TSTP Solution File: GEO068-2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO068-2 : 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 : n019.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 22:45:54 EDT 2023
% Result : Unsatisfiable 99.10s 99.25s
% Output : CNFRefutation 99.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 35
% Syntax : Number of formulae : 157 ( 50 unt; 17 typ; 0 def)
% Number of atoms : 362 ( 139 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 338 ( 116 ~; 222 |; 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 : 35 ( 8 >; 27 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-6 aty)
% Number of variables : 221 ( 18 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,
colinear: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
u: $i ).
tff(decl_34,type,
v: $i ).
tff(decl_35,type,
u1: $i ).
tff(decl_36,type,
v1: $i ).
tff(decl_37,type,
w: $i ).
tff(decl_38,type,
w1: $i ).
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(v_to_w_equals_v1_to_w1,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',reflexivity_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(u_to_w_equals_u1_to_w1,hypothesis,
equidistant(u,w,u1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_w_equals_u1_to_w1) ).
cnf(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
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(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
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(colinearity4,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
cnf(uvw_colinear,hypothesis,
colinear(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uvw_colinear) ).
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(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(prove_u1v1w1_colinear,negated_conjecture,
~ colinear(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_u1v1w1_colinear) ).
cnf(colinearity1,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity1) ).
cnf(colinearity3,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity3) ).
cnf(colinearity2,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-1.ax',colinearity2) ).
cnf(c_0_18,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_19,hypothesis,
equidistant(v,w,v1,w1),
v_to_w_equals_v1_to_w1 ).
cnf(c_0_20,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_21,hypothesis,
( equidistant(X1,X2,v1,w1)
| ~ equidistant(v,w,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_23,hypothesis,
equidistant(w,v,v1,w1),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_24,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_25,hypothesis,
equidistant(v1,w1,v,w),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_27,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_28,hypothesis,
equidistant(u,w,u1,w1),
u_to_w_equals_u1_to_w1 ).
cnf(c_0_29,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1 ).
cnf(c_0_30,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_31,hypothesis,
( equidistant(X1,X2,v,w)
| ~ equidistant(v1,w1,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_32,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,hypothesis,
( equidistant(X1,X2,u1,w1)
| ~ equidistant(u,w,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_28]) ).
cnf(c_0_34,hypothesis,
( equidistant(X1,X2,u1,v1)
| ~ equidistant(u,v,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_35,hypothesis,
( X1 = v1
| equidistant(X2,w1,X3,w)
| ~ between(X4,v,X3)
| ~ between(X1,v1,X2)
| ~ equidistant(v1,X2,v,X3)
| ~ equidistant(X1,w1,X4,w)
| ~ equidistant(X1,v1,X4,v) ),
inference(spm,[status(thm)],[c_0_30,c_0_25]) ).
cnf(c_0_36,hypothesis,
equidistant(X1,extension(X2,X1,v1,w1),v,w),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,hypothesis,
equidistant(w,u,u1,w1),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_38,hypothesis,
equidistant(v,u,u1,v1),
inference(spm,[status(thm)],[c_0_34,c_0_20]) ).
cnf(c_0_39,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_40,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_41,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2 ).
cnf(c_0_42,axiom,
( between(X1,X2,X3)
| between(X2,X3,X1)
| between(X3,X1,X2)
| ~ colinear(X1,X2,X3) ),
colinearity4 ).
cnf(c_0_43,hypothesis,
colinear(u,v,w),
uvw_colinear ).
cnf(c_0_44,hypothesis,
( X1 = v1
| equidistant(extension(X2,v1,v1,w1),w1,w,w)
| ~ between(X1,v1,extension(X2,v1,v1,w1))
| ~ between(X3,v,w)
| ~ equidistant(X1,w1,X3,w)
| ~ equidistant(X1,v1,X3,v) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,hypothesis,
equidistant(u1,w1,u,w),
inference(spm,[status(thm)],[c_0_22,c_0_37]) ).
cnf(c_0_46,hypothesis,
equidistant(u1,v1,u,v),
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_47,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1 ).
cnf(c_0_48,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_49,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_50,plain,
( inner_pasch(X1,X2,X3,X1,X4) = X1
| ~ between(X4,X1,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,hypothesis,
( between(u,v,w)
| between(v,w,u)
| between(w,u,v) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,hypothesis,
( v1 = u1
| equidistant(extension(X1,v1,v1,w1),w1,w,w)
| ~ between(u1,v1,extension(X1,v1,v1,w1))
| ~ between(u,v,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]) ).
