%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO205+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n031.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 04:19:54 PM UTC 2026
% Result : Theorem 6.24s 4.57s
% Output : CNFRefutation 6.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 22 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 148 ( 54 ~; 70 |; 9 &)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 118 ( 3 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& equal_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& equal_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(ax2,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
fof(ax1,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax1) ).
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(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
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(ceq2,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(c_0_13,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& equal_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& equal_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_14,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])]) ).
fof(c_0_15,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& equal_lines(esk2_0,esk3_0)
& ( ~ convergent_lines(esk1_0,esk3_0)
| ~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_17,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_19,plain,
! [X97] : ~ convergent_lines(X97,X97),
inference(variable_rename,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
fof(c_0_23,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
cnf(c_0_24,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_25,plain,
! [X130,X131] : ~ convergent_lines(parallel_through_point(X131,X130),X131),
inference(variable_rename,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
fof(c_0_27,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_28,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
fof(c_0_30,plain,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax2]) ).
cnf(c_0_31,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
convergent_lines(parallel_through_point(esk2_0,X1),esk1_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X168,X169] :
( ( ~ equal_lines(X168,X169)
| ~ distinct_lines(X168,X169) )
& ( distinct_lines(X168,X169)
| equal_lines(X168,X169) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).
fof(c_0_34,plain,
! [X101,X102,X103] :
( ~ distinct_lines(X101,X102)
| distinct_lines(X101,X103)
| distinct_lines(X102,X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
cnf(c_0_35,negated_conjecture,
( convergent_lines(parallel_through_point(esk2_0,X1),X2)
| distinct_lines(esk1_0,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_36,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
cnf(c_0_37,plain,
( ~ equal_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
equal_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_39,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
distinct_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
fof(c_0_41,plain,
! [X166,X167] :
( ( ~ equal_points(X166,X167)
| ~ distinct_points(X166,X167) )
& ( distinct_points(X166,X167)
| equal_points(X166,X167) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
fof(c_0_42,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_43,negated_conjecture,
~ distinct_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( distinct_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,negated_conjecture,
( ~ convergent_lines(esk1_0,esk3_0)
| ~ equal_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_46,plain,
( distinct_points(X1,X2)
| equal_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( convergent_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
fof(c_0_48,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_49,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_42]) ).
cnf(c_0_50,negated_conjecture,
distinct_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_43,c_0_47]) ).
fof(c_0_53,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_54,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_48])]) ).
cnf(c_0_55,negated_conjecture,
( apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X2,esk1_0)
| apart_point_and_line(X2,esk3_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
fof(c_0_57,plain,
! [X111,X112] :
( ~ convergent_lines(X111,X112)
| ~ apart_point_and_line(intersection_point(X111,X112),X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])]) ).
cnf(c_0_58,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_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),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_60,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_61,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_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_58,c_0_59]),c_0_52])]) ).
cnf(c_0_63,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_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_61,c_0_62]),c_0_52])]) ).
cnf(c_0_65,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
fof(c_0_66,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_67,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| distinct_lines(esk3_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_65]),c_0_18])]) ).
fof(c_0_68,plain,
! [X96] : ~ distinct_lines(X96,X96),
inference(variable_rename,[status(thm)],[c_0_66]) ).
cnf(c_0_69,negated_conjecture,
distinct_lines(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_67]),c_0_18])]) ).
cnf(c_0_70,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_71,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_69]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO205+3 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.15/0.32 % Computer : n031.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 17:49:53 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 6.24/4.57 % Version : CSE_E---1.7
% 6.24/4.57 % Problem : theBenchmark.p
% 6.24/4.57 % SZS status Theorem for theBenchmark.p
% 6.24/4.57 % SZS output start CNFRefutation
% See solution above
% 6.24/4.59 % Total time : 3.370s
%------------------------------------------------------------------------------