TSTP Solution File: NUM388+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM388+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n014.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 11:30:15 EDT 2023
% Result : Theorem 1.84s 1.16s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 13 unt; 0 def)
% Number of atoms : 180 ( 1 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 184 ( 62 ~; 49 |; 54 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 92 ( 1 sgn; 54 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ordinal(X0)
=> ( epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(f7,axiom,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( in(X1,X0)
=> subset(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(f24,conjecture,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( epsilon_transitive(X2)
=> ( ( in(X0,X1)
& in(X2,X0) )
=> in(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_ordinal1) ).
fof(f25,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> ! [X1] :
( ordinal(X1)
=> ! [X2] :
( epsilon_transitive(X2)
=> ( ( in(X0,X1)
& in(X2,X0) )
=> in(X2,X1) ) ) ) ),
inference(negated_conjecture,[],[f24]) ).
fof(f27,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f28,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f32,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f43,plain,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f49,plain,
! [X0] :
( epsilon_transitive(X0)
<=> ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X0,X1)
& in(X2,X0)
& epsilon_transitive(X2) )
& ordinal(X1) )
& ordinal(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f51,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X0,X1)
& in(X2,X0)
& epsilon_transitive(X2) )
& ordinal(X1) )
& ordinal(X0) ),
inference(flattening,[],[f50]) ).
fof(f53,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f56,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f59,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f61,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X1] :
( subset(X1,X0)
| ~ in(X1,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f62,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( ~ subset(X1,X0)
& in(X1,X0) )
=> ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0] :
( ( epsilon_transitive(X0)
| ( ~ subset(sK0(X0),X0)
& in(sK0(X0),X0) ) )
& ( ! [X2] :
( subset(X2,X0)
| ~ in(X2,X0) )
| ~ epsilon_transitive(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f62,f63]) ).
fof(f89,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X0,X1)
& in(X2,X0)
& epsilon_transitive(X2) )
& ordinal(X1) )
& ordinal(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(sK13,X1)
& in(X2,sK13)
& epsilon_transitive(X2) )
& ordinal(X1) )
& ordinal(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( ? [X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(sK13,X1)
& in(X2,sK13)
& epsilon_transitive(X2) )
& ordinal(X1) )
=> ( ? [X2] :
( ~ in(X2,sK14)
& in(sK13,sK14)
& in(X2,sK13)
& epsilon_transitive(X2) )
& ordinal(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
( ? [X2] :
( ~ in(X2,sK14)
& in(sK13,sK14)
& in(X2,sK13)
& epsilon_transitive(X2) )
=> ( ~ in(sK15,sK14)
& in(sK13,sK14)
& in(sK15,sK13)
& epsilon_transitive(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
( ~ in(sK15,sK14)
& in(sK13,sK14)
& in(sK15,sK13)
& epsilon_transitive(sK15)
& ordinal(sK14)
& ordinal(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f51,f91,f90,f89]) ).
fof(f93,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f96,plain,
! [X0] :
( epsilon_transitive(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f102,plain,
! [X2,X0] :
( subset(X2,X0)
| ~ in(X2,X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f134,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f136,plain,
in(sK15,sK13),
inference(cnf_transformation,[],[f92]) ).
fof(f137,plain,
in(sK13,sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f138,plain,
~ in(sK15,sK14),
inference(cnf_transformation,[],[f92]) ).
fof(f140,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f142,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f143,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f146,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
cnf(c_52,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_57,plain,
( ~ in(X0,X1)
| ~ epsilon_transitive(X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_86,negated_conjecture,
~ in(sK15,sK14),
inference(cnf_transformation,[],[f138]) ).
cnf(c_87,negated_conjecture,
in(sK13,sK14),
inference(cnf_transformation,[],[f137]) ).
cnf(c_88,negated_conjecture,
in(sK15,sK13),
inference(cnf_transformation,[],[f136]) ).
cnf(c_90,negated_conjecture,
ordinal(sK14),
inference(cnf_transformation,[],[f134]) ).
