%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO266+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n012.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 04:20:12 PM UTC 2026
% Result : Theorem 1.12s 1.62s
% Output : CNFRefutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 86 ( 37 ~; 37 |; 5 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 54 ( 2 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X4,X5] :
( unequally_directed_opposite_lines(X4,X5)
<=> unequally_directed_opposite_lines(X5,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(a1_defns,axiom,
! [X1,X2] :
( unequally_directed_opposite_lines(X1,X2)
<=> unequally_directed_lines(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',a1_defns) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/GEO009+0.ax',ax11_basics) ).
fof(ax8_basics,axiom,
! [X4,X5] :
( unequally_directed_lines(X4,X5)
| unequally_directed_lines(X4,reverse_line(X5)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax8_basics) ).
fof(a4_defns,axiom,
! [X1,X2] :
( equally_directed_lines(X1,X2)
<=> ~ unequally_directed_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',a4_defns) ).
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/sandbox2/benchmark/Axioms/GEO009+0.ax',ax6_basics) ).
fof(ax5_basics,axiom,
! [X4] : equally_directed_lines(X4,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO009+0.ax',ax5_basics) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5] :
( unequally_directed_opposite_lines(X4,X5)
<=> unequally_directed_opposite_lines(X5,X4) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_9,negated_conjecture,
( ( ~ unequally_directed_opposite_lines(esk1_0,esk2_0)
| ~ unequally_directed_opposite_lines(esk2_0,esk1_0) )
& ( unequally_directed_opposite_lines(esk1_0,esk2_0)
| unequally_directed_opposite_lines(esk2_0,esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X92,X93] :
( ( ~ unequally_directed_opposite_lines(X92,X93)
| unequally_directed_lines(X92,reverse_line(X93)) )
& ( ~ unequally_directed_lines(X92,reverse_line(X93))
| unequally_directed_opposite_lines(X92,X93) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1_defns])]) ).
cnf(c_0_11,negated_conjecture,
( ~ unequally_directed_opposite_lines(esk1_0,esk2_0)
| ~ unequally_directed_opposite_lines(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,plain,
( unequally_directed_opposite_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X133,X134] :
( ~ unequally_directed_lines(X133,X134)
| ~ unequally_directed_lines(X133,reverse_line(X134))
| left_convergent_lines(X133,X134)
| left_convergent_lines(X133,reverse_line(X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax9_basics])]) ).
fof(c_0_14,plain,
! [X137,X138] :
( ~ left_convergent_lines(X137,X138)
& ~ left_convergent_lines(X137,reverse_line(X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax11_basics])]) ).
cnf(c_0_15,plain,
( unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_opposite_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( unequally_directed_opposite_lines(esk1_0,esk2_0)
| unequally_directed_opposite_lines(esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
( ~ unequally_directed_lines(esk2_0,reverse_line(esk1_0))
| ~ unequally_directed_opposite_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_18,plain,
! [X131,X132] :
( unequally_directed_lines(X131,X132)
| unequally_directed_lines(X131,reverse_line(X132)) ),
inference(variable_rename,[status(thm)],[ax8_basics]) ).
cnf(c_0_19,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_13]) ).
cnf(c_0_20,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( unequally_directed_lines(esk2_0,reverse_line(esk1_0))
| unequally_directed_opposite_lines(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( ~ unequally_directed_lines(esk2_0,reverse_line(esk1_0))
| ~ unequally_directed_lines(esk1_0,reverse_line(esk2_0)) ),
inference(spm,[status(thm)],[c_0_17,c_0_12]) ).
cnf(c_0_23,plain,
( unequally_directed_lines(X1,X2)
| unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X1,X2] :
( equally_directed_lines(X1,X2)
<=> ~ unequally_directed_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4_defns]) ).
cnf(c_0_25,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( unequally_directed_lines(esk2_0,reverse_line(esk1_0))
| unequally_directed_lines(esk1_0,reverse_line(esk2_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
fof(c_0_27,plain,
! [X125,X126,X127] :
( ~ unequally_directed_lines(X125,X126)
| unequally_directed_lines(X125,X127)
| unequally_directed_lines(X126,X127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6_basics])]) ).
cnf(c_0_28,negated_conjecture,
( unequally_directed_lines(esk2_0,esk1_0)
| ~ unequally_directed_lines(esk1_0,reverse_line(esk2_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_29,plain,
! [X98,X99] :
( ( ~ equally_directed_lines(X98,X99)
| ~ unequally_directed_lines(X98,X99) )
& ( unequally_directed_lines(X98,X99)
| equally_directed_lines(X98,X99) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
fof(c_0_30,plain,
! [X124] : equally_directed_lines(X124,X124),
inference(variable_rename,[status(thm)],[ax5_basics]) ).
cnf(c_0_31,negated_conjecture,
( unequally_directed_lines(esk1_0,reverse_line(esk2_0))
| ~ unequally_directed_lines(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
( unequally_directed_lines(X1,X3)
| unequally_directed_lines(X2,X3)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( unequally_directed_lines(esk1_0,esk2_0)
| unequally_directed_lines(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_34,plain,
( ~ equally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
equally_directed_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( ~ unequally_directed_lines(esk1_0,esk2_0)
| ~ unequally_directed_lines(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( unequally_directed_lines(esk2_0,X1)
| unequally_directed_lines(esk1_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_32]) ).
cnf(c_0_38,plain,
~ unequally_directed_lines(X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
~ unequally_directed_lines(esk1_0,esk2_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_37]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GEO266+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n012.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Mon May 4 17:51:01 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.12/1.62 % Version : CSE_E---1.7
% 1.12/1.62 % Problem : theBenchmark.p
% 1.12/1.62 % SZS status Theorem for theBenchmark.p
% 1.12/1.62 % SZS output start CNFRefutation
% See solution above
% 1.12/1.62 % Total time : 1.362s
%------------------------------------------------------------------------------