%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRA010+2 : TPTP v9.2.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 : Tue May 5 04:22:56 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 65 ( 14 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 71 ( 23 ~; 25 |; 15 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 44 ( 13 sgn 21 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complete_means_sequential_pairs_and_triangles,conjecture,
( complete
=> ! [X4,X2,X3] :
( ( path(X2,X3,X4)
& ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(sequential_pairs_and_triangles,axiom,
! [X4,X2,X3] :
( ( path(X2,X3,X4)
& ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(c_0_2,negated_conjecture,
~ ( complete
=> ! [X4,X2,X3] :
( ( path(X2,X3,X4)
& ! [X7,X8] :
( ( on_path(X7,X4)
& on_path(X8,X4)
& sequential(X7,X8) )
=> ? [X9] : triangle(X7,X8,X9) ) )
=> number_of_in(sequential_pairs,X4) = number_of_in(triangles,X4) ) ),
inference(assume_negation,[status(cth)],[complete_means_sequential_pairs_and_triangles]) ).
fof(c_0_3,plain,
! [X153,X154,X155,X158] :
( ( on_path(esk7_1(X153),X153)
| ~ path(X154,X155,X153)
| number_of_in(sequential_pairs,X153) = number_of_in(triangles,X153) )
& ( on_path(esk8_1(X153),X153)
| ~ path(X154,X155,X153)
| number_of_in(sequential_pairs,X153) = number_of_in(triangles,X153) )
& ( sequential(esk7_1(X153),esk8_1(X153))
| ~ path(X154,X155,X153)
| number_of_in(sequential_pairs,X153) = number_of_in(triangles,X153) )
& ( ~ triangle(esk7_1(X153),esk8_1(X153),X158)
| ~ path(X154,X155,X153)
| number_of_in(sequential_pairs,X153) = number_of_in(triangles,X153) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[sequential_pairs_and_triangles])])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X170,X171] :
( complete
& path(esk11_0,esk12_0,esk10_0)
& ( ~ on_path(X170,esk10_0)
| ~ on_path(X171,esk10_0)
| ~ sequential(X170,X171)
| triangle(X170,X171,esk13_2(X170,X171)) )
& number_of_in(sequential_pairs,esk10_0) != number_of_in(triangles,esk10_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])]) ).
cnf(c_0_5,plain,
( number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ triangle(esk7_1(X1),esk8_1(X1),X2)
| ~ path(X3,X4,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( triangle(X1,X2,esk13_2(X1,X2))
| ~ on_path(X1,esk10_0)
| ~ on_path(X2,esk10_0)
| ~ sequential(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( sequential(esk7_1(X1),esk8_1(X1))
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,plain,
( on_path(esk8_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
path(esk11_0,esk12_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
number_of_in(sequential_pairs,esk10_0) != number_of_in(triangles,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,plain,
( on_path(esk7_1(X1),X1)
| number_of_in(sequential_pairs,X1) = number_of_in(triangles,X1)
| ~ path(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_12,negated_conjecture,
( number_of_in(triangles,X1) = number_of_in(sequential_pairs,X1)
| ~ on_path(esk8_1(X1),esk10_0)
| ~ on_path(esk7_1(X1),esk10_0)
| ~ path(X2,X3,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]) ).
cnf(c_0_13,negated_conjecture,
on_path(esk8_1(esk10_0),esk10_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_14,negated_conjecture,
on_path(esk7_1(esk10_0),esk10_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_9]),c_0_10]) ).
cnf(c_0_15,negated_conjecture,
~ path(X1,X2,esk10_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14])]),c_0_10]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_9,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA010+2 : TPTP v9.2.1. Bugfixed v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:06:43 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.367s
%------------------------------------------------------------------------------