%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO209+2 : 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 : n022.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 04:19:55 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 29 ~; 25 |; 13 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 44 ( 0 sgn 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X6,X7,X8,X9] :
( ( apart_point_and_line(X6,X7)
& ~ apart_point_and_line(X6,X8)
& ~ apart_point_and_line(X6,X9)
& ~ convergent_lines(X8,X7)
& ~ convergent_lines(X9,X7) )
=> ~ distinct_lines(X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+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/GEO008+0.ax',apart5) ).
fof(cup1,axiom,
! [X1,X2,X3] :
( distinct_lines(X2,X3)
=> ( apart_point_and_line(X1,X2)
| apart_point_and_line(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).
fof(apart6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
fof(c_0_5,negated_conjecture,
~ ! [X6,X7,X8,X9] :
( ( apart_point_and_line(X6,X7)
& ~ apart_point_and_line(X6,X8)
& ~ apart_point_and_line(X6,X9)
& ~ convergent_lines(X8,X7)
& ~ convergent_lines(X9,X7) )
=> ~ distinct_lines(X8,X9) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_6,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_7,plain,
! [X57,X58,X59] :
( ~ distinct_lines(X57,X58)
| distinct_lines(X57,X59)
| distinct_lines(X58,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(c_0_8,negated_conjecture,
( apart_point_and_line(esk1_0,esk2_0)
& ~ apart_point_and_line(esk1_0,esk3_0)
& ~ apart_point_and_line(esk1_0,esk4_0)
& ~ convergent_lines(esk3_0,esk2_0)
& ~ convergent_lines(esk4_0,esk2_0)
& distinct_lines(esk3_0,esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_9,plain,
! [X52] : ~ distinct_lines(X52,X52),
inference(variable_rename,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
distinct_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X85,X86,X87] :
( ~ distinct_lines(X86,X87)
| apart_point_and_line(X85,X86)
| apart_point_and_line(X85,X87)
| convergent_lines(X86,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
cnf(c_0_13,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_15,plain,
! [X60,X61,X62] :
( ~ convergent_lines(X60,X61)
| convergent_lines(X60,X62)
| convergent_lines(X61,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
cnf(c_0_16,plain,
( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
distinct_lines(esk4_0,esk3_0),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( apart_point_and_line(X1,esk4_0)
| apart_point_and_line(X1,esk3_0)
| convergent_lines(esk4_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ convergent_lines(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
( apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X1,esk4_0)
| convergent_lines(esk4_0,X2)
| convergent_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
~ convergent_lines(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
~ apart_point_and_line(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_24,negated_conjecture,
( apart_point_and_line(X1,esk4_0)
| apart_point_and_line(X1,esk3_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
~ apart_point_and_line(esk1_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO209+2 : 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 : n022.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 17:47:51 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------