%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO215+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 : n004.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 04:19:57 PM UTC 2026
% Result : Theorem 1.34s 1.75s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 20 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 143 ( 45 ~; 80 |; 8 &)
% ( 0 <=>; 10 =>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 3 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X6,X7,X8] :
( convergent_lines(X6,X7)
=> ( unorthogonal_lines(X6,X8)
| unorthogonal_lines(X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
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(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(ouo1,axiom,
! [X9,X6,X7,X8] :
( distinct_lines(X6,X7)
=> ( apart_point_and_line(X9,X6)
| apart_point_and_line(X9,X7)
| unorthogonal_lines(X6,X8)
| unorthogonal_lines(X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ouo1) ).
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(oac1,axiom,
! [X6,X7,X8] :
( ( convergent_lines(X6,X7)
& unorthogonal_lines(X6,X7) )
=> ( ( convergent_lines(X6,X8)
& unorthogonal_lines(X6,X8) )
| ( convergent_lines(X7,X8)
& unorthogonal_lines(X7,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(c_0_10,negated_conjecture,
~ ! [X6,X7,X8] :
( convergent_lines(X6,X7)
=> ( unorthogonal_lines(X6,X8)
| unorthogonal_lines(X7,X8) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_11,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ unorthogonal_lines(esk1_0,esk3_0)
& ~ unorthogonal_lines(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_12,plain,
! [X106,X107] :
( convergent_lines(X106,X107)
| unorthogonal_lines(X106,X107) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(c_0_13,plain,
! [X75,X76,X77] :
( ~ convergent_lines(X75,X76)
| convergent_lines(X75,X77)
| convergent_lines(X76,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
cnf(c_0_14,negated_conjecture,
~ unorthogonal_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_17,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
convergent_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_19,plain,
! [X68] : ~ convergent_lines(X68,X68),
inference(variable_rename,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk3_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
fof(c_0_23,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
cnf(c_0_24,negated_conjecture,
( convergent_lines(X1,esk3_0)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_25,plain,
! [X99,X100] : ~ convergent_lines(parallel_through_point(X100,X99),X100),
inference(variable_rename,[status(thm)],[c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( convergent_lines(X1,esk3_0)
| convergent_lines(esk2_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
fof(c_0_27,plain,
! [X96,X97,X98] :
( ~ convergent_lines(X96,X97)
| distinct_lines(X97,X98)
| convergent_lines(X96,X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_28,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_30,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
convergent_lines(parallel_through_point(esk3_0,X1),esk2_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_33,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(c_0_34,plain,
! [X115,X116,X117,X118] :
( ~ distinct_lines(X116,X117)
| apart_point_and_line(X115,X116)
| apart_point_and_line(X115,X117)
| unorthogonal_lines(X116,X118)
| unorthogonal_lines(X117,X118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
cnf(c_0_35,negated_conjecture,
( convergent_lines(parallel_through_point(esk3_0,X1),X2)
| distinct_lines(esk2_0,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
fof(c_0_37,plain,
! [X82,X83] :
( ~ convergent_lines(X82,X83)
| ~ apart_point_and_line(intersection_point(X82,X83),X82) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])]) ).
cnf(c_0_38,plain,
( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| unorthogonal_lines(X1,X4)
| unorthogonal_lines(X2,X4)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
distinct_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_36]) ).
fof(c_0_41,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
cnf(c_0_42,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| unorthogonal_lines(esk3_0,X1)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X2,esk3_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk3_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_40]) ).
fof(c_0_45,plain,
! [X84,X85] :
( ~ convergent_lines(X84,X85)
| ~ apart_point_and_line(intersection_point(X84,X85),X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])]) ).
cnf(c_0_46,negated_conjecture,
( unorthogonal_lines(esk3_0,X1)
| unorthogonal_lines(esk2_0,X1)
| apart_point_and_line(intersection_point(esk3_0,X2),esk2_0)
| ~ convergent_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
convergent_lines(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_21,c_0_29]) ).
cnf(c_0_48,negated_conjecture,
( convergent_lines(X1,esk3_0)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
fof(c_0_49,plain,
! [X108,X109,X110] :
( ( convergent_lines(X109,X110)
| convergent_lines(X108,X110)
| ~ convergent_lines(X108,X109)
| ~ unorthogonal_lines(X108,X109) )
& ( unorthogonal_lines(X109,X110)
| convergent_lines(X108,X110)
| ~ convergent_lines(X108,X109)
| ~ unorthogonal_lines(X108,X109) )
& ( convergent_lines(X109,X110)
| unorthogonal_lines(X108,X110)
| ~ convergent_lines(X108,X109)
| ~ unorthogonal_lines(X108,X109) )
& ( unorthogonal_lines(X109,X110)
| unorthogonal_lines(X108,X110)
| ~ convergent_lines(X108,X109)
| ~ unorthogonal_lines(X108,X109) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
cnf(c_0_50,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| unorthogonal_lines(esk3_0,X1)
| apart_point_and_line(intersection_point(esk3_0,esk2_0),esk2_0) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
( convergent_lines(X1,esk3_0)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_48]) ).
cnf(c_0_53,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_54,negated_conjecture,
( unorthogonal_lines(esk3_0,X1)
| unorthogonal_lines(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_47])]) ).
cnf(c_0_55,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( unorthogonal_lines(esk2_0,X1)
| unorthogonal_lines(X1,X2)
| convergent_lines(esk3_0,X2)
| ~ convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,negated_conjecture,
convergent_lines(esk3_0,esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_55]) ).
cnf(c_0_58,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_59,negated_conjecture,
( unorthogonal_lines(esk2_0,esk1_0)
| unorthogonal_lines(esk1_0,X1)
| convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_58]) ).
cnf(c_0_61,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_62,negated_conjecture,
unorthogonal_lines(esk2_0,esk1_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_59]),c_0_21]) ).
cnf(c_0_63,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
( unorthogonal_lines(esk1_0,X1)
| unorthogonal_lines(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63])]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_64]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO215+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
% 0.16/0.33 % Computer : n004.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 17:49:02 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.34/1.75 % Version : CSE_E---1.7
% 1.34/1.75 % Problem : theBenchmark.p
% 1.34/1.75 % SZS status Theorem for theBenchmark.p
% 1.34/1.75 % SZS output start CNFRefutation
% See solution above
% 1.34/1.75 % Total time : 1.374s
%------------------------------------------------------------------------------