%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO171+1 : 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 : n027.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 04:19:39 PM UTC 2026
% Result : Theorem 0.22s 1.60s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 17 unt; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 129 ( 57 ~; 53 |; 2 &)
% ( 0 <=>; 17 =>; 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; 2 con; 0-2 aty)
% Number of variables : 118 ( 0 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(con,conjecture,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
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(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(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(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(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+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/GEO006+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/GEO006+0.ax',apart4) ).
fof(i_0_15,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(i_0_16,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(i_0_17,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
fof(i_0_18,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
fof(i_0_19,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_20,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_21,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_22,negated_conjecture,
~ ! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(i_0_23,plain,
! [X61,X62,X63,X64] :
( ~ distinct_points(X61,X62)
| ~ distinct_lines(X63,X64)
| apart_point_and_line(X61,X63)
| apart_point_and_line(X61,X64)
| apart_point_and_line(X62,X63)
| apart_point_and_line(X62,X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_24,plain,
! [X57,X58] :
( ~ convergent_lines(X57,X58)
| ~ apart_point_and_line(intersection_point(X57,X58),X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_15])]) ).
fof(i_0_25,plain,
! [X59,X60] :
( ~ convergent_lines(X59,X60)
| ~ apart_point_and_line(intersection_point(X59,X60),X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])]) ).
fof(i_0_26,plain,
! [X53,X54] :
( ~ distinct_points(X53,X54)
| ~ apart_point_and_line(X53,line_connecting(X53,X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_17])]) ).
fof(i_0_27,plain,
! [X55,X56] :
( ~ distinct_points(X55,X56)
| ~ apart_point_and_line(X56,line_connecting(X55,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])]) ).
fof(i_0_28,plain,
! [X50,X51,X52] :
( ~ convergent_lines(X50,X51)
| convergent_lines(X50,X52)
| convergent_lines(X51,X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(i_0_29,plain,
! [X68,X69,X70] :
( ~ apart_point_and_line(X68,X69)
| distinct_lines(X69,X70)
| apart_point_and_line(X68,X70) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_30,plain,
! [X71,X72,X73] :
( ~ convergent_lines(X71,X72)
| distinct_lines(X72,X73)
| convergent_lines(X71,X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_31,plain,
! [X47,X48,X49] :
( ~ distinct_lines(X47,X48)
| distinct_lines(X47,X49)
| distinct_lines(X48,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_32,plain,
! [X65,X66,X67] :
( ~ apart_point_and_line(X65,X66)
| distinct_points(X65,X67)
| apart_point_and_line(X67,X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_33,plain,
! [X44,X45,X46] :
( ~ distinct_points(X44,X45)
| distinct_points(X44,X46)
| distinct_points(X45,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_34,plain,
! [X43] : ~ convergent_lines(X43,X43),
inference(variable_rename,[status(thm)],[i_0_19]) ).
fof(i_0_35,plain,
! [X42] : ~ distinct_lines(X42,X42),
inference(variable_rename,[status(thm)],[i_0_20]) ).
fof(i_0_36,plain,
! [X41] : ~ distinct_points(X41,X41),
inference(variable_rename,[status(thm)],[i_0_21]) ).
fof(i_0_37,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ distinct_lines(esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_22])])]) ).
cnf(i_0_38,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_23]),
[final] ).
cnf(i_0_39,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_40,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_41,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_42,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_43,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_44,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_45,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_46,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_47,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_48,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_49,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_50,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_51,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_52,negated_conjecture,
~ distinct_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_53,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_54,plain,
convergent_lines(esk2_0,esk1_0),
inference(scs_inference,[],[i_0_53,i_0_49,i_0_43]) ).
cnf(i_0_55,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_49]) ).
cnf(i_0_56,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_57,plain,
$false,
inference(scs_inference,[],[i_0_52,i_0_53,i_0_49,i_0_55,i_0_43,i_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO171+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n027.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 17:45:04 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 0.22/1.60 % Version : CSE_E---1.7
% 0.22/1.60 % Problem : theBenchmark.p
% 0.22/1.60 % SZS status Theorem for theBenchmark.p
% 0.22/1.60 % SZS output start CNFRefutation
% See solution above
% 0.22/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------