TSTP Solution File: GEO034-2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO034-2 : 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 : n027.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 22:45:39 EDT 2023
% Result : Unsatisfiable 2.36s 2.52s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 27
% Syntax : Number of formulae : 92 ( 40 unt; 14 typ; 0 def)
% Number of atoms : 168 ( 43 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 165 ( 75 ~; 90 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 7 >; 25 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-6 aty)
% Number of variables : 171 ( 24 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(decl_23,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(decl_24,type,
between: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
inner_pasch: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_26,type,
lower_dimension_point_1: $i ).
tff(decl_27,type,
lower_dimension_point_2: $i ).
tff(decl_28,type,
lower_dimension_point_3: $i ).
tff(decl_29,type,
euclid1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_30,type,
euclid2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_31,type,
continuous: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
u: $i ).
tff(decl_33,type,
v: $i ).
tff(decl_34,type,
w: $i ).
tff(decl_35,type,
x: $i ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
cnf(inner_pasch2,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(inner_pasch1,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(transitivity_for_equidistance,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(outer_five_segment,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(w_to_v_equals_w_to_x,hypothesis,
equidistant(w,v,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_to_v_equals_w_to_x) ).
cnf(u_to_v_equals_u_to_x,hypothesis,
equidistant(u,v,u,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u_to_x) ).
cnf(prove_v_is_x,negated_conjecture,
v != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_is_x) ).
cnf(c_0_13,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_14,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2 ).
cnf(c_0_15,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_16,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_17,plain,
( inner_pasch(X1,X2,X3,X1,X4) = X1
| ~ between(X4,X1,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_19,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_20,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1 ).
cnf(c_0_22,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_23,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_24,hypothesis,
( inner_pasch(v,X1,w,v,u) = v
| ~ between(v,X1,w) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,plain,
( inner_pasch(X1,X2,X3,X4,X2) = X2
| ~ between(X2,X4,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_27,axiom,
( X1 = X2
| equidistant(X5,X7,X6,X8)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X2,X5,X4,X6)
| ~ equidistant(X1,X7,X3,X8)
| ~ equidistant(X2,X7,X4,X8)
| ~ between(X1,X2,X5)
| ~ between(X3,X4,X6) ),
outer_five_segment ).
cnf(c_0_28,hypothesis,
equidistant(w,v,w,x),
w_to_v_equals_w_to_x ).
cnf(c_0_29,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,hypothesis,
inner_pasch(v,w,w,v,u) = v,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( inner_pasch(X1,X2,X3,X3,X2) = X2
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_32,hypothesis,
( X1 = w
| equidistant(X2,v,X3,x)
| ~ between(X4,w,X3)
| ~ between(X1,w,X2)
| ~ equidistant(w,X2,w,X3)
| ~ equidistant(X1,v,X4,x)
| ~ equidistant(X1,w,X4,w) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_34,hypothesis,
between(w,v,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_18]),c_0_25])]) ).
cnf(c_0_35,plain,
inner_pasch(X1,X2,extension(X1,X2,X3,X4),extension(X1,X2,X3,X4),X2) = X2,
inference(spm,[status(thm)],[c_0_31,c_0_19]) ).
cnf(c_0_36,hypothesis,
( X1 = w
| equidistant(X2,v,X2,x)
| ~ between(X3,w,X2)
| ~ between(X1,w,X2)
| ~ equidistant(X1,v,X3,x)
| ~ equidistant(X1,w,X3,w) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,hypothesis,
equidistant(u,v,u,x),
u_to_v_equals_u_to_x ).
cnf(c_0_38,hypothesis,
( inner_pasch(X1,w,u,v,w) = w
| ~ between(X1,w,u) ),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_39,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_35]),c_0_25]),c_0_19])]) ).
cnf(c_0_40,plain,
equidistant(X1,X1,X2,X2),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_41,hypothesis,
( w = u
| equidistant(X1,v,X1,x)
| ~ between(u,w,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33])]) ).
cnf(c_0_42,hypothesis,
inner_pasch(extension(u,w,X1,X2),w,u,v,w) = w,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
( equidistant(X1,X2,X3,X3)
| ~ equidistant(X4,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_40]) ).
cnf(c_0_44,hypothesis,
( w = u
| X1 = w
| equidistant(X2,v,X2,x)
| ~ between(u,w,X1)
| ~ between(X1,w,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_41]),c_0_33])]) ).
cnf(c_0_45,hypothesis,
between(v,w,extension(u,w,X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_42]),c_0_34]),c_0_39])]) ).
cnf(c_0_46,hypothesis,
( equidistant(X1,X2,u,x)
| ~ equidistant(u,v,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_47,hypothesis,
( equidistant(X1,X2,w,x)
| ~ equidistant(w,v,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_48,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_49,hypothesis,
( w = u
| X1 = w
| equidistant(v,x,X2,X2)
| ~ between(u,w,X1)
| ~ between(X1,w,v) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
v != x,
prove_v_is_x ).
