TSTP Solution File: GEO084+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GEO084+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 : Wed Aug 30 23:09:16 EDT 2023
% Result : Theorem 0.42s 1.14s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 7 unt; 0 def)
% Number of atoms : 183 ( 11 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 214 ( 73 ~; 75 |; 53 &)
% ( 6 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 100 ( 0 sgn; 70 !; 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(f17,conjecture,
! [X1,X3,X5,X2] :
( ( meet(X2,X1,X3)
& part_of(X3,X5)
& part_of(X1,X5) )
=> part_of(sum(X1,X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_6_2) ).
fof(f18,negated_conjecture,
~ ! [X1,X3,X5,X2] :
( ( meet(X2,X1,X3)
& part_of(X3,X5)
& part_of(X1,X5) )
=> part_of(sum(X1,X3),X5) ),
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,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) )
=> part_of(sum(X0,X1),X2) ),
inference(rectify,[],[f18]) ).
fof(f35,plain,
! [X0,X1] :
( part_of(X1,X0)
<=> ! [X2] :
( incident_c(X2,X0)
| ~ incident_c(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f54,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f55,plain,
? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) ),
inference(flattening,[],[f54]) ).
fof(f56,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,[],[f35]) ).
fof(f57,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,[],[f56]) ).
fof(f58,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(f59,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])],[f57,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) ) ) )
& ( ! [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(f61,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,[],[f60]) ).
fof(f62,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,[],[f61]) ).
fof(f63,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(f64,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])],[f62,f63]) ).
fof(f93,plain,
( ? [X0,X1,X2,X3] :
( ~ part_of(sum(X0,X1),X2)
& meet(X3,X0,X1)
& part_of(X1,X2)
& part_of(X0,X2) )
=> ( ~ part_of(sum(sK13,sK14),sK15)
& meet(sK16,sK13,sK14)
& part_of(sK14,sK15)
& part_of(sK13,sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
( ~ part_of(sum(sK13,sK14),sK15)
& meet(sK16,sK13,sK14)
& part_of(sK14,sK15)
& part_of(sK13,sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f55,f93]) ).
fof(f95,plain,
! [X3,X0,X1] :
( incident_c(X3,X0)
| ~ incident_c(X3,X1)
| ~ part_of(X1,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f96,plain,
! [X0,X1] :
( part_of(X1,X0)
| incident_c(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f97,plain,
! [X0,X1] :
( part_of(X1,X0)
| ~ incident_c(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f59]) ).
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,[],[f64]) ).
fof(f136,plain,
part_of(sK13,sK15),
inference(cnf_transformation,[],[f94]) ).
fof(f137,plain,
part_of(sK14,sK15),
inference(cnf_transformation,[],[f94]) ).
fof(f139,plain,
~ part_of(sum(sK13,sK14),sK15),
inference(cnf_transformation,[],[f94]) ).
fof(f142,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,[],[f142]) ).
cnf(c_90,negated_conjecture,
~ part_of(sum(sK13,sK14),sK15),
inference(cnf_transformation,[],[f139]) ).
cnf(c_92,negated_conjecture,
part_of(sK14,sK15),
inference(cnf_transformation,[],[f137]) ).
cnf(c_93,negated_conjecture,
part_of(sK13,sK15),
inference(cnf_transformation,[],[f136]) ).
cnf(c_2010,plain,
( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sK15)
| part_of(sum(sK13,sK14),sK15) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_2016,plain,
( incident_c(sK0(sK15,sum(sK13,sK14)),sum(sK13,sK14))
| part_of(sum(sK13,sK14),sK15) ),
inference(instantiation,[status(thm)],[c_50]) ).
cnf(c_2210,plain,
( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sum(sK13,sK14))
| incident_c(sK0(sK15,sum(sK13,sK14)),sK13)
| incident_c(sK0(sK15,sum(sK13,sK14)),sK14) ),
inference(instantiation,[status(thm)],[c_57]) ).
cnf(c_6758,plain,
( ~ incident_c(sK0(sK15,sum(sK13,sK14)),X0)
| ~ part_of(X0,sK15)
| incident_c(sK0(sK15,sum(sK13,sK14)),sK15) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_6759,plain,
( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sK13)
| ~ part_of(sK13,sK15)
| incident_c(sK0(sK15,sum(sK13,sK14)),sK15) ),
inference(instantiation,[status(thm)],[c_6758]) ).
cnf(c_10056,plain,
( ~ incident_c(sK0(sK15,sum(sK13,sK14)),sK14)
| ~ part_of(sK14,sK15)
| incident_c(sK0(sK15,sum(sK13,sK14)),sK15) ),
inference(instantiation,[status(thm)],[c_6758]) ).
cnf(c_10057,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_10056,c_6759,c_2210,c_2016,c_2010,c_90,c_92,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : GEO084+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.14 % Command : run_iprover %s %d THM
% 0.11/0.35 % Computer : n028.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8042.1875MB
% 0.11/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Tue Aug 29 21:37:41 EDT 2023
% 0.11/0.35 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.42/1.14 % SZS status Started for theBenchmark.p
% 0.42/1.14 % SZS status Theorem for theBenchmark.p
% 0.42/1.14
% 0.42/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.42/1.14
% 0.42/1.14 ------ iProver source info
% 0.42/1.14
% 0.42/1.14 git: date: 2023-05-31 18:12:56 +0000
% 0.42/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.42/1.14 git: non_committed_changes: false
% 0.42/1.14 git: last_make_outside_of_git: false
% 0.42/1.14
% 0.42/1.14 ------ Parsing...
% 0.42/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.42/1.14
% 0.42/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.42/1.14
% 0.42/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.42/1.14
% 0.42/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.42/1.14 ------ Proving...
% 0.42/1.14 ------ Problem Properties
% 0.42/1.14
% 0.42/1.14
% 0.42/1.14 clauses 45
% 0.42/1.14 conjectures 4
% 0.42/1.14 EPR 16
% 0.42/1.14 Horn 29
% 0.42/1.14 unary 5
% 0.42/1.14 binary 16
% 0.42/1.14 lits 133
% 0.42/1.14 lits eq 12
% 0.42/1.14 fd_pure 0
% 0.42/1.14 fd_pseudo 0
% 0.42/1.14 fd_cond 0
% 0.42/1.14 fd_pseudo_cond 7
% 0.42/1.14 AC symbols 0
% 0.42/1.14
% 0.42/1.14 ------ Schedule dynamic 5 is on
% 0.42/1.14
% 0.42/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.42/1.14
% 0.42/1.14
% 0.42/1.14 ------
% 0.42/1.14 Current options:
% 0.42/1.14 ------
% 0.42/1.14
% 0.42/1.14
% 0.42/1.14
% 0.42/1.14
% 0.42/1.14 ------ Proving...
% 0.42/1.14
% 0.42/1.14
% 0.42/1.14 % SZS status Theorem for theBenchmark.p
% 0.42/1.14
% 0.42/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.42/1.14
% 0.42/1.14
%------------------------------------------------------------------------------