cnf(c_0_53,plain,
( inner_pasch(X1,X2,X3,X4,X2) = X2
| ~ between(X2,X4,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_47]) ).
cnf(c_0_54,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,hypothesis,
( inner_pasch(u,X1,v,u,w) = u
| between(v,w,u)
| between(u,v,w)
| ~ between(u,X1,v) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,hypothesis,
equidistant(v,w,w1,v1),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_57,hypothesis,
equidistant(v1,w1,w,v),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_58,hypothesis,
( extension(X1,v1,v1,w1) = w1
| v1 = u1
| ~ between(u1,v1,extension(X1,v1,v1,w1))
| ~ between(u,v,w) ),
inference(spm,[status(thm)],[c_0_39,c_0_52]) ).
cnf(c_0_59,plain,
( inner_pasch(X1,X2,X3,X3,X2) = X2
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_60,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| between(u,v,w)
| between(v,w,u) ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_61,hypothesis,
equidistant(w1,v1,w,v),
inference(spm,[status(thm)],[c_0_22,c_0_56]) ).
cnf(c_0_62,hypothesis,
( equidistant(X1,X2,w,v)
| ~ equidistant(v1,w1,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_57]) ).
cnf(c_0_63,hypothesis,
( extension(u1,v1,v1,w1) = w1
| v1 = u1
| ~ between(u,v,w) ),
inference(spm,[status(thm)],[c_0_58,c_0_48]) ).
cnf(c_0_64,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| inner_pasch(v,w,u,u,w) = w
| between(u,v,w) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,negated_conjecture,
~ colinear(u1,v1,w1),
prove_u1v1w1_colinear ).
cnf(c_0_66,axiom,
( colinear(X1,X2,X3)
| ~ between(X1,X2,X3) ),
colinearity1 ).
cnf(c_0_67,hypothesis,
( X1 = w1
| equidistant(X2,v1,X3,v)
| ~ between(X4,w,X3)
| ~ between(X1,w1,X2)
| ~ equidistant(w1,X2,w,X3)
| ~ equidistant(X1,v1,X4,v)
| ~ equidistant(X1,w1,X4,w) ),
inference(spm,[status(thm)],[c_0_30,c_0_61]) ).
cnf(c_0_68,hypothesis,
equidistant(X1,extension(X2,X1,v1,w1),w,v),
inference(spm,[status(thm)],[c_0_62,c_0_32]) ).
cnf(c_0_69,axiom,
( colinear(X2,X3,X1)
| ~ between(X1,X2,X3) ),
colinearity3 ).
cnf(c_0_70,hypothesis,
( inner_pasch(v,w,u,u,w) = w
| inner_pasch(u,v,v,u,w) = u
| extension(u1,v1,v1,w1) = w1
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
~ between(u1,v1,w1),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,hypothesis,
( inner_pasch(w,u,v,v,u) = u
| between(v,w,u)
| between(u,v,w) ),
inference(spm,[status(thm)],[c_0_59,c_0_51]) ).
cnf(c_0_73,hypothesis,
( X1 = w1
| equidistant(extension(X2,w1,v1,w1),v1,v,v)
| ~ between(X1,w1,extension(X2,w1,v1,w1))
| ~ between(X3,w,v)
| ~ equidistant(X1,v1,X3,v)
| ~ equidistant(X1,w1,X3,w) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,negated_conjecture,
~ between(w1,u1,v1),
inference(spm,[status(thm)],[c_0_65,c_0_69]) ).
cnf(c_0_75,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| inner_pasch(v,w,u,u,w) = w
| v1 = u1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_70]),c_0_71]) ).
cnf(c_0_76,hypothesis,
( inner_pasch(w,u,v,v,u) = u
| inner_pasch(v,w,u,u,w) = w
| between(u,v,w) ),
inference(spm,[status(thm)],[c_0_59,c_0_72]) ).
cnf(c_0_77,hypothesis,
( w1 = u1
| equidistant(extension(X1,w1,v1,w1),v1,v,v)
| ~ between(u1,w1,extension(X1,w1,v1,w1))
| ~ between(u,w,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_45]),c_0_46])]) ).
