%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO230+1 : TPTP v9.2.1. Bugfixed v6.4.0.
% 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 : n006.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 04:20:02 PM UTC 2026
% Result : Theorem 1.62s 1.84s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 47 ( 18 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 112 ( 41 ~; 59 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 10 sgn 39 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(oaguc1,axiom,
! [X1,X4,X2,X3] :
( ( distinct_points(X1,X4)
& distinct_lines(X2,X3) )
=> ( left_apart_point(X1,X2)
| left_apart_point(X4,X2)
| left_apart_point(X1,X3)
| left_apart_point(X4,X3)
| left_apart_point(X1,reverse_line(X2))
| left_apart_point(X4,reverse_line(X2))
| left_apart_point(X1,reverse_line(X3))
| left_apart_point(X4,reverse_line(X3)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oaguc1) ).
fof(oag10,axiom,
! [X1,X2] :
~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag10) ).
fof(con,conjecture,
! [X1,X4] :
( distinct_points(X1,X4)
=> ( ~ distinct_lines(line_connecting(X1,X4),line_connecting(X4,X1))
& ~ unequally_directed_lines(line_connecting(X4,X1),line_connecting(X1,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(oag6,axiom,
! [X2,X3,X6] :
( unequally_directed_lines(X2,X3)
=> ( unequally_directed_lines(X2,X6)
| unequally_directed_lines(X3,X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag6) ).
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/sandbox/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/sandbox/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(oagco9,axiom,
! [X1,X4] : ~ unequally_directed_lines(line_connecting(X1,X4),reverse_line(line_connecting(X4,X1))),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oagco9) ).
fof(oag5,axiom,
! [X2] : ~ unequally_directed_lines(X2,X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO007+0.ax',oag5) ).
fof(c_0_8,plain,
! [X135,X136,X137,X138] :
( ~ distinct_points(X135,X136)
| ~ distinct_lines(X137,X138)
| left_apart_point(X135,X137)
| left_apart_point(X136,X137)
| left_apart_point(X135,X138)
| left_apart_point(X136,X138)
| left_apart_point(X135,reverse_line(X137))
| left_apart_point(X136,reverse_line(X137))
| left_apart_point(X135,reverse_line(X138))
| left_apart_point(X136,reverse_line(X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oaguc1])]) ).
fof(c_0_9,plain,
! [X113,X114] :
( ~ left_apart_point(X113,X114)
& ~ left_apart_point(X113,reverse_line(X114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag10])]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X4] :
( distinct_points(X1,X4)
=> ( ~ distinct_lines(line_connecting(X1,X4),line_connecting(X4,X1))
& ~ unequally_directed_lines(line_connecting(X4,X1),line_connecting(X1,X4)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
cnf(c_0_11,plain,
( left_apart_point(X1,X3)
| left_apart_point(X2,X3)
| left_apart_point(X1,X4)
| left_apart_point(X2,X4)
| left_apart_point(X1,reverse_line(X3))
| left_apart_point(X2,reverse_line(X3))
| left_apart_point(X1,reverse_line(X4))
| left_apart_point(X2,reverse_line(X4))
| ~ distinct_points(X1,X2)
| ~ distinct_lines(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
~ left_apart_point(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& ( distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(line_connecting(esk2_0,esk1_0),line_connecting(esk1_0,esk2_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_14,plain,
( ~ distinct_lines(X1,X2)
| ~ distinct_points(X3,X4) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(line_connecting(esk2_0,esk1_0),line_connecting(esk1_0,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X103,X104,X105] :
( ~ unequally_directed_lines(X103,X104)
| unequally_directed_lines(X103,X105)
| unequally_directed_lines(X104,X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag6])]) ).
cnf(c_0_17,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),line_connecting(esk1_0,esk2_0))
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X111,X112] :
( ~ unequally_directed_lines(X111,X112)
| ~ unequally_directed_lines(X111,reverse_line(X112))
| left_convergent_lines(X111,X112)
| left_convergent_lines(X111,reverse_line(X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag9])]) ).
fof(c_0_20,plain,
! [X115,X116] :
( ~ left_convergent_lines(X115,X116)
& ~ left_convergent_lines(X115,reverse_line(X116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag11])]) ).
cnf(c_0_21,plain,
( unequally_directed_lines(X1,X3)
| unequally_directed_lines(X2,X3)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
unequally_directed_lines(line_connecting(esk2_0,esk1_0),line_connecting(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,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_19]) ).
cnf(c_0_24,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),X1)
| unequally_directed_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_23,c_0_24]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),X1)
| unequally_directed_lines(line_connecting(esk1_0,esk2_0),X2)
| unequally_directed_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
fof(c_0_28,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_29,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),X1)
| unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(line_connecting(esk1_0,esk2_0),X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_30,plain,
! [X131,X132] : ~ unequally_directed_lines(line_connecting(X131,X132),reverse_line(line_connecting(X132,X131))),
inference(variable_rename,[status(thm)],[c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),X1)
| unequally_directed_lines(line_connecting(esk2_0,esk1_0),X2)
| unequally_directed_lines(X2,reverse_line(X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
fof(c_0_32,plain,
! [X2] : ~ unequally_directed_lines(X2,X2),
inference(fof_simplification,[status(thm)],[oag5]) ).
cnf(c_0_33,plain,
~ unequally_directed_lines(line_connecting(X1,X2),reverse_line(line_connecting(X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),X1)
| unequally_directed_lines(X1,reverse_line(X1)) ),
inference(ef,[status(thm)],[c_0_31]) ).
fof(c_0_35,plain,
! [X102] : ~ unequally_directed_lines(X102,X102),
inference(variable_rename,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( unequally_directed_lines(line_connecting(esk1_0,esk2_0),reverse_line(X1))
| unequally_directed_lines(line_connecting(esk2_0,esk1_0),X2)
| ~ unequally_directed_lines(X2,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,negated_conjecture,
unequally_directed_lines(line_connecting(esk2_0,esk1_0),line_connecting(X1,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
~ unequally_directed_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),reverse_line(X1))
| ~ unequally_directed_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_40,negated_conjecture,
unequally_directed_lines(line_connecting(esk1_0,esk2_0),reverse_line(line_connecting(X1,X1))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_41,negated_conjecture,
unequally_directed_lines(line_connecting(esk2_0,esk1_0),reverse_line(reverse_line(line_connecting(X1,X1)))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
~ unequally_directed_lines(line_connecting(esk2_0,esk1_0),reverse_line(line_connecting(X1,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( unequally_directed_lines(line_connecting(esk1_0,esk2_0),X1)
| unequally_directed_lines(line_connecting(esk2_0,esk1_0),X2)
| unequally_directed_lines(X2,X3)
| unequally_directed_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_44,negated_conjecture,
( unequally_directed_lines(X1,reverse_line(line_connecting(X2,X2)))
| unequally_directed_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_38]) ).
cnf(c_0_45,negated_conjecture,
~ unequally_directed_lines(line_connecting(esk1_0,esk2_0),line_connecting(X1,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO230+1 : TPTP v9.2.1. Bugfixed v6.4.0.
% 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 : n006.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 17:49:46 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.62/1.84 % Version : CSE_E---1.7
% 1.62/1.84 % Problem : theBenchmark.p
% 1.62/1.84 % SZS status Theorem for theBenchmark.p
% 1.62/1.84 % SZS output start CNFRefutation
% See solution above
% 1.62/1.84 % Total time : 1.374s
%------------------------------------------------------------------------------