TSTP Solution File: SYN036+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYN036+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 18:01:51 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 49
% Syntax : Number of formulae : 168 ( 1 unt; 0 def)
% Number of atoms : 642 ( 0 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 769 ( 295 ~; 329 |; 69 &)
% ( 54 <=>; 20 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 29 prp; 0-1 aty)
% Number of functors : 20 ( 20 usr; 18 con; 0-1 aty)
% Number of variables : 200 ( 124 !; 76 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f270,plain,
$false,
inference(avatar_sat_refutation,[],[f83,f91,f101,f111,f120,f121,f137,f145,f155,f165,f174,f175,f179,f183,f188,f189,f193,f197,f202,f203,f204,f205,f208,f213,f215,f219,f223,f225,f229,f233,f239,f243,f246,f249,f251,f259,f261,f263,f269]) ).
fof(f269,plain,
( ~ spl24_2
| ~ spl24_29 ),
inference(avatar_contradiction_clause,[],[f268]) ).
fof(f268,plain,
( $false
| ~ spl24_2
| ~ spl24_29 ),
inference(subsumption_resolution,[],[f267,f74]) ).
fof(f74,plain,
( ! [X1] : ~ big_p(X1)
| ~ spl24_2 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f73,plain,
( spl24_2
<=> ! [X1] : ~ big_p(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_2])]) ).
fof(f267,plain,
( ! [X0] : big_p(X0)
| ~ spl24_2
| ~ spl24_29 ),
inference(subsumption_resolution,[],[f196,f74]) ).
fof(f196,plain,
( ! [X0] :
( big_p(sK22(X0))
| big_p(X0) )
| ~ spl24_29 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f195,plain,
( spl24_29
<=> ! [X0] :
( big_p(sK22(X0))
| big_p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_29])]) ).
fof(f263,plain,
( ~ spl24_2
| ~ spl24_5 ),
inference(avatar_contradiction_clause,[],[f262]) ).
fof(f262,plain,
( $false
| ~ spl24_2
| ~ spl24_5 ),
inference(resolution,[],[f74,f87]) ).
fof(f87,plain,
( big_p(sK5)
| ~ spl24_5 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f85,plain,
( spl24_5
<=> big_p(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_5])]) ).
fof(f261,plain,
( ~ spl24_14
| ~ spl24_22 ),
inference(avatar_contradiction_clause,[],[f260]) ).
fof(f260,plain,
( $false
| ~ spl24_14
| ~ spl24_22 ),
inference(subsumption_resolution,[],[f164,f128]) ).
fof(f128,plain,
( ! [X1] : ~ big_q(X1)
| ~ spl24_14 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f127,plain,
( spl24_14
<=> ! [X1] : ~ big_q(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_14])]) ).
fof(f164,plain,
( big_q(sK17)
| ~ spl24_22 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f162,plain,
( spl24_22
<=> big_q(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_22])]) ).
fof(f259,plain,
( ~ spl24_14
| ~ spl24_24 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f258,plain,
( $false
| ~ spl24_14
| ~ spl24_24 ),
inference(subsumption_resolution,[],[f173,f128]) ).
fof(f173,plain,
( big_q(sK18)
| ~ spl24_24 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f171,plain,
( spl24_24
<=> big_q(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_24])]) ).
fof(f251,plain,
( spl24_3
| ~ spl24_6 ),
inference(avatar_contradiction_clause,[],[f250]) ).
fof(f250,plain,
( $false
| spl24_3
| ~ spl24_6 ),
inference(subsumption_resolution,[],[f78,f90]) ).
fof(f90,plain,
( ! [X2] : big_q(X2)
| ~ spl24_6 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f89,plain,
( spl24_6
<=> ! [X2] : big_q(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_6])]) ).
fof(f78,plain,
( ~ big_q(sK4)
| spl24_3 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f76,plain,
( spl24_3
<=> big_q(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_3])]) ).
fof(f249,plain,
( ~ spl24_2
| ~ spl24_12 ),
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f248,plain,
( $false
| ~ spl24_2
| ~ spl24_12 ),
inference(subsumption_resolution,[],[f119,f74]) ).
fof(f119,plain,
( big_p(sK10)
| ~ spl24_12 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f117,plain,
( spl24_12
<=> big_p(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_12])]) ).
