TSTP Solution File: GEO093+1 by iProver---3.9
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%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GEO093+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.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 02:16:23 EDT 2024
% Result : Theorem 17.37s 3.15s
% Output : CNFRefutation 17.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 226 ( 21 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 256 ( 87 ~; 93 |; 62 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 119 ( 0 sgn 78 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X1)
=> incident_c(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).
fof(f2,axiom,
! [X0,X1,X3] :
( sum(X1,X3) = X0
<=> ! [X4] :
( incident_c(X4,X0)
<=> ( incident_c(X4,X3)
| incident_c(X4,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_defn) ).
fof(f8,axiom,
! [X0,X1] :
( ( X0 != X1
& part_of(X1,X0) )
=> open(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1) ).
fof(f17,conjecture,
! [X0,X1,X3,X2] :
( ( meet(X2,X1,X3)
& part_of(X3,X0)
& part_of(X1,X0)
& open(X0) )
=> open(sum(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',proposition_2_14_2) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X3,X2] :
( ( meet(X2,X1,X3)
& part_of(X3,X0)
& part_of(X1,X0)
& open(X0) )
=> open(sum(X1,X3)) ),
inference(negated_conjecture,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( sum(X1,X2) = X0
<=> ! [X3] :
( incident_c(X3,X0)
<=> ( incident_c(X3,X2)
| incident_c(X3,X1) ) ) ),
inference(rectify,[],[f2]) ).
fof(f32,plain,
~ ! [X0,X1,X2,X3] :
( ( meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0) )
=> open(sum(X1,X2)) ),
inference(rectify,[],[f18]) ).
fof(f34,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0,X1] :
( open(X1)
| X0 = X1
| ~ part_of(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f41,plain,
! [X0,X1] :
( open(X1)
| X0 = X1
| ~ part_of(X1,X0) ),
inference(flattening,[],[f40]) ).
fof(f52,plain,
? [X0,X1,X2,X3] :
( ~ open(sum(X1,X2))
& meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f53,plain,
? [X0,X1,X2,X3] :
( ~ open(sum(X1,X2))
& meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) )
| ~ part_of(X1,X0) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ? [X2] :
( ~ incident_c(X2,X0)
& incident_c(X2,X1) )
=> ( ~ incident_c(sK0(X0,X1),X0)
& incident_c(sK0(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f57,plain,
! [X0,X1] :
( ( part_of(X1,X0)
| ( ~ incident_c(sK0(X0,X1),X0)
& incident_c(sK0(X0,X1),X1) ) )
& ( ! [X3] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1) )
| ~ part_of(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f55,f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X3] :
( ( incident_c(X3,X0)
| ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) ) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| ~ incident_c(X3,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(flattening,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(rectify,[],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ incident_c(X3,X2)
& ~ incident_c(X3,X1) )
| ~ incident_c(X3,X0) )
& ( incident_c(X3,X2)
| incident_c(X3,X1)
| incident_c(X3,X0) ) )
=> ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
& ~ incident_c(sK1(X0,X1,X2),X1) )
| ~ incident_c(sK1(X0,X1,X2),X0) )
& ( incident_c(sK1(X0,X1,X2),X2)
| incident_c(sK1(X0,X1,X2),X1)
| incident_c(sK1(X0,X1,X2),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( sum(X1,X2) = X0
| ( ( ( ~ incident_c(sK1(X0,X1,X2),X2)
& ~ incident_c(sK1(X0,X1,X2),X1) )
| ~ incident_c(sK1(X0,X1,X2),X0) )
& ( incident_c(sK1(X0,X1,X2),X2)
| incident_c(sK1(X0,X1,X2),X1)
| incident_c(sK1(X0,X1,X2),X0) ) ) )
& ( ! [X4] :
( ( incident_c(X4,X0)
| ( ~ incident_c(X4,X2)
& ~ incident_c(X4,X1) ) )
& ( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0) ) )
| sum(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f60,f61]) ).
