%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO254+1 : TPTP v9.2.1. Bugfixed v6.4.0.
% 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 : 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 04:20:09 PM UTC 2026
% Result : Theorem 1.44s 1.77s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 62 ( 19 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 175 ( 65 ~; 79 |; 24 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 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 : 101 ( 4 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bf_def,axiom,
! [X2,X1,X4] :
( before_on_line(X2,X1,X4)
<=> ( distinct_points(X1,X4)
& ~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) )
& ~ ( left_apart_point(X4,X2)
| left_apart_point(X4,reverse_line(X2)) )
& ~ unequally_directed_lines(X2,line_connecting(X1,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',bf_def) ).
fof(con,conjecture,
! [X1,X4,X2] :
( ( distinct_points(X1,X4)
& ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X4,X2) )
=> ( before_on_line(X2,X1,X4)
& before_on_line(X2,X4,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(oag10,axiom,
! [X1,X2] :
~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag10) ).
fof(oag1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag1) ).
fof(oag2,axiom,
! [X1,X4,X5] :
( distinct_points(X1,X4)
=> ( distinct_points(X1,X5)
| distinct_points(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag2) ).
fof(oag9,axiom,
! [X2,X3] :
( ( unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) )
=> ( left_convergent_lines(X2,X3)
| left_convergent_lines(X2,reverse_line(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag9) ).
fof(oag11,axiom,
! [X2,X3] :
~ ( left_convergent_lines(X2,X3)
| left_convergent_lines(X2,reverse_line(X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(oag6,axiom,
! [X2,X3,X6] :
( unequally_directed_lines(X2,X3)
=> ( unequally_directed_lines(X2,X6)
| unequally_directed_lines(X3,X6) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag6) ).
fof(oagco9,axiom,
! [X1,X4] : ~ unequally_directed_lines(line_connecting(X1,X4),reverse_line(line_connecting(X4,X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco9) ).
fof(oag5,axiom,
! [X2] : ~ unequally_directed_lines(X2,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag5) ).
fof(c_0_10,plain,
! [X2,X1,X4] :
( before_on_line(X2,X1,X4)
<=> ( distinct_points(X1,X4)
& ~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) )
& ~ ( left_apart_point(X4,X2)
| left_apart_point(X4,reverse_line(X2)) )
& ~ unequally_directed_lines(X2,line_connecting(X1,X4)) ) ),
inference(fof_simplification,[status(thm)],[bf_def]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X4,X2] :
( ( distinct_points(X1,X4)
& ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X4,X2) )
=> ( before_on_line(X2,X1,X4)
& before_on_line(X2,X4,X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_12,plain,
! [X88,X89,X90] :
( ( distinct_points(X89,X90)
| ~ before_on_line(X88,X89,X90) )
& ( ~ left_apart_point(X89,X88)
| ~ before_on_line(X88,X89,X90) )
& ( ~ left_apart_point(X89,reverse_line(X88))
| ~ before_on_line(X88,X89,X90) )
& ( ~ left_apart_point(X90,X88)
| ~ before_on_line(X88,X89,X90) )
& ( ~ left_apart_point(X90,reverse_line(X88))
| ~ before_on_line(X88,X89,X90) )
& ( ~ unequally_directed_lines(X88,line_connecting(X89,X90))
| ~ before_on_line(X88,X89,X90) )
& ( ~ distinct_points(X89,X90)
| left_apart_point(X89,X88)
| left_apart_point(X89,reverse_line(X88))
| left_apart_point(X90,X88)
| left_apart_point(X90,reverse_line(X88))
| unequally_directed_lines(X88,line_connecting(X89,X90))
| before_on_line(X88,X89,X90) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_13,plain,
! [X114,X115] :
( ~ left_apart_point(X114,X115)
& ~ left_apart_point(X114,reverse_line(X115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag10])]) ).
fof(c_0_14,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[oag1]) ).
fof(c_0_15,plain,
! [X96,X97,X98] :
( ~ distinct_points(X96,X97)
| distinct_points(X96,X98)
| distinct_points(X97,X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag2])]) ).
fof(c_0_16,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& ~ apart_point_and_line(esk1_0,esk3_0)
& ~ apart_point_and_line(esk2_0,esk3_0)
& ( ~ before_on_line(esk3_0,esk1_0,esk2_0)
| ~ before_on_line(esk3_0,esk2_0,esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_17,plain,
( left_apart_point(X1,X3)
| left_apart_point(X1,reverse_line(X3))
| left_apart_point(X2,X3)
| left_apart_point(X2,reverse_line(X3))
| unequally_directed_lines(X3,line_connecting(X1,X2))
| before_on_line(X3,X1,X2)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
~ left_apart_point(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X95] : ~ distinct_points(X95,X95),
inference(variable_rename,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( before_on_line(X1,X2,X3)
| unequally_directed_lines(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_23,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( ~ before_on_line(esk3_0,esk1_0,esk2_0)
| ~ before_on_line(esk3_0,esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( before_on_line(X1,esk1_0,esk2_0)
| unequally_directed_lines(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
distinct_points(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X112,X113] :
( ~ unequally_directed_lines(X112,X113)
| ~ unequally_directed_lines(X112,reverse_line(X113))
| left_convergent_lines(X112,X113)
| left_convergent_lines(X112,reverse_line(X113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag9])]) ).
