%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO172+1 : TPTP v9.2.1. Released v3.3.0.
% 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 : n016.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 04:19:40 PM UTC 2026
% Result : Theorem 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 51 ( 15 unt; 0 def)
% Number of atoms : 122 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 113 ( 42 ~; 53 |; 8 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 5 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ apart_point_and_line(X3,X1)
& ~ apart_point_and_line(X3,X2) )
=> ~ distinct_points(X3,intersection_point(X1,X2)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).
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/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ apart_point_and_line(X3,X1)
& ~ apart_point_and_line(X3,X2) )
=> ~ distinct_points(X3,intersection_point(X1,X2)) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_10,plain,
! [X51,X52,X53] :
( ~ convergent_lines(X51,X52)
| convergent_lines(X51,X53)
| convergent_lines(X52,X53) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(c_0_11,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ apart_point_and_line(esk3_0,esk1_0)
& ~ apart_point_and_line(esk3_0,esk2_0)
& distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
fof(c_0_12,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_13,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X44] : ~ convergent_lines(X44,X44),
inference(variable_rename,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( convergent_lines(esk2_0,X1)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_20,plain,
! [X72,X73,X74] :
( ~ convergent_lines(X72,X73)
| distinct_lines(X73,X74)
| convergent_lines(X72,X74) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_21,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(esk2_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_22,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
fof(c_0_24,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_25,plain,
! [X48,X49,X50] :
( ~ distinct_lines(X48,X49)
| distinct_lines(X48,X50)
| distinct_lines(X49,X50) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
cnf(c_0_26,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,X2)
| distinct_lines(esk1_0,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
fof(c_0_27,plain,
! [X43] : ~ distinct_lines(X43,X43),
inference(variable_rename,[status(thm)],[c_0_24]) ).
cnf(c_0_28,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( convergent_lines(X1,esk2_0)
| distinct_lines(esk1_0,esk2_0) ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_30,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( convergent_lines(X1,esk2_0)
| distinct_lines(esk1_0,X2)
| distinct_lines(esk2_0,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( convergent_lines(X1,esk2_0)
| distinct_lines(esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( convergent_lines(X1,X2)
| distinct_lines(esk2_0,esk1_0)
| distinct_lines(esk2_0,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
fof(c_0_34,plain,
! [X62,X63,X64,X65] :
( ~ distinct_points(X62,X63)
| ~ distinct_lines(X64,X65)
| apart_point_and_line(X62,X64)
| apart_point_and_line(X62,X65)
| apart_point_and_line(X63,X64)
| apart_point_and_line(X63,X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_35,negated_conjecture,
( distinct_lines(esk2_0,esk1_0)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
fof(c_0_36,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
cnf(c_0_37,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_34]) ).
cnf(c_0_38,negated_conjecture,
distinct_lines(esk2_0,esk1_0),
inference(ef,[status(thm)],[c_0_35]) ).
fof(c_0_39,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(c_0_40,plain,
! [X58,X59] :
( ~ convergent_lines(X58,X59)
| ~ apart_point_and_line(intersection_point(X58,X59),X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_36])]) ).
cnf(c_0_41,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X2,esk1_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
distinct_points(esk3_0,intersection_point(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_43,negated_conjecture,
~ apart_point_and_line(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_44,negated_conjecture,
~ apart_point_and_line(esk3_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_45,plain,
! [X60,X61] :
( ~ convergent_lines(X60,X61)
| ~ apart_point_and_line(intersection_point(X60,X61),X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])]) ).
cnf(c_0_46,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_47,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44]) ).
cnf(c_0_48,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_49,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_14])]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO172+1 : TPTP v9.2.1. Released v3.3.0.
% 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
% 0.17/0.33 % Computer : n016.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon May 4 18:00:36 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Theorem for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------