TSTP Solution File: SET764+4 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n021.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 : Thu Aug 31 15:09:31 EDT 2023
% Result : Theorem 3.94s 1.23s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 11 unt; 0 def)
% Number of atoms : 115 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 126 ( 53 ~; 36 |; 24 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 94 ( 6 sgn; 65 !; 14 ?)
% 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(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
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] :
( maps(X5,X0,X1)
=> equal_set(inverse_image2(X5,empty_set),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa14) ).
fof(f30,negated_conjecture,
~ ! [X5,X0,X1] :
( maps(X5,X0,X1)
=> equal_set(inverse_image2(X5,empty_set),empty_set) ),
inference(negated_conjecture,[],[f29]) ).
fof(f34,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
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] :
( maps(X0,X1,X2)
=> equal_set(inverse_image2(X0,empty_set),empty_set) ),
inference(rectify,[],[f30]) ).
fof(f59,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f60,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f61,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f62,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f61]) ).
fof(f70,plain,
? [X0,X1,X2] :
( ~ equal_set(inverse_image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) ),
inference(ennf_transformation,[],[f57]) ).
fof(f71,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,[],[f60]) ).
fof(f72,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,[],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f74,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])],[f72,f73]) ).
fof(f109,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(f110,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,[],[f109]) ).
fof(f111,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(f112,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])],[f110,f111]) ).
fof(f118,plain,
( ? [X0,X1,X2] :
( ~ equal_set(inverse_image2(X0,empty_set),empty_set)
& maps(X0,X1,X2) )
=> ( ~ equal_set(inverse_image2(sK9,empty_set),empty_set)
& maps(sK9,sK10,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
( ~ equal_set(inverse_image2(sK9,empty_set),empty_set)
& maps(sK9,sK10,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f70,f118]) ).
fof(f121,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f123,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f132,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f34]) ).
fof(f163,plain,
! [X2,X0,X1] :
( member(sK7(X0,X1,X2),X1)
| ~ member(X2,inverse_image2(X0,X1)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f171,plain,
~ equal_set(inverse_image2(sK9,empty_set),empty_set),
inference(cnf_transformation,[],[f119]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_61,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f132]) ).
cnf(c_94,plain,
( ~ member(X0,inverse_image2(X1,X2))
| member(sK7(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_99,negated_conjecture,
~ equal_set(inverse_image2(sK9,empty_set),empty_set),
inference(cnf_transformation,[],[f171]) ).
cnf(c_840,plain,
( inverse_image2(sK9,empty_set) != X0
| X1 != empty_set
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_99]) ).
cnf(c_841,plain,
( ~ subset(inverse_image2(sK9,empty_set),empty_set)
| ~ subset(empty_set,inverse_image2(sK9,empty_set)) ),
inference(unflattening,[status(thm)],[c_840]) ).
cnf(c_995,plain,
( ~ subset(inverse_image2(sK9,empty_set),empty_set)
| ~ subset(empty_set,inverse_image2(sK9,empty_set)) ),
inference(prop_impl_just,[status(thm)],[c_841]) ).
cnf(c_2639,plain,
subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_61]) ).
cnf(c_2645,plain,
~ subset(inverse_image2(sK9,empty_set),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_995,c_2639]) ).
cnf(c_3343,plain,
~ member(X0,inverse_image2(X1,empty_set)),
inference(superposition,[status(thm)],[c_94,c_61]) ).
cnf(c_3460,plain,
subset(inverse_image2(X0,empty_set),X1),
inference(superposition,[status(thm)],[c_50,c_3343]) ).
cnf(c_3465,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_2645,c_3460]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET764+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.14/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 15:04:27 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.50 Running first-order theorem proving
% 0.20/0.50 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.94/1.23 % SZS status Started for theBenchmark.p
% 3.94/1.23 % SZS status Theorem for theBenchmark.p
% 3.94/1.23
% 3.94/1.23 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.94/1.23
% 3.94/1.23 ------ iProver source info
% 3.94/1.23
% 3.94/1.23 git: date: 2023-05-31 18:12:56 +0000
% 3.94/1.23 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.94/1.23 git: non_committed_changes: false
% 3.94/1.23 git: last_make_outside_of_git: false
% 3.94/1.23
% 3.94/1.23 ------ Parsing...
% 3.94/1.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.94/1.23
% 3.94/1.23 ------ 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
% 3.94/1.23
% 3.94/1.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.94/1.23
% 3.94/1.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.94/1.23 ------ Proving...
% 3.94/1.23 ------ Problem Properties
% 3.94/1.23
% 3.94/1.23
% 3.94/1.23 clauses 50
% 3.94/1.23 conjectures 0
% 3.94/1.23 EPR 3
% 3.94/1.23 Horn 45
% 3.94/1.23 unary 4
% 3.94/1.23 binary 28
% 3.94/1.23 lits 127
% 3.94/1.23 lits eq 4
% 3.94/1.23 fd_pure 0
% 3.94/1.23 fd_pseudo 0
% 3.94/1.23 fd_cond 0
% 3.94/1.23 fd_pseudo_cond 3
% 3.94/1.23 AC symbols 0
% 3.94/1.23
% 3.94/1.23 ------ Schedule dynamic 5 is on
% 3.94/1.23
% 3.94/1.23 ------ no conjectures: strip conj schedule
% 3.94/1.23
% 3.94/1.23 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.94/1.23
% 3.94/1.23
% 3.94/1.23 ------
% 3.94/1.23 Current options:
% 3.94/1.23 ------
% 3.94/1.23
% 3.94/1.23
% 3.94/1.23
% 3.94/1.23
% 3.94/1.23 ------ Proving...
% 3.94/1.23
% 3.94/1.23
% 3.94/1.23 % SZS status Theorem for theBenchmark.p
% 3.94/1.23
% 3.94/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.94/1.23
% 3.94/1.23
%------------------------------------------------------------------------------