fof(c_0_29,plain,
! [X116,X117] :
( ~ left_convergent_lines(X116,X117)
& ~ left_convergent_lines(X116,reverse_line(X117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag11])]) ).
fof(c_0_30,plain,
! [X104,X105,X106] :
( ~ unequally_directed_lines(X104,X105)
| unequally_directed_lines(X104,X106)
| unequally_directed_lines(X105,X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag6])]) ).
cnf(c_0_31,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0))
| ~ before_on_line(esk3_0,esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( before_on_line(X1,esk2_0,esk1_0)
| unequally_directed_lines(X1,line_connecting(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_33,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_28]) ).
cnf(c_0_34,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( unequally_directed_lines(X1,X3)
| unequally_directed_lines(X2,X3)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(line_connecting(esk1_0,esk2_0),X1)
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_39,plain,
! [X1,X4] : ~ unequally_directed_lines(line_connecting(X1,X4),reverse_line(line_connecting(X4,X1))),
inference(fof_simplification,[status(thm)],[oagco9]) ).
cnf(c_0_40,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(esk3_0,reverse_line(X1))
| ~ unequally_directed_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_41,plain,
! [X132,X133] : ~ unequally_directed_lines(line_connecting(X132,X133),reverse_line(line_connecting(X133,X132))),
inference(variable_rename,[status(thm)],[c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_43,plain,
~ unequally_directed_lines(line_connecting(X1,X2),reverse_line(line_connecting(X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),X1)
| unequally_directed_lines(esk3_0,reverse_line(X2))
| unequally_directed_lines(esk3_0,X2)
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( unequally_directed_lines(esk3_0,reverse_line(line_connecting(esk1_0,esk2_0)))
| unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( unequally_directed_lines(esk3_0,reverse_line(line_connecting(esk1_0,esk2_0)))
| unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(ef,[status(thm)],[c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( unequally_directed_lines(reverse_line(line_connecting(esk1_0,esk2_0)),X1)
| unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0))
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0))
| unequally_directed_lines(esk3_0,reverse_line(X1))
| ~ unequally_directed_lines(reverse_line(line_connecting(esk1_0,esk2_0)),X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_47]) ).
cnf(c_0_49,negated_conjecture,
( unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1)
| ~ unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_45]) ).
fof(c_0_50,plain,
! [X2] : ~ unequally_directed_lines(X2,X2),
inference(fof_simplification,[status(thm)],[oag5]) ).
cnf(c_0_51,negated_conjecture,
( unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_47]),c_0_49]) ).
fof(c_0_52,plain,
! [X103] : ~ unequally_directed_lines(X103,X103),
inference(variable_rename,[status(thm)],[c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( unequally_directed_lines(reverse_line(X1),X2)
| unequally_directed_lines(esk3_0,X1)
| unequally_directed_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_54,plain,
~ unequally_directed_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( unequally_directed_lines(reverse_line(X1),X2)
| unequally_directed_lines(esk3_0,X3)
| unequally_directed_lines(esk3_0,X1)
| unequally_directed_lines(X3,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(esk3_0,X2)
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(X1,X2))
| unequally_directed_lines(esk3_0,line_connecting(X2,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_56]) ).
cnf(c_0_58,negated_conjecture,
unequally_directed_lines(esk3_0,line_connecting(X1,X1)),
inference(ef,[status(thm)],[c_0_57]) ).
cnf(c_0_59,negated_conjecture,
( unequally_directed_lines(line_connecting(X1,X1),X2)
| unequally_directed_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_60,negated_conjecture,
unequally_directed_lines(esk3_0,reverse_line(line_connecting(X1,X1))),
inference(spm,[status(thm)],[c_0_43,c_0_59]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_60]),c_0_58])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO254+1 : TPTP v9.2.1. Bugfixed v6.4.0.
% 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
% 0.16/0.32 % Computer : n007.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 17:49:54 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.44/1.77 % Version : CSE_E---1.7
% 1.44/1.77 % Problem : theBenchmark.p
% 1.44/1.77 % SZS status Theorem for theBenchmark.p
% 1.44/1.77 % SZS output start CNFRefutation
% See solution above
% 1.44/1.77 % Total time : 1.371s
%------------------------------------------------------------------------------