cnf(c_93,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_94,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_96,plain,
( ~ element(X0,powerset(X1))
| ~ in(X2,X0)
| element(X2,X1) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_99,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_116,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_94]) ).
cnf(c_136,plain,
( ~ ordinal(X0)
| epsilon_transitive(X0) ),
inference(prop_impl_just,[status(thm)],[c_52]) ).
cnf(c_218,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| element(X0,X2) ),
inference(bin_hyper_res,[status(thm)],[c_96,c_116]) ).
cnf(c_466,plain,
( X0 != sK14
| epsilon_transitive(X0) ),
inference(resolution_lifted,[status(thm)],[c_136,c_90]) ).
cnf(c_467,plain,
epsilon_transitive(sK14),
inference(unflattening,[status(thm)],[c_466]) ).
cnf(c_1700,plain,
~ empty(sK14),
inference(superposition,[status(thm)],[c_87,c_99]) ).
cnf(c_1770,plain,
( ~ subset(sK13,X0)
| element(sK15,X0) ),
inference(superposition,[status(thm)],[c_88,c_218]) ).
cnf(c_1791,plain,
( ~ epsilon_transitive(sK14)
| subset(sK13,sK14) ),
inference(superposition,[status(thm)],[c_87,c_57]) ).
cnf(c_1795,plain,
subset(sK13,sK14),
inference(forward_subsumption_resolution,[status(thm)],[c_1791,c_467]) ).
cnf(c_1816,plain,
element(sK15,sK14),
inference(superposition,[status(thm)],[c_1795,c_1770]) ).
cnf(c_1817,plain,
( in(sK15,sK14)
| empty(sK14) ),
inference(superposition,[status(thm)],[c_1816,c_93]) ).
cnf(c_1818,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1817,c_1700,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM388+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n014.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 : Fri Aug 25 15:38:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.84/1.16 % SZS status Started for theBenchmark.p
% 1.84/1.16 % SZS status Theorem for theBenchmark.p
% 1.84/1.16
% 1.84/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.84/1.16
% 1.84/1.16 ------ iProver source info
% 1.84/1.16
% 1.84/1.16 git: date: 2023-05-31 18:12:56 +0000
% 1.84/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.84/1.16 git: non_committed_changes: false
% 1.84/1.16 git: last_make_outside_of_git: false
% 1.84/1.16
% 1.84/1.16 ------ Parsing...
% 1.84/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.84/1.16
% 1.84/1.16 ------ Preprocessing... sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e
% 1.84/1.16
% 1.84/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.84/1.16
% 1.84/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.84/1.16 ------ Proving...
% 1.84/1.16 ------ Problem Properties
% 1.84/1.16
% 1.84/1.16
% 1.84/1.16 clauses 28
% 1.84/1.16 conjectures 4
% 1.84/1.16 EPR 23
% 1.84/1.16 Horn 26
% 1.84/1.16 unary 15
% 1.84/1.16 binary 8
% 1.84/1.16 lits 46
% 1.84/1.16 lits eq 2
% 1.84/1.16 fd_pure 0
% 1.84/1.16 fd_pseudo 0
% 1.84/1.16 fd_cond 1
% 1.84/1.16 fd_pseudo_cond 1
% 1.84/1.16 AC symbols 0
% 1.84/1.16
% 1.84/1.16 ------ Schedule dynamic 5 is on
% 1.84/1.16
% 1.84/1.16 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.84/1.16
% 1.84/1.16
% 1.84/1.16 ------
% 1.84/1.16 Current options:
% 1.84/1.16 ------
% 1.84/1.16
% 1.84/1.16
% 1.84/1.16
% 1.84/1.16
% 1.84/1.16 ------ Proving...
% 1.84/1.16
% 1.84/1.16
% 1.84/1.16 % SZS status Theorem for theBenchmark.p
% 1.84/1.16
% 1.84/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.84/1.16
% 1.84/1.16
%------------------------------------------------------------------------------