%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO200+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 04:19:51 PM UTC 2026
% Result : Theorem 1.14s 1.62s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 82 ( 32 ~; 39 |; 2 &)
% ( 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 : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con,conjecture,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ distinct_lines(line_connecting(X1,X2),line_connecting(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
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(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+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/GEO006+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/GEO006+0.ax',cu1) ).
fof(ci1,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(c_0_8,negated_conjecture,
~ ! [X1,X2] :
( distinct_points(X1,X2)
=> ~ distinct_lines(line_connecting(X1,X2),line_connecting(X2,X1)) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_9,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(c_0_10,plain,
! [X47,X48,X49] :
( ~ distinct_lines(X47,X48)
| distinct_lines(X47,X49)
| distinct_lines(X48,X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(c_0_11,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk2_0,esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X42] : ~ distinct_lines(X42,X42),
inference(variable_rename,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,negated_conjecture,
distinct_lines(line_connecting(esk1_0,esk2_0),line_connecting(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_16,plain,
! [X44,X45,X46] :
( ~ distinct_points(X44,X45)
| distinct_points(X44,X46)
| distinct_points(X45,X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(c_0_17,plain,
! [X61,X62,X63,X64] :
( ~ distinct_points(X61,X62)
| ~ distinct_lines(X63,X64)
| apart_point_and_line(X61,X63)
| apart_point_and_line(X61,X64)
| apart_point_and_line(X62,X63)
| apart_point_and_line(X62,X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_18,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( distinct_lines(line_connecting(esk1_0,esk2_0),X1)
| distinct_lines(line_connecting(esk2_0,esk1_0),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,plain,
! [X41] : ~ distinct_points(X41,X41),
inference(variable_rename,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_23,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
cnf(c_0_24,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_17]) ).
cnf(c_0_25,negated_conjecture,
distinct_lines(line_connecting(esk2_0,esk1_0),line_connecting(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_28,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
fof(c_0_29,plain,
! [X53,X54] :
( ~ distinct_points(X53,X54)
| ~ apart_point_and_line(X53,line_connecting(X53,X54)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])]) ).
cnf(c_0_30,negated_conjecture,
( apart_point_and_line(X1,line_connecting(esk2_0,esk1_0))
| apart_point_and_line(X1,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(X2,line_connecting(esk2_0,esk1_0))
| apart_point_and_line(X2,line_connecting(esk1_0,esk2_0))
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
distinct_points(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_32,plain,
! [X55,X56] :
( ~ distinct_points(X55,X56)
| ~ apart_point_and_line(X56,line_connecting(X55,X56)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])]) ).
cnf(c_0_33,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( apart_point_and_line(esk1_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk2_0,esk1_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk2_0,esk1_0))
| apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk1_0,line_connecting(esk2_0,esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_22])]) ).
cnf(c_0_37,negated_conjecture,
( apart_point_and_line(esk2_0,line_connecting(esk1_0,esk2_0))
| apart_point_and_line(esk2_0,line_connecting(esk2_0,esk1_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_31])]) ).
cnf(c_0_38,negated_conjecture,
apart_point_and_line(esk2_0,line_connecting(esk2_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_37]),c_0_22])]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_38]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : GEO200+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Mon May 4 17:47:16 EDT 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 1.14/1.62 % Version : CSE_E---1.7
% 1.14/1.62 % Problem : theBenchmark.p
% 1.14/1.62 % SZS status Theorem for theBenchmark.p
% 1.14/1.62 % SZS output start CNFRefutation
% See solution above
% 1.14/1.62 % Total time : 1.361s
%------------------------------------------------------------------------------