TSTP Solution File: GEO254+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO254+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 22:47:30 EDT 2023
% Result : Theorem 0.21s 0.64s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 29
% Syntax : Number of formulae : 81 ( 19 unt; 19 typ; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 175 ( 65 ~; 79 |; 24 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 16 >; 17 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 4 sgn; 51 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
apart_point_and_line: ( $i * $i ) > $o ).
tff(decl_23,type,
left_apart_point: ( $i * $i ) > $o ).
tff(decl_24,type,
reverse_line: $i > $i ).
tff(decl_25,type,
convergent_lines: ( $i * $i ) > $o ).
tff(decl_26,type,
unequally_directed_lines: ( $i * $i ) > $o ).
tff(decl_27,type,
divides_points: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
before_on_line: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
distinct_points: ( $i * $i ) > $o ).
tff(decl_30,type,
line_connecting: ( $i * $i ) > $i ).
tff(decl_31,type,
between_on_line: ( $i * $i * $i * $i ) > $o ).
tff(decl_32,type,
distinct_lines: ( $i * $i ) > $o ).
tff(decl_33,type,
line: $i > $o ).
tff(decl_34,type,
left_convergent_lines: ( $i * $i ) > $o ).
tff(decl_35,type,
point: $i > $o ).
tff(decl_36,type,
intersection_point: ( $i * $i ) > $i ).
tff(decl_37,type,
parallel_through_point: ( $i * $i ) > $i ).
tff(decl_38,type,
esk1_0: $i ).
tff(decl_39,type,
esk2_0: $i ).
tff(decl_40,type,
esk3_0: $i ).
fof(bf_def,axiom,
! [X2,X1,X4] :
( before_on_line(X2,X1,X4)
<=> ( distinct_points(X1,X4)
& ~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) )
& ~ ( left_apart_point(X4,X2)
| left_apart_point(X4,reverse_line(X2)) )
& ~ unequally_directed_lines(X2,line_connecting(X1,X4)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',bf_def) ).
fof(con,conjecture,
! [X1,X4,X2] :
( ( distinct_points(X1,X4)
& ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X4,X2) )
=> ( before_on_line(X2,X1,X4)
& before_on_line(X2,X4,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
fof(oag10,axiom,
! [X1,X2] :
~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag10) ).
fof(oag1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag1) ).
fof(oag2,axiom,
! [X1,X4,X5] :
( distinct_points(X1,X4)
=> ( distinct_points(X1,X5)
| distinct_points(X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag2) ).
fof(oag9,axiom,
! [X2,X3] :
( ( unequally_directed_lines(X2,X3)
& unequally_directed_lines(X2,reverse_line(X3)) )
=> ( left_convergent_lines(X2,X3)
| left_convergent_lines(X2,reverse_line(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag9) ).
fof(oag11,axiom,
! [X2,X3] :
~ ( left_convergent_lines(X2,X3)
| left_convergent_lines(X2,reverse_line(X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag11) ).
fof(oag6,axiom,
! [X2,X3,X6] :
( unequally_directed_lines(X2,X3)
=> ( unequally_directed_lines(X2,X6)
| unequally_directed_lines(X3,X6) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag6) ).
fof(oagco9,axiom,
! [X1,X4] : ~ unequally_directed_lines(line_connecting(X1,X4),reverse_line(line_connecting(X4,X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oagco9) ).
fof(oag5,axiom,
! [X2] : ~ unequally_directed_lines(X2,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO007+0.ax',oag5) ).