fof(f93,plain,
( ? [X0,X1,X2,X3] :
( ~ open(sum(X1,X2))
& meet(X3,X1,X2)
& part_of(X2,X0)
& part_of(X1,X0)
& open(X0) )
=> ( ~ open(sum(sK14,sK15))
& meet(sK16,sK14,sK15)
& part_of(sK15,sK13)
& part_of(sK14,sK13)
& open(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ~ open(sum(sK14,sK15))
& meet(sK16,sK14,sK15)
& part_of(sK15,sK13)
& part_of(sK14,sK13)
& open(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f53,f93]) ).
fof(f95,plain,
! [X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f96,plain,
! [X0,X1] :
( part_of(X1,X0)
| incident_c(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f97,plain,
! [X0,X1] :
( part_of(X1,X0)
| ~ incident_c(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f98,plain,
! [X2,X0,X1,X4] :
( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,X0)
| sum(X1,X2) != X0 ),
inference(cnf_transformation,[],[f62]) ).
fof(f125,plain,
! [X0,X1] :
( open(X1)
| X0 = X1
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f137,plain,
open(sK13),
inference(cnf_transformation,[],[f94]) ).
fof(f138,plain,
part_of(sK14,sK13),
inference(cnf_transformation,[],[f94]) ).
fof(f139,plain,
part_of(sK15,sK13),
inference(cnf_transformation,[],[f94]) ).
fof(f141,plain,
~ open(sum(sK14,sK15)),
inference(cnf_transformation,[],[f94]) ).
fof(f144,plain,
! [X2,X1,X4] :
( incident_c(X4,X2)
| incident_c(X4,X1)
| ~ incident_c(X4,sum(X1,X2)) ),
inference(equality_resolution,[],[f98]) ).
cnf(c_49,plain,
( ~ incident_c(sK0(X0,X1),X0)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_50,plain,
( incident_c(sK0(X0,X1),X1)
| part_of(X1,X0) ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_51,plain,
( ~ part_of(X0,X1)
| ~ incident_c(X2,X0)
| incident_c(X2,X1) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_57,plain,
( ~ incident_c(X0,sum(X1,X2))
| incident_c(X0,X1)
| incident_c(X0,X2) ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_79,plain,
( ~ part_of(X0,X1)
| X0 = X1
| open(X0) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_91,negated_conjecture,
~ open(sum(sK14,sK15)),
inference(cnf_transformation,[],[f141]) ).
cnf(c_93,negated_conjecture,
part_of(sK15,sK13),
inference(cnf_transformation,[],[f139]) ).
cnf(c_94,negated_conjecture,
part_of(sK14,sK13),
inference(cnf_transformation,[],[f138]) ).
cnf(c_95,negated_conjecture,
open(sK13),
inference(cnf_transformation,[],[f137]) ).
cnf(c_455,plain,
( sum(sK14,sK15) != X0
| ~ part_of(X0,X1)
| X0 = X1 ),
inference(resolution_lifted,[status(thm)],[c_79,c_91]) ).
cnf(c_456,plain,
( ~ part_of(sum(sK14,sK15),X0)
| sum(sK14,sK15) = X0 ),
inference(unflattening,[status(thm)],[c_455]) ).
cnf(c_457,plain,
( ~ part_of(sum(sK14,sK15),sK13)
| sum(sK14,sK15) = sK13 ),
inference(instantiation,[status(thm)],[c_456]) ).
cnf(c_469,plain,
sum(sK14,sK15) != sK13,
inference(resolution_lifted,[status(thm)],[c_91,c_95]) ).
cnf(c_1267,plain,
( incident_c(sK0(X0,sum(sK14,sK15)),sum(sK14,sK15))
| part_of(sum(sK14,sK15),X0) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_1268,plain,
( ~ incident_c(sK0(X0,sum(sK14,sK15)),X0)
| part_of(sum(sK14,sK15),X0) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_1269,plain,
( ~ incident_c(sK0(sK13,sum(sK14,sK15)),sK13)
| part_of(sum(sK14,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_1268]) ).
