%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO181+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 : n023.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 04:19:44 PM UTC 2026
% Result : Theorem 1.22s 1.91s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 12 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 25 ~; 51 |; 5 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> apart_point_and_line(X2,line_connecting(X1,X3)) ) ),
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/GEO008+0.ax',ceq2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart4) ).
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/GEO008+0.ax',cu1) ).
fof(con1,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> apart_point_and_line(X2,line_connecting(X1,X3)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_7,plain,
! [X64,X65,X66] :
( ~ apart_point_and_line(X64,X65)
| distinct_lines(X65,X66)
| apart_point_and_line(X64,X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(c_0_8,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0))
& ~ apart_point_and_line(esk2_0,line_connecting(esk1_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_9,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_10,plain,
! [X42,X43,X44] :
( ~ distinct_points(X42,X43)
| distinct_points(X42,X44)
| distinct_points(X43,X44) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(c_0_11,plain,
! [X57,X58,X59,X60] :
( ~ distinct_points(X57,X58)
| ~ distinct_lines(X59,X60)
| apart_point_and_line(X57,X59)
| apart_point_and_line(X57,X60)
| apart_point_and_line(X58,X59)
| apart_point_and_line(X58,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_12,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
apart_point_and_line(esk3_0,line_connecting(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_14,plain,
! [X39] : ~ distinct_points(X39,X39),
inference(variable_rename,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,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_11]) ).
cnf(c_0_18,negated_conjecture,
( apart_point_and_line(esk3_0,X1)
| distinct_lines(line_connecting(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
fof(c_0_21,plain,
! [X51,X52,X53] :
( ( distinct_points(X53,X51)
| ~ apart_point_and_line(X53,line_connecting(X51,X52))
| ~ distinct_points(X51,X52) )
& ( distinct_points(X53,X52)
| ~ apart_point_and_line(X53,line_connecting(X51,X52))
| ~ distinct_points(X51,X52) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
cnf(c_0_22,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,X3)
| apart_point_and_line(X1,X3)
| apart_point_and_line(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
distinct_points(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X3,X2))
| ~ distinct_points(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk3_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk1_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_16])]),c_0_19]) ).
cnf(c_0_28,negated_conjecture,
distinct_points(esk3_0,esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_13]),c_0_16])]) ).
cnf(c_0_29,negated_conjecture,
( apart_point_and_line(esk1_0,X1)
| apart_point_and_line(esk2_0,X1)
| apart_point_and_line(esk3_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_16])]),c_0_19]) ).
cnf(c_0_30,negated_conjecture,
( distinct_points(esk3_0,X1)
| distinct_points(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(X1,X2))
| apart_point_and_line(esk1_0,line_connecting(X1,X2))
| distinct_points(esk3_0,X2)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_32,negated_conjecture,
distinct_points(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
~ apart_point_and_line(esk2_0,line_connecting(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_34,negated_conjecture,
apart_point_and_line(esk1_0,line_connecting(esk1_0,esk3_0)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_19]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_32])]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.27 % Problem : GEO181+2 : TPTP v9.2.1. Released v3.3.0.
% 0.10/0.27 % 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
% 0.12/0.48 % Computer : n023.cluster.edu
% 0.12/0.48 % Model : x86_64 x86_64
% 0.12/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.48 % Memory : 8042.1875MB
% 0.12/0.48 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.48 % CPULimit : 300
% 0.12/0.48 % WCLimit : 300
% 0.12/0.48 % DateTime : Mon May 4 17:47:08 EDT 2026
% 0.12/0.48 % CPUTime :
% 0.12/0.49 % start to proof: theBenchmark
% 1.22/1.91 % Version : CSE_E---1.7
% 1.22/1.91 % Problem : theBenchmark.p
% 1.22/1.91 % SZS status Theorem for theBenchmark.p
% 1.22/1.91 % SZS output start CNFRefutation
% See solution above
% 1.22/1.92 % Total time : 1.385s
%------------------------------------------------------------------------------