%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO255+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 : n008.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 04:20:09 PM UTC 2026
% Result : Theorem 1.88s 1.93s
% Output : CNFRefutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 15 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 112 ( 45 ~; 48 |; 13 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 99 ( 3 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a4_defns,axiom,
! [X1,X2] :
( equally_directed_lines(X1,X2)
<=> ~ unequally_directed_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',a4_defns) ).
fof(ax5_basics,axiom,
! [X4] : equally_directed_lines(X4,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax5_basics) ).
fof(ax8_basics,axiom,
! [X4,X5] :
( unequally_directed_lines(X4,X5)
| unequally_directed_lines(X4,reverse_line(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax8_basics) ).
fof(ax9_basics,axiom,
! [X4,X5] :
( ( unequally_directed_lines(X4,X5)
& unequally_directed_lines(X4,reverse_line(X5)) )
=> ( left_convergent_lines(X4,X5)
| left_convergent_lines(X4,reverse_line(X5)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax9_basics) ).
fof(ax11_basics,axiom,
! [X4,X5] :
~ ( left_convergent_lines(X4,X5)
| left_convergent_lines(X4,reverse_line(X5)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(ax6_basics,axiom,
! [X4,X5,X8] :
( unequally_directed_lines(X4,X5)
=> ( unequally_directed_lines(X4,X8)
| unequally_directed_lines(X5,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax6_basics) ).
fof(ax4_defns,axiom,
! [X4,X3,X6] :
( before_on_line(X4,X3,X6)
<=> ( distinct_points(X3,X6)
& incident_point_and_line(X3,X4)
& incident_point_and_line(X6,X4)
& equally_directed_lines(X4,line_connecting(X3,X6)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax4_defns) ).
fof(con,conjecture,
! [X4,X3,X6] :
~ ( before_on_line(X4,X3,X6)
& before_on_line(X4,X6,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ax9_cons_objs,axiom,
! [X3,X6] :
( distinct_points(X3,X6)
=> equally_directed_lines(line_connecting(X3,X6),reverse_line(line_connecting(X6,X3))) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO009+0.ax',ax9_cons_objs) ).
fof(c_0_9,plain,
! [X1,X2] :
( equally_directed_lines(X1,X2)
<=> ~ unequally_directed_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4_defns]) ).
fof(c_0_10,plain,
! [X99,X100] :
( ( ~ equally_directed_lines(X99,X100)
| ~ unequally_directed_lines(X99,X100) )
& ( unequally_directed_lines(X99,X100)
| equally_directed_lines(X99,X100) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).
fof(c_0_11,plain,
! [X125] : equally_directed_lines(X125,X125),
inference(variable_rename,[status(thm)],[ax5_basics]) ).
cnf(c_0_12,plain,
( ~ equally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
equally_directed_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X132,X133] :
( unequally_directed_lines(X132,X133)
| unequally_directed_lines(X132,reverse_line(X133)) ),
inference(variable_rename,[status(thm)],[ax8_basics]) ).
fof(c_0_15,plain,
! [X134,X135] :
( ~ unequally_directed_lines(X134,X135)
| ~ unequally_directed_lines(X134,reverse_line(X135))
| left_convergent_lines(X134,X135)
| left_convergent_lines(X134,reverse_line(X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9_basics])]) ).
fof(c_0_16,plain,
! [X138,X139] :
( ~ left_convergent_lines(X138,X139)
& ~ left_convergent_lines(X138,reverse_line(X139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11_basics])]) ).
fof(c_0_17,plain,
! [X126,X127,X128] :
( ~ unequally_directed_lines(X126,X127)
| unequally_directed_lines(X126,X128)
| unequally_directed_lines(X127,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6_basics])]) ).
cnf(c_0_18,plain,
~ unequally_directed_lines(X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( left_convergent_lines(X1,X2)
| left_convergent_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( unequally_directed_lines(X1,X3)
| unequally_directed_lines(X2,X3)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
unequally_directed_lines(reverse_line(X1),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_20,c_0_21]),c_0_21]) ).