fof(c_0_10,plain,
! [X2,X1,X4] :
( before_on_line(X2,X1,X4)
<=> ( distinct_points(X1,X4)
& ~ ( left_apart_point(X1,X2)
| left_apart_point(X1,reverse_line(X2)) )
& ~ ( left_apart_point(X4,X2)
| left_apart_point(X4,reverse_line(X2)) )
& ~ unequally_directed_lines(X2,line_connecting(X1,X4)) ) ),
inference(fof_simplification,[status(thm)],[bf_def]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X4,X2] :
( ( distinct_points(X1,X4)
& ~ apart_point_and_line(X1,X2)
& ~ apart_point_and_line(X4,X2) )
=> ( before_on_line(X2,X1,X4)
& before_on_line(X2,X4,X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(c_0_12,plain,
! [X14,X15,X16] :
( ( distinct_points(X15,X16)
| ~ before_on_line(X14,X15,X16) )
& ( ~ left_apart_point(X15,X14)
| ~ before_on_line(X14,X15,X16) )
& ( ~ left_apart_point(X15,reverse_line(X14))
| ~ before_on_line(X14,X15,X16) )
& ( ~ left_apart_point(X16,X14)
| ~ before_on_line(X14,X15,X16) )
& ( ~ left_apart_point(X16,reverse_line(X14))
| ~ before_on_line(X14,X15,X16) )
& ( ~ unequally_directed_lines(X14,line_connecting(X15,X16))
| ~ before_on_line(X14,X15,X16) )
& ( ~ distinct_points(X15,X16)
| left_apart_point(X15,X14)
| left_apart_point(X15,reverse_line(X14))
| left_apart_point(X16,X14)
| left_apart_point(X16,reverse_line(X14))
| unequally_directed_lines(X14,line_connecting(X15,X16))
| before_on_line(X14,X15,X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_13,plain,
! [X40,X41] :
( ~ left_apart_point(X40,X41)
& ~ left_apart_point(X40,reverse_line(X41)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag10])]) ).
fof(c_0_14,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[oag1]) ).
fof(c_0_15,plain,
! [X22,X23,X24] :
( ~ distinct_points(X22,X23)
| distinct_points(X22,X24)
| distinct_points(X23,X24) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag2])]) ).
fof(c_0_16,negated_conjecture,
( distinct_points(esk1_0,esk2_0)
& ~ apart_point_and_line(esk1_0,esk3_0)
& ~ apart_point_and_line(esk2_0,esk3_0)
& ( ~ before_on_line(esk3_0,esk1_0,esk2_0)
| ~ before_on_line(esk3_0,esk2_0,esk1_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_17,plain,
( left_apart_point(X1,X3)
| left_apart_point(X1,reverse_line(X3))
| left_apart_point(X2,X3)
| left_apart_point(X2,reverse_line(X3))
| unequally_directed_lines(X3,line_connecting(X1,X2))
| before_on_line(X3,X1,X2)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
~ left_apart_point(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_19,plain,
! [X21] : ~ distinct_points(X21,X21),
inference(variable_rename,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
distinct_points(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( before_on_line(X1,X2,X3)
| unequally_directed_lines(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_23,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( distinct_points(esk1_0,X1)
| distinct_points(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( ~ before_on_line(esk3_0,esk1_0,esk2_0)
| ~ before_on_line(esk3_0,esk2_0,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( before_on_line(X1,esk1_0,esk2_0)
| unequally_directed_lines(X1,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
distinct_points(esk2_0,esk1_0),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X38,X39] :
( ~ unequally_directed_lines(X38,X39)
| ~ unequally_directed_lines(X38,reverse_line(X39))
| left_convergent_lines(X38,X39)
| left_convergent_lines(X38,reverse_line(X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag9])]) ).
fof(c_0_29,plain,
! [X42,X43] :
( ~ left_convergent_lines(X42,X43)
& ~ left_convergent_lines(X42,reverse_line(X43)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag11])]) ).
fof(c_0_30,plain,
! [X30,X31,X32] :
( ~ unequally_directed_lines(X30,X31)
| unequally_directed_lines(X30,X32)
| unequally_directed_lines(X31,X32) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oag6])]) ).
cnf(c_0_31,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0))
| ~ before_on_line(esk3_0,esk2_0,esk1_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
( before_on_line(X1,esk2_0,esk1_0)
| unequally_directed_lines(X1,line_connecting(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_33,plain,
( left_convergent_lines(X1,X2)
| left_convergent_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2)
| ~ unequally_directed_lines(X1,reverse_line(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
~ left_convergent_lines(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( unequally_directed_lines(X1,X3)
| unequally_directed_lines(X2,X3)
| ~ unequally_directed_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( ~ unequally_directed_lines(X1,reverse_line(X2))
| ~ unequally_directed_lines(X1,X2) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(line_connecting(esk1_0,esk2_0),X1)
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_39,plain,
! [X1,X4] : ~ unequally_directed_lines(line_connecting(X1,X4),reverse_line(line_connecting(X4,X1))),
inference(fof_simplification,[status(thm)],[oagco9]) ).
