%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO224+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n012.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 04:20:01 PM UTC 2026
% Result : Theorem 1.11s 1.61s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 39 ~; 27 |; 10 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 3 sgn 35 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2] :
( ( point(X1)
& line(X2) )
=> ? [X3] :
( point(X3)
& incident_point_and_line(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(a4,axiom,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(int1,axiom,
! [X6,X7] :
( ( line(X6)
& line(X7)
& convergent_lines(X6,X7) )
=> point(intersection_point(X6,X7)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',int1) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(orth1,axiom,
! [X6,X9] :
( ( line(X6)
& point(X9) )
=> line(orthogonal_through_point(X6,X9)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',orth1) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( ( point(X1)
& line(X2) )
=> ? [X3] :
( point(X3)
& incident_point_and_line(X3,X2) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_8,plain,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4]) ).
fof(c_0_9,negated_conjecture,
! [X178] :
( point(esk1_0)
& line(esk2_0)
& ( ~ point(X178)
| ~ incident_point_and_line(X178,esk2_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_10,plain,
! [X172,X173] :
( ( ~ incident_point_and_line(X172,X173)
| ~ apart_point_and_line(X172,X173) )
& ( apart_point_and_line(X172,X173)
| incident_point_and_line(X172,X173) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_11,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
cnf(c_0_12,negated_conjecture,
( ~ point(X1)
| ~ incident_point_and_line(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( apart_point_and_line(X1,X2)
| incident_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X160,X161] :
( ~ line(X160)
| ~ line(X161)
| ~ convergent_lines(X160,X161)
| point(intersection_point(X160,X161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int1])]) ).
fof(c_0_15,plain,
! [X113,X114] :
( ~ convergent_lines(X113,X114)
| ~ apart_point_and_line(intersection_point(X113,X114),X114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_16,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( point(intersection_point(X1,X2))
| ~ line(X1)
| ~ line(X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
cnf(c_0_19,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( apart_point_and_line(intersection_point(X1,X2),esk2_0)
| ~ line(X2)
| ~ line(X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
line(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_22,plain,
! [X164,X165] :
( ~ line(X164)
| ~ point(X165)
| line(orthogonal_through_point(X164,X165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[orth1])]) ).
fof(c_0_23,plain,
! [X142,X143] : ~ unorthogonal_lines(orthogonal_through_point(X143,X142),X143),
inference(variable_rename,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X137,X138] :
( convergent_lines(X137,X138)
| unorthogonal_lines(X137,X138) ),
inference(variable_rename,[status(thm)],[occu1]) ).
cnf(c_0_25,negated_conjecture,
( ~ line(X1)
| ~ convergent_lines(X1,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
( line(orthogonal_through_point(X1,X2))
| ~ line(X1)
| ~ point(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( ~ line(X1)
| ~ point(X2)
| ~ convergent_lines(orthogonal_through_point(X1,X2),esk2_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
point(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_32,negated_conjecture,
~ point(X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_21])]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_31,c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GEO224+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.08/0.24 % Computer : n012.cluster.edu
% 0.08/0.24 % Model : x86_64 x86_64
% 0.08/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.24 % Memory : 8042.1875MB
% 0.08/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.24 % CPULimit : 300
% 0.08/0.24 % WCLimit : 300
% 0.08/0.24 % DateTime : Mon May 4 17:48:16 EDT 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.25 % start to proof: theBenchmark
% 1.11/1.61 % Version : CSE_E---1.7
% 1.11/1.61 % Problem : theBenchmark.p
% 1.11/1.61 % SZS status Theorem for theBenchmark.p
% 1.11/1.61 % SZS output start CNFRefutation
% See solution above
% 1.11/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------