%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO201+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 : n023.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 3.64s 3.13s
% Output : CNFRefutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 21 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 111 ( 42 ~; 54 |; 3 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 96 ( 3 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2] :
( convergent_lines(X1,X2)
=> equal_points(intersection_point(X1,X2),intersection_point(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(ax1,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
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(c_0_11,negated_conjecture,
~ ! [X1,X2] :
( convergent_lines(X1,X2)
=> equal_points(intersection_point(X1,X2),intersection_point(X2,X1)) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_12,plain,
! [X103,X104,X105] :
( ~ convergent_lines(X103,X104)
| convergent_lines(X103,X105)
| convergent_lines(X104,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(c_0_13,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk2_0,esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_14,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_15,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X96] : ~ convergent_lines(X96,X96),
inference(variable_rename,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
fof(c_0_21,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
cnf(c_0_22,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_23,plain,
! [X129,X130] : ~ convergent_lines(parallel_through_point(X130,X129),X130),
inference(variable_rename,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(esk2_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
fof(c_0_25,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
fof(c_0_26,plain,
! [X124,X125,X126] :
( ~ convergent_lines(X124,X125)
| distinct_lines(X125,X126)
| convergent_lines(X124,X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_27,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_24]) ).
fof(c_0_29,plain,
! [X165,X166] :
( ( ~ equal_points(X165,X166)
| ~ distinct_points(X165,X166) )
& ( distinct_points(X165,X166)
| equal_points(X165,X166) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])]) ).
cnf(c_0_30,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
convergent_lines(parallel_through_point(esk1_0,X1),esk2_0),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_32,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_33,plain,
! [X97,X98,X99] :
( ~ distinct_points(X97,X98)
| distinct_points(X97,X99)
| distinct_points(X98,X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
cnf(c_0_34,negated_conjecture,
~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_35,plain,
( distinct_points(X1,X2)
| equal_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_36,plain,
! [X114,X115,X116,X117] :
( ~ distinct_points(X114,X115)
| ~ distinct_lines(X116,X117)
| apart_point_and_line(X114,X116)
| apart_point_and_line(X114,X117)
| apart_point_and_line(X115,X116)
| apart_point_and_line(X115,X117) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_37,negated_conjecture,
( convergent_lines(parallel_through_point(esk1_0,X1),X2)
| distinct_lines(esk2_0,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_38,plain,
! [X94] : ~ distinct_points(X94,X94),
inference(variable_rename,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_41,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
cnf(c_0_42,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_36]) ).
cnf(c_0_43,negated_conjecture,
distinct_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_44,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),X1)
| distinct_points(intersection_point(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_46,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(c_0_47,plain,
! [X110,X111] :
( ~ convergent_lines(X110,X111)
| ~ apart_point_and_line(intersection_point(X110,X111),X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
cnf(c_0_48,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X2,esk1_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
distinct_points(intersection_point(esk2_0,esk1_0),intersection_point(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_50,plain,
! [X112,X113] :
( ~ convergent_lines(X112,X113)
| ~ apart_point_and_line(intersection_point(X112,X113),X113) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])]) ).
cnf(c_0_51,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(intersection_point(esk2_0,esk1_0),esk1_0)
| apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0)
| apart_point_and_line(intersection_point(esk2_0,esk1_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_16])]) ).
cnf(c_0_55,negated_conjecture,
( apart_point_and_line(intersection_point(esk2_0,esk1_0),esk1_0)
| apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_16])]) ).
cnf(c_0_56,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_57,negated_conjecture,
apart_point_and_line(intersection_point(esk2_0,esk1_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_55]),c_0_56])]) ).
cnf(c_0_58,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_57]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO201+3 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.17/0.34 % Computer : n023.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 17:49:08 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 3.64/3.13 % Version : CSE_E---1.7
% 3.64/3.13 % Problem : theBenchmark.p
% 3.64/3.13 % SZS status Theorem for theBenchmark.p
% 3.64/3.13 % SZS output start CNFRefutation
% See solution above
% 3.64/3.14 % Total time : 2.374s
%------------------------------------------------------------------------------