatar_contradiction_clause,[],[f193]) ).
fof(f195,plain,
( ! [X0] : big_p(X0)
| ~ spl13_10
| ~ spl13_19 ),
inference(forward_subsumption_resolution,[],[f191,f104]) ).
fof(f196,plain,
( $false
| ~ spl13_10
| ~ spl13_19 ),
inference(forward_subsumption_resolution,[],[f195,f104]) ).
fof(f197,plain,
( ~ spl13_10
| ~ spl13_19 ),
inference(avatar_contradiction_clause,[],[f196]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f75]) ).
cnf(s2,plain,
( spl13_1
| spl13_3 ),
inference(sat_conversion,[],[f79]) ).
cnf(s3,plain,
( ~ spl13_1
| ~ spl13_4
| spl13_5 ),
inference(sat_conversion,[],[f87]) ).
cnf(s4,plain,
( ~ spl13_1
| spl13_4
| spl13_6 ),
inference(sat_conversion,[],[f91]) ).
cnf(s5,plain,
( spl13_7
| spl13_8 ),
inference(sat_conversion,[],[f98]) ).
cnf(s6,plain,
( spl13_9
| spl13_10 ),
inference(sat_conversion,[],[f105]) ).
cnf(s7,plain,
( spl13_6
| ~ spl13_11
| ~ spl13_12 ),
inference(sat_conversion,[],[f114]) ).
cnf(s8,plain,
( spl13_8
| ~ spl13_11
| spl13_13 ),
inference(sat_conversion,[],[f119]) ).
cnf(s9,plain,
( spl13_11
| ~ spl13_12
| spl13_13 ),
inference(sat_conversion,[],[f120]) ).
cnf(s10,plain,
( spl13_6
| spl13_8
| spl13_11 ),
inference(sat_conversion,[],[f121]) ).
cnf(s11,plain,
( spl13_10
| ~ spl13_14 ),
inference(sat_conversion,[],[f126]) ).
cnf(s12,plain,
( spl13_14
| spl13_15 ),
inference(sat_conversion,[],[f131]) ).
cnf(s13,plain,
( spl13_16
| ~ spl13_17 ),
inference(sat_conversion,[],[f140]) ).
cnf(s14,plain,
( spl13_5
| ~ spl13_16 ),
inference(sat_conversion,[],[f141]) ).
cnf(s16,plain,
( ~ spl13_1
| spl13_11
| spl13_14
| spl13_16
| spl13_18 ),
inference(sat_conversion,[],[f147]) ).
cnf(s18,plain,
( spl13_1
| ~ spl13_11
| spl13_14
| spl13_16
| spl13_18 ),
inference(sat_conversion,[],[f149]) ).
cnf(s19,plain,
( ~ spl13_1
| spl13_11
| spl13_14
| ~ spl13_16
| spl13_19 ),
inference(sat_conversion,[],[f153]) ).
cnf(s20,plain,
( ~ spl13_1
| spl13_11
| ~ spl13_14
| spl13_16
| spl13_19 ),
inference(sat_conversion,[],[f154]) ).
cnf(s22,plain,
( spl13_1
| ~ spl13_11
| ~ spl13_14
| spl13_16
| spl13_19 ),
inference(sat_conversion,[],[f156]) ).
cnf(s23,plain,
( ~ spl13_1
| ~ spl13_11
| spl13_14
| ~ spl13_16
| spl13_18 ),
inference(sat_conversion,[],[f157]) ).
cnf(s27,plain,
( ~ spl13_1
| ~ spl13_11
| ~ spl13_14
| ~ spl13_16
| spl13_19 ),
inference(sat_conversion,[],[f161]) ).
cnf(s28,plain,
( ~ spl13_1
| ~ spl13_11
| spl13_14
| spl13_16
| spl13_19 ),
inference(sat_conversion,[],[f162]) ).
cnf(s30,plain,
( spl13_1
| spl13_11
| spl13_14
| spl13_16
| spl13_19 ),
inference(sat_conversion,[],[f164]) ).
cnf(s31,plain,
( ~ spl13_8
| ~ spl13_10 ),
inference(sat_conversion,[],[f166]) ).
cnf(s32,plain,
( ~ spl13_10
| ~ spl13_15 ),
inference(sat_conversion,[],[f168]) ).
cnf(s33,plain,
( ~ spl13_7
| ~ spl13_9
| spl13_19 ),
inference(sat_conversion,[],[f171]) ).
cnf(s34,plain,
( ~ spl13_8
| spl13_12 ),
inference(sat_conversion,[],[f173]) ).
cnf(s35,plain,
( ~ spl13_6
| ~ spl13_13 ),
inference(sat_conversion,[],[f175]) ).
