TSTP Solution File: GEO222+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO222+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 22:47:15 EDT 2023
% Result : Theorem 0.58s 0.63s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 62 ( 18 unt; 18 typ; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 100 ( 40 ~; 44 |; 9 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 16 >; 14 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 87 ( 6 sgn; 48 !; 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,
point: $i > $o ).
tff(decl_32,type,
line: $i > $o ).
tff(decl_33,type,
equal_points: ( $i * $i ) > $o ).
tff(decl_34,type,
equal_lines: ( $i * $i ) > $o ).
tff(decl_35,type,
parallel_lines: ( $i * $i ) > $o ).
tff(decl_36,type,
incident_point_and_line: ( $i * $i ) > $o ).
tff(decl_37,type,
orthogonal_lines: ( $i * $i ) > $o ).
tff(decl_38,type,
esk1_0: $i ).
tff(decl_39,type,
esk2_0: $i ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(couo1,axiom,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(con,conjecture,
! [X9,X6] : parallel_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(a3,axiom,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).
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(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(c_0_9,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(c_0_10,plain,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[couo1]) ).
fof(c_0_11,plain,
! [X58,X59] : ~ unorthogonal_lines(orthogonal_through_point(X59,X58),X59),
inference(variable_rename,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X53,X54] :
( convergent_lines(X53,X54)
| unorthogonal_lines(X53,X54) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(c_0_13,plain,
! [X71,X72,X73] :
( unorthogonal_lines(X71,X72)
| unorthogonal_lines(X71,X73)
| ~ convergent_lines(X72,X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])]) ).
cnf(c_0_14,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_16,negated_conjecture,
~ ! [X9,X6] : parallel_lines(X6,orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_17,plain,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_18,plain,
! [X55,X56,X57] :
( ( convergent_lines(X56,X57)
| convergent_lines(X55,X57)
| ~ convergent_lines(X55,X56)
| ~ unorthogonal_lines(X55,X56) )
& ( unorthogonal_lines(X56,X57)
| convergent_lines(X55,X57)
| ~ convergent_lines(X55,X56)
| ~ unorthogonal_lines(X55,X56) )
& ( convergent_lines(X56,X57)
| unorthogonal_lines(X55,X57)
| ~ convergent_lines(X55,X56)
| ~ unorthogonal_lines(X55,X56) )
& ( unorthogonal_lines(X56,X57)
| unorthogonal_lines(X55,X57)
| ~ convergent_lines(X55,X56)
| ~ unorthogonal_lines(X55,X56) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
cnf(c_0_19,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_21,negated_conjecture,
~ parallel_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_16])])]) ).
fof(c_0_22,plain,
! [X86,X87] :
( ( ~ parallel_lines(X86,X87)
| ~ convergent_lines(X86,X87) )
& ( convergent_lines(X86,X87)
| parallel_lines(X86,X87) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
fof(c_0_23,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(c_0_24,plain,
! [X41,X42,X43] :
( ~ convergent_lines(X41,X42)
| distinct_lines(X42,X43)
| convergent_lines(X41,X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
cnf(c_0_25,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( unorthogonal_lines(X1,orthogonal_through_point(X2,X3))
| unorthogonal_lines(X1,X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
~ parallel_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( convergent_lines(X1,X2)
| parallel_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_29,plain,
! [X13] : ~ convergent_lines(X13,X13),
inference(variable_rename,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( unorthogonal_lines(orthogonal_through_point(X1,X2),X3)
| unorthogonal_lines(X4,X1)
| unorthogonal_lines(X4,X3)
| ~ convergent_lines(X4,orthogonal_through_point(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
convergent_lines(esk2_0,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_33,plain,
! [X44,X45] :
( ~ distinct_lines(X44,X45)
| convergent_lines(X44,X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
cnf(c_0_34,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( convergent_lines(orthogonal_through_point(X1,X2),X3)
| distinct_lines(X1,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
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,orthogonal_through_point(esk2_0,esk1_0))
| unorthogonal_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
distinct_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_40,negated_conjecture,
unorthogonal_lines(esk2_0,orthogonal_through_point(esk2_0,esk1_0)),
inference(spm,[status(thm)],[c_0_14,c_0_36]) ).
cnf(c_0_41,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,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_39,c_0_40]),c_0_41])]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_42]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO222+3 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 23:10:31 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.42/0.60 start to proof: theBenchmark
% 0.58/0.63 % Version : CSE_E---1.5
% 0.58/0.63 % Problem : theBenchmark.p
% 0.58/0.63 % Proof found
% 0.58/0.63 % SZS status Theorem for theBenchmark.p
% 0.58/0.63 % SZS output start Proof
% See solution above
% 0.58/0.63 % Total time : 0.020000 s
% 0.58/0.63 % SZS output end Proof
% 0.58/0.63 % Total time : 0.024000 s
%------------------------------------------------------------------------------