cnf(c_0_40,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(esk3_0,X1)
| ~ unequally_directed_lines(line_connecting(esk1_0,esk2_0),reverse_line(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_41,plain,
! [X58,X59] : ~ unequally_directed_lines(line_connecting(X58,X59),reverse_line(line_connecting(X59,X58))),
inference(variable_rename,[status(thm)],[c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk2_0,esk1_0))
| unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_43,plain,
~ unequally_directed_lines(line_connecting(X1,X2),reverse_line(line_connecting(X2,X1))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_44,negated_conjecture,
( unequally_directed_lines(line_connecting(esk2_0,esk1_0),X1)
| unequally_directed_lines(esk3_0,reverse_line(X2))
| unequally_directed_lines(esk3_0,X2)
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( unequally_directed_lines(esk3_0,reverse_line(line_connecting(esk1_0,esk2_0)))
| unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
( unequally_directed_lines(esk3_0,reverse_line(line_connecting(esk1_0,esk2_0)))
| unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0)) ),
inference(ef,[status(thm)],[c_0_45]) ).
cnf(c_0_47,negated_conjecture,
( unequally_directed_lines(reverse_line(line_connecting(esk1_0,esk2_0)),X1)
| unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0))
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0))
| unequally_directed_lines(esk3_0,X1)
| ~ unequally_directed_lines(reverse_line(line_connecting(esk1_0,esk2_0)),reverse_line(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_47]) ).
cnf(c_0_49,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(esk1_0,esk2_0))
| unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_47]) ).
fof(c_0_50,plain,
! [X2] : ~ unequally_directed_lines(X2,X2),
inference(fof_simplification,[status(thm)],[oag5]) ).
cnf(c_0_51,negated_conjecture,
( unequally_directed_lines(esk3_0,reverse_line(X1))
| unequally_directed_lines(esk3_0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_49]),c_0_45]) ).
fof(c_0_52,plain,
! [X29] : ~ unequally_directed_lines(X29,X29),
inference(variable_rename,[status(thm)],[c_0_50]) ).
cnf(c_0_53,negated_conjecture,
( unequally_directed_lines(reverse_line(X1),X2)
| unequally_directed_lines(esk3_0,X1)
| unequally_directed_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_54,plain,
~ unequally_directed_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( unequally_directed_lines(reverse_line(X1),X2)
| unequally_directed_lines(esk3_0,X3)
| unequally_directed_lines(esk3_0,X1)
| unequally_directed_lines(X3,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_53]) ).
cnf(c_0_56,negated_conjecture,
( unequally_directed_lines(X1,reverse_line(X2))
| unequally_directed_lines(esk3_0,X2)
| unequally_directed_lines(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,negated_conjecture,
( unequally_directed_lines(esk3_0,line_connecting(X1,X2))
| unequally_directed_lines(esk3_0,line_connecting(X2,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_56]) ).
cnf(c_0_58,negated_conjecture,
unequally_directed_lines(esk3_0,line_connecting(X1,X1)),
inference(ef,[status(thm)],[c_0_57]) ).
cnf(c_0_59,negated_conjecture,
( unequally_directed_lines(line_connecting(X1,X1),X2)
| unequally_directed_lines(esk3_0,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_58]) ).
cnf(c_0_60,negated_conjecture,
~ unequally_directed_lines(esk3_0,reverse_line(line_connecting(X1,X1))),
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_61,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_59]),c_0_60]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO254+1 : TPTP v8.1.2. Bugfixed v6.4.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n021.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 23:21:00 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 0.21/0.64 % Version : CSE_E---1.5
% 0.21/0.64 % Problem : theBenchmark.p
% 0.21/0.64 % Proof found
% 0.21/0.64 % SZS status Theorem for theBenchmark.p
% 0.21/0.64 % SZS output start Proof
% See solution above
% 0.55/0.64 % Total time : 0.042000 s
% 0.55/0.64 % SZS output end Proof
% 0.55/0.64 % Total time : 0.046000 s
%------------------------------------------------------------------------------