TSTP Solution File: SET731+4 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET731+4 : TPTP v8.2.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 : Mon Jun 24 14:35:34 EDT 2024
% Result : Theorem 10.24s 2.16s
% Output : CNFRefutation 10.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 63 ( 10 unt; 0 def)
% Number of atoms : 236 ( 34 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 281 ( 108 ~; 91 |; 58 &)
% ( 11 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 181 ( 0 sgn 105 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X2,X0] :
( member(X2,singleton(X0))
<=> X0 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
fof(f18,axiom,
! [X5,X0,X1] :
( surjective(X5,X0,X1)
<=> ! [X4] :
( member(X4,X1)
=> ? [X3] :
( apply(X5,X3,X4)
& member(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f22,axiom,
! [X5,X0,X4] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).
fof(f29,conjecture,
! [X5,X9,X0,X1,X10] :
( ( ! [X2,X4] :
( ( member(X4,X10)
& member(X2,X0) )
=> ( apply(X9,X2,X4)
<=> apply(X5,X2,X4) ) )
& image2(X5,X0) = X10
& subset(X10,X1)
& maps(X5,X0,X1) )
=> surjective(X9,X0,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII22) ).
fof(f30,negated_conjecture,
~ ! [X5,X9,X0,X1,X10] :
( ( ! [X2,X4] :
( ( member(X4,X10)
& member(X2,X0) )
=> ( apply(X9,X2,X4)
<=> apply(X5,X2,X4) ) )
& image2(X5,X0) = X10
& subset(X10,X1)
& maps(X5,X0,X1) )
=> surjective(X9,X0,X10) ),
inference(negated_conjecture,[],[f29]) ).
fof(f36,plain,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ),
inference(rectify,[],[f8]) ).
fof(f46,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) ) ),
inference(rectify,[],[f18]) ).
fof(f50,plain,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(rectify,[],[f22]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6] :
( ( member(X6,X4)
& member(X5,X2) )
=> ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) ) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> surjective(X1,X2,X4) ),
inference(rectify,[],[f30]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ! [X3] :
( member(X3,X2)
=> ? [X4] :
( apply(X0,X4,X3)
& member(X4,X1) ) )
=> surjective(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f66,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ? [X3] :
( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
& member(X3,X2) ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f69,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(ennf_transformation,[],[f57]) ).
fof(f70,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( apply(X1,X5,X6)
<=> apply(X0,X5,X6) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(flattening,[],[f69]) ).
fof(f82,plain,
! [X0,X1] :
( ( member(X0,singleton(X1))
| X0 != X1 )
& ( X0 = X1
| ~ member(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f99,plain,
! [X0,X1,X2] :
( ? [X3] :
( ! [X4] :
( ~ apply(X0,X4,X3)
| ~ member(X4,X1) )
& member(X3,X2) )
=> ( ! [X4] :
( ~ apply(X0,X4,sK5(X0,X1,X2))
| ~ member(X4,X1) )
& member(sK5(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X0,X1,X2] :
( surjective(X0,X1,X2)
| ( ! [X4] :
( ~ apply(X0,X4,sK5(X0,X1,X2))
| ~ member(X4,X1) )
& member(sK5(X0,X1,X2),X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f66,f99]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(rectify,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
=> ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ( apply(X0,sK6(X0,X1,X2),X2)
& member(sK6(X0,X1,X2),X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f103,f104]) ).
fof(f120,plain,
? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( ( apply(X1,X5,X6)
| ~ apply(X0,X5,X6) )
& ( apply(X0,X5,X6)
| ~ apply(X1,X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) ),
inference(nnf_transformation,[],[f70]) ).
fof(f121,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ surjective(X1,X2,X4)
& ! [X5,X6] :
( ( ( apply(X1,X5,X6)
| ~ apply(X0,X5,X6) )
& ( apply(X0,X5,X6)
| ~ apply(X1,X5,X6) ) )
| ~ member(X6,X4)
| ~ member(X5,X2) )
& image2(X0,X2) = X4
& subset(X4,X3)
& maps(X0,X2,X3) )
=> ( ~ surjective(sK11,sK12,sK14)
& ! [X6,X5] :
( ( ( apply(sK11,X5,X6)
| ~ apply(sK10,X5,X6) )
& ( apply(sK10,X5,X6)
| ~ apply(sK11,X5,X6) ) )
| ~ member(X6,sK14)
| ~ member(X5,sK12) )
& sK14 = image2(sK10,sK12)
& subset(sK14,sK13)
& maps(sK10,sK12,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f122,plain,
( ~ surjective(sK11,sK12,sK14)
& ! [X5,X6] :
( ( ( apply(sK11,X5,X6)
| ~ apply(sK10,X5,X6) )
& ( apply(sK10,X5,X6)
| ~ apply(sK11,X5,X6) ) )
| ~ member(X6,sK14)
| ~ member(X5,sK12) )
& sK14 = image2(sK10,sK12)
& subset(sK14,sK13)
& maps(sK10,sK12,sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14])],[f120,f121]) ).