cnf(s36,plain,
( ~ spl13_3
| ~ spl13_6 ),
inference(sat_conversion,[],[f178]) ).
cnf(s37,plain,
( ~ spl13_5
| spl13_17 ),
inference(sat_conversion,[],[f180]) ).
cnf(s38,plain,
( ~ spl13_2
| ~ spl13_5 ),
inference(sat_conversion,[],[f183]) ).
cnf(s40,plain,
( ~ spl13_18
| ~ spl13_19 ),
inference(sat_conversion,[],[f185]) ).
cnf(s41,plain,
( ~ spl13_8
| ~ spl13_19 ),
inference(sat_conversion,[],[f190]) ).
cnf(s42,plain,
( ~ spl13_5
| ~ spl13_6 ),
inference(sat_conversion,[],[f194]) ).
cnf(s43,plain,
( ~ spl13_10
| ~ spl13_19 ),
inference(sat_conversion,[],[f197]) ).
cnf(s44,plain,
( ~ spl13_8
| spl13_1 ),
inference(rat,[],[s30,s11,s7,s31,s34,s41,s36,s2,s14,s38,s1]) ).
cnf(s45,plain,
( spl13_10
| spl13_1 ),
inference(rat,[],[s40,s33,s18,s6,s11,s14,s38,s1,s5,s10,s44,s36,s2]) ).
cnf(s46,plain,
spl13_1,
inference(rat,[],[s12,s22,s32,s43,s45,s10,s44,s14,s38,s36,s1,s2]) ).
cnf(s47,plain,
( ~ spl13_11
| spl13_18
| spl13_8
| spl13_14 ),
inference(rat,[],[s3,s4,s37,s35,s13,s8,s23,s46]) ).
cnf(s48,plain,
( spl13_18
| spl13_14
| spl13_8 ),
inference(rat,[],[s42,s14,s10,s16,s47,s46]) ).
cnf(s49,plain,
( spl13_10
| ~ spl13_7 ),
inference(rat,[],[s48,s40,s41,s33,s6,s11]) ).
cnf(s50,plain,
( ~ spl13_11
| ~ spl13_10 ),
inference(rat,[],[s3,s4,s37,s35,s13,s8,s27,s43,s31,s12,s32,s46]) ).
cnf(s51,plain,
~ spl13_10,
inference(rat,[],[s42,s14,s10,s20,s50,s12,s31,s32,s43,s46]) ).
cnf(s52,plain,
~ spl13_14,
inference(rat,[],[s11,s51]) ).
cnf(s54,plain,
~ spl13_7,
inference(rat,[],[s49,s51]) ).
cnf(s56,plain,
spl13_8,
inference(rat,[],[s5,s54]) ).
cnf(s57,plain,
~ spl13_19,
inference(rat,[],[s41,s56]) ).
cnf(s58,plain,
spl13_12,
inference(rat,[],[s34,s56]) ).
cnf(s59,plain,
~ spl13_11,
inference(rat,[],[s42,s14,s7,s28,s58,s52,s57,s46]) ).
cnf(s60,plain,
~ spl13_16,
inference(rat,[],[s19,s57,s46,s52,s59]) ).
cnf(s61,plain,
spl13_13,
inference(rat,[],[s9,s58,s59]) ).
cnf(s62,plain,
~ spl13_17,
inference(rat,[],[s13,s60]) ).
cnf(s64,plain,
~ spl13_6,
inference(rat,[],[s35,s61]) ).
cnf(s65,plain,
~ spl13_5,
inference(rat,[],[s37,s62]) ).
cnf(s66,plain,
spl13_4,
inference(rat,[],[s4,s46,s64]) ).
cnf(s67,plain,
$false,
inference(rat,[],[s3,s46,s65,s66]) ).
fof(f198,plain,
$false,
inference(avatar_sat_refutation,[],[s67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n026.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:24:27 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.26 % (3938174)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (3938180)% WARNING: option uhcvi not known.
% 0.20/0.26 % (3938180)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2417172546:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.26 % (3938180) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3938174-3938180"...
% 0.20/0.26 % (3938180)...printing done.
% 0.20/0.26 % (3938180)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (3938180)------------------------------
% 0.20/0.27 % (3938180)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (3938180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (3938180)CaDiCaL version: 2.1.3
% 0.20/0.27 % (3938180)Termination reason: Refutation
% 0.20/0.27 % (3938180)Time elapsed: 0.003 s
% 0.20/0.27 % (3938180)Peak memory usage: 12 MB
% 0.20/0.27 % (3938180)Instructions burned: 5 (million)
% 0.20/0.27 % (3938174)Success in time 0.03 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------