fof(f246,plain,
( ~ spl24_6
| spl24_11 ),
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f245,plain,
( $false
| ~ spl24_6
| spl24_11 ),
inference(resolution,[],[f90,f115]) ).
fof(f115,plain,
( ~ big_q(sK11)
| spl24_11 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f113,plain,
( spl24_11
<=> big_q(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_11])]) ).
fof(f243,plain,
( ~ spl24_6
| ~ spl24_14 ),
inference(avatar_contradiction_clause,[],[f242]) ).
fof(f242,plain,
( $false
| ~ spl24_6
| ~ spl24_14 ),
inference(subsumption_resolution,[],[f90,f128]) ).
fof(f239,plain,
( ~ spl24_2
| ~ spl24_30 ),
inference(avatar_contradiction_clause,[],[f238]) ).
fof(f238,plain,
( $false
| ~ spl24_2
| ~ spl24_30 ),
inference(subsumption_resolution,[],[f201,f74]) ).
fof(f201,plain,
( big_p(sK23)
| ~ spl24_30 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f199,plain,
( spl24_30
<=> big_p(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_30])]) ).
fof(f233,plain,
( ~ spl24_14
| ~ spl24_17 ),
inference(avatar_contradiction_clause,[],[f230]) ).
fof(f230,plain,
( $false
| ~ spl24_14
| ~ spl24_17 ),
inference(resolution,[],[f128,f141]) ).
fof(f141,plain,
( big_q(sK13)
| ~ spl24_17 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f139,plain,
( spl24_17
<=> big_q(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_17])]) ).
fof(f229,plain,
( ~ spl24_18
| ~ spl24_28 ),
inference(avatar_contradiction_clause,[],[f228]) ).
fof(f228,plain,
( $false
| ~ spl24_18
| ~ spl24_28 ),
inference(subsumption_resolution,[],[f227,f144]) ).
fof(f144,plain,
( ! [X2] : big_p(X2)
| ~ spl24_18 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f143,plain,
( spl24_18
<=> ! [X2] : big_p(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_18])]) ).
fof(f227,plain,
( ! [X0] : ~ big_p(X0)
| ~ spl24_18
| ~ spl24_28 ),
inference(subsumption_resolution,[],[f192,f144]) ).
fof(f192,plain,
( ! [X0] :
( ~ big_p(sK22(X0))
| ~ big_p(X0) )
| ~ spl24_28 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f191,plain,
( spl24_28
<=> ! [X0] :
( ~ big_p(sK22(X0))
| ~ big_p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_28])]) ).
fof(f225,plain,
( ~ spl24_18
| spl24_30 ),
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f224,plain,
( $false
| ~ spl24_18
| spl24_30 ),
inference(subsumption_resolution,[],[f200,f144]) ).
fof(f200,plain,
( ~ big_p(sK23)
| spl24_30 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f223,plain,
( ~ spl24_18
| spl24_23 ),
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f222,plain,
( $false
| ~ spl24_18
| spl24_23 ),
inference(subsumption_resolution,[],[f169,f144]) ).
fof(f169,plain,
( ~ big_p(sK19)
| spl24_23 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f167,plain,
( spl24_23
<=> big_p(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_23])]) ).
fof(f219,plain,
( spl24_15
| ~ spl24_18 ),
inference(avatar_contradiction_clause,[],[f218]) ).
fof(f218,plain,
( $false
| spl24_15
| ~ spl24_18 ),
inference(resolution,[],[f144,f132]) ).
fof(f132,plain,
( ~ big_p(sK12)
| spl24_15 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f130,plain,
( spl24_15
<=> big_p(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_15])]) ).
fof(f215,plain,
( ~ spl24_2
| ~ spl24_10 ),
inference(avatar_contradiction_clause,[],[f214]) ).
fof(f214,plain,
( $false
| ~ spl24_2
| ~ spl24_10 ),
inference(subsumption_resolution,[],[f110,f74]) ).
fof(f110,plain,
( big_p(sK9)
| ~ spl24_10 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f108,plain,
( spl24_10
<=> big_p(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_10])]) ).
fof(f213,plain,
( ~ spl24_6
| ~ spl24_25 ),
inference(avatar_contradiction_clause,[],[f212]) ).
fof(f212,plain,
( $false
| ~ spl24_6
| ~ spl24_25 ),
inference(subsumption_resolution,[],[f211,f90]) ).