fof(f138,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f139,plain,
! [X0,X1] :
( member(X0,singleton(X1))
| X0 != X1 ),
inference(cnf_transformation,[],[f82]) ).
fof(f156,plain,
! [X2,X0,X1] :
( surjective(X0,X1,X2)
| member(sK5(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
! [X2,X0,X1,X4] :
( surjective(X0,X1,X2)
| ~ apply(X0,X4,sK5(X0,X1,X2))
| ~ member(X4,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f160,plain,
! [X2,X0,X1] :
( member(sK6(X0,X1,X2),X1)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f161,plain,
! [X2,X0,X1] :
( apply(X0,sK6(X0,X1,X2),X2)
| ~ member(X2,image2(X0,X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f176,plain,
sK14 = image2(sK10,sK12),
inference(cnf_transformation,[],[f122]) ).
fof(f178,plain,
! [X6,X5] :
( apply(sK11,X5,X6)
| ~ apply(sK10,X5,X6)
| ~ member(X6,sK14)
| ~ member(X5,sK12) ),
inference(cnf_transformation,[],[f122]) ).
fof(f179,plain,
~ surjective(sK11,sK12,sK14),
inference(cnf_transformation,[],[f122]) ).
fof(f180,plain,
! [X1] : member(X1,singleton(X1)),
inference(equality_resolution,[],[f139]) ).
cnf(c_64,plain,
member(X0,singleton(X0)),
inference(cnf_transformation,[],[f180]) ).
cnf(c_65,plain,
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_82,plain,
( ~ apply(X0,X1,sK5(X0,X2,X3))
| ~ member(X1,X2)
| surjective(X0,X2,X3) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_83,plain,
( member(sK5(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_87,plain,
( ~ member(X0,image2(X1,X2))
| apply(X1,sK6(X1,X2,X0),X0) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_88,plain,
( ~ member(X0,image2(X1,X2))
| member(sK6(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_100,negated_conjecture,
~ surjective(sK11,sK12,sK14),
inference(cnf_transformation,[],[f179]) ).
cnf(c_101,negated_conjecture,
( ~ apply(sK10,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK14)
| apply(sK11,X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_103,negated_conjecture,
image2(sK10,sK12) = sK14,
inference(cnf_transformation,[],[f176]) ).
cnf(c_229,plain,
( member(sK5(X0,X1,X2),X2)
| surjective(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
cnf(c_652,plain,
( X0 != sK11
| X1 != sK12
| X2 != sK14
| ~ apply(X0,X3,sK5(X0,X1,X2))
| ~ member(X3,X1) ),
inference(resolution_lifted,[status(thm)],[c_82,c_100]) ).
cnf(c_653,plain,
( ~ apply(sK11,X0,sK5(sK11,sK12,sK14))
| ~ member(X0,sK12) ),
inference(unflattening,[status(thm)],[c_652]) ).
cnf(c_661,plain,
( X0 != sK11
| X1 != sK12
| X2 != sK14
| member(sK5(X0,X1,X2),X2) ),
inference(resolution_lifted,[status(thm)],[c_229,c_100]) ).
cnf(c_662,plain,
member(sK5(sK11,sK12,sK14),sK14),
inference(unflattening,[status(thm)],[c_661]) ).
cnf(c_869,plain,
( ~ member(X0,sK12)
| ~ apply(sK11,X0,sK5(sK11,sK12,sK14)) ),
inference(prop_impl_just,[status(thm)],[c_653]) ).
cnf(c_870,plain,
( ~ apply(sK11,X0,sK5(sK11,sK12,sK14))
| ~ member(X0,sK12) ),
inference(renaming,[status(thm)],[c_869]) ).
cnf(c_1371,negated_conjecture,
( ~ apply(sK10,X0,X1)
| ~ member(X0,sK12)
| ~ member(X1,sK14)
| apply(sK11,X0,X1) ),
inference(demodulation,[status(thm)],[c_101]) ).
cnf(c_1376,plain,
( X0 != X1
| X2 != X3
| ~ member(X1,X3)
| member(X0,X2) ),
theory(equality) ).
cnf(c_6615,plain,
( X0 != sK5(sK11,sK12,sK14)
| X1 != sK14
| ~ member(sK5(sK11,sK12,sK14),sK14)
| member(X0,X1) ),
inference(instantiation,[status(thm)],[c_1376]) ).
cnf(c_8270,plain,
( ~ member(sK6(sK10,X0,X1),sK12)
| ~ member(X1,image2(sK10,X0))
| ~ member(X1,sK14)
| apply(sK11,sK6(sK10,X0,X1),X1) ),
inference(resolution,[status(thm)],[c_87,c_1371]) ).
