TSTP Solution File: GEO077-4 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO077-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 22:45:57 EDT 2023
% Result : Unsatisfiable 0.54s 0.64s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 82 ( 36 unt; 19 typ; 0 def)
% Number of atoms : 188 ( 56 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 218 ( 93 ~; 125 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 57 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
line_from_to: ( $i * $i ) > $i ).
tff(decl_23,type,
on: ( $i * $i ) > $o ).
tff(decl_24,type,
point: $i > $o ).
tff(decl_25,type,
line: $i > $o ).
tff(decl_26,type,
point_1_on_line: $i > $i ).
tff(decl_27,type,
point_2_on_line: $i > $i ).
tff(decl_28,type,
point_not_on_line: $i > $i ).
tff(decl_29,type,
at_least_one_line: $i ).
tff(decl_30,type,
plane: $i > $o ).
tff(decl_31,type,
point_on_plane: $i > $i ).
tff(decl_32,type,
point_not_on_plane: $i > $i ).
tff(decl_33,type,
plane_for_points: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
collinear: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
common_point_on_planes: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
line_through_3_points: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
point1: $i ).
tff(decl_38,type,
point2: $i ).
tff(decl_39,type,
point3: $i ).
tff(decl_40,type,
a_line: $i ).
cnf(axiom_G1B,axiom,
( on(X1,line_from_to(X2,X1))
| X2 = X1
| ~ point(X2)
| ~ point(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1B) ).
cnf(point3,hypothesis,
point(point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3) ).
cnf(axiom_G1C,axiom,
( line(line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1C) ).
cnf(point2,hypothesis,
point(point2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2) ).
cnf(point2_not_point3,hypothesis,
point2 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_not_point3) ).
cnf(axiom_G1A,axiom,
( on(X1,line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1A) ).
cnf(axiom_G1D,axiom,
( X1 = X3
| X2 = X4
| ~ on(X1,X2)
| ~ on(X3,X2)
| ~ on(X1,X4)
| ~ on(X3,X4)
| ~ point(X1)
| ~ point(X3)
| ~ line(X2)
| ~ line(X4) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G1D) ).
cnf(axiom_G10B,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X2,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10B) ).
cnf(prove_points_noncollinear,negated_conjecture,
collinear(point1,point2,point3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_points_noncollinear) ).
cnf(point1,hypothesis,
point(point1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1) ).
cnf(point1_not_point3,hypothesis,
point1 != point3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point3) ).
cnf(point1_not_point2,hypothesis,
point1 != point2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_not_point2) ).
cnf(axiom_G10D,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| line(line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10D) ).
cnf(axiom_G10C,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X3,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10C) ).
cnf(axiom_G10A,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X1,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO003-0.ax',axiom_G10A) ).
cnf(point2_on_line,hypothesis,
on(point2,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point2_on_line) ).
cnf(line,hypothesis,
line(a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',line) ).
cnf(point1_on_line,hypothesis,
on(point1,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point1_on_line) ).
cnf(point3_not_on_line,hypothesis,
~ on(point3,a_line),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',point3_not_on_line) ).
cnf(c_0_19,axiom,
( on(X1,line_from_to(X2,X1))
| X2 = X1
| ~ point(X2)
| ~ point(X1) ),
axiom_G1B ).
cnf(c_0_20,hypothesis,
point(point3),
point3 ).
cnf(c_0_21,axiom,
( line(line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
axiom_G1C ).
cnf(c_0_22,hypothesis,
point(point2),
point2 ).
cnf(c_0_23,hypothesis,
( X1 = point3
| on(X1,line_from_to(point3,X1))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
point2 != point3,
point2_not_point3 ).
cnf(c_0_25,hypothesis,
( X1 = point2
| line(line_from_to(X1,point2))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
( on(X1,line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
axiom_G1A ).
cnf(c_0_27,axiom,
( X1 = X3
| X2 = X4
| ~ on(X1,X2)
| ~ on(X3,X2)
| ~ on(X1,X4)
| ~ on(X3,X4)
| ~ point(X1)
| ~ point(X3)
| ~ line(X2)
| ~ line(X4) ),
axiom_G1D ).
cnf(c_0_28,hypothesis,
on(point2,line_from_to(point3,point2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_24]) ).
cnf(c_0_29,hypothesis,
line(line_from_to(point3,point2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_20]),c_0_24]) ).
cnf(c_0_30,hypothesis,
( X1 = point2
| on(X1,line_from_to(X1,point2))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_31,hypothesis,
( X1 = line_from_to(point3,point2)
| X2 = point2
| ~ line(X1)
| ~ point(X2)
| ~ on(X2,line_from_to(point3,point2))
| ~ on(point2,X1)
| ~ on(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_22])]) ).
