%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO194+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 : 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 04:19:49 PM UTC 2026
% Result : Theorem 1.16s 1.63s
% Output : CNFRefutation 1.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 35 ~; 47 |; 9 &)
% ( 0 <=>; 12 =>; 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 : 79 ( 0 sgn 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X3,X2)
& convergent_lines(X1,X3) )
=> ( apart_point_and_line(intersection_point(X1,X2),X3)
=> apart_point_and_line(intersection_point(X1,X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ceq2,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
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(ceq1,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_points(X1,X3)
| apart_point_and_line(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
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(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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(c_0_9,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& convergent_lines(X3,X2)
& convergent_lines(X1,X3) )
=> ( apart_point_and_line(intersection_point(X1,X2),X3)
=> apart_point_and_line(intersection_point(X1,X3),X2) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_10,plain,
! [X69,X70,X71] :
( ~ apart_point_and_line(X69,X70)
| distinct_lines(X70,X71)
| apart_point_and_line(X69,X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(c_0_11,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& convergent_lines(esk3_0,esk2_0)
& convergent_lines(esk1_0,esk3_0)
& apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
& ~ apart_point_and_line(intersection_point(esk1_0,esk3_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,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(c_0_13,plain,
! [X66,X67,X68] :
( ~ apart_point_and_line(X66,X67)
| distinct_points(X66,X68)
| apart_point_and_line(X68,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
cnf(c_0_14,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,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])]) ).
fof(c_0_17,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_12])]) ).
cnf(c_0_18,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_21,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_22,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
( apart_point_and_line(X1,X2)
| distinct_lines(esk3_0,X2)
| distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
fof(c_0_26,plain,
! [X43] : ~ distinct_lines(X43,X43),
inference(variable_rename,[status(thm)],[c_0_20]) ).
fof(c_0_27,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_28,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_21]) ).
cnf(c_0_29,negated_conjecture,
( convergent_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(X2,X1))
| ~ convergent_lines(X2,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_33,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_34,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_27])]) ).
cnf(c_0_35,negated_conjecture,
( apart_point_and_line(X1,esk2_0)
| apart_point_and_line(X2,esk2_0)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| convergent_lines(esk1_0,X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_37,negated_conjecture,
~ apart_point_and_line(intersection_point(esk1_0,esk3_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_38,plain,
! [X44] : ~ convergent_lines(X44,X44),
inference(variable_rename,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk2_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),X1)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| convergent_lines(esk1_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_41,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_42,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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31])]),c_0_41]) ).
cnf(c_0_43,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_39,c_0_42]),c_0_23])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_43]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GEO194+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 17:49:01 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.16/1.63 % Version : CSE_E---1.7
% 1.16/1.63 % Problem : theBenchmark.p
% 1.16/1.63 % SZS status Theorem for theBenchmark.p
% 1.16/1.63 % SZS output start CNFRefutation
% See solution above
% 1.16/1.63 % Total time : 1.362s
%------------------------------------------------------------------------------