TSTP Solution File: NUM386+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 11:30:14 EDT 2023
% Result : Theorem 1.90s 1.17s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 229 ( 70 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 279 ( 105 ~; 119 |; 45 &)
% ( 6 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 102 ( 2 sgn; 75 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f7,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f8,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f28,conjecture,
! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_ordinal1) ).
fof(f29,negated_conjecture,
~ ! [X0,X1] :
( in(X0,succ(X1))
<=> ( X0 = X1
| in(X0,X1) ) ),
inference(negated_conjecture,[],[f28]) ).
fof(f52,plain,
? [X0,X1] :
( in(X0,succ(X1))
<~> ( X0 = X1
| in(X0,X1) ) ),
inference(ennf_transformation,[],[f29]) ).
fof(f59,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f60,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK0(X0,X1) != X0
| ~ in(sK0(X0,X1),X1) )
& ( sK0(X0,X1) = X0
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f60,f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(flattening,[],[f63]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ( ( ( ~ in(sK1(X0,X1,X2),X1)
& ~ in(sK1(X0,X1,X2),X0) )
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(sK1(X0,X1,X2),X1)
| in(sK1(X0,X1,X2),X0)
| in(sK1(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X1)
& ~ in(X4,X0) ) )
& ( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2) ) )
| set_union2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f65,f66]) ).
fof(f90,plain,
? [X0,X1] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f91,plain,
? [X0,X1] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ? [X0,X1] :
( ( ( X0 != X1
& ~ in(X0,X1) )
| ~ in(X0,succ(X1)) )
& ( X0 = X1
| in(X0,X1)
| in(X0,succ(X1)) ) )
=> ( ( ( sK13 != sK14
& ~ in(sK13,sK14) )
| ~ in(sK13,succ(sK14)) )
& ( sK13 = sK14
| in(sK13,sK14)
| in(sK13,succ(sK14)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ( ( sK13 != sK14
& ~ in(sK13,sK14) )
| ~ in(sK13,succ(sK14)) )
& ( sK13 = sK14
| in(sK13,sK14)
| in(sK13,succ(sK14)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f91,f92]) ).
fof(f100,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f101,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f102,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f62]) ).
fof(f105,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f106,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f140,plain,
( sK13 = sK14
| in(sK13,sK14)
| in(sK13,succ(sK14)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f141,plain,
( ~ in(sK13,sK14)
| ~ in(sK13,succ(sK14)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f142,plain,
( sK13 != sK14
| ~ in(sK13,succ(sK14)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f150,plain,
( sK13 != sK14
| ~ in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(definition_unfolding,[],[f142,f100]) ).
fof(f151,plain,
( ~ in(sK13,sK14)
| ~ in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(definition_unfolding,[],[f141,f100]) ).
fof(f152,plain,
( sK13 = sK14
| in(sK13,sK14)
| in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(definition_unfolding,[],[f140,f100]) ).
fof(f153,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f102]) ).
fof(f154,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f153]) ).
fof(f155,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f101]) ).
fof(f156,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f107]) ).
fof(f157,plain,
! [X0,X1,X4] :
( in(X4,set_union2(X0,X1))
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f106]) ).
fof(f158,plain,
! [X0,X1,X4] :
( in(X4,X1)
| in(X4,X0)
| ~ in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f105]) ).
cnf(c_55,plain,
in(X0,singleton(X0)),
inference(cnf_transformation,[],[f154]) ).
cnf(c_56,plain,
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f155]) ).
cnf(c_60,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X2,X1)) ),
inference(cnf_transformation,[],[f156]) ).
cnf(c_61,plain,
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_62,plain,
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(cnf_transformation,[],[f158]) ).
cnf(c_92,negated_conjecture,
( sK13 != sK14
| ~ in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_93,negated_conjecture,
( ~ in(sK13,set_union2(sK14,singleton(sK14)))
| ~ in(sK13,sK14) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_94,negated_conjecture,
( sK13 = sK14
| in(sK13,set_union2(sK14,singleton(sK14)))
| in(sK13,sK14) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_218,plain,
~ in(sK13,sK14),
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_61]) ).
