%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO226+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 : n017.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 04:20:01 PM UTC 2026
% Result : Theorem 0.29s 1.63s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_28)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X8,X9] :
( ( line(X8)
& line(X9)
& convergent_lines(X8,X9) )
=> ? [X1] :
( point(X1)
=> ( ~ apart_point_and_line(X1,X8)
& ~ apart_point_and_line(X1,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(con1,axiom,
! [X6,X7] :
( ( point(X6)
& point(X7)
& distinct_points(X6,X7) )
=> line(line_connecting(X6,X7)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',con1) ).
fof(orth1,axiom,
! [X8,X6] :
( ( line(X8)
& point(X6) )
=> line(orthogonal_through_point(X8,X6)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',orth1) ).
fof(par1,axiom,
! [X8,X6] :
( ( line(X8)
& point(X6) )
=> line(parallel_through_point(X8,X6)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+5.ax',par1) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
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(con1_001,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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).
fof(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(i_0_16,negated_conjecture,
~ ! [X8,X9] :
( ( line(X8)
& line(X9)
& convergent_lines(X8,X9) )
=> ? [X1] :
( point(X1)
=> ( ~ apart_point_and_line(X1,X8)
& ~ apart_point_and_line(X1,X9) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_17,plain,
! [X81,X82] :
( ~ point(X81)
| ~ point(X82)
| ~ distinct_points(X81,X82)
| line(line_connecting(X81,X82)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])]) ).
fof(i_0_18,negated_conjecture,
! [X91] :
( line(esk1_0)
& line(esk2_0)
& convergent_lines(esk1_0,esk2_0)
& point(X91)
& ( apart_point_and_line(X91,esk1_0)
| apart_point_and_line(X91,esk2_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_16])])])]) ).
fof(i_0_19,plain,
! [X87,X88] :
( ~ line(X87)
| ~ point(X88)
| line(orthogonal_through_point(X87,X88)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[orth1])]) ).
fof(i_0_20,plain,
! [X85,X86] :
( ~ line(X85)
| ~ point(X86)
| line(parallel_through_point(X85,X86)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[par1])]) ).
fof(i_0_21,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_22,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_23,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_24,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_25,plain,
! [X63,X64,X65] :
( ( distinct_points(X65,X63)
| ~ apart_point_and_line(X65,line_connecting(X63,X64))
| ~ distinct_points(X63,X64) )
& ( distinct_points(X65,X64)
| ~ apart_point_and_line(X65,line_connecting(X63,X64))
| ~ distinct_points(X63,X64) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
fof(i_0_26,plain,
! [X66,X67,X68] :
( ( ~ apart_point_and_line(X68,X66)
| distinct_points(X68,intersection_point(X66,X67))
| ~ convergent_lines(X66,X67) )
& ( ~ apart_point_and_line(X68,X67)
| distinct_points(X68,intersection_point(X66,X67))
| ~ convergent_lines(X66,X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
cnf(i_0_27,plain,
( line(line_connecting(X1,X2))
| ~ point(X1)
| ~ point(X2)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_17]) ).
cnf(i_0_28,negated_conjecture,
point(X1),
inference(split_conjunct,[status(thm)],[i_0_18]) ).
fof(i_0_29,plain,
! [X60,X61,X62] :
( ~ convergent_lines(X60,X61)
| convergent_lines(X60,X62)
| convergent_lines(X61,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
fof(i_0_30,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_31,plain,
! [X57,X58,X59] :
( ~ distinct_lines(X57,X58)
| distinct_lines(X57,X59)
| distinct_lines(X58,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_32,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_33,plain,
! [X54,X55,X56] :
( ~ distinct_points(X54,X55)
| distinct_points(X54,X56)
| distinct_points(X55,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
cnf(i_0_34,plain,
( line(orthogonal_through_point(X1,X2))
| ~ line(X1)
| ~ point(X2) ),
inference(split_conjunct,[status(thm)],[i_0_19]) ).
cnf(i_0_35,plain,
( line(parallel_through_point(X1,X2))
| ~ line(X1)
| ~ point(X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]) ).
fof(i_0_36,plain,
! [X79,X80] :
( ~ convergent_lines(X79,X80)
| distinct_lines(X79,X80) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_37,plain,
! [X53] : ~ convergent_lines(X53,X53),
inference(variable_rename,[status(thm)],[i_0_21]) ).
fof(i_0_38,plain,
! [X52] : ~ distinct_lines(X52,X52),
inference(variable_rename,[status(thm)],[i_0_22]) ).
fof(i_0_39,plain,
! [X51] : ~ distinct_points(X51,X51),
inference(variable_rename,[status(thm)],[i_0_23]) ).
cnf(i_0_40,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_24]),
[final] ).
cnf(i_0_41,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_25]),
[final] ).
cnf(i_0_42,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_25]),
[final] ).
cnf(i_0_43,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_26]),
[final] ).
cnf(i_0_44,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_26]),
[final] ).
cnf(i_0_45,negated_conjecture,
( line(line_connecting(X1,X2))
| ~ distinct_points(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_27,c_0_28]),c_0_28])]),
[final] ).
cnf(i_0_46,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_47,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_48,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_49,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_50,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_51,negated_conjecture,
( line(orthogonal_through_point(X1,X2))
| ~ line(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[i_0_34,c_0_28])]),
[final] ).
cnf(i_0_52,negated_conjecture,
( line(parallel_through_point(X1,X2))
| ~ line(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[i_0_35,c_0_28])]),
[final] ).
cnf(i_0_53,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_54,negated_conjecture,
( apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_55,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_56,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_57,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_58,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_59,negated_conjecture,
line(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_60,negated_conjecture,
line(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_18]),
[final] ).
cnf(i_0_61,plain,
distinct_lines(esk1_0,esk2_0),
inference(scs_inference,[],[i_0_58,i_0_53]) ).
cnf(i_0_62,plain,
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_63,plain,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0),
inference(scs_inference,[],[i_0_58,i_0_57,i_0_53,i_0_43]) ).
cnf(i_0_64,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_65,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_43]) ).
cnf(i_0_66,plain,
~ apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0),
inference(scs_inference,[],[i_0_58,i_0_57,i_0_64,i_0_53,i_0_43,i_0_44]) ).
cnf(i_0_67,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_68,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_69,plain,
convergent_lines(esk2_0,esk1_0),
inference(scs_inference,[],[i_0_58,i_0_55,i_0_57,i_0_64,i_0_53,i_0_43,i_0_44,i_0_46]) ).
cnf(i_0_70,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_55]) ).
cnf(i_0_71,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_46]) ).
cnf(i_0_72,plain,
distinct_lines(esk2_0,esk1_0),
inference(scs_inference,[],[i_0_58,i_0_55,i_0_56,i_0_57,i_0_64,i_0_53,i_0_43,i_0_44,i_0_46,i_0_48]) ).
cnf(i_0_73,plain,
~ distinct_lines(X1,X1),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_74,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_75,plain,
$false,
inference(scs_inference,[],[i_0_58,i_0_55,i_0_56,i_0_57,i_0_64,i_0_53,i_0_43,i_0_44,i_0_46,i_0_48,i_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO226+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
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 17:47:57 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.29/1.63 % Version : CSE_E---1.7
% 0.29/1.63 % Problem : theBenchmark.p
% 0.29/1.63 % SZS status Theorem for theBenchmark.p
% 0.29/1.63 % SZS output start CNFRefutation
% See solution above
% 0.29/1.67 % Total time : 1.275s
%------------------------------------------------------------------------------