TSTP Solution File: GEO205+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO205+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n006.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 : Wed Aug 30 22:47:02 EDT 2023
% Result : Theorem 0.14s 0.55s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 80 ( 20 unt; 9 typ; 0 def)
% Number of atoms : 168 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 49 ~; 78 |; 7 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 114 ( 0 sgn; 65 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
distinct_points: ( $i * $i ) > $o ).
tff(decl_23,type,
distinct_lines: ( $i * $i ) > $o ).
tff(decl_24,type,
convergent_lines: ( $i * $i ) > $o ).
tff(decl_25,type,
line_connecting: ( $i * $i ) > $i ).
tff(decl_26,type,
apart_point_and_line: ( $i * $i ) > $o ).
tff(decl_27,type,
intersection_point: ( $i * $i ) > $i ).
tff(decl_28,type,
esk1_0: $i ).
tff(decl_29,type,
esk2_0: $i ).
tff(decl_30,type,
esk3_0: $i ).
fof(con,conjecture,
! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& ~ distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(ax6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ax6) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(ceq3,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( distinct_lines(X2,X3)
| convergent_lines(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart5) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',cu1) ).
fof(ci4,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci4) ).
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',ci3) ).
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/sandbox2/benchmark/Axioms/GEO006+0.ax',ceq2) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
( ( convergent_lines(X1,X2)
& ~ distinct_lines(X2,X3) )
=> ( convergent_lines(X1,X3)
& ~ distinct_points(intersection_point(X1,X2),intersection_point(X1,X3)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_13,plain,
! [X15,X16,X17] :
( ~ convergent_lines(X15,X16)
| convergent_lines(X15,X17)
| convergent_lines(X16,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(c_0_14,negated_conjecture,
( convergent_lines(esk1_0,esk2_0)
& ~ distinct_lines(esk2_0,esk3_0)
& ( ~ convergent_lines(esk1_0,esk3_0)
| distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_15,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_16,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X8] : ~ convergent_lines(X8,X8),
inference(variable_rename,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_20,plain,
! [X36,X37,X38] :
( ~ convergent_lines(X36,X37)
| distinct_lines(X37,X38)
| convergent_lines(X36,X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_21,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_19]) ).
fof(c_0_23,plain,
! [X9,X10,X11] :
( ~ distinct_points(X9,X10)
| distinct_points(X9,X11)
| distinct_points(X10,X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
cnf(c_0_24,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),intersection_point(esk1_0,esk3_0))
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,negated_conjecture,
~ distinct_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_29,negated_conjecture,
( convergent_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_30,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(esk1_0,X2)
| convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
fof(c_0_31,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
cnf(c_0_32,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),X1)
| distinct_points(intersection_point(esk1_0,esk3_0),X1)
| ~ convergent_lines(esk1_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,negated_conjecture,
convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( convergent_lines(X1,esk1_0)
| convergent_lines(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
fof(c_0_35,plain,
! [X6] : ~ distinct_points(X6,X6),
inference(variable_rename,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk3_0),X1)
| distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]) ).
fof(c_0_37,plain,
! [X12,X13,X14] :
( ~ distinct_lines(X12,X13)
| distinct_lines(X12,X14)
| distinct_lines(X13,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
cnf(c_0_38,negated_conjecture,
convergent_lines(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_21,c_0_34]) ).
cnf(c_0_39,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,negated_conjecture,
( distinct_points(intersection_point(esk1_0,esk2_0),X1)
| distinct_points(intersection_point(esk1_0,esk3_0),X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_36]) ).
cnf(c_0_41,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_42,negated_conjecture,
( convergent_lines(esk2_0,X1)
| distinct_lines(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( distinct_points(X1,intersection_point(esk1_0,esk3_0))
| distinct_points(intersection_point(esk1_0,esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_44,plain,
! [X26,X27,X28,X29] :
( ~ distinct_points(X26,X27)
| ~ distinct_lines(X28,X29)
| apart_point_and_line(X26,X28)
| apart_point_and_line(X26,X29)
| apart_point_and_line(X27,X28)
| apart_point_and_line(X27,X29) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
cnf(c_0_45,negated_conjecture,
( convergent_lines(esk2_0,X1)
| distinct_lines(esk1_0,X2)
| distinct_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( distinct_points(X1,intersection_point(esk1_0,esk3_0))
| distinct_points(intersection_point(esk1_0,esk2_0),X2)
| distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
fof(c_0_47,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
cnf(c_0_48,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_44]) ).
cnf(c_0_49,negated_conjecture,
distinct_lines(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_45]),c_0_21]) ).
cnf(c_0_50,negated_conjecture,
( distinct_points(X1,intersection_point(esk1_0,esk2_0))
| distinct_points(X1,intersection_point(esk1_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_39,c_0_46]) ).
fof(c_0_51,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(c_0_52,plain,
! [X24,X25] :
( ~ convergent_lines(X24,X25)
| ~ apart_point_and_line(intersection_point(X24,X25),X25) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])]) ).
cnf(c_0_53,negated_conjecture,
( apart_point_and_line(X1,esk1_0)
| apart_point_and_line(X1,esk3_0)
| apart_point_and_line(X2,esk1_0)
| apart_point_and_line(X2,esk3_0)
| ~ distinct_points(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,negated_conjecture,
distinct_points(intersection_point(esk1_0,esk3_0),intersection_point(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_39,c_0_50]) ).
fof(c_0_55,plain,
! [X22,X23] :
( ~ convergent_lines(X22,X23)
| ~ apart_point_and_line(intersection_point(X22,X23),X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])]) ).
cnf(c_0_56,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
fof(c_0_58,plain,
! [X33,X34,X35] :
( ~ apart_point_and_line(X33,X34)
| distinct_lines(X34,X35)
| apart_point_and_line(X33,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
cnf(c_0_59,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_60,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk3_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_33])]) ).
cnf(c_0_61,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_62,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk3_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_33])]) ).
cnf(c_0_63,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| apart_point_and_line(intersection_point(esk1_0,esk2_0),X1)
| distinct_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
fof(c_0_64,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_65,negated_conjecture,
( apart_point_and_line(intersection_point(esk1_0,esk2_0),esk1_0)
| distinct_lines(esk3_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_63]),c_0_17])]) ).
fof(c_0_66,plain,
! [X7] : ~ distinct_lines(X7,X7),
inference(variable_rename,[status(thm)],[c_0_64]) ).
cnf(c_0_67,negated_conjecture,
distinct_lines(esk3_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_65]),c_0_17])]) ).
cnf(c_0_68,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_69,negated_conjecture,
( distinct_lines(esk3_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO205+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.09/0.30 % Computer : n006.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Aug 29 23:36:51 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.14/0.52 start to proof: theBenchmark
% 0.14/0.55 % Version : CSE_E---1.5
% 0.14/0.55 % Problem : theBenchmark.p
% 0.14/0.55 % Proof found
% 0.14/0.55 % SZS status Theorem for theBenchmark.p
% 0.14/0.55 % SZS output start Proof
% See solution above
% 0.14/0.55 % Total time : 0.022000 s
% 0.14/0.55 % SZS output end Proof
% 0.14/0.55 % Total time : 0.024000 s
%------------------------------------------------------------------------------