%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO223+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 : n028.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 04:20:00 PM UTC 2026
% Result : Theorem 1.93s 1.90s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 67 ( 33 unt; 0 def)
% Number of atoms : 157 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 147 ( 57 ~; 77 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 128 ( 8 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X9,X6] : ~ distinct_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
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/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
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/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(ooc2,axiom,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).
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(cp2,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).
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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
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/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(c_0_13,negated_conjecture,
~ ! [X9,X6] : ~ distinct_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_14,plain,
! [X96,X97,X98] :
( ~ distinct_lines(X97,X98)
| apart_point_and_line(X96,X97)
| apart_point_and_line(X96,X98)
| convergent_lines(X97,X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
fof(c_0_15,negated_conjecture,
distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_16,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_17,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(c_0_18,plain,
! [X108,X109,X110,X111] :
( ~ distinct_lines(X109,X110)
| apart_point_and_line(X108,X109)
| apart_point_and_line(X108,X110)
| unorthogonal_lines(X109,X111)
| unorthogonal_lines(X110,X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
fof(c_0_19,plain,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
inference(fof_simplification,[status(thm)],[ooc2]) ).
fof(c_0_20,plain,
! [X71,X72,X73] :
( ~ convergent_lines(X71,X72)
| convergent_lines(X71,X73)
| convergent_lines(X72,X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
cnf(c_0_21,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)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(c_0_24,plain,
! [X62] : ~ distinct_points(X62,X62),
inference(variable_rename,[status(thm)],[c_0_16]) ).
fof(c_0_25,plain,
! [X77,X78,X79] :
( ( ~ apart_point_and_line(X79,X77)
| distinct_points(X79,intersection_point(X77,X78))
| ~ convergent_lines(X77,X78) )
& ( ~ apart_point_and_line(X79,X78)
| distinct_points(X79,intersection_point(X77,X78))
| ~ convergent_lines(X77,X78) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
fof(c_0_26,plain,
! [X104,X105] : ~ unorthogonal_lines(orthogonal_through_point(X105,X104),X105),
inference(variable_rename,[status(thm)],[c_0_17]) ).
cnf(c_0_27,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_18]) ).
fof(c_0_28,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_29,plain,
! [X106,X107] : ~ apart_point_and_line(X106,orthogonal_through_point(X107,X106)),
inference(variable_rename,[status(thm)],[c_0_19]) ).
cnf(c_0_30,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,negated_conjecture,
( apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
| convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_32,plain,
! [X94,X95] : ~ apart_point_and_line(X94,parallel_through_point(X95,X94)),
inference(variable_rename,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_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)],[c_0_25]) ).
cnf(c_0_35,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X1)
| apart_point_and_line(X2,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X2,parallel_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
fof(c_0_37,plain,
! [X64] : ~ convergent_lines(X64,X64),
inference(variable_rename,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,negated_conjecture,
( apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X2)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_41,plain,
! [X99,X100] :
( convergent_lines(X99,X100)
| unorthogonal_lines(X99,X100) ),
inference(variable_rename,[status(thm)],[occu1]) ).
cnf(c_0_42,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_43,negated_conjecture,
( unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,negated_conjecture,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_46,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_48,negated_conjecture,
( unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
| apart_point_and_line(intersection_point(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),parallel_through_point(esk2_0,esk1_0))
| ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
fof(c_0_51,plain,
! [X101,X102,X103] :
( ( convergent_lines(X102,X103)
| convergent_lines(X101,X103)
| ~ convergent_lines(X101,X102)
| ~ unorthogonal_lines(X101,X102) )
& ( unorthogonal_lines(X102,X103)
| convergent_lines(X101,X103)
| ~ convergent_lines(X101,X102)
| ~ unorthogonal_lines(X101,X102) )
& ( convergent_lines(X102,X103)
| unorthogonal_lines(X101,X103)
| ~ convergent_lines(X101,X102)
| ~ unorthogonal_lines(X101,X102) )
& ( unorthogonal_lines(X102,X103)
| unorthogonal_lines(X101,X103)
| ~ convergent_lines(X101,X102)
| ~ unorthogonal_lines(X101,X102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
cnf(c_0_52,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_47]) ).
cnf(c_0_53,negated_conjecture,
( unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
| apart_point_and_line(intersection_point(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),parallel_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_55,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_56,negated_conjecture,
unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_49])]) ).
cnf(c_0_57,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| convergent_lines(X1,X4)
| convergent_lines(X4,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_54]) ).
fof(c_0_58,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
cnf(c_0_59,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| ~ convergent_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
( convergent_lines(X1,orthogonal_through_point(X2,X3))
| convergent_lines(X2,X1) ),
inference(spm,[status(thm)],[c_0_44,c_0_57]) ).
fof(c_0_61,plain,
! [X92,X93] : ~ convergent_lines(parallel_through_point(X93,X92),X93),
inference(variable_rename,[status(thm)],[c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,parallel_through_point(esk2_0,esk1_0))
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_64,negated_conjecture,
convergent_lines(esk2_0,parallel_through_point(esk2_0,esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_62]),c_0_63]) ).
cnf(c_0_65,negated_conjecture,
( convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_64]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_65]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO223+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
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon May 4 17:48:46 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 1.93/1.90 % Version : CSE_E---1.7
% 1.93/1.90 % Problem : theBenchmark.p
% 1.93/1.90 % SZS status Theorem for theBenchmark.p
% 1.93/1.90 % SZS output start CNFRefutation
% See solution above
% 1.93/1.90 % Total time : 1.372s
%------------------------------------------------------------------------------