%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO209+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n013.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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 66 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 19 ~; 16 |; 15 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 42 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X9,X6,X7,X8] :
( ( apart_point_and_line(X9,X6)
& incident_point_and_line(X9,X7)
& incident_point_and_line(X9,X8)
& parallel_lines(X7,X6)
& parallel_lines(X8,X6) )
=> equal_lines(X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(ax2,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',ax2) ).
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(a3,axiom,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(c_0_5,negated_conjecture,
~ ! [X9,X6,X7,X8] :
( ( apart_point_and_line(X9,X6)
& incident_point_and_line(X9,X7)
& incident_point_and_line(X9,X8)
& parallel_lines(X7,X6)
& parallel_lines(X8,X6) )
=> equal_lines(X7,X8) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_6,plain,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax2]) ).
fof(c_0_7,negated_conjecture,
( apart_point_and_line(esk1_0,esk2_0)
& incident_point_and_line(esk1_0,esk3_0)
& incident_point_and_line(esk1_0,esk4_0)
& parallel_lines(esk3_0,esk2_0)
& parallel_lines(esk4_0,esk2_0)
& ~ equal_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_8,plain,
! [X169,X170] :
( ( ~ equal_lines(X169,X170)
| ~ distinct_lines(X169,X170) )
& ( distinct_lines(X169,X170)
| equal_lines(X169,X170) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_9,plain,
! [X102,X103,X104] :
( ~ distinct_lines(X102,X103)
| distinct_lines(X102,X104)
| distinct_lines(X103,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
cnf(c_0_10,negated_conjecture,
~ equal_lines(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( distinct_lines(X1,X2)
| equal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_13,plain,
! [X129,X130] :
( ~ distinct_lines(X129,X130)
| convergent_lines(X129,X130) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_14,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
distinct_lines(esk3_0,esk4_0),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_16,plain,
! [X171,X172] :
( ( ~ parallel_lines(X171,X172)
| ~ convergent_lines(X171,X172) )
& ( convergent_lines(X171,X172)
| parallel_lines(X171,X172) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])]) ).
cnf(c_0_17,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_lines(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,plain,
( ~ parallel_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
parallel_lines(esk4_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
( convergent_lines(esk4_0,X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
parallel_lines(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
~ convergent_lines(esk4_0,esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( convergent_lines(esk4_0,X1)
| convergent_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
~ convergent_lines(esk3_0,esk2_0),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
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+3 : TPTP v9.2.1. Released v4.0.0.
% 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 : n013.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 17:47:26 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------