cnf(c_0_78,negated_conjecture,
( inner_pasch(v,w,u,u,w) = w
| inner_pasch(u,v,v,u,w) = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_54])]) ).
cnf(c_0_79,plain,
( X1 = X2
| equidistant(X3,X4,X5,X4)
| ~ between(X6,X2,X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X2,X3,X2,X5)
| ~ equidistant(X1,X4,X6,X4)
| ~ equidistant(X1,X2,X6,X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_80,plain,
equidistant(X1,extension(X2,X1,X3,X4),X4,X3),
inference(spm,[status(thm)],[c_0_22,c_0_32]) ).
cnf(c_0_81,hypothesis,
( inner_pasch(v,w,u,u,w) = w
| inner_pasch(w,u,v,v,u) = u
| extension(u1,v1,v1,w1) = w1
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_63,c_0_76]) ).
cnf(c_0_82,hypothesis,
( extension(X1,w1,v1,w1) = v1
| w1 = u1
| ~ between(u1,w1,extension(X1,w1,v1,w1))
| ~ between(u,w,v) ),
inference(spm,[status(thm)],[c_0_39,c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( inner_pasch(u,v,v,u,w) = u
| between(u,w,v)
| ~ between(v,w,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_78]),c_0_54])]) ).
cnf(c_0_84,plain,
( X1 = X2
| equidistant(extension(X3,X2,X4,X2),X5,X4,X5)
| ~ between(X1,X2,extension(X3,X2,X4,X2))
| ~ between(X6,X2,X4)
| ~ equidistant(X1,X5,X6,X5)
| ~ equidistant(X1,X2,X6,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,hypothesis,
( inner_pasch(w,u,v,v,u) = u
| inner_pasch(v,w,u,u,w) = w
| v1 = u1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_81]),c_0_71]) ).
cnf(c_0_86,hypothesis,
( extension(u1,w1,v1,w1) = v1
| w1 = u1
| ~ between(u,w,v) ),
inference(spm,[status(thm)],[c_0_82,c_0_48]) ).
cnf(c_0_87,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| between(u,v,w)
| between(u,w,v) ),
inference(spm,[status(thm)],[c_0_83,c_0_60]) ).
cnf(c_0_88,plain,
( X1 = X2
| equidistant(extension(X3,X2,X4,X2),X5,X4,X5)
| ~ between(X1,X2,extension(X3,X2,X4,X2))
| ~ between(X1,X2,X4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_24]),c_0_24])]) ).
cnf(c_0_89,negated_conjecture,
( inner_pasch(v,w,u,u,w) = w
| inner_pasch(w,u,v,v,u) = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_85]),c_0_54])]) ).
cnf(c_0_90,plain,
inner_pasch(X1,X2,extension(X1,X2,X3,X4),extension(X1,X2,X3,X4),X2) = X2,
inference(spm,[status(thm)],[c_0_59,c_0_48]) ).
cnf(c_0_91,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| extension(u1,w1,v1,w1) = v1
| w1 = u1
| between(u,v,w) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_92,axiom,
( colinear(X3,X1,X2)
| ~ between(X1,X2,X3) ),
colinearity2 ).
cnf(c_0_93,plain,
( extension(X1,X2,X3,X2) = X3
| X4 = X2
| ~ between(X4,X2,extension(X1,X2,X3,X2))
| ~ between(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_88]) ).
cnf(c_0_94,negated_conjecture,
( inner_pasch(v,w,u,u,w) = w
| between(v,u,w)
| ~ between(w,u,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_89]),c_0_54])]) ).
cnf(c_0_95,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_41,c_0_90]),c_0_54]),c_0_48])]) ).
cnf(c_0_96,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| extension(u1,w1,v1,w1) = v1
| extension(u1,v1,v1,w1) = w1
| w1 = u1
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_63,c_0_91]) ).
cnf(c_0_97,negated_conjecture,
~ between(v1,w1,u1),
inference(spm,[status(thm)],[c_0_65,c_0_92]) ).
cnf(c_0_98,plain,
( extension(X1,X2,X3,X2) = X3
| X1 = X2
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_93,c_0_48]) ).
cnf(c_0_99,hypothesis,
( inner_pasch(v,w,u,u,w) = w
| between(u,v,w)
| between(v,u,w) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_51]),c_0_59]) ).
cnf(c_0_100,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| extension(u1,v1,v1,w1) = w1
| v1 = u1
| w1 = u