TSTP Solution File: GRA010+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n003.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 00:03:12 EDT 2023
% Result : Theorem 1.17s 1.24s
% Output : CNFRefutation 1.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 5 unt; 0 def)
% Number of atoms : 159 ( 32 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 191 ( 68 ~; 64 |; 43 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 119 ( 16 sgn; 67 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f18,conjecture,
( complete
=> ! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(rectify,[],[f16]) ).
fof(f35,plain,
~ ( complete
=> ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(rectify,[],[f19]) ).
fof(f57,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f58,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f35]) ).
fof(f60,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
& complete ),
inference(flattening,[],[f59]) ).
fof(f84,plain,
! [X0] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
& sequential(sK6(X0),sK7(X0))
& on_path(sK7(X0),X0)
& on_path(sK6(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
& sequential(sK6(X0),sK7(X0))
& on_path(sK7(X0),X0)
& on_path(sK6(X0),X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f58,f84]) ).
fof(f86,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
& path(X1,X2,X0) )
=> ( number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8)
& ! [X4,X3] :
( ? [X5] : triangle(X3,X4,X5)
| ~ sequential(X3,X4)
| ~ on_path(X4,sK8)
| ~ on_path(X3,sK8) )
& path(sK9,sK10,sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
=> triangle(X3,X4,sK11(X3,X4)) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8)
& ! [X3,X4] :
( triangle(X3,X4,sK11(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK8)
| ~ on_path(X3,sK8) )
& path(sK9,sK10,sK8)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f60,f87,f86]) ).
fof(f140,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK6(X0),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f141,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK7(X0),X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f142,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK6(X0),sK7(X0))
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f143,plain,
! [X2,X0,X1,X5] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ triangle(sK6(X0),sK7(X0),X5)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f146,plain,
path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f88]) ).
fof(f147,plain,
! [X3,X4] :
( triangle(X3,X4,sK11(X3,X4))
| ~ sequential(X3,X4)
| ~ on_path(X4,sK8)
| ~ on_path(X3,sK8) ),
inference(cnf_transformation,[],[f88]) ).
fof(f148,plain,
number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8),
inference(cnf_transformation,[],[f88]) ).
cnf(c_100,plain,
( ~ triangle(sK6(X0),sK7(X0),X1)
| ~ path(X2,X3,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_101,plain,
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| sequential(sK6(X2),sK7(X2)) ),
inference(cnf_transformation,[],[f142]) ).
cnf(c_102,plain,
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| on_path(sK7(X2),X2) ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_103,plain,
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| on_path(sK6(X2),X2) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_105,negated_conjecture,
number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8),
inference(cnf_transformation,[],[f148]) ).
cnf(c_106,negated_conjecture,
( ~ sequential(X0,X1)
| ~ on_path(X0,sK8)
| ~ on_path(X1,sK8)
| triangle(X0,X1,sK11(X0,X1)) ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_107,negated_conjecture,
path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f146]) ).
cnf(c_1239,plain,
( sK11(X1,X2) != X3
| sK6(X0) != X1
| sK7(X0) != X2
| ~ path(X4,X5,X0)
| ~ sequential(X1,X2)
| ~ on_path(X1,sK8)
| ~ on_path(X2,sK8)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(resolution_lifted,[status(thm)],[c_100,c_106]) ).
cnf(c_1240,plain,
( ~ sequential(sK6(X0),sK7(X0))
| ~ path(X1,X2,X0)
| ~ on_path(sK6(X0),sK8)
| ~ on_path(sK7(X0),sK8)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(unflattening,[status(thm)],[c_1239]) ).
cnf(c_1252,plain,
( ~ path(X0,X1,X2)
| ~ on_path(sK6(X2),sK8)
| ~ on_path(sK7(X2),sK8)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1240,c_101]) ).
cnf(c_3189,plain,
( ~ on_path(sK6(sK8),sK8)
| ~ on_path(sK7(sK8),sK8)
| number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8) ),
inference(superposition,[status(thm)],[c_107,c_1252]) ).
cnf(c_3190,plain,
( ~ on_path(sK6(sK8),sK8)
| ~ on_path(sK7(sK8),sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3189,c_105]) ).
cnf(c_3911,plain,
( ~ path(sK9,sK10,sK8)
| number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| on_path(sK7(sK8),sK8) ),
inference(instantiation,[status(thm)],[c_102]) ).
cnf(c_3941,plain,
( ~ path(sK9,sK10,sK8)
| number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| on_path(sK6(sK8),sK8) ),
inference(instantiation,[status(thm)],[c_103]) ).
cnf(c_3942,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3941,c_3911,c_3190,c_105,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n003.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
% 0.21/0.36 % CPULimit : 300
% 0.21/0.36 % WCLimit : 300
% 0.21/0.36 % DateTime : Sun Aug 27 03:19:54 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.17/1.24 % SZS status Started for theBenchmark.p
% 1.17/1.24 % SZS status Theorem for theBenchmark.p
% 1.17/1.24
% 1.17/1.24 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.17/1.24
% 1.17/1.24 ------ iProver source info
% 1.17/1.24
% 1.17/1.24 git: date: 2023-05-31 18:12:56 +0000
% 1.17/1.24 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.17/1.24 git: non_committed_changes: false
% 1.17/1.24 git: last_make_outside_of_git: false
% 1.17/1.24
% 1.17/1.24 ------ Parsing...
% 1.17/1.24 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.17/1.24
% 1.17/1.24 ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 1.17/1.24
% 1.17/1.24 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.17/1.24
% 1.17/1.24 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.17/1.24 ------ Proving...
% 1.17/1.24 ------ Problem Properties
% 1.17/1.24
% 1.17/1.24
% 1.17/1.24 clauses 55
% 1.17/1.24 conjectures 2
% 1.17/1.24 EPR 14
% 1.17/1.24 Horn 37
% 1.17/1.24 unary 4
% 1.17/1.24 binary 13
% 1.17/1.24 lits 178
% 1.17/1.24 lits eq 46
% 1.17/1.24 fd_pure 0
% 1.17/1.24 fd_pseudo 0
% 1.17/1.24 fd_cond 0
% 1.17/1.24 fd_pseudo_cond 5
% 1.17/1.24 AC symbols 0
% 1.17/1.24
% 1.17/1.24 ------ Schedule dynamic 5 is on
% 1.17/1.24
% 1.17/1.24 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.17/1.24
% 1.17/1.24
% 1.17/1.24 ------
% 1.17/1.24 Current options:
% 1.17/1.24 ------
% 1.17/1.24
% 1.17/1.24
% 1.17/1.24
% 1.17/1.24
% 1.17/1.24 ------ Proving...
% 1.17/1.24
% 1.17/1.24
% 1.17/1.24 % SZS status Theorem for theBenchmark.p
% 1.17/1.24
% 1.17/1.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.17/1.24
% 1.17/1.24
%------------------------------------------------------------------------------