TSTP Solution File: GEO219+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO219+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 : n028.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 22:47:13 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 27
% Syntax : Number of formulae : 63 ( 13 unt; 19 typ; 0 def)
% Number of atoms : 112 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 118 ( 50 ~; 47 |; 11 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn; 44 !; 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 ).
tff(decl_40,type,
esk3_0: $i ).
fof(a5,axiom,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(con,conjecture,
! [X6,X7,X8] :
( ( orthogonal_lines(X6,X7)
& parallel_lines(X6,X8) )
=> orthogonal_lines(X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(cotno1,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+4.ax',cotno1) ).
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(a3,axiom,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(c_0_8,plain,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a5]) ).
fof(c_0_9,negated_conjecture,
~ ! [X6,X7,X8] :
( ( orthogonal_lines(X6,X7)
& parallel_lines(X6,X8) )
=> orthogonal_lines(X7,X8) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(c_0_10,plain,
! [X90,X91] :
( ( ~ orthogonal_lines(X90,X91)
| ~ unorthogonal_lines(X90,X91) )
& ( unorthogonal_lines(X90,X91)
| orthogonal_lines(X90,X91) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])]) ).
fof(c_0_11,negated_conjecture,
( orthogonal_lines(esk1_0,esk2_0)
& parallel_lines(esk1_0,esk3_0)
& ~ orthogonal_lines(esk2_0,esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_12,plain,
( ~ orthogonal_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,negated_conjecture,
orthogonal_lines(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X53,X54] :
( convergent_lines(X53,X54)
| unorthogonal_lines(X53,X54) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(c_0_15,plain,
! [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) ) ),
inference(fof_simplification,[status(thm)],[cotno1]) ).
fof(c_0_16,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_17,negated_conjecture,
~ unorthogonal_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_20,plain,
! [X68,X69,X70] :
( ( convergent_lines(X68,X70)
| convergent_lines(X68,X69)
| ~ convergent_lines(X69,X70)
| ~ unorthogonal_lines(X69,X70) )
& ( unorthogonal_lines(X68,X70)
| convergent_lines(X68,X69)
| ~ convergent_lines(X69,X70)
| ~ unorthogonal_lines(X69,X70) )
& ( convergent_lines(X68,X70)
| unorthogonal_lines(X68,X69)
| ~ convergent_lines(X69,X70)
| ~ unorthogonal_lines(X69,X70) )
& ( unorthogonal_lines(X68,X70)
| unorthogonal_lines(X68,X69)
| ~ convergent_lines(X69,X70)
| ~ unorthogonal_lines(X69,X70) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
cnf(c_0_21,negated_conjecture,
~ orthogonal_lines(esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,plain,
( unorthogonal_lines(X1,X2)
| orthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_23,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_24,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,negated_conjecture,
convergent_lines(esk1_0,esk2_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_26,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_19])]) ).
fof(c_0_27,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
cnf(c_0_28,plain,
( convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
unorthogonal_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( convergent_lines(esk1_0,X1)
| distinct_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( ~ parallel_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
parallel_lines(esk1_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_34,plain,
! [X13] : ~ convergent_lines(X13,X13),
inference(variable_rename,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( convergent_lines(X1,esk3_0)
| convergent_lines(X1,esk2_0)
| ~ convergent_lines(esk2_0,esk3_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
( convergent_lines(esk1_0,X1)
| convergent_lines(esk2_0,X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
~ convergent_lines(esk1_0,esk3_0),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( convergent_lines(X1,esk2_0)
| convergent_lines(X1,esk3_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]) ).
cnf(c_0_40,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_41,negated_conjecture,
convergent_lines(esk2_0,esk3_0),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( unorthogonal_lines(X1,esk2_0)
| convergent_lines(X1,esk3_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_29]),c_0_41])]) ).
cnf(c_0_43,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_42]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO219+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 22:45:56 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.017000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.019000 s
%------------------------------------------------------------------------------