fof(f211,plain,
( ! [X0] : ~ big_q(X0)
| ~ spl24_6
| ~ spl24_25 ),
inference(subsumption_resolution,[],[f178,f90]) ).
fof(f178,plain,
( ! [X0] :
( ~ big_q(sK20(X0))
| ~ big_q(X0) )
| ~ spl24_25 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f177,plain,
( spl24_25
<=> ! [X0] :
( ~ big_q(sK20(X0))
| ~ big_q(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_25])]) ).
fof(f208,plain,
( ~ spl24_14
| ~ spl24_26 ),
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f207,plain,
( $false
| ~ spl24_14
| ~ spl24_26 ),
inference(subsumption_resolution,[],[f206,f128]) ).
fof(f206,plain,
( ! [X0] : big_q(X0)
| ~ spl24_14
| ~ spl24_26 ),
inference(subsumption_resolution,[],[f182,f128]) ).
fof(f182,plain,
( ! [X0] :
( big_q(sK20(X0))
| big_q(X0) )
| ~ spl24_26 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f181,plain,
( spl24_26
<=> ! [X0] :
( big_q(sK20(X0))
| big_q(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_26])]) ).
fof(f205,plain,
( spl24_16
| spl24_4 ),
inference(avatar_split_clause,[],[f66,f80,f134]) ).
fof(f134,plain,
( spl24_16
<=> sP2 ),
introduced(avatar_definition,[new_symbols(naming,[spl24_16])]) ).
fof(f80,plain,
( spl24_4
<=> sP3 ),
introduced(avatar_definition,[new_symbols(naming,[spl24_4])]) ).
fof(f66,plain,
( sP3
| sP2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
( ( ~ sP3
| ~ sP2 )
& ( sP3
| sP2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,plain,
( sP2
<~> sP3 ),
inference(definition_folding,[],[f3,f7,f6,f5,f4]) ).
fof(f4,plain,
( sP0
<=> ? [X0] :
! [X1] :
( big_p(X0)
<=> big_p(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f5,plain,
( sP1
<=> ? [X4] :
! [X5] :
( big_q(X4)
<=> big_q(X5) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f6,plain,
( sP2
<=> ( sP0
<=> ( ? [X2] : big_q(X2)
<=> ! [X3] : big_p(X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f7,plain,
( sP3
<=> ( sP1
<=> ( ? [X6] : big_p(X6)
<=> ! [X7] : big_q(X7) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
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(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,[],[f1]) ).
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(f204,plain,
( ~ spl24_16
| ~ spl24_4 ),
inference(avatar_split_clause,[],[f67,f80,f134]) ).
fof(f67,plain,
( ~ sP3
| ~ sP2 ),
inference(cnf_transformation,[],[f41]) ).
fof(f203,plain,
( ~ spl24_13
| ~ spl24_30
| spl24_18 ),
inference(avatar_split_clause,[],[f62,f143,f199,f123]) ).
fof(f123,plain,
( spl24_13
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl24_13])]) ).
fof(f62,plain,
! [X3] :
( big_p(X3)
| ~ big_p(sK23)
| ~ sP0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ( sP0
| ! [X0] :
( ( ~ big_p(sK22(X0))
| ~ big_p(X0) )
& ( big_p(sK22(X0))
| big_p(X0) ) ) )
& ( ! [X3] :
( ( big_p(sK23)
| ~ big_p(X3) )
& ( big_p(X3)
| ~ big_p(sK23) ) )
| ~ sP0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f37,f39,f38]) ).
fof(f38,plain,
! [X0] :
( ? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) )
=> ( ( ~ big_p(sK22(X0))
| ~ big_p(X0) )
& ( big_p(sK22(X0))
| big_p(X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
( ? [X2] :
! [X3] :
( ( big_p(X2)
| ~ big_p(X3) )
& ( big_p(X3)
| ~ big_p(X2) ) )
=> ! [X3] :
( ( big_p(sK23)
| ~ big_p(X3) )
& ( big_p(X3)
| ~ big_p(sK23) ) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
( ( sP0
| ! [X0] :
? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) ) )
& ( ? [X2] :
! [X3] :
( ( big_p(X2)
| ~ big_p(X3) )
& ( big_p(X3)
| ~ big_p(X2) ) )
| ~ sP0 ) ),
inference(rectify,[],[f36]) ).