cnf(c_1270,plain,
( incident_c(sK0(sK13,sum(sK14,sK15)),sum(sK14,sK15))
| part_of(sum(sK14,sK15),sK13) ),
inference(instantiation,[status(thm)],[c_1267]) ).
cnf(c_1496,plain,
( ~ incident_c(sK0(X0,sum(sK14,sK15)),sum(sK14,sK15))
| incident_c(sK0(X0,sum(sK14,sK15)),sK14)
| incident_c(sK0(X0,sum(sK14,sK15)),sK15) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_1497,plain,
( ~ incident_c(sK0(sK13,sum(sK14,sK15)),sum(sK14,sK15))
| incident_c(sK0(sK13,sum(sK14,sK15)),sK14)
| incident_c(sK0(sK13,sum(sK14,sK15)),sK15) ),
inference(instantiation,[status(thm)],[c_1496]) ).
cnf(c_3440,plain,
( ~ incident_c(sK0(X0,sum(sK14,sK15)),sK14)
| ~ part_of(sK14,X1)
| incident_c(sK0(X0,sum(sK14,sK15)),X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_3441,plain,
( ~ incident_c(sK0(sK13,sum(sK14,sK15)),sK14)
| ~ part_of(sK14,sK13)
| incident_c(sK0(sK13,sum(sK14,sK15)),sK13) ),
inference(instantiation,[status(thm)],[c_3440]) ).
cnf(c_3476,plain,
( ~ incident_c(sK0(X0,sum(sK14,sK15)),sK15)
| ~ part_of(sK15,X1)
| incident_c(sK0(X0,sum(sK14,sK15)),X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_3477,plain,
( ~ incident_c(sK0(sK13,sum(sK14,sK15)),sK15)
| ~ part_of(sK15,sK13)
| incident_c(sK0(sK13,sum(sK14,sK15)),sK13) ),
inference(instantiation,[status(thm)],[c_3476]) ).
cnf(c_3478,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3477,c_3441,c_1497,c_1270,c_1269,c_469,c_457,c_93,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO093+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 01:17:46 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.43 Running first-order theorem proving
% 0.17/0.43 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.37/3.15 % SZS status Started for theBenchmark.p
% 17.37/3.15 % SZS status Theorem for theBenchmark.p
% 17.37/3.15
% 17.37/3.15 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.37/3.15
% 17.37/3.15 ------ iProver source info
% 17.37/3.15
% 17.37/3.15 git: date: 2024-05-02 19:28:25 +0000
% 17.37/3.15 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.37/3.15 git: non_committed_changes: false
% 17.37/3.15
% 17.37/3.15 ------ Parsing...
% 17.37/3.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.37/3.15
% 17.37/3.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 17.37/3.15
% 17.37/3.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.37/3.15
% 17.37/3.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.37/3.15 ------ Proving...
% 17.37/3.15 ------ Problem Properties
% 17.37/3.15
% 17.37/3.15
% 17.37/3.15 clauses 47
% 17.37/3.15 conjectures 5
% 17.37/3.15 EPR 18
% 17.37/3.15 Horn 31
% 17.37/3.15 unary 6
% 17.37/3.15 binary 17
% 17.37/3.15 lits 136
% 17.37/3.15 lits eq 12
% 17.37/3.15 fd_pure 0
% 17.37/3.15 fd_pseudo 0
% 17.37/3.15 fd_cond 0
% 17.37/3.15 fd_pseudo_cond 7
% 17.37/3.15 AC symbols 0
% 17.37/3.15
% 17.37/3.15 ------ Input Options Time Limit: Unbounded
% 17.37/3.15
% 17.37/3.15
% 17.37/3.15 ------
% 17.37/3.15 Current options:
% 17.37/3.15 ------
% 17.37/3.15
% 17.37/3.15
% 17.37/3.15
% 17.37/3.15
% 17.37/3.15 ------ Proving...
% 17.37/3.15
% 17.37/3.15
% 17.37/3.15 % SZS status Theorem for theBenchmark.p
% 17.37/3.15
% 17.37/3.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.37/3.15
% 17.37/3.16
%------------------------------------------------------------------------------