%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO223+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n007.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 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 57 ( 24 unt; 0 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 119 ( 47 ~; 55 |; 9 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 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 : 108 ( 8 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X9,X6] : equal_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ax2,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(couo1,axiom,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
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(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(c_0_11,negated_conjecture,
~ ! [X9,X6] : equal_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_12,plain,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax2]) ).
fof(c_0_13,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(c_0_14,negated_conjecture,
~ equal_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_11])])]) ).
fof(c_0_15,plain,
! [X167,X168] :
( ( ~ equal_lines(X167,X168)
| ~ distinct_lines(X167,X168) )
& ( distinct_lines(X167,X168)
| equal_lines(X167,X168) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
fof(c_0_16,plain,
! [X141,X142] : ~ unorthogonal_lines(orthogonal_through_point(X142,X141),X142),
inference(variable_rename,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X136,X137] :
( convergent_lines(X136,X137)
| unorthogonal_lines(X136,X137) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(c_0_18,plain,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[couo1]) ).
fof(c_0_19,plain,
! [X127,X128] :
( ~ distinct_lines(X127,X128)
| convergent_lines(X127,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_20,negated_conjecture,
~ equal_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_14]) ).
cnf(c_0_21,plain,
( distinct_lines(X1,X2)
| equal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_23,plain,
! [X124,X125,X126] :
( ~ convergent_lines(X124,X125)
| distinct_lines(X125,X126)
| convergent_lines(X124,X126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_24,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_26,plain,
! [X154,X155,X156] :
( unorthogonal_lines(X154,X155)
| unorthogonal_lines(X154,X156)
| ~ convergent_lines(X155,X156) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).
cnf(c_0_27,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
distinct_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_20,c_0_21]) ).
fof(c_0_29,plain,
! [X96] : ~ convergent_lines(X96,X96),
inference(variable_rename,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
fof(c_0_32,plain,
! [X138,X139,X140] :
( ( convergent_lines(X139,X140)
| convergent_lines(X138,X140)
| ~ convergent_lines(X138,X139)
| ~ unorthogonal_lines(X138,X139) )
& ( unorthogonal_lines(X139,X140)
| convergent_lines(X138,X140)
| ~ convergent_lines(X138,X139)
| ~ unorthogonal_lines(X138,X139) )
& ( convergent_lines(X139,X140)
| unorthogonal_lines(X138,X140)
| ~ convergent_lines(X138,X139)
| ~ unorthogonal_lines(X138,X139) )
& ( unorthogonal_lines(X139,X140)
| unorthogonal_lines(X138,X140)
| ~ convergent_lines(X138,X139)
| ~ unorthogonal_lines(X138,X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
cnf(c_0_33,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,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_27,c_0_28]) ).
cnf(c_0_35,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| distinct_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( unorthogonal_lines(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| unorthogonal_lines(X1,parallel_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
distinct_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| unorthogonal_lines(X2,parallel_through_point(esk2_0,esk1_0))
| convergent_lines(X2,X1)
| ~ convergent_lines(X2,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_41,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),parallel_through_point(esk2_0,esk1_0))
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| convergent_lines(orthogonal_through_point(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,negated_conjecture,
unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),parallel_through_point(esk2_0,esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_42]),c_0_35]) ).
cnf(c_0_45,plain,
( convergent_lines(X1,X2)
| distinct_lines(orthogonal_through_point(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_41]) ).
fof(c_0_46,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
cnf(c_0_47,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| ~ convergent_lines(orthogonal_through_point(esk2_0,esk1_0),parallel_through_point(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_45]) ).
fof(c_0_49,plain,
! [X129,X130] : ~ convergent_lines(parallel_through_point(X130,X129),X130),
inference(variable_rename,[status(thm)],[c_0_46]) ).
fof(c_0_50,plain,
! [X103,X104,X105] :
( ~ convergent_lines(X103,X104)
| convergent_lines(X103,X105)
| convergent_lines(X104,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
cnf(c_0_51,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_47,c_0_48]) ).
cnf(c_0_52,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_54,negated_conjecture,
convergent_lines(esk2_0,parallel_through_point(esk2_0,esk1_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_51]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( convergent_lines(parallel_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_55]),c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO223+3 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.16/0.33 % Computer : n007.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 17:47:39 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------