fof(f36,plain,
( ( sP0
| ! [X0] :
? [X1] :
( ( ~ big_p(X1)
| ~ big_p(X0) )
& ( big_p(X1)
| big_p(X0) ) ) )
& ( ? [X0] :
! [X1] :
( ( big_p(X0)
| ~ big_p(X1) )
& ( big_p(X1)
| ~ big_p(X0) ) )
| ~ sP0 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f202,plain,
( ~ spl24_13
| spl24_2
| spl24_30 ),
inference(avatar_split_clause,[],[f63,f199,f73,f123]) ).
fof(f63,plain,
! [X3] :
( big_p(sK23)
| ~ big_p(X3)
| ~ sP0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f197,plain,
( spl24_29
| spl24_13 ),
inference(avatar_split_clause,[],[f64,f123,f195]) ).
fof(f64,plain,
! [X0] :
( sP0
| big_p(sK22(X0))
| big_p(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f193,plain,
( spl24_28
| spl24_13 ),
inference(avatar_split_clause,[],[f65,f123,f191]) ).
fof(f65,plain,
! [X0] :
( sP0
| ~ big_p(sK22(X0))
| ~ big_p(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f189,plain,
( ~ spl24_1
| ~ spl24_27
| spl24_6 ),
inference(avatar_split_clause,[],[f58,f89,f185,f69]) ).
fof(f69,plain,
( spl24_1
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl24_1])]) ).
fof(f185,plain,
( spl24_27
<=> big_q(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl24_27])]) ).
fof(f58,plain,
! [X3] :
( big_q(X3)
| ~ big_q(sK21)
| ~ sP1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
( ( sP1
| ! [X0] :
( ( ~ big_q(sK20(X0))
| ~ big_q(X0) )
& ( big_q(sK20(X0))
| big_q(X0) ) ) )
& ( ! [X3] :
( ( big_q(sK21)
| ~ big_q(X3) )
& ( big_q(X3)
| ~ big_q(sK21) ) )
| ~ sP1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f32,f34,f33]) ).
fof(f33,plain,
! [X0] :
( ? [X1] :
( ( ~ big_q(X1)
| ~ big_q(X0) )
& ( big_q(X1)
| big_q(X0) ) )
=> ( ( ~ big_q(sK20(X0))
| ~ big_q(X0) )
& ( big_q(sK20(X0))
| big_q(X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( ? [X2] :
! [X3] :
( ( big_q(X2)
| ~ big_q(X3) )
& ( big_q(X3)
| ~ big_q(X2) ) )
=> ! [X3] :
( ( big_q(sK21)
| ~ big_q(X3) )
& ( big_q(X3)
| ~ big_q(sK21) ) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
( ( sP1
| ! [X0] :
? [X1] :
( ( ~ big_q(X1)
| ~ big_q(X0) )
& ( big_q(X1)
| big_q(X0) ) ) )
& ( ? [X2] :
! [X3] :
( ( big_q(X2)
| ~ big_q(X3) )
& ( big_q(X3)
| ~ big_q(X2) ) )
| ~ sP1 ) ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
( ( sP1
| ! [X4] :
? [X5] :
( ( ~ big_q(X5)
| ~ big_q(X4) )
& ( big_q(X5)
| big_q(X4) ) ) )
& ( ? [X4] :
! [X5] :
( ( big_q(X4)
| ~ big_q(X5) )
& ( big_q(X5)
| ~ big_q(X4) ) )
| ~ sP1 ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f188,plain,
( ~ spl24_1
| spl24_14
| spl24_27 ),
inference(avatar_split_clause,[],[f59,f185,f127,f69]) ).
fof(f59,plain,
! [X3] :
( big_q(sK21)
| ~ big_q(X3)
| ~ sP1 ),
inference(cnf_transformation,[],[f35]) ).
fof(f183,plain,
( spl24_26
| spl24_1 ),
inference(avatar_split_clause,[],[f60,f69,f181]) ).
fof(f60,plain,
! [X0] :
( sP1
| big_q(sK20(X0))
| big_q(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f179,plain,
( spl24_25
| spl24_1 ),
inference(avatar_split_clause,[],[f61,f69,f177]) ).
