%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO196+2 : TPTP v9.2.1. Released v3.3.0.
% 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 : n001.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 04:19:50 PM UTC 2026
% Result : Theorem 1.34s 1.61s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 86 ( 39 unt; 0 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 215 ( 95 ~; 91 |; 16 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 157 ( 0 sgn 71 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X4,X5)
& ~ apart_point_and_line(intersection_point(X1,X2),X4)
& ~ apart_point_and_line(intersection_point(X1,X2),X5) )
=> ( ~ apart_point_and_line(intersection_point(X4,X5),X1)
& ~ apart_point_and_line(intersection_point(X4,X5),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO008+0.ax',cu1) ).
fof(con1,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',con1) ).
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/sandbox2/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(apart6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart6) ).
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/GEO008+0.ax',ceq2) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart5) ).
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/GEO008+0.ax',ceq1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(i_0_13,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( convergent_lines(X1,X2)
& convergent_lines(X4,X5)
& ~ apart_point_and_line(intersection_point(X1,X2),X4)
& ~ apart_point_and_line(intersection_point(X1,X2),X5) )
=> ( ~ apart_point_and_line(intersection_point(X4,X5),X1)
& ~ apart_point_and_line(intersection_point(X4,X5),X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_14,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_15,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_16,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_17,plain,
! [X58,X59,X60,X61] :
( ~ distinct_points(X58,X59)
| ~ distinct_lines(X60,X61)
| apart_point_and_line(X58,X60)
| apart_point_and_line(X58,X61)
| apart_point_and_line(X59,X60)
| apart_point_and_line(X59,X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_18,plain,
! [X52,X53,X54] :
( ( distinct_points(X54,X52)
| ~ apart_point_and_line(X54,line_connecting(X52,X53))
| ~ distinct_points(X52,X53) )
& ( distinct_points(X54,X53)
| ~ apart_point_and_line(X54,line_connecting(X52,X53))
| ~ distinct_points(X52,X53) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
fof(i_0_19,plain,
! [X55,X56,X57] :
( ( ~ apart_point_and_line(X57,X55)
| distinct_points(X57,intersection_point(X55,X56))
| ~ convergent_lines(X55,X56) )
& ( ~ apart_point_and_line(X57,X56)
| distinct_points(X57,intersection_point(X55,X56))
| ~ convergent_lines(X55,X56) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
fof(i_0_20,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& convergent_lines(esk3_0,esk4_0)
& ~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
& ~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0)
& ( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
| apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_13])])]) ).
fof(i_0_21,plain,
! [X49,X50,X51] :
( ~ convergent_lines(X49,X50)
| convergent_lines(X49,X51)
| convergent_lines(X50,X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
fof(i_0_22,plain,
! [X65,X66,X67] :
( ~ apart_point_and_line(X65,X66)
| distinct_lines(X66,X67)
| apart_point_and_line(X65,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_23,plain,
! [X46,X47,X48] :
( ~ distinct_lines(X46,X47)
| distinct_lines(X46,X48)
| distinct_lines(X47,X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_24,plain,
! [X62,X63,X64] :
( ~ apart_point_and_line(X62,X63)
| distinct_points(X62,X64)
| apart_point_and_line(X64,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_25,plain,
! [X43,X44,X45] :
( ~ distinct_points(X43,X44)
| distinct_points(X43,X45)
| distinct_points(X44,X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_26,plain,
! [X68,X69] :
( ~ convergent_lines(X68,X69)
| distinct_lines(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_27,plain,
! [X42] : ~ convergent_lines(X42,X42),
inference(variable_rename,[status(thm)],[i_0_14]) ).
fof(i_0_28,plain,
! [X41] : ~ distinct_lines(X41,X41),
inference(variable_rename,[status(thm)],[i_0_15]) ).
fof(i_0_29,plain,
! [X40] : ~ distinct_points(X40,X40),
inference(variable_rename,[status(thm)],[i_0_16]) ).
cnf(i_0_30,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)],[i_0_17]),
[final] ).
cnf(i_0_31,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_32,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X3,X2))
| ~ distinct_points(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_33,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_34,plain,
( distinct_points(X1,intersection_point(X3,X2))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]),
[final] ).
cnf(i_0_35,negated_conjecture,
( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0)
| apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_36,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_37,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_38,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_39,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_40,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_41,negated_conjecture,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk4_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_42,negated_conjecture,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_43,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_44,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_45,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_46,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_47,negated_conjecture,
convergent_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_48,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_49,plain,
distinct_lines(esk3_0,esk4_0),
inference(scs_inference,[],[i_0_47,i_0_43]) ).
