TSTP Solution File: NUM410+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n016.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 11:30:18 EDT 2023
% Result : Theorem 0.93s 1.18s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 0 def)
% Number of atoms : 119 ( 3 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 143 ( 61 ~; 47 |; 22 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 31 ( 1 sgn; 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f9,axiom,
! [X0,X1] :
( ( transfinite_sequence(X1)
& function(X1)
& relation(X1) )
=> ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f36,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f40,conjecture,
! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).
fof(f41,negated_conjecture,
~ ! [X0] :
( ( function(X0)
& relation(X0) )
=> ( ordinal(relation_dom(X0))
=> transfinite_sequence_of(X0,relation_rng(X0)) ) ),
inference(negated_conjecture,[],[f40]) ).
fof(f47,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f36]) ).
fof(f67,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f68,plain,
! [X0] :
( ( transfinite_sequence(X0)
<=> ordinal(relation_dom(X0)) )
| ~ function(X0)
| ~ relation(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f70,plain,
! [X0,X1] :
( ( transfinite_sequence_of(X1,X0)
<=> subset(relation_rng(X1),X0) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f81,plain,
? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& function(X0)
& relation(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f82,plain,
? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& function(X0)
& relation(X0) ),
inference(flattening,[],[f81]) ).
fof(f89,plain,
! [X0] :
( ( ( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0)) )
& ( ordinal(relation_dom(X0))
| ~ transfinite_sequence(X0) ) )
| ~ function(X0)
| ~ relation(X0) ),
inference(nnf_transformation,[],[f68]) ).
fof(f90,plain,
! [X0,X1] :
( ( ( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0) )
& ( subset(relation_rng(X1),X0)
| ~ transfinite_sequence_of(X1,X0) ) )
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f70]) ).
fof(f124,plain,
( ? [X0] :
( ~ transfinite_sequence_of(X0,relation_rng(X0))
& ordinal(relation_dom(X0))
& function(X0)
& relation(X0) )
=> ( ~ transfinite_sequence_of(sK16,relation_rng(sK16))
& ordinal(relation_dom(sK16))
& function(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
( ~ transfinite_sequence_of(sK16,relation_rng(sK16))
& ordinal(relation_dom(sK16))
& function(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f82,f124]) ).
fof(f138,plain,
! [X0] :
( transfinite_sequence(X0)
| ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f140,plain,
! [X0,X1] :
( transfinite_sequence_of(X1,X0)
| ~ subset(relation_rng(X1),X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f197,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f47]) ).
fof(f202,plain,
relation(sK16),
inference(cnf_transformation,[],[f125]) ).
fof(f203,plain,
function(sK16),
inference(cnf_transformation,[],[f125]) ).
fof(f204,plain,
ordinal(relation_dom(sK16)),
inference(cnf_transformation,[],[f125]) ).
fof(f205,plain,
~ transfinite_sequence_of(sK16,relation_rng(sK16)),
inference(cnf_transformation,[],[f125]) ).
cnf(c_58,plain,
( ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| transfinite_sequence(X0) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_60,plain,
( ~ subset(relation_rng(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence(X0)
| transfinite_sequence_of(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_118,plain,
subset(X0,X0),
inference(cnf_transformation,[],[f197]) ).
cnf(c_123,negated_conjecture,
~ transfinite_sequence_of(sK16,relation_rng(sK16)),
inference(cnf_transformation,[],[f205]) ).
cnf(c_124,negated_conjecture,
ordinal(relation_dom(sK16)),
inference(cnf_transformation,[],[f204]) ).
cnf(c_125,negated_conjecture,
function(sK16),
inference(cnf_transformation,[],[f203]) ).
cnf(c_126,negated_conjecture,
relation(sK16),
inference(cnf_transformation,[],[f202]) ).
cnf(c_1006,plain,
( relation_rng(sK16) != X1
| X0 != sK16
| ~ subset(relation_rng(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence(X0) ),
inference(resolution_lifted,[status(thm)],[c_60,c_123]) ).
cnf(c_1007,plain,
( ~ subset(relation_rng(sK16),relation_rng(sK16))
| ~ function(sK16)
| ~ relation(sK16)
| ~ transfinite_sequence(sK16) ),
inference(unflattening,[status(thm)],[c_1006]) ).
cnf(c_1008,plain,
( ~ subset(relation_rng(sK16),relation_rng(sK16))
| ~ transfinite_sequence(sK16) ),
inference(global_subsumption_just,[status(thm)],[c_1007,c_126,c_125,c_1007]) ).
cnf(c_1014,plain,
~ transfinite_sequence(sK16),
inference(forward_subsumption_resolution,[status(thm)],[c_1008,c_118]) ).
cnf(c_1045,plain,
( X0 != sK16
| ~ ordinal(relation_dom(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution_lifted,[status(thm)],[c_58,c_1014]) ).
cnf(c_1046,plain,
( ~ ordinal(relation_dom(sK16))
| ~ function(sK16)
| ~ relation(sK16) ),
inference(unflattening,[status(thm)],[c_1045]) ).
cnf(c_1047,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1046,c_124,c_125,c_126]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM410+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n016.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 : Fri Aug 25 10:01:25 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.93/1.18 % SZS status Started for theBenchmark.p
% 0.93/1.18 % SZS status Theorem for theBenchmark.p
% 0.93/1.18
% 0.93/1.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.93/1.18
% 0.93/1.18 ------ iProver source info
% 0.93/1.18
% 0.93/1.18 git: date: 2023-05-31 18:12:56 +0000
% 0.93/1.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.93/1.18 git: non_committed_changes: false
% 0.93/1.18 git: last_make_outside_of_git: false
% 0.93/1.18
% 0.93/1.18 ------ Parsing...
% 0.93/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.93/1.18
% 0.93/1.18 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s
% 0.93/1.18
% 0.93/1.18 % SZS status Theorem for theBenchmark.p
% 0.93/1.18
% 0.93/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.93/1.18
% 0.93/1.18
%------------------------------------------------------------------------------