fof(f61,plain,
! [X0] :
( sP1
| ~ big_q(sK20(X0))
| ~ big_q(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f175,plain,
( ~ spl24_16
| ~ spl24_13
| spl24_14
| spl24_18 ),
inference(avatar_split_clause,[],[f50,f143,f127,f123,f134]) ).
fof(f50,plain,
! [X14,X15] :
( big_p(X14)
| ~ big_q(X15)
| ~ sP0
| ~ sP2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
( ( sP2
| ( ( ( ( ~ big_p(sK12)
| ! [X1] : ~ big_q(X1) )
& ( ! [X2] : big_p(X2)
| big_q(sK13) ) )
| ~ sP0 )
& ( ( ( big_q(sK14)
| ~ big_p(sK15) )
& ( ! [X6] : big_p(X6)
| ! [X7] : ~ big_q(X7) ) )
| sP0 ) ) )
& ( ( ( sP0
| ( ( ~ big_p(sK16)
| ! [X9] : ~ big_q(X9) )
& ( ! [X10] : big_p(X10)
| big_q(sK17) ) ) )
& ( ( ( big_q(sK18)
| ~ big_p(sK19) )
& ( ! [X14] : big_p(X14)
| ! [X15] : ~ big_q(X15) ) )
| ~ sP0 ) )
| ~ sP2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16,sK17,sK18,sK19])],[f21,f29,f28,f27,f26,f25,f24,f23,f22]) ).
fof(f22,plain,
( ? [X0] : ~ big_p(X0)
=> ~ big_p(sK12) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
( ? [X3] : big_q(X3)
=> big_q(sK13) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( ? [X4] : big_q(X4)
=> big_q(sK14) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
( ? [X5] : ~ big_p(X5)
=> ~ big_p(sK15) ),
introduced(choice_axiom,[]) ).
fof(f26,plain,
( ? [X8] : ~ big_p(X8)
=> ~ big_p(sK16) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
( ? [X11] : big_q(X11)
=> big_q(sK17) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
( ? [X12] : big_q(X12)
=> big_q(sK18) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( ? [X13] : ~ big_p(X13)
=> ~ big_p(sK19) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
( ( sP2
| ( ( ( ( ? [X0] : ~ big_p(X0)
| ! [X1] : ~ big_q(X1) )
& ( ! [X2] : big_p(X2)
| ? [X3] : big_q(X3) ) )
| ~ sP0 )
& ( ( ( ? [X4] : big_q(X4)
| ? [X5] : ~ big_p(X5) )
& ( ! [X6] : big_p(X6)
| ! [X7] : ~ big_q(X7) ) )
| sP0 ) ) )
& ( ( ( sP0
| ( ( ? [X8] : ~ big_p(X8)
| ! [X9] : ~ big_q(X9) )
& ( ! [X10] : big_p(X10)
| ? [X11] : big_q(X11) ) ) )
& ( ( ( ? [X12] : big_q(X12)
| ? [X13] : ~ big_p(X13) )
& ( ! [X14] : big_p(X14)
| ! [X15] : ~ big_q(X15) ) )
| ~ sP0 ) )
| ~ sP2 ) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
( ( sP2
| ( ( ( ( ? [X3] : ~ big_p(X3)
| ! [X2] : ~ big_q(X2) )
& ( ! [X3] : big_p(X3)
| ? [X2] : big_q(X2) ) )
| ~ sP0 )
& ( ( ( ? [X2] : big_q(X2)
| ? [X3] : ~ big_p(X3) )
& ( ! [X3] : big_p(X3)
| ! [X2] : ~ big_q(X2) ) )
| sP0 ) ) )
& ( ( ( sP0
| ( ( ? [X3] : ~ big_p(X3)
| ! [X2] : ~ big_q(X2) )
& ( ! [X3] : big_p(X3)
| ? [X2] : big_q(X2) ) ) )
& ( ( ( ? [X2] : big_q(X2)
| ? [X3] : ~ big_p(X3) )
& ( ! [X3] : big_p(X3)
| ! [X2] : ~ big_q(X2) ) )
| ~ sP0 ) )
| ~ sP2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f174,plain,
( ~ spl24_16
| ~ spl24_13
| ~ spl24_23
| spl24_24 ),
inference(avatar_split_clause,[],[f51,f171,f167,f123,f134]) ).
