%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO205+2 : 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 : n011.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 04:19:53 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 17 unt; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 131 ( 46 ~; 67 |; 8 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 95 ( 0 sgn 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart5) ).
fof(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& ~ distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(apart6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
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/GEO008+0.ax',cu1) ).
fof(con2,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( ( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2) )
=> distinct_points(X3,intersection_point(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
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/sandbox/benchmark/Axioms/GEO008+0.ax',ceq1) ).
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/GEO008+0.ax',ceq2) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(c_0_10,plain,
! [X45,X46,X47] :
( ~ distinct_lines(X45,X46)
| distinct_lines(X45,X47)
| distinct_lines(X46,X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(c_0_11,plain,
! [X67,X68] :
( ~ convergent_lines(X67,X68)
| distinct_lines(X67,X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& ~ distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
cnf(c_0_13,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ distinct_lines(esk2_0,esk3_0)
& ( ~ convergent_lines(esk1_0,esk3_0)
| distinct_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_12])])]) ).
fof(c_0_16,plain,
! [X48,X49,X50] :
( ~ convergent_lines(X48,X49)
| convergent_lines(X48,X50)
| convergent_lines(X49,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
cnf(c_0_17,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
~ distinct_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_22,plain,
! [X57,X58,X59,X60] :
( ~ distinct_points(X57,X58)
| ~ distinct_lines(X59,X60)
| apart_point_and_line(X57,X59)
| apart_point_and_line(X57,X60)
| apart_point_and_line(X58,X59)
| apart_point_and_line(X58,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_23,negated_conjecture,
( distinct_lines(esk2_0,X1)
| distinct_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ convergent_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_25,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
fof(c_0_26,plain,
! [X39] : ~ distinct_points(X39,X39),
inference(variable_rename,[status(thm)],[c_0_21]) ).
fof(c_0_27,plain,
! [X54,X55,X56] :
( ( ~ apart_point_and_line(X56,X54)
| distinct_points(X56,intersection_point(X54,X55))
| ~ convergent_lines(X54,X55) )
& ( ~ apart_point_and_line(X56,X55)
| distinct_points(X56,intersection_point(X54,X55))
| ~ convergent_lines(X54,X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
cnf(c_0_28,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_22]) ).
cnf(c_0_29,negated_conjecture,
distinct_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( distinct_points(X1,intersection_point(X3,X2))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,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_28,c_0_29]) ).
cnf(c_0_35,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_30,c_0_31])]) ).
cnf(c_0_36,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,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_34,c_0_35]) ).
fof(c_0_39,plain,
! [X61,X62,X63] :
( ~ apart_point_and_line(X61,X62)
| distinct_points(X61,X63)
| apart_point_and_line(X63,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
cnf(c_0_40,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_36]) ).
cnf(c_0_41,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_37,c_0_38]),c_0_31])]) ).
cnf(c_0_42,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_43,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_40,c_0_41]),c_0_31])]) ).
cnf(c_0_44,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(X1,esk3_0)
| distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_45,plain,
! [X64,X65,X66] :
( ~ apart_point_and_line(X64,X65)
| distinct_lines(X65,X66)
| apart_point_and_line(X64,X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
cnf(c_0_46,negated_conjecture,
( apart_point_and_line(X1,esk3_0)
| distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_44]),c_0_18])]) ).
cnf(c_0_47,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_48,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0),
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
fof(c_0_49,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_50,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_51,plain,
! [X40] : ~ distinct_lines(X40,X40),
inference(variable_rename,[status(thm)],[c_0_49]) ).
cnf(c_0_52,negated_conjecture,
distinct_lines(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_50]),c_0_18])]) ).
cnf(c_0_53,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO205+2 : 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
% 0.16/0.33 % Computer : n011.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:47:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------