cnf(c_0_32,hypothesis,
on(point3,line_from_to(point3,point2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_24]) ).
cnf(c_0_33,hypothesis,
( X1 = point3
| on(X1,line_from_to(X1,point3))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_34,hypothesis,
( X1 = point3
| line(line_from_to(X1,point3))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_35,hypothesis,
( X1 = point2
| on(X1,line_from_to(point2,X1))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_36,hypothesis,
( X1 = line_from_to(point3,point2)
| ~ line(X1)
| ~ on(point2,X1)
| ~ on(point3,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_20])]),c_0_24]) ).
cnf(c_0_37,hypothesis,
on(point2,line_from_to(point2,point3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_24]) ).
cnf(c_0_38,hypothesis,
line(line_from_to(point2,point3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_22]),c_0_24]) ).
cnf(c_0_39,hypothesis,
on(point3,line_from_to(point2,point3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_24]) ).
cnf(c_0_40,hypothesis,
line_from_to(point3,point2) = line_from_to(point2,point3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]) ).
cnf(c_0_41,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X2,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10B ).
cnf(c_0_42,negated_conjecture,
collinear(point1,point2,point3),
prove_points_noncollinear ).
cnf(c_0_43,hypothesis,
point(point1),
point1 ).
cnf(c_0_44,hypothesis,
point1 != point3,
point1_not_point3 ).
cnf(c_0_45,hypothesis,
point1 != point2,
point1_not_point2 ).
cnf(c_0_46,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| line(line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10D ).
cnf(c_0_47,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X3,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10C ).
cnf(c_0_48,hypothesis,
( X1 = line_from_to(point2,point3)
| ~ line(X1)
| ~ on(point2,X1)
| ~ on(point3,X1) ),
inference(rw,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
on(point2,line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_20]),c_0_22]),c_0_43])]),c_0_24]),c_0_44]),c_0_45]) ).
cnf(c_0_50,negated_conjecture,
line(line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_42]),c_0_20]),c_0_22]),c_0_43])]),c_0_24]),c_0_44]),c_0_45]) ).
cnf(c_0_51,negated_conjecture,
on(point3,line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_42]),c_0_20]),c_0_22]),c_0_43])]),c_0_24]),c_0_44]),c_0_45]) ).
cnf(c_0_52,negated_conjecture,
line_from_to(point2,point3) = line_through_3_points(point1,point2,point3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51])]) ).
cnf(c_0_53,axiom,
( X1 = X2
| X1 = X3
| X2 = X3
| on(X1,line_through_3_points(X1,X2,X3))
| ~ point(X1)
| ~ point(X2)
| ~ point(X3)
| ~ collinear(X1,X2,X3) ),
axiom_G10A ).
cnf(c_0_54,hypothesis,
( X1 = line_through_3_points(point1,point2,point3)
| X2 = point2
| ~ line(X1)
| ~ point(X2)
| ~ on(X2,line_through_3_points(point1,point2,point3))
| ~ on(point2,X1)
| ~ on(X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_40]),c_0_40]),c_0_52]),c_0_52]) ).
cnf(c_0_55,negated_conjecture,
on(point1,line_through_3_points(point1,point2,point3)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_42]),c_0_20]),c_0_22]),c_0_43])]),c_0_24]),c_0_44]),c_0_45]) ).
cnf(c_0_56,negated_conjecture,
( X1 = line_through_3_points(point1,point2,point3)
| ~ line(X1)
| ~ on(point2,X1)
| ~ on(point1,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_43])]),c_0_45]) ).
cnf(c_0_57,hypothesis,
on(point2,a_line),
point2_on_line ).
cnf(c_0_58,hypothesis,
line(a_line),
line ).
cnf(c_0_59,hypothesis,
on(point1,a_line),
point1_on_line ).
cnf(c_0_60,hypothesis,
line_through_3_points(point1,point2,point3) = a_line,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59])]) ).
cnf(c_0_61,hypothesis,
~ on(point3,a_line),
point3_not_on_line ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_60]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO077-4 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n022.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 22:57:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.54/0.64 % Version : CSE_E---1.5
% 0.54/0.64 % Problem : theBenchmark.p
% 0.54/0.64 % Proof found
% 0.54/0.64 % SZS status Theorem for theBenchmark.p
% 0.54/0.64 % SZS output start Proof
% See solution above
% 0.54/0.64 % Total time : 0.067000 s
% 0.54/0.64 % SZS output end Proof
% 0.54/0.64 % Total time : 0.071000 s
%------------------------------------------------------------------------------