cnf(i_0_50,plain,
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_51,plain,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0),
inference(scs_inference,[],[i_0_47,i_0_46,i_0_43,i_0_33]) ).
cnf(i_0_52,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_53,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_54,plain,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk4_0),
inference(scs_inference,[],[i_0_47,i_0_46,i_0_52,i_0_43,i_0_33,i_0_34]) ).
cnf(i_0_55,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_56,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_57,plain,
convergent_lines(esk4_0,esk3_0),
inference(scs_inference,[],[i_0_47,i_0_44,i_0_46,i_0_52,i_0_43,i_0_33,i_0_34,i_0_36]) ).
cnf(i_0_58,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_59,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_60,plain,
distinct_lines(esk4_0,esk3_0),
inference(scs_inference,[],[i_0_47,i_0_44,i_0_45,i_0_46,i_0_52,i_0_43,i_0_33,i_0_34,i_0_36,i_0_38]) ).
cnf(i_0_61,plain,
~ distinct_lines(X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_62,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_63,plain,
~ distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk3_0,esk4_0)),
inference(scs_inference,[],[i_0_41,i_0_47,i_0_42,i_0_44,i_0_45,i_0_46,i_0_52,i_0_43,i_0_33,i_0_34,i_0_36,i_0_38,i_0_30]) ).
cnf(i_0_64,plain,
( apart_point_and_line(X1,X2)
| ~ distinct_points(X3,X1)
| ~ distinct_lines(X4,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_65,plain,
distinct_lines(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_48,i_0_43]) ).
cnf(i_0_66,plain,
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_67,plain,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0),
inference(scs_inference,[],[i_0_48,i_0_46,i_0_43,i_0_33]) ).
cnf(i_0_68,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_69,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_70,plain,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0),
inference(scs_inference,[],[i_0_48,i_0_46,i_0_68,i_0_43,i_0_33,i_0_34]) ).
cnf(i_0_71,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_72,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_73,plain,
convergent_lines(esk2_0,esk1_0),
inference(scs_inference,[],[i_0_48,i_0_44,i_0_46,i_0_68,i_0_43,i_0_33,i_0_34,i_0_36]) ).
cnf(i_0_74,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_75,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_36]) ).
cnf(i_0_76,plain,
distinct_lines(esk2_0,esk1_0),
inference(scs_inference,[],[i_0_48,i_0_44,i_0_45,i_0_46,i_0_68,i_0_43,i_0_33,i_0_34,i_0_36,i_0_38]) ).
cnf(i_0_77,plain,
~ distinct_lines(X1,X1),
inference(rename_variables,[],[i_0_45]) ).
cnf(i_0_78,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(rename_variables,[],[i_0_38]) ).
cnf(i_0_79,plain,
~ distinct_points(intersection_point(esk3_0,esk4_0),intersection_point(esk1_0,esk2_0)),
inference(scs_inference,[],[i_0_51,i_0_42,i_0_41,i_0_54,i_0_49,i_0_30]) ).
cnf(i_0_80,plain,
( apart_point_and_line(X1,X2)
| ~ distinct_points(X3,X1)
| ~ distinct_lines(X4,X2)
| apart_point_and_line(X3,X4)
| apart_point_and_line(X3,X2)
| apart_point_and_line(X1,X4) ),
inference(rename_variables,[],[i_0_30]) ).
cnf(i_0_81,plain,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk1_0),
inference(scs_inference,[],[i_0_51,i_0_42,i_0_41,i_0_48,i_0_54,i_0_49,i_0_30,i_0_33]) ).
cnf(i_0_82,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_33]) ).
cnf(i_0_83,plain,
~ apart_point_and_line(intersection_point(esk3_0,esk4_0),esk2_0),
inference(scs_inference,[],[i_0_51,i_0_42,i_0_41,i_0_48,i_0_54,i_0_49,i_0_30,i_0_33,i_0_34]) ).
cnf(i_0_84,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_34]) ).
cnf(i_0_85,plain,
$false,
inference(scs_inference,[],[i_0_51,i_0_42,i_0_41,i_0_48,i_0_54,i_0_49,i_0_30,i_0_33,i_0_34,i_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO196+2 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.16/0.33 % Computer : n001.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 17:47:48 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.61 % Version : CSE_E---1.7
% 1.34/1.61 % Problem : theBenchmark.p
% 1.34/1.61 % SZS status Theorem for theBenchmark.p
% 1.34/1.61 % SZS output start CNFRefutation
% See solution above
% 1.43/1.70 % Total time : 1.269s
%------------------------------------------------------------------------------