TSTP Solution File: SET679+3 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n004.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 15:09:05 EDT 2023
% Result : Theorem 2.94s 1.14s
% Output : CNFRefutation 2.94s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f140)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( not_equal(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(f23,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f24,conjecture,
! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> not_equal(identity_relation_of(X0),empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_46) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ( ilf_type(X0,set_type)
& ~ empty(X0) )
=> not_equal(identity_relation_of(X0),empty_set) ),
inference(negated_conjecture,[],[f24]) ).
fof(f27,plain,
! [X0] :
( ! [X1] :
( ( member(X1,X0)
<=> member(ordered_pair(X1,X1),identity_relation_of(X0)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( not_equal(X0,X1)
<=> X0 != X1 )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f51,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f52,plain,
? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ilf_type(X0,set_type)
& ~ empty(X0) ),
inference(flattening,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,X0)
| ~ member(ordered_pair(X1,X1),identity_relation_of(X0)) )
& ( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f27]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( ( not_equal(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ not_equal(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f63,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK1(X0),X0)
& ilf_type(sK1(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK1(X0),X0)
& ilf_type(sK1(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f63,f64]) ).
fof(f86,plain,
( ? [X0] :
( ~ not_equal(identity_relation_of(X0),empty_set)
& ilf_type(X0,set_type)
& ~ empty(X0) )
=> ( ~ not_equal(identity_relation_of(sK9),empty_set)
& ilf_type(sK9,set_type)
& ~ empty(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ~ not_equal(identity_relation_of(sK9),empty_set)
& ilf_type(sK9,set_type)
& ~ empty(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f52,f86]) ).
fof(f88,plain,
! [X0,X1] :
( member(ordered_pair(X1,X1),identity_relation_of(X0))
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f90,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f28]) ).
fof(f102,plain,
! [X0,X1] :
( not_equal(X0,X1)
| X0 = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f61]) ).
fof(f105,plain,
! [X0] :
( empty(X0)
| member(sK1(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f132,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f23]) ).
fof(f133,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f87]) ).
fof(f135,plain,
~ not_equal(identity_relation_of(sK9),empty_set),
inference(cnf_transformation,[],[f87]) ).
cnf(c_50,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_51,plain,
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_53,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_62,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1
| not_equal(X1,X0) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_64,plain,
( ~ ilf_type(X0,set_type)
| member(sK1(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_92,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f132]) ).
cnf(c_93,negated_conjecture,
~ not_equal(identity_relation_of(sK9),empty_set),
inference(cnf_transformation,[],[f135]) ).
cnf(c_95,negated_conjecture,
~ empty(sK9),
inference(cnf_transformation,[],[f133]) ).
cnf(c_145,plain,
~ member(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_51,c_92,c_51]) ).
cnf(c_187,plain,
( ~ ilf_type(X1,set_type)
| X0 = X1
| not_equal(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_92,c_62]) ).
cnf(c_188,plain,
( ~ ilf_type(X0,set_type)
| X1 = X0
| not_equal(X0,X1) ),
inference(renaming,[status(thm)],[c_187]) ).
cnf(c_189,plain,
( X1 = X0
| not_equal(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_188,c_92,c_188]) ).
cnf(c_190,plain,
( X0 = X1
| not_equal(X1,X0) ),
inference(renaming,[status(thm)],[c_189]) ).
cnf(c_218,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_92,c_53]) ).
cnf(c_220,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_218]) ).
cnf(c_279,plain,
( X0 = X1
| not_equal(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_190]) ).
cnf(c_365,plain,
( ~ member(X0,X1)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_220,c_92]) ).
cnf(c_652,plain,
( identity_relation_of(sK9) != X1
| X0 != empty_set
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_279,c_93]) ).
cnf(c_653,plain,
empty_set = identity_relation_of(sK9),
inference(unflattening,[status(thm)],[c_652]) ).
cnf(c_914,plain,
( ~ member(X0,X1)
| member(ordered_pair(X0,X0),identity_relation_of(X1)) ),
inference(prop_impl_just,[status(thm)],[c_365]) ).
cnf(c_938,plain,
( empty(X0)
| member(sK1(X0),X0) ),
inference(prop_impl_just,[status(thm)],[c_92,c_64]) ).
cnf(c_939,plain,
( member(sK1(X0),X0)
| empty(X0) ),
inference(renaming,[status(thm)],[c_938]) ).
cnf(c_2181,plain,
( ~ member(X0,sK9)
| member(ordered_pair(X0,X0),empty_set) ),
inference(superposition,[status(thm)],[c_653,c_914]) ).
cnf(c_2185,plain,
~ member(X0,sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2181,c_145]) ).
cnf(c_2194,plain,
empty(sK9),
inference(superposition,[status(thm)],[c_939,c_2185]) ).
cnf(c_2197,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2194,c_95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET679+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 12:54:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.94/1.14 % SZS status Started for theBenchmark.p
% 2.94/1.14 % SZS status Theorem for theBenchmark.p
% 2.94/1.14
% 2.94/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.94/1.14
% 2.94/1.14 ------ iProver source info
% 2.94/1.14
% 2.94/1.14 git: date: 2023-05-31 18:12:56 +0000
% 2.94/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.94/1.14 git: non_committed_changes: false
% 2.94/1.14 git: last_make_outside_of_git: false
% 2.94/1.14
% 2.94/1.14 ------ Parsing...
% 2.94/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.94/1.14
% 2.94/1.14 ------ 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
% 2.94/1.14
% 2.94/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.94/1.14
% 2.94/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.94/1.14 ------ Proving...
% 2.94/1.14 ------ Problem Properties
% 2.94/1.14
% 2.94/1.14
% 2.94/1.14 clauses 31
% 2.94/1.14 conjectures 1
% 2.94/1.14 EPR 9
% 2.94/1.14 Horn 25
% 2.94/1.14 unary 9
% 2.94/1.14 binary 17
% 2.94/1.14 lits 58
% 2.94/1.14 lits eq 6
% 2.94/1.14 fd_pure 0
% 2.94/1.14 fd_pseudo 0
% 2.94/1.14 fd_cond 0
% 2.94/1.14 fd_pseudo_cond 3
% 2.94/1.14 AC symbols 0
% 2.94/1.14
% 2.94/1.14 ------ Schedule dynamic 5 is on
% 2.94/1.14
% 2.94/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.94/1.14
% 2.94/1.14
% 2.94/1.14 ------
% 2.94/1.14 Current options:
% 2.94/1.14 ------
% 2.94/1.14
% 2.94/1.14
% 2.94/1.14
% 2.94/1.14
% 2.94/1.14 ------ Proving...
% 2.94/1.14
% 2.94/1.14
% 2.94/1.14 % SZS status Theorem for theBenchmark.p
% 2.94/1.14
% 2.94/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.94/1.14
% 2.94/1.14
%------------------------------------------------------------------------------