cnf(c_9483,plain,
member(sK5(sK11,sK12,sK14),singleton(sK5(sK11,sK12,sK14))),
inference(instantiation,[status(thm)],[c_64]) ).
cnf(c_10948,plain,
( ~ member(X0,singleton(sK5(sK11,sK12,sK14)))
| X0 = sK5(sK11,sK12,sK14) ),
inference(instantiation,[status(thm)],[c_65]) ).
cnf(c_10950,plain,
( sK5(sK11,sK12,sK14) != sK5(sK11,sK12,sK14)
| X0 != sK14
| ~ member(sK5(sK11,sK12,sK14),sK14)
| member(sK5(sK11,sK12,sK14),X0) ),
inference(instantiation,[status(thm)],[c_6615]) ).
cnf(c_17527,plain,
( ~ member(sK5(sK11,sK12,sK14),singleton(sK5(sK11,sK12,sK14)))
| sK5(sK11,sK12,sK14) = sK5(sK11,sK12,sK14) ),
inference(instantiation,[status(thm)],[c_10948]) ).
cnf(c_23020,plain,
( ~ member(sK6(sK10,X0,sK5(sK11,sK12,sK14)),sK12)
| ~ member(sK5(sK11,sK12,sK14),image2(sK10,X0))
| ~ member(sK5(sK11,sK12,sK14),sK14) ),
inference(resolution,[status(thm)],[c_870,c_8270]) ).
cnf(c_24853,plain,
( ~ member(sK5(sK11,sK12,sK14),image2(sK10,X0))
| ~ member(sK6(sK10,X0,sK5(sK11,sK12,sK14)),sK12) ),
inference(global_subsumption_just,[status(thm)],[c_23020,c_662,c_23020]) ).
cnf(c_24854,plain,
( ~ member(sK6(sK10,X0,sK5(sK11,sK12,sK14)),sK12)
| ~ member(sK5(sK11,sK12,sK14),image2(sK10,X0)) ),
inference(renaming,[status(thm)],[c_24853]) ).
cnf(c_24864,plain,
~ member(sK5(sK11,sK12,sK14),image2(sK10,sK12)),
inference(resolution,[status(thm)],[c_24854,c_88]) ).
cnf(c_25419,plain,
( sK5(sK11,sK12,sK14) != sK5(sK11,sK12,sK14)
| image2(sK10,sK12) != sK14
| ~ member(sK5(sK11,sK12,sK14),sK14)
| member(sK5(sK11,sK12,sK14),image2(sK10,sK12)) ),
inference(instantiation,[status(thm)],[c_10950]) ).
cnf(c_25421,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_25419,c_24864,c_17527,c_9483,c_662,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET731+4 : TPTP v8.2.0. Bugfixed v2.2.1.
% 0.03/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Jun 23 16:07:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.24/2.16 % SZS status Started for theBenchmark.p
% 10.24/2.16 % SZS status Theorem for theBenchmark.p
% 10.24/2.16
% 10.24/2.16 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 10.24/2.16
% 10.24/2.16 ------ iProver source info
% 10.24/2.16
% 10.24/2.16 git: date: 2024-06-12 09:56:46 +0000
% 10.24/2.16 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 10.24/2.16 git: non_committed_changes: false
% 10.24/2.16
% 10.24/2.16 ------ Parsing...
% 10.24/2.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 10.24/2.16
% 10.24/2.16 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 10.24/2.16
% 10.24/2.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 10.24/2.16
% 10.24/2.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.24/2.16 ------ Proving...
% 10.24/2.16 ------ Problem Properties
% 10.24/2.16
% 10.24/2.16
% 10.24/2.16 clauses 56
% 10.24/2.16 conjectures 4
% 10.24/2.16 EPR 7
% 10.24/2.16 Horn 51
% 10.24/2.16 unary 8
% 10.24/2.16 binary 28
% 10.24/2.16 lits 139
% 10.24/2.16 lits eq 6
% 10.24/2.16 fd_pure 0
% 10.24/2.16 fd_pseudo 0
% 10.24/2.16 fd_cond 0
% 10.24/2.16 fd_pseudo_cond 3
% 10.24/2.16 AC symbols 0
% 10.24/2.16
% 10.24/2.16 ------ Input Options Time Limit: Unbounded
% 10.24/2.16
% 10.24/2.16
% 10.24/2.16 ------
% 10.24/2.16 Current options:
% 10.24/2.16 ------
% 10.24/2.16
% 10.24/2.16
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% 10.24/2.16
% 10.24/2.16 ------ Proving...
% 10.24/2.16
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% 10.24/2.16 % SZS status Theorem for theBenchmark.p
% 10.24/2.16
% 10.24/2.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 10.24/2.16
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