%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO203+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 04:19:52 PM UTC 2026
% Result : Theorem 1.72s 1.86s
% Output : CNFRefutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 6 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 26 ~; 29 |; 8 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
=> ~ distinct_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(cu1,axiom,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_lines(X4,X5) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(ci1,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X1,X3)
& distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) )
=> ~ distinct_lines(line_connecting(intersection_point(X1,X2),intersection_point(X1,X3)),X1) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_6,plain,
! [X62,X63,X64,X65] :
( ~ distinct_points(X62,X63)
| ~ distinct_lines(X64,X65)
| apart_point_and_line(X62,X64)
| apart_point_and_line(X62,X65)
| apart_point_and_line(X63,X64)
| apart_point_and_line(X63,X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(c_0_7,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& convergent_lines(esk1_0,esk3_0)
& distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
& distinct_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
cnf(c_0_9,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X4)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X4)
| ~ distinct_points(X1,X2)
| ~ distinct_lines(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
distinct_lines(line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
fof(c_0_12,plain,
! [X56,X57] :
( ~ distinct_points(X56,X57)
| ~ apart_point_and_line(X57,line_connecting(X56,X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
cnf(c_0_13,negated_conjecture,
( apart_point_and_line(X1,line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(X2,line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X2,esk1_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(c_0_16,plain,
! [X54,X55] :
( ~ distinct_points(X54,X55)
| ~ apart_point_and_line(X54,line_connecting(X54,X55)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_17,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_19,plain,
! [X58,X59] :
( ~ convergent_lines(X58,X59)
| ~ apart_point_and_line(intersection_point(X58,X59),X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_20,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),line_connecting(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)))
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_14])]) ).
cnf(c_0_22,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_14])]) ).
cnf(c_0_24,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_25,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_26,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO203+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n007.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 17:47:23 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.72/1.86 % Version : CSE_E---1.7
% 1.72/1.86 % Problem : theBenchmark.p
% 1.72/1.86 % SZS status Theorem for theBenchmark.p
% 1.72/1.86 % SZS output start CNFRefutation
% See solution above
% 1.72/1.86 % Total time : 1.371s
%------------------------------------------------------------------------------