cnf(c_0_25,plain,
( unequally_directed_lines(reverse_line(X1),X2)
| unequally_directed_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_26,plain,
! [X110,X111,X112] :
( ( distinct_points(X111,X112)
| ~ before_on_line(X110,X111,X112) )
& ( incident_point_and_line(X111,X110)
| ~ before_on_line(X110,X111,X112) )
& ( incident_point_and_line(X112,X110)
| ~ before_on_line(X110,X111,X112) )
& ( equally_directed_lines(X110,line_connecting(X111,X112))
| ~ before_on_line(X110,X111,X112) )
& ( ~ distinct_points(X111,X112)
| ~ incident_point_and_line(X111,X110)
| ~ incident_point_and_line(X112,X110)
| ~ equally_directed_lines(X110,line_connecting(X111,X112))
| before_on_line(X110,X111,X112) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4_defns])])]) ).
cnf(c_0_27,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(reverse_line(X1),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
unequally_directed_lines(X1,reverse_line(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_29,plain,
( equally_directed_lines(X1,line_connecting(X2,X3))
| ~ before_on_line(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,negated_conjecture,
~ ! [X4,X3,X6] :
~ ( before_on_line(X4,X3,X6)
& before_on_line(X4,X6,X3) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_0_31,plain,
( unequally_directed_lines(X1,reverse_line(reverse_line(X2)))
| unequally_directed_lines(reverse_line(X1),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_19]) ).
cnf(c_0_32,plain,
unequally_directed_lines(X1,reverse_line(reverse_line(reverse_line(X1)))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,plain,
! [X154,X155] :
( ~ distinct_points(X154,X155)
| equally_directed_lines(line_connecting(X154,X155),reverse_line(line_connecting(X155,X154))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9_cons_objs])]) ).
cnf(c_0_34,plain,
( ~ before_on_line(X1,X2,X3)
| ~ unequally_directed_lines(X1,line_connecting(X2,X3)) ),
inference(spm,[status(thm)],[c_0_12,c_0_29]) ).
cnf(c_0_35,plain,
( unequally_directed_lines(reverse_line(X1),X2)
| unequally_directed_lines(X1,X3)
| unequally_directed_lines(X3,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
fof(c_0_36,negated_conjecture,
( before_on_line(esk1_0,esk2_0,esk3_0)
& before_on_line(esk1_0,esk3_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
cnf(c_0_37,plain,
( unequally_directed_lines(reverse_line(X1),X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_31]) ).
cnf(c_0_38,plain,
~ unequally_directed_lines(X1,reverse_line(reverse_line(X1))),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_39,plain,
( unequally_directed_lines(reverse_line(X1),X2)
| unequally_directed_lines(X3,X1)
| unequally_directed_lines(X3,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_40,plain,
( equally_directed_lines(line_connecting(X1,X2),reverse_line(line_connecting(X2,X1)))
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( unequally_directed_lines(line_connecting(X1,X2),X3)
| unequally_directed_lines(reverse_line(X4),X3)
| ~ before_on_line(X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
before_on_line(esk1_0,esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
( distinct_points(X1,X2)
| ~ before_on_line(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_44,plain,
( ~ unequally_directed_lines(X1,reverse_line(reverse_line(X2)))
| ~ unequally_directed_lines(reverse_line(X1),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_37]) ).
cnf(c_0_45,plain,
( unequally_directed_lines(X1,reverse_line(reverse_line(reverse_line(X2))))
| unequally_directed_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( ~ distinct_points(X1,X2)
| ~ unequally_directed_lines(line_connecting(X1,X2),reverse_line(line_connecting(X2,X1))) ),
inference(spm,[status(thm)],[c_0_12,c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( unequally_directed_lines(line_connecting(esk3_0,esk2_0),X1)
| unequally_directed_lines(reverse_line(esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
distinct_points(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_43,c_0_42]) ).
cnf(c_0_49,plain,
( unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(reverse_line(X1),reverse_line(X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,negated_conjecture,
unequally_directed_lines(reverse_line(esk1_0),reverse_line(line_connecting(esk2_0,esk3_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_51,negated_conjecture,
unequally_directed_lines(esk1_0,line_connecting(esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,negated_conjecture,
before_on_line(esk1_0,esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_51]),c_0_52])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO255+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.13/0.32 % Computer : n008.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Mon May 4 17:50:44 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.88/1.93 % Version : CSE_E---1.7
% 1.88/1.93 % Problem : theBenchmark.p
% 1.88/1.93 % SZS status Theorem for theBenchmark.p
% 1.88/1.93 % SZS output start CNFRefutation
% See solution above
% 1.88/1.94 % Total time : 1.372s
%------------------------------------------------------------------------------