fof(f51,plain,
( big_q(sK18)
| ~ big_p(sK19)
| ~ sP0
| ~ sP2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f165,plain,
( ~ spl24_16
| spl24_22
| spl24_18
| spl24_13 ),
inference(avatar_split_clause,[],[f52,f123,f143,f162,f134]) ).
fof(f52,plain,
! [X10] :
( sP0
| big_p(X10)
| big_q(sK17)
| ~ sP2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f155,plain,
( spl24_13
| spl24_14
| spl24_18
| spl24_16 ),
inference(avatar_split_clause,[],[f54,f134,f143,f127,f123]) ).
fof(f54,plain,
! [X6,X7] :
( sP2
| big_p(X6)
| ~ big_q(X7)
| sP0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f145,plain,
( ~ spl24_13
| spl24_17
| spl24_18
| spl24_16 ),
inference(avatar_split_clause,[],[f56,f134,f143,f139,f123]) ).
fof(f56,plain,
! [X2] :
( sP2
| big_p(X2)
| big_q(sK13)
| ~ sP0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f137,plain,
( ~ spl24_13
| spl24_14
| ~ spl24_15
| spl24_16 ),
inference(avatar_split_clause,[],[f57,f134,f130,f127,f123]) ).
fof(f57,plain,
! [X1] :
( sP2
| ~ big_p(sK12)
| ~ big_q(X1)
| ~ sP0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f121,plain,
( ~ spl24_4
| ~ spl24_1
| spl24_2
| spl24_6 ),
inference(avatar_split_clause,[],[f42,f89,f73,f69,f80]) ).
fof(f42,plain,
! [X14,X15] :
( big_q(X14)
| ~ big_p(X15)
| ~ sP1
| ~ sP3 ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
( ( sP3
| ( ( ( ( ~ big_q(sK4)
| ! [X1] : ~ big_p(X1) )
& ( ! [X2] : big_q(X2)
| big_p(sK5) ) )
| ~ sP1 )
& ( ( ( big_p(sK6)
| ~ big_q(sK7) )
& ( ! [X6] : big_q(X6)
| ! [X7] : ~ big_p(X7) ) )
| sP1 ) ) )
& ( ( ( sP1
| ( ( ~ big_q(sK8)
| ! [X9] : ~ big_p(X9) )
& ( ! [X10] : big_q(X10)
| big_p(sK9) ) ) )
& ( ( ( big_p(sK10)
| ~ big_q(sK11) )
& ( ! [X14] : big_q(X14)
| ! [X15] : ~ big_p(X15) ) )
| ~ sP1 ) )
| ~ sP3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f10,f18,f17,f16,f15,f14,f13,f12,f11]) ).
fof(f11,plain,
( ? [X0] : ~ big_q(X0)
=> ~ big_q(sK4) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
( ? [X3] : big_p(X3)
=> big_p(sK5) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
( ? [X4] : big_p(X4)
=> big_p(sK6) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
( ? [X5] : ~ big_q(X5)
=> ~ big_q(sK7) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
( ? [X8] : ~ big_q(X8)
=> ~ big_q(sK8) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ? [X11] : big_p(X11)
=> big_p(sK9) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ? [X12] : big_p(X12)
=> big_p(sK10) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
( ? [X13] : ~ big_q(X13)
=> ~ big_q(sK11) ),
introduced(choice_axiom,[]) ).
fof(f10,plain,
( ( sP3
| ( ( ( ( ? [X0] : ~ big_q(X0)
| ! [X1] : ~ big_p(X1) )
& ( ! [X2] : big_q(X2)
| ? [X3] : big_p(X3) ) )
| ~ sP1 )
& ( ( ( ? [X4] : big_p(X4)
| ? [X5] : ~ big_q(X5) )
& ( ! [X6] : big_q(X6)
| ! [X7] : ~ big_p(X7) ) )
| sP1 ) ) )
& ( ( ( sP1
| ( ( ? [X8] : ~ big_q(X8)
| ! [X9] : ~ big_p(X9) )
& ( ! [X10] : big_q(X10)
| ? [X11] : big_p(X11) ) ) )
& ( ( ( ? [X12] : big_p(X12)
| ? [X13] : ~ big_q(X13) )
& ( ! [X14] : big_q(X14)
| ! [X15] : ~ big_p(X15) ) )
| ~ sP1 ) )
| ~ sP3 ) ),
inference(rectify,[],[f9]) ).
