%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO202+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 : n018.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 9.09s 6.17s
% Output : CNFRefutation 9.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 22 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 147 ( 47 ~; 79 |; 8 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 136 ( 8 sgn 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( distinct_points(X1,X2)
& distinct_points(X1,X3)
& convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
=> equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
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(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
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(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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ceq1,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_points(X1,X3)
| apart_point_and_line(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(cp2,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(ceq2,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
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(c_0_14,negated_conjecture,
~ ! [X1,X2,X3] :
( ( distinct_points(X1,X2)
& distinct_points(X1,X3)
& convergent_lines(line_connecting(X1,X2),line_connecting(X1,X3)) )
=> equal_points(intersection_point(line_connecting(X1,X2),line_connecting(X1,X3)),X1) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_15,plain,
! [X98,X99,X100] :
( ~ distinct_points(X98,X99)
| distinct_points(X98,X100)
| distinct_points(X99,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(c_0_16,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& distinct_points(esk1_0,esk3_0)
& convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0))
& ~ equal_points(intersection_point(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_17,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
cnf(c_0_18,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
distinct_points(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X95] : ~ distinct_points(X95,X95),
inference(variable_rename,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk3_0,X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
fof(c_0_24,plain,
! [X125,X126,X127] :
( ~ convergent_lines(X125,X126)
| distinct_lines(X126,X127)
| convergent_lines(X125,X127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_25,negated_conjecture,
( distinct_points(X1,esk3_0)
| distinct_points(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_26,plain,
! [X115,X116,X117,X118] :
( ~ distinct_points(X115,X116)
| ~ distinct_lines(X117,X118)
| apart_point_and_line(X115,X117)
| apart_point_and_line(X115,X118)
| apart_point_and_line(X116,X117)
| apart_point_and_line(X116,X118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_27,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
convergent_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_29,negated_conjecture,
( distinct_points(X1,esk3_0)
| distinct_points(esk1_0,X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
fof(c_0_30,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_31,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_26]) ).
cnf(c_0_32,negated_conjecture,
( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| distinct_lines(line_connecting(esk1_0,esk3_0),X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( distinct_points(X1,esk1_0)
| distinct_points(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
fof(c_0_34,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
fof(c_0_35,plain,
! [X97] : ~ convergent_lines(X97,X97),
inference(variable_rename,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| convergent_lines(line_connecting(esk1_0,esk2_0),X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
distinct_points(esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
fof(c_0_38,plain,
! [X109,X110] :
( ~ distinct_points(X109,X110)
| ~ apart_point_and_line(X110,line_connecting(X109,X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])]) ).
cnf(c_0_39,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk3_0,X1)
| convergent_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
fof(c_0_41,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_42,plain,
! [X119,X120,X121] :
( ~ apart_point_and_line(X119,X120)
| distinct_points(X119,X121)
| apart_point_and_line(X121,X120) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
cnf(c_0_43,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_45,plain,
! [X107,X108] :
( ~ distinct_points(X107,X108)
| ~ apart_point_and_line(X107,line_connecting(X107,X108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
cnf(c_0_46,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_19])]) ).
cnf(c_0_48,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_50,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(c_0_51,plain,
! [X122,X123,X124] :
( ~ apart_point_and_line(X122,X123)
| distinct_lines(X123,X124)
| apart_point_and_line(X122,X124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
cnf(c_0_52,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_19])]) ).
cnf(c_0_53,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_54,plain,
! [X132,X133] : ~ apart_point_and_line(X132,parallel_through_point(X133,X132)),
inference(variable_rename,[status(thm)],[c_0_50]) ).
cnf(c_0_55,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| distinct_points(esk3_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_52]),c_0_53])]) ).
fof(c_0_57,plain,
! [X128,X129] :
( ~ distinct_lines(X128,X129)
| convergent_lines(X128,X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_58,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( apart_point_and_line(X1,X2)
| distinct_lines(line_connecting(esk1_0,esk2_0),X2)
| distinct_points(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_60,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(c_0_61,plain,
! [X104,X105,X106] :
( ~ convergent_lines(X104,X105)
| convergent_lines(X104,X106)
| convergent_lines(X105,X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
cnf(c_0_62,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),parallel_through_point(X1,X2))
| distinct_points(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
fof(c_0_64,plain,
! [X130,X131] : ~ convergent_lines(parallel_through_point(X131,X130),X131),
inference(variable_rename,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,negated_conjecture,
( convergent_lines(line_connecting(esk1_0,esk2_0),parallel_through_point(X1,X2))
| distinct_points(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| convergent_lines(parallel_through_point(X2,X3),X1)
| distinct_points(esk3_0,X3) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
( convergent_lines(line_connecting(esk1_0,esk2_0),X1)
| distinct_points(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_70,negated_conjecture,
distinct_points(esk3_0,X1),
inference(spm,[status(thm)],[c_0_39,c_0_69]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_22,c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO202+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
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 17:48:17 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 9.09/6.17 % Version : CSE_E---1.7
% 9.09/6.17 % Problem : theBenchmark.p
% 9.09/6.17 % SZS status Theorem for theBenchmark.p
% 9.09/6.17 % SZS output start CNFRefutation
% See solution above
% 9.16/6.20 % Total time : 4.373s
%------------------------------------------------------------------------------