%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO208+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 04:19:54 PM UTC 2026
% Result : Theorem 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 18
% Syntax : Number of formulae : 71 ( 27 unt; 0 def)
% Number of atoms : 158 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 166 ( 79 ~; 61 |; 8 &)
% ( 0 <=>; 18 =>; 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 145 ( 2 sgn 101 !; 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(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
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(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,X3] :
( ( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X1,X3)
& ~ convergent_lines(X2,X3) )
=> ~ distinct_lines(X2,X3) ),
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(cup1,axiom,
! [X1,X2,X3] :
( distinct_lines(X2,X3)
=> ( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cup1) ).
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_18,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_19,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_20,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_21,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_22,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(i_0_23,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(i_0_24,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_25,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_26,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_27,negated_conjecture,
~ ! [X1,X2,X3] :
( ( ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X1,X3)
& ~ convergent_lines(X2,X3) )
=> ~ distinct_lines(X2,X3) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_28,plain,
! [X69,X70,X71,X72] :
( ~ distinct_points(X69,X70)
| ~ distinct_lines(X71,X72)
| apart_point_and_line(X69,X71)
| apart_point_and_line(X69,X72)
| apart_point_and_line(X70,X71)
| apart_point_and_line(X70,X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_29,plain,
! [X65,X66] :
( ~ convergent_lines(X65,X66)
| ~ apart_point_and_line(intersection_point(X65,X66),X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_18])]) ).
fof(i_0_30,plain,
! [X67,X68] :
( ~ convergent_lines(X67,X68)
| ~ apart_point_and_line(intersection_point(X67,X68),X68) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_19])]) ).
fof(i_0_31,plain,
! [X61,X62] :
( ~ distinct_points(X61,X62)
| ~ apart_point_and_line(X61,line_connecting(X61,X62)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_20])]) ).
fof(i_0_32,plain,
! [X63,X64] :
( ~ distinct_points(X63,X64)
| ~ apart_point_and_line(X64,line_connecting(X63,X64)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_21])]) ).
fof(i_0_33,plain,
! [X86,X87,X88] :
( ~ distinct_lines(X87,X88)
| apart_point_and_line(X86,X87)
| apart_point_and_line(X86,X88)
| convergent_lines(X87,X88) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
fof(i_0_34,plain,
! [X82,X83] : ~ convergent_lines(parallel_through_point(X83,X82),X83),
inference(variable_rename,[status(thm)],[i_0_22]) ).
fof(i_0_35,plain,
! [X84,X85] : ~ apart_point_and_line(X84,parallel_through_point(X85,X84)),
inference(variable_rename,[status(thm)],[i_0_23]) ).
fof(i_0_36,plain,
! [X58,X59,X60] :
( ~ convergent_lines(X58,X59)
| convergent_lines(X58,X60)
| convergent_lines(X59,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(i_0_37,plain,
! [X76,X77,X78] :
( ~ apart_point_and_line(X76,X77)
| distinct_lines(X77,X78)
| apart_point_and_line(X76,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_38,plain,
! [X79,X80,X81] :
( ~ convergent_lines(X79,X80)
| distinct_lines(X80,X81)
| convergent_lines(X79,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_39,plain,
! [X55,X56,X57] :
( ~ distinct_lines(X55,X56)
| distinct_lines(X55,X57)
| distinct_lines(X56,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_40,plain,
! [X73,X74,X75] :
( ~ apart_point_and_line(X73,X74)
| distinct_points(X73,X75)
| apart_point_and_line(X75,X74) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_41,plain,
! [X52,X53,X54] :
( ~ distinct_points(X52,X53)
| distinct_points(X52,X54)
| distinct_points(X53,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_42,plain,
! [X51] : ~ convergent_lines(X51,X51),
inference(variable_rename,[status(thm)],[i_0_24]) ).
fof(i_0_43,plain,
! [X50] : ~ distinct_lines(X50,X50),
inference(variable_rename,[status(thm)],[i_0_25]) ).
fof(i_0_44,plain,
! [X49] : ~ distinct_points(X49,X49),
inference(variable_rename,[status(thm)],[i_0_26]) ).
fof(i_0_45,negated_conjecture,
( ~ apart_point_and_line(esk1_0,esk2_0)
& ~ apart_point_and_line(esk1_0,esk3_0)
& ~ convergent_lines(esk2_0,esk3_0)
& distinct_lines(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_27])])]) ).
cnf(i_0_46,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_28]),
[final] ).
cnf(i_0_47,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_48,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_49,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_50,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_51,plain,
( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_52,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_53,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_54,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_55,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_56,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_57,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_58,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_59,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_60,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_61,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_62,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_63,negated_conjecture,
~ apart_point_and_line(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_64,negated_conjecture,
~ apart_point_and_line(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_65,negated_conjecture,
~ convergent_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_66,negated_conjecture,
distinct_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_67,plain,
distinct_lines(esk3_0,esk2_0),
inference(scs_inference,[],[i_0_66,i_0_61,i_0_57]) ).
cnf(i_0_68,plain,
~ distinct_lines(X1,X1),
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_69,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_70,plain,
$false,
inference(scs_inference,[],[i_0_63,i_0_64,i_0_65,i_0_66,i_0_61,i_0_57,i_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO208+1 : 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
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:48:05 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Theorem for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.27/1.64 % Total time : 1.272s
%------------------------------------------------------------------------------