TSTP Solution File: SET754+4 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET754+4 : TPTP v8.1.2. 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 : Fri May 3 03:01:26 EDT 2024
% Result : Theorem 17.71s 3.19s
% Output : CNFRefutation 17.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 7 unt; 0 def)
% Number of atoms : 239 ( 6 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 273 ( 95 ~; 87 |; 64 &)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 192 ( 0 sgn 135 !; 31 ?)
% 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(f12,axiom,
! [X5,X0,X1] :
( maps(X5,X0,X1)
<=> ( ! [X2,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X2,X0) )
=> ( ( apply(X5,X2,X7)
& apply(X5,X2,X6) )
=> X6 = X7 ) )
& ! [X2] :
( member(X2,X0)
=> ? [X4] :
( apply(X5,X2,X4)
& member(X4,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maps) ).
fof(f22,axiom,
! [X5,X0,X4] :
( member(X4,image2(X5,X0))
<=> ? [X2] :
( apply(X5,X2,X4)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image2) ).
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,X10] :
( ( subset(X10,X0)
& maps(X5,X0,X1) )
=> subset(X10,inverse_image2(X5,image2(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa04) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1,X10] :
( ( subset(X10,X0)
& maps(X5,X0,X1) )
=> subset(X10,inverse_image2(X5,image2(X5,X10))) ),
inference(negated_conjecture,[],[f29]) ).
fof(f40,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
<=> ( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) ) ) ) ),
inference(rectify,[],[f12]) ).
fof(f50,plain,
! [X0,X1,X2] :
( member(X2,image2(X0,X1))
<=> ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1) ) ),
inference(rectify,[],[f22]) ).
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] :
( ( subset(X3,X1)
& maps(X0,X1,X2) )
=> subset(X3,inverse_image2(X0,image2(X0,X3))) ),
inference(rectify,[],[f30]) ).
fof(f58,plain,
! [X0,X1,X2] :
( maps(X0,X1,X2)
=> ( ! [X3,X4,X5] :
( ( member(X5,X2)
& member(X4,X2)
& member(X3,X1) )
=> ( ( apply(X0,X3,X5)
& apply(X0,X3,X4) )
=> X4 = X5 ) )
& ! [X6] :
( member(X6,X1)
=> ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f40]) ).
fof(f59,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f58]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(flattening,[],[f61]) ).
fof(f67,plain,
? [X0,X1,X2,X3] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& subset(X3,X1)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f57]) ).
fof(f68,plain,
? [X0,X1,X2,X3] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& subset(X3,X1)
& 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(f91,plain,
! [X0,X2,X6] :
( ? [X7] :
( apply(X0,X6,X7)
& member(X7,X2) )
=> ( apply(X0,X6,sK3(X0,X2,X6))
& member(sK3(X0,X2,X6),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ! [X3,X4,X5] :
( X4 = X5
| ~ apply(X0,X3,X5)
| ~ apply(X0,X3,X4)
| ~ member(X5,X2)
| ~ member(X4,X2)
| ~ member(X3,X1) )
& ! [X6] :
( ( apply(X0,X6,sK3(X0,X2,X6))
& member(sK3(X0,X2,X6),X2) )
| ~ member(X6,X1) ) )
| ~ maps(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f62,f91]) ).
fof(f98,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(f99,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,[],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ? [X4] :
( apply(X0,X4,X2)
& member(X4,X1) )
=> ( apply(X0,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( member(X2,image2(X0,X1))
| ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1) ) )
& ( ( apply(X0,sK5(X0,X1,X2),X2)
& member(sK5(X0,X1,X2),X1) )
| ~ member(X2,image2(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f99,f100]) ).
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] :
( ~ subset(X3,inverse_image2(X0,image2(X0,X3)))
& subset(X3,X1)
& maps(X0,X1,X2) )
=> ( ~ subset(sK12,inverse_image2(sK9,image2(sK9,sK12)))
& subset(sK12,sK10)
& maps(sK9,sK10,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
( ~ subset(sK12,inverse_image2(sK9,image2(sK9,sK12)))
& subset(sK12,sK10)
& maps(sK9,sK10,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[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(f145,plain,
! [X2,X0,X1,X6] :
( apply(X0,X6,sK3(X0,X2,X6))
| ~ member(X6,X1)
| ~ maps(X0,X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f155,plain,
! [X2,X3,X0,X1] :
( member(X2,image2(X0,X1))
| ~ apply(X0,X3,X2)
| ~ member(X3,X1) ),
inference(cnf_transformation,[],[f101]) ).
