TSTP Solution File: GEO222+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO222+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 22:47:14 EDT 2023
% Result : Theorem 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of formulae : 67 ( 25 unt; 11 typ; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 130 ( 51 ~; 65 |; 7 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 9 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 107 ( 4 sgn; 59 !; 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,
parallel_through_point: ( $i * $i ) > $i ).
tff(decl_29,type,
unorthogonal_lines: ( $i * $i ) > $o ).
tff(decl_30,type,
orthogonal_through_point: ( $i * $i ) > $i ).
tff(decl_31,type,
esk1_0: $i ).
tff(decl_32,type,
esk2_0: $i ).
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(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
fof(con,conjecture,
! [X9,X6] : ~ convergent_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X9),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(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart1) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(ouo1,axiom,
! [X9,X6,X7,X8] :
( distinct_lines(X6,X7)
=> ( apart_point_and_line(X9,X6)
| apart_point_and_line(X9,X7)
| unorthogonal_lines(X6,X8)
| unorthogonal_lines(X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).
fof(con2,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( ( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2) )
=> distinct_points(X3,intersection_point(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).
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(oac1,axiom,
! [X6,X7,X8] :
( ( convergent_lines(X6,X7)
& unorthogonal_lines(X6,X7) )
=> ( ( convergent_lines(X6,X8)
& unorthogonal_lines(X6,X8) )
| ( convergent_lines(X7,X8)
& unorthogonal_lines(X7,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(c_0_12,plain,
! [X16,X17,X18] :
( ~ distinct_lines(X16,X17)
| distinct_lines(X16,X18)
| distinct_lines(X17,X18) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(c_0_13,plain,
! [X38,X39] :
( ~ convergent_lines(X38,X39)
| distinct_lines(X38,X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(c_0_14,negated_conjecture,
~ ! [X9,X6] : ~ convergent_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_15,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
cnf(c_0_16,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,negated_conjecture,
convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_19,plain,
! [X11] : ~ distinct_lines(X11,X11),
inference(variable_rename,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( distinct_lines(X1,X2)
| distinct_lines(X3,X2)
| ~ convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(c_0_23,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(c_0_24,plain,
! [X56,X57,X58,X59] :
( ~ distinct_lines(X57,X58)
| apart_point_and_line(X56,X57)
| apart_point_and_line(X56,X58)
| unorthogonal_lines(X57,X59)
| unorthogonal_lines(X58,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
cnf(c_0_25,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_27,plain,
! [X10] : ~ distinct_points(X10,X10),
inference(variable_rename,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X25,X26,X27] :
( ( ~ apart_point_and_line(X27,X25)
| distinct_points(X27,intersection_point(X25,X26))
| ~ convergent_lines(X25,X26) )
& ( ~ apart_point_and_line(X27,X26)
| distinct_points(X27,intersection_point(X25,X26))
| ~ convergent_lines(X25,X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
fof(c_0_29,plain,
! [X52,X53] : ~ unorthogonal_lines(orthogonal_through_point(X53,X52),X53),
inference(variable_rename,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2)
| unorthogonal_lines(X1,X4)
| unorthogonal_lines(X2,X4)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,negated_conjecture,
distinct_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_32,plain,
! [X47,X48] :
( convergent_lines(X47,X48)
| unorthogonal_lines(X47,X48) ),
inference(variable_rename,[status(thm)],[occu1]) ).
cnf(c_0_33,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( distinct_points(X1,intersection_point(X3,X2))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
| unorthogonal_lines(esk2_0,X1)
| apart_point_and_line(X2,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X2,esk2_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_37,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_38,plain,
! [X19,X20,X21] :
( ~ convergent_lines(X19,X20)
| convergent_lines(X19,X21)
| convergent_lines(X20,X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
cnf(c_0_39,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_41,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X2)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_42,negated_conjecture,
( unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0))
| apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
| apart_point_and_line(X1,esk2_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_43,plain,
! [X12] : ~ convergent_lines(X12,X12),
inference(variable_rename,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_35,c_0_39]) ).
fof(c_0_46,plain,
! [X49,X50,X51] :
( ( convergent_lines(X50,X51)
| convergent_lines(X49,X51)
| ~ convergent_lines(X49,X50)
| ~ unorthogonal_lines(X49,X50) )
& ( unorthogonal_lines(X50,X51)
| convergent_lines(X49,X51)
| ~ convergent_lines(X49,X50)
| ~ unorthogonal_lines(X49,X50) )
& ( convergent_lines(X50,X51)
| unorthogonal_lines(X49,X51)
| ~ convergent_lines(X49,X50)
| ~ unorthogonal_lines(X49,X50) )
& ( unorthogonal_lines(X50,X51)
| unorthogonal_lines(X49,X51)
| ~ convergent_lines(X49,X50)
| ~ unorthogonal_lines(X49,X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
cnf(c_0_47,plain,
( ~ apart_point_and_line(intersection_point(X1,X2),X1)
| ~ convergent_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_40]) ).
cnf(c_0_48,negated_conjecture,
( unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0))
| apart_point_and_line(intersection_point(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),esk2_0)
| ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_50,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| convergent_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,negated_conjecture,
unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_21])]) ).
cnf(c_0_53,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
| convergent_lines(esk2_0,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_54]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : GEO222+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 21:54:37 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.64 % Version : CSE_E---1.5
% 0.20/0.64 % Problem : theBenchmark.p
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark.p
% 0.20/0.64 % SZS output start Proof
% See solution above
% 0.20/0.64 % Total time : 0.045000 s
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time : 0.048000 s
%------------------------------------------------------------------------------