cnf(c_416,plain,
( in(sK13,set_union2(sK14,singleton(sK14)))
| sK13 = sK14 ),
inference(prop_impl_just,[status(thm)],[c_94,c_218]) ).
cnf(c_417,plain,
( sK13 = sK14
| in(sK13,set_union2(sK14,singleton(sK14))) ),
inference(renaming,[status(thm)],[c_416]) ).
cnf(c_1444,plain,
( sK13 = sK14
| in(sK13,singleton(sK14))
| in(sK13,sK14) ),
inference(superposition,[status(thm)],[c_417,c_62]) ).
cnf(c_1451,plain,
( sK13 = sK14
| in(sK13,singleton(sK14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1444,c_218]) ).
cnf(c_1544,plain,
sK13 = sK14,
inference(forward_subsumption_resolution,[status(thm)],[c_1451,c_56]) ).
cnf(c_1547,plain,
( sK14 != sK14
| ~ in(sK14,set_union2(sK14,singleton(sK14))) ),
inference(demodulation,[status(thm)],[c_92,c_1544]) ).
cnf(c_1548,plain,
~ in(sK14,set_union2(sK14,singleton(sK14))),
inference(equality_resolution_simp,[status(thm)],[c_1547]) ).
cnf(c_1549,plain,
~ in(sK14,singleton(sK14)),
inference(superposition,[status(thm)],[c_60,c_1548]) ).
cnf(c_1551,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1549,c_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM386+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 14:59:56 EDT 2023
% 0.14/0.35 % 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
% 1.90/1.17 % SZS status Started for theBenchmark.p
% 1.90/1.17 % SZS status Theorem for theBenchmark.p
% 1.90/1.17
% 1.90/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.90/1.17
% 1.90/1.17 ------ iProver source info
% 1.90/1.17
% 1.90/1.17 git: date: 2023-05-31 18:12:56 +0000
% 1.90/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.90/1.17 git: non_committed_changes: false
% 1.90/1.17 git: last_make_outside_of_git: false
% 1.90/1.17
% 1.90/1.17 ------ Parsing...
% 1.90/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.90/1.17
% 1.90/1.17 ------ Preprocessing... sup_sim: 0 sf_s rm: 20 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e
% 1.90/1.17
% 1.90/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.90/1.17
% 1.90/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.90/1.17 ------ Proving...
% 1.90/1.17 ------ Problem Properties
% 1.90/1.17
% 1.90/1.17
% 1.90/1.17 clauses 30
% 1.90/1.17 conjectures 1
% 1.90/1.17 EPR 11
% 1.90/1.17 Horn 25
% 1.90/1.17 unary 12
% 1.90/1.17 binary 11
% 1.90/1.17 lits 56
% 1.90/1.17 lits eq 15
% 1.90/1.17 fd_pure 0
% 1.90/1.17 fd_pseudo 0
% 1.90/1.17 fd_cond 1
% 1.90/1.17 fd_pseudo_cond 6
% 1.90/1.17 AC symbols 0
% 1.90/1.17
% 1.90/1.17 ------ Schedule dynamic 5 is on
% 1.90/1.17
% 1.90/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.90/1.17
% 1.90/1.17
% 1.90/1.17 ------
% 1.90/1.17 Current options:
% 1.90/1.17 ------
% 1.90/1.17
% 1.90/1.17
% 1.90/1.17
% 1.90/1.17
% 1.90/1.17 ------ Proving...
% 1.90/1.17
% 1.90/1.17
% 1.90/1.17 % SZS status Theorem for theBenchmark.p
% 1.90/1.17
% 1.90/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.90/1.17
% 1.90/1.17
%------------------------------------------------------------------------------