cnf(c_0_51,hypothesis,
inner_pasch(v,w,extension(u,w,X1,X2),extension(u,w,X1,X2),w) = w,
inference(spm,[status(thm)],[c_0_31,c_0_45]) ).
cnf(c_0_52,hypothesis,
equidistant(v,u,u,x),
inference(spm,[status(thm)],[c_0_46,c_0_23]) ).
cnf(c_0_53,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_54,hypothesis,
equidistant(extension(X1,X2,w,v),X2,w,x),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,hypothesis,
( w = u
| X1 = w
| ~ between(u,w,X1)
| ~ between(X1,w,v) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_49]),c_0_50]) ).
cnf(c_0_56,hypothesis,
between(extension(u,w,X1,X2),w,v),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_51]),c_0_25]),c_0_45])]) ).
cnf(c_0_57,hypothesis,
equidistant(u,x,u,v),
inference(spm,[status(thm)],[c_0_29,c_0_52]) ).
cnf(c_0_58,hypothesis,
equidistant(w,x,extension(X1,X2,w,v),X2),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,hypothesis,
( extension(u,w,X1,X2) = w
| w = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_19]),c_0_56])]) ).
cnf(c_0_60,hypothesis,
( X1 = u
| equidistant(X2,v,X3,x)
| ~ between(X4,u,X3)
| ~ between(X1,u,X2)
| ~ equidistant(u,X2,u,X3)
| ~ equidistant(X1,v,X4,x)
| ~ equidistant(X1,u,X4,u) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_61,hypothesis,
equidistant(u,v,x,u),
inference(spm,[status(thm)],[c_0_29,c_0_57]) ).
cnf(c_0_62,hypothesis,
( w = u
| equidistant(w,x,w,w) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_63,hypothesis,
( X1 = u
| equidistant(X2,v,X2,x)
| ~ between(X3,u,X2)
| ~ between(X1,u,X2)
| ~ equidistant(X1,v,X3,x)
| ~ equidistant(X1,u,X3,u) ),
inference(spm,[status(thm)],[c_0_60,c_0_33]) ).
cnf(c_0_64,hypothesis,
equidistant(x,u,v,u),
inference(spm,[status(thm)],[c_0_29,c_0_61]) ).
cnf(c_0_65,hypothesis,
( w = u
| ~ between(u,w,x) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_41]),c_0_50]) ).
cnf(c_0_66,hypothesis,
( w = u
| x = w ),
inference(spm,[status(thm)],[c_0_15,c_0_62]) ).
cnf(c_0_67,hypothesis,
( x = u
| equidistant(X1,v,X1,x)
| ~ between(v,u,X1)
| ~ between(x,u,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_23]),c_0_64])]) ).
cnf(c_0_68,hypothesis,
w = u,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_25])]) ).
cnf(c_0_69,plain,
( inner_pasch(X1,X2,X1,X1,X3) = X1
| ~ between(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_25]) ).
cnf(c_0_70,hypothesis,
( x = u
| equidistant(v,x,X1,X1)
| ~ between(v,u,v)
| ~ between(x,u,v) ),
inference(spm,[status(thm)],[c_0_43,c_0_67]) ).
cnf(c_0_71,hypothesis,
between(u,v,u),
inference(rw,[status(thm)],[c_0_34,c_0_68]) ).
cnf(c_0_72,plain,
inner_pasch(X1,X1,X1,X1,X2) = X1,
inference(spm,[status(thm)],[c_0_69,c_0_25]) ).
cnf(c_0_73,hypothesis,
( x = u
| ~ between(v,u,v)
| ~ between(x,u,v) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_70]),c_0_50]) ).
cnf(c_0_74,hypothesis,
v = u,
inference(spm,[status(thm)],[c_0_13,c_0_71]) ).
cnf(c_0_75,plain,
between(X1,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_72]),c_0_25]),c_0_25])]) ).
cnf(c_0_76,hypothesis,
x = u,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74]),c_0_74]),c_0_75]),c_0_74]),c_0_25])]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_74]),c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GEO034-2 : 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
% 0.13/0.35 % Computer : n027.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 23:00:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.22/0.58 start to proof: theBenchmark
% 2.36/2.52 % Version : CSE_E---1.5
% 2.36/2.52 % Problem : theBenchmark.p
% 2.36/2.52 % Proof found
% 2.36/2.52 % SZS status Theorem for theBenchmark.p
% 2.36/2.52 % SZS output start Proof
% See solution above
% 2.36/2.53 % Total time : 1.899000 s
% 2.36/2.53 % SZS output end Proof
% 2.36/2.53 % Total time : 1.902000 s
%------------------------------------------------------------------------------