%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO186+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 : n009.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 04:19:46 PM UTC 2026
% Result : Theorem 2.23s 2.00s
% Output : CNFRefutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 44 ~; 46 |; 13 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 94 ( 3 sgn 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& convergent_lines(X4,X5)
& incident_point_and_line(X1,X4)
& incident_point_and_line(X1,X5) )
=> equal_points(X1,intersection_point(X4,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(ax1,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(a4,axiom,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(cu1,axiom,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_lines(X4,X5) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(c_0_10,negated_conjecture,
~ ! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& convergent_lines(X4,X5)
& incident_point_and_line(X1,X4)
& incident_point_and_line(X1,X5) )
=> equal_points(X1,intersection_point(X4,X5)) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_11,plain,
! [X105,X106,X107] :
( ~ convergent_lines(X105,X106)
| convergent_lines(X105,X107)
| convergent_lines(X106,X107) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(c_0_12,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& convergent_lines(esk3_0,esk4_0)
& incident_point_and_line(esk1_0,esk3_0)
& incident_point_and_line(esk1_0,esk4_0)
& ~ equal_points(esk1_0,intersection_point(esk3_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_13,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_14,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
convergent_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,plain,
! [X98] : ~ convergent_lines(X98,X98),
inference(variable_rename,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( convergent_lines(esk3_0,X1)
| convergent_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( convergent_lines(esk3_0,X1)
| convergent_lines(esk4_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
fof(c_0_20,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
cnf(c_0_21,negated_conjecture,
( convergent_lines(X1,esk4_0)
| convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_22,plain,
! [X131,X132] : ~ convergent_lines(parallel_through_point(X132,X131),X132),
inference(variable_rename,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( convergent_lines(X1,esk4_0)
| convergent_lines(esk3_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_21]) ).
fof(c_0_24,plain,
! [X126,X127,X128] :
( ~ convergent_lines(X126,X127)
| distinct_lines(X127,X128)
| convergent_lines(X126,X128) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_25,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( convergent_lines(X1,esk3_0)
| convergent_lines(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_27,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
convergent_lines(parallel_through_point(esk4_0,X1),esk3_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_29,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
fof(c_0_30,plain,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4]) ).
fof(c_0_31,plain,
! [X116,X117,X118,X119] :
( ~ distinct_points(X116,X117)
| ~ distinct_lines(X118,X119)
| apart_point_and_line(X116,X118)
| apart_point_and_line(X116,X119)
| apart_point_and_line(X117,X118)
| apart_point_and_line(X117,X119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_32,negated_conjecture,
( convergent_lines(parallel_through_point(esk4_0,X1),X2)
| distinct_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,plain,
! [X167,X168] :
( ( ~ equal_points(X167,X168)
| ~ distinct_points(X167,X168) )
& ( distinct_points(X167,X168)
| equal_points(X167,X168) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
fof(c_0_34,plain,
! [X173,X174] :
( ( ~ incident_point_and_line(X173,X174)
| ~ apart_point_and_line(X173,X174) )
& ( apart_point_and_line(X173,X174)
| incident_point_and_line(X173,X174) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])]) ).
fof(c_0_35,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
cnf(c_0_36,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X4)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X4)
| ~ distinct_points(X1,X2)
| ~ distinct_lines(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,negated_conjecture,
distinct_lines(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_25,c_0_32]) ).
cnf(c_0_38,negated_conjecture,
~ equal_points(esk1_0,intersection_point(esk3_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_39,plain,
( distinct_points(X1,X2)
| equal_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
( ~ incident_point_and_line(X1,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
incident_point_and_line(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_42,negated_conjecture,
incident_point_and_line(esk1_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_43,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(c_0_44,plain,
! [X114,X115] :
( ~ convergent_lines(X114,X115)
| ~ apart_point_and_line(intersection_point(X114,X115),X115) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])]) ).
cnf(c_0_45,negated_conjecture,
( apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk4_0)
| apart_point_and_line(X2,esk3_0)
| apart_point_and_line(X2,esk4_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
distinct_points(esk1_0,intersection_point(esk3_0,esk4_0)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
~ apart_point_and_line(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
~ apart_point_and_line(esk1_0,esk4_0),
inference(spm,[status(thm)],[c_0_40,c_0_42]) ).
fof(c_0_49,plain,
! [X112,X113] :
( ~ convergent_lines(X112,X113)
| ~ apart_point_and_line(intersection_point(X112,X113),X112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])]) ).
cnf(c_0_50,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
( apart_point_and_line(intersection_point(esk3_0,esk4_0),esk4_0)
| apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]) ).
cnf(c_0_52,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
apart_point_and_line(intersection_point(esk3_0,esk4_0),esk3_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_15])]) ).
cnf(c_0_54,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO186+3 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.16/0.33 % Computer : n009.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 17:46:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.23/2.00 % Version : CSE_E---1.7
% 2.23/2.00 % Problem : theBenchmark.p
% 2.23/2.00 % SZS status Theorem for theBenchmark.p
% 2.23/2.00 % SZS output start CNFRefutation
% See solution above
% 2.23/2.01 % Total time : 1.371s
%------------------------------------------------------------------------------