fof(f9,plain,
( ( sP3
| ( ( ( ( ? [X7] : ~ big_q(X7)
| ! [X6] : ~ big_p(X6) )
& ( ! [X7] : big_q(X7)
| ? [X6] : big_p(X6) ) )
| ~ sP1 )
& ( ( ( ? [X6] : big_p(X6)
| ? [X7] : ~ big_q(X7) )
& ( ! [X7] : big_q(X7)
| ! [X6] : ~ big_p(X6) ) )
| sP1 ) ) )
& ( ( ( sP1
| ( ( ? [X7] : ~ big_q(X7)
| ! [X6] : ~ big_p(X6) )
& ( ! [X7] : big_q(X7)
| ? [X6] : big_p(X6) ) ) )
& ( ( ( ? [X6] : big_p(X6)
| ? [X7] : ~ big_q(X7) )
& ( ! [X7] : big_q(X7)
| ! [X6] : ~ big_p(X6) ) )
| ~ sP1 ) )
| ~ sP3 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f120,plain,
( ~ spl24_4
| ~ spl24_1
| ~ spl24_11
| spl24_12 ),
inference(avatar_split_clause,[],[f43,f117,f113,f69,f80]) ).
fof(f43,plain,
( big_p(sK10)
| ~ big_q(sK11)
| ~ sP1
| ~ sP3 ),
inference(cnf_transformation,[],[f19]) ).
fof(f111,plain,
( ~ spl24_4
| spl24_10
| spl24_6
| spl24_1 ),
inference(avatar_split_clause,[],[f44,f69,f89,f108,f80]) ).
fof(f44,plain,
! [X10] :
( sP1
| big_q(X10)
| big_p(sK9)
| ~ sP3 ),
inference(cnf_transformation,[],[f19]) ).
fof(f101,plain,
( spl24_1
| spl24_2
| spl24_6
| spl24_4 ),
inference(avatar_split_clause,[],[f46,f80,f89,f73,f69]) ).
fof(f46,plain,
! [X6,X7] :
( sP3
| big_q(X6)
| ~ big_p(X7)
| sP1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f91,plain,
( ~ spl24_1
| spl24_5
| spl24_6
| spl24_4 ),
inference(avatar_split_clause,[],[f48,f80,f89,f85,f69]) ).
fof(f48,plain,
! [X2] :
( sP3
| big_q(X2)
| big_p(sK5)
| ~ sP1 ),
inference(cnf_transformation,[],[f19]) ).
fof(f83,plain,
( ~ spl24_1
| spl24_2
| ~ spl24_3
| spl24_4 ),
inference(avatar_split_clause,[],[f49,f80,f76,f73,f69]) ).
fof(f49,plain,
! [X1] :
( sP3
| ~ big_q(sK4)
| ~ big_p(X1)
| ~ sP1 ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN036+2 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 01:48:21 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (27957)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (27959)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (27960)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.37 % (27963)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37 % (27962)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37 % (27961)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37 % (27958)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 % (27964)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [2,1]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [3,1]
% 0.14/0.37 % (27963)First to succeed.
% 0.14/0.37 TRYING [4]
% 0.14/0.37 TRYING [4]
% 0.14/0.37 TRYING [1,1]
% 0.14/0.37 TRYING [2,2]
% 0.14/0.38 TRYING [2,1]
% 0.14/0.38 TRYING [5]
% 0.14/0.38 TRYING [3,2]
% 0.14/0.38 TRYING [5]
% 0.14/0.38 % (27962)Also succeeded, but the first one will report.
% 0.14/0.38 TRYING [3,1]
% 0.14/0.38 TRYING [4,1]
% 0.14/0.38 % (27960)Also succeeded, but the first one will report.
% 0.14/0.38 % (27963)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (27963)------------------------------
% 0.14/0.38 % (27963)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (27963)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (27963)Memory used [KB]: 893
% 0.14/0.38 % (27963)Time elapsed: 0.007 s
% 0.14/0.38 % (27963)Instructions burned: 9 (million)
% 0.14/0.38 % (27963)------------------------------
% 0.14/0.38 % (27963)------------------------------
% 0.14/0.38 % (27957)Success in time 0.011 s
%------------------------------------------------------------------------------