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(f167,plain,
maps(sK9,sK10,sK11),
inference(cnf_transformation,[],[f117]) ).
fof(f168,plain,
subset(sK12,sK10),
inference(cnf_transformation,[],[f117]) ).
fof(f169,plain,
~ subset(sK12,inverse_image2(sK9,image2(sK9,sK12))),
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_76,plain,
( ~ maps(X0,X1,X2)
| ~ member(X3,X1)
| apply(X0,X3,sK3(X0,X2,X3)) ),
inference(cnf_transformation,[],[f145]) ).
cnf(c_84,plain,
( ~ apply(X0,X1,X2)
| ~ member(X1,X3)
| member(X2,image2(X0,X3)) ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_91,plain,
( ~ apply(X0,X1,X2)
| ~ member(X2,X3)
| member(X1,inverse_image2(X0,X3)) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_98,negated_conjecture,
~ subset(sK12,inverse_image2(sK9,image2(sK9,sK12))),
inference(cnf_transformation,[],[f169]) ).
cnf(c_99,negated_conjecture,
subset(sK12,sK10),
inference(cnf_transformation,[],[f168]) ).
cnf(c_100,negated_conjecture,
maps(sK9,sK10,sK11),
inference(cnf_transformation,[],[f167]) ).
cnf(c_237,plain,
( ~ member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),inverse_image2(sK9,image2(sK9,sK12)))
| subset(sK12,inverse_image2(sK9,image2(sK9,sK12))) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_238,plain,
( member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK12)
| subset(sK12,inverse_image2(sK9,image2(sK9,sK12))) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_450,plain,
( ~ maps(sK9,sK10,sK11)
| ~ member(X0,sK10)
| apply(sK9,X0,sK3(sK9,sK11,X0)) ),
inference(instantiation,[status(thm)],[c_76]) ).
cnf(c_543,plain,
( ~ member(X0,X1)
| ~ subset(X1,sK10)
| member(X0,sK10) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_1535,plain,
( ~ apply(sK9,X0,sK3(sK9,sK11,X0))
| ~ member(sK3(sK9,sK11,X0),X1)
| member(X0,inverse_image2(sK9,X1)) ),
inference(instantiation,[status(thm)],[c_91]) ).
cnf(c_1536,plain,
( ~ apply(sK9,X0,sK3(sK9,sK11,X0))
| ~ member(X0,X1)
| member(sK3(sK9,sK11,X0),image2(sK9,X1)) ),
inference(instantiation,[status(thm)],[c_84]) ).
cnf(c_6709,plain,
( ~ apply(sK9,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))))
| ~ member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK12)
| member(sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))),image2(sK9,sK12)) ),
inference(instantiation,[status(thm)],[c_1536]) ).
cnf(c_7050,plain,
( ~ member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK12)
| ~ subset(sK12,sK10)
| member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK10) ),
inference(instantiation,[status(thm)],[c_543]) ).
cnf(c_7819,plain,
( ~ member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK10)
| ~ maps(sK9,sK10,sK11)
| apply(sK9,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))))) ),
inference(instantiation,[status(thm)],[c_450]) ).
cnf(c_8398,plain,
( ~ apply(sK9,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))))
| ~ member(sK3(sK9,sK11,sK0(sK12,inverse_image2(sK9,image2(sK9,sK12)))),image2(sK9,sK12))
| member(sK0(sK12,inverse_image2(sK9,image2(sK9,sK12))),inverse_image2(sK9,image2(sK9,sK12))) ),
inference(instantiation,[status(thm)],[c_1535]) ).
cnf(c_8399,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_8398,c_7819,c_7050,c_6709,c_238,c_237,c_98,c_100,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET754+4 : TPTP v8.1.2. 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 : Thu May 2 20:45:31 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 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
% 17.71/3.19 % SZS status Started for theBenchmark.p
% 17.71/3.19 % SZS status Theorem for theBenchmark.p
% 17.71/3.19
% 17.71/3.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.71/3.19
% 17.71/3.19 ------ iProver source info
% 17.71/3.19
% 17.71/3.19 git: date: 2024-05-02 19:28:25 +0000
% 17.71/3.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.71/3.19 git: non_committed_changes: false
% 17.71/3.19
% 17.71/3.19 ------ Parsing...
% 17.71/3.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.71/3.19
% 17.71/3.19 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e
% 17.71/3.19
% 17.71/3.19 ------ Preprocessing...
% 17.71/3.19
% 17.71/3.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.71/3.19 ------ Proving...
% 17.71/3.19 ------ Problem Properties
% 17.71/3.19
% 17.71/3.19
% 17.71/3.19 clauses 52
% 17.71/3.19 conjectures 5
% 17.71/3.19 EPR 5
% 17.71/3.19 Horn 47
% 17.71/3.19 unary 7
% 17.71/3.19 binary 25
% 17.71/3.19 lits 131
% 17.71/3.19 lits eq 4
% 17.71/3.19 fd_pure 0
% 17.71/3.19 fd_pseudo 0
% 17.71/3.19 fd_cond 0
% 17.71/3.19 fd_pseudo_cond 3
% 17.71/3.19 AC symbols 0
% 17.71/3.19
% 17.71/3.19 ------ Input Options Time Limit: Unbounded
% 17.71/3.19
% 17.71/3.19
% 17.71/3.19 ------
% 17.71/3.19 Current options:
% 17.71/3.19 ------
% 17.71/3.19
% 17.71/3.19
% 17.71/3.19
% 17.71/3.19
% 17.71/3.19 ------ Proving...
% 17.71/3.19
% 17.71/3.19
% 17.71/3.19 % SZS status Theorem for theBenchmark.p
% 17.71/3.19
% 17.71/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.71/3.19
% 17.71/3.20
%------------------------------------------------------------------------------