TSTP Solution File: SET347+4 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET347+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 03:00:30 EDT 2024
% Result : Theorem 3.43s 1.17s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 104 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 114 ( 49 ~; 36 |; 20 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 69 ( 4 sgn 49 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).
fof(f6,axiom,
! [X2] : ~ member(X2,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
fof(f10,axiom,
! [X2,X0] :
( member(X2,sum(X0))
<=> ? [X4] :
( member(X2,X4)
& member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum) ).
fof(f12,conjecture,
equal_set(sum(empty_set),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI38) ).
fof(f13,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(negated_conjecture,[],[f12]) ).
fof(f17,plain,
! [X0] : ~ member(X0,empty_set),
inference(rectify,[],[f6]) ).
fof(f21,plain,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
inference(rectify,[],[f10]) ).
fof(f23,plain,
~ equal_set(sum(empty_set),empty_set),
inference(flattening,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f26,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f29,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,[],[f25]) ).
fof(f30,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,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f32,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])],[f30,f31]) ).
fof(f43,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X2] :
( member(X0,X2)
& member(X2,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
| ~ member(X0,sum(X1)) ) ),
inference(rectify,[],[f43]) ).
fof(f45,plain,
! [X0,X1] :
( ? [X3] :
( member(X0,X3)
& member(X3,X1) )
=> ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( ( member(X0,sum(X1))
| ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) ) )
& ( ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) )
| ~ member(X0,sum(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f44,f45]) ).
fof(f52,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f54,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f63,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f17]) ).
fof(f72,plain,
! [X0,X1] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f78,plain,
~ equal_set(sum(empty_set),empty_set),
inference(cnf_transformation,[],[f23]) ).
cnf(c_50,plain,
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
cnf(c_61,plain,
~ member(X0,empty_set),
inference(cnf_transformation,[],[f63]) ).
cnf(c_72,plain,
( ~ member(X0,sum(X1))
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f72]) ).
cnf(c_76,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(cnf_transformation,[],[f78]) ).
cnf(c_422,plain,
( sum(empty_set) != X0
| X1 != empty_set
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
cnf(c_423,plain,
( ~ subset(sum(empty_set),empty_set)
| ~ subset(empty_set,sum(empty_set)) ),
inference(unflattening,[status(thm)],[c_422]) ).
cnf(c_488,plain,
( ~ subset(sum(empty_set),empty_set)
| ~ subset(empty_set,sum(empty_set)) ),
inference(prop_impl_just,[status(thm)],[c_423]) ).
cnf(c_1283,plain,
subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_61]) ).
cnf(c_1298,plain,
~ subset(sum(empty_set),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_488,c_1283]) ).
cnf(c_1405,plain,
~ member(X0,sum(empty_set)),
inference(superposition,[status(thm)],[c_72,c_61]) ).
cnf(c_1427,plain,
subset(sum(empty_set),X0),
inference(superposition,[status(thm)],[c_50,c_1405]) ).
cnf(c_1430,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1298,c_1427]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET347+4 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 2 20:56:22 EDT 2024
% 0.13/0.35 % 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
% 3.43/1.17 % SZS status Started for theBenchmark.p
% 3.43/1.17 % SZS status Theorem for theBenchmark.p
% 3.43/1.17
% 3.43/1.17 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.43/1.17
% 3.43/1.17 ------ iProver source info
% 3.43/1.17
% 3.43/1.17 git: date: 2024-05-02 19:28:25 +0000
% 3.43/1.17 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.43/1.17 git: non_committed_changes: false
% 3.43/1.17
% 3.43/1.17 ------ Parsing...
% 3.43/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.43/1.17
% 3.43/1.17 ------ 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
% 3.43/1.17
% 3.43/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.43/1.17
% 3.43/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.43/1.17 ------ Proving...
% 3.43/1.17 ------ Problem Properties
% 3.43/1.17
% 3.43/1.17
% 3.43/1.17 clauses 27
% 3.43/1.17 conjectures 0
% 3.43/1.17 EPR 2
% 3.43/1.17 Horn 22
% 3.43/1.17 unary 4
% 3.43/1.17 binary 16
% 3.43/1.17 lits 57
% 3.43/1.17 lits eq 3
% 3.43/1.17 fd_pure 0
% 3.43/1.17 fd_pseudo 0
% 3.43/1.17 fd_cond 0
% 3.43/1.17 fd_pseudo_cond 2
% 3.43/1.17 AC symbols 0
% 3.43/1.17
% 3.43/1.17 ------ Schedule dynamic 5 is on
% 3.43/1.17
% 3.43/1.17 ------ no conjectures: strip conj schedule
% 3.43/1.17
% 3.43/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.43/1.17
% 3.43/1.17
% 3.43/1.17 ------
% 3.43/1.17 Current options:
% 3.43/1.17 ------
% 3.43/1.17
% 3.43/1.17
% 3.43/1.17
% 3.43/1.17
% 3.43/1.17 ------ Proving...
% 3.43/1.17
% 3.43/1.17
% 3.43/1.17 % SZS status Theorem for theBenchmark.p
% 3.43/1.17
% 3.43/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.43/1.17
% 3.43/1.17
%------------------------------------------------------------------------------