TSTP Solution File: SET755+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n006.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 : Fri May 3 03:01:26 EDT 2024
% Result : Theorem 91.90s 13.01s
% Output : CNFRefutation 91.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 159 ( 4 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 171 ( 61 ~; 52 |; 47 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 122 ( 0 sgn 70 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
fof(f24,axiom,
! [X5,X1,X2] :
( member(X2,inverse_image2(X5,X1))
<=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_image2) ).
fof(f29,conjecture,
! [X5,X0,X1,X2,X4] :
( ( subset(X2,X4)
& subset(X4,X1)
& subset(X2,X1)
& maps(X5,X0,X1) )
=> subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa05) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1,X2,X4] :
( ( subset(X2,X4)
& subset(X4,X1)
& subset(X2,X1)
& maps(X5,X0,X1) )
=> subset(inverse_image2(X5,X2),inverse_image2(X5,X4)) ),
inference(negated_conjecture,[],[f29]) ).
fof(f52,plain,
! [X0,X1,X2] :
( member(X2,inverse_image2(X0,X1))
<=> ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f57,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> subset(inverse_image2(X0,X3),inverse_image2(X0,X4)) ),
inference(rectify,[],[f30]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f67,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f57]) ).
fof(f68,plain,
? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f70,f71]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X3] :
( apply(X0,X2,X3)
& member(X3,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X2,X4)
& member(X4,X1) )
=> ( apply(X0,X2,sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ( member(X2,inverse_image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1) ) )
& ( ( apply(X0,X2,sK7(X0,X1,X2))
& member(sK7(X0,X1,X2),X1) )
| ~ member(X2,inverse_image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f108,f109]) ).
fof(f116,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ subset(inverse_image2(X0,X3),inverse_image2(X0,X4))
& subset(X3,X4)
& subset(X4,X2)
& subset(X3,X2)
& maps(X0,X1,X2) )
=> ( ~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))
& subset(sK12,sK13)
& subset(sK13,sK11)
& subset(sK12,sK11)
& maps(sK9,sK10,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
( ~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))
& subset(sK12,sK13)
& subset(sK13,sK11)
& subset(sK12,sK11)
& maps(sK9,sK10,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f68,f116]) ).
fof(f118,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f119,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f120,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f160,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f161,plain,
! [X2,X0,X1] :
( apply(X0,X2,sK7(X0,X1,X2))
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f162,plain,
! [X2,X3,X0,X1] :
( member(X2,inverse_image2(X0,X1))
| ~ apply(X0,X2,X3)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f170,plain,
subset(sK12,sK13),
inference(cnf_transformation,[],[f117]) ).
fof(f171,plain,
~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),
inference(cnf_transformation,[],[f117]) ).
cnf(c_49,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_91,plain,
( ~ apply(X0,X1,X2)
| ~ member(X2,X3)
| member(X1,inverse_image2(X0,X3)) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_92,plain,
( ~ member(X0,inverse_image2(X1,X2))
| apply(X1,X0,sK7(X1,X2,X0)) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_93,plain,
( ~ member(X0,inverse_image2(X1,X2))
| member(sK7(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f160]) ).
cnf(c_98,negated_conjecture,
~ subset(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),
inference(cnf_transformation,[],[f171]) ).
cnf(c_99,negated_conjecture,
subset(sK12,sK13),
inference(cnf_transformation,[],[f170]) ).
cnf(c_150,plain,
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_49]) ).
cnf(c_154,plain,
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_50]) ).
cnf(c_155,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_154]) ).
cnf(c_838,plain,
( inverse_image2(sK9,sK12) != X0
| inverse_image2(sK9,sK13) != X1
| member(sK0(X0,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_155,c_98]) ).
cnf(c_839,plain,
member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12)),
inference(unflattening,[status(thm)],[c_838]) ).
cnf(c_843,plain,
( inverse_image2(sK9,sK12) != X0
| inverse_image2(sK9,sK13) != X1
| ~ member(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_150,c_98]) ).
cnf(c_844,plain,
~ member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK13)),
inference(unflattening,[status(thm)],[c_843]) ).
cnf(c_3337,plain,
( ~ member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12))
| apply(sK9,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)))) ),
inference(instantiation,[status(thm)],[c_92]) ).
cnf(c_3338,plain,
( ~ member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK12))
| member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK12) ),
inference(instantiation,[status(thm)],[c_93]) ).
cnf(c_11398,plain,
( ~ apply(sK9,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))))
| ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),X0)
| member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,X0)) ),
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_11432,plain,
( ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK12)
| ~ subset(sK12,X0)
| member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),X0) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_21058,plain,
( ~ apply(sK9,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))))
| ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK13)
| member(sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13)),inverse_image2(sK9,sK13)) ),
inference(instantiation,[status(thm)],[c_11398]) ).
cnf(c_28285,plain,
( ~ member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK12)
| ~ subset(sK12,sK13)
| member(sK7(sK9,sK12,sK0(inverse_image2(sK9,sK12),inverse_image2(sK9,sK13))),sK13) ),
inference(instantiation,[status(thm)],[c_11432]) ).
cnf(c_28286,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_28285,c_21058,c_3337,c_3338,c_844,c_839,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.06 % Problem : SET755+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.04/0.07 % Command : run_iprover %s %d THM
% 0.08/0.25 % Computer : n006.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Thu May 2 20:14:04 EDT 2024
% 0.08/0.25 % CPUTime :
% 0.11/0.32 Running first-order theorem proving
% 0.11/0.32 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 91.90/13.01 % SZS status Started for theBenchmark.p
% 91.90/13.01 % SZS status Theorem for theBenchmark.p
% 91.90/13.01
% 91.90/13.01 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 91.90/13.01
% 91.90/13.01 ------ iProver source info
% 91.90/13.01
% 91.90/13.01 git: date: 2024-05-02 19:28:25 +0000
% 91.90/13.01 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 91.90/13.01 git: non_committed_changes: false
% 91.90/13.01
% 91.90/13.01 ------ Parsing...
% 91.90/13.01 ------ Clausification by vclausify_rel & Parsing by iProver...
% 91.90/13.01
% 91.90/13.01 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 91.90/13.01
% 91.90/13.01 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 91.90/13.01
% 91.90/13.01 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 91.90/13.01 ------ Proving...
% 91.90/13.01 ------ Problem Properties
% 91.90/13.01
% 91.90/13.01
% 91.90/13.01 clauses 53
% 91.90/13.01 conjectures 4
% 91.90/13.01 EPR 6
% 91.90/13.01 Horn 48
% 91.90/13.01 unary 8
% 91.90/13.01 binary 27
% 91.90/13.01 lits 129
% 91.90/13.01 lits eq 4
% 91.90/13.01 fd_pure 0
% 91.90/13.01 fd_pseudo 0
% 91.90/13.01 fd_cond 0
% 91.90/13.01 fd_pseudo_cond 3
% 91.90/13.01 AC symbols 0
% 91.90/13.01
% 91.90/13.01 ------ Input Options Time Limit: Unbounded
% 91.90/13.01
% 91.90/13.01
% 91.90/13.01 ------
% 91.90/13.01 Current options:
% 91.90/13.01 ------
% 91.90/13.01
% 91.90/13.01
% 91.90/13.01
% 91.90/13.01
% 91.90/13.01 ------ Proving...
% 91.90/13.01
% 91.90/13.01
% 91.90/13.01 % SZS status Theorem for theBenchmark.p
% 91.90/13.01
% 91.90/13.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 91.90/13.01
% 91.90/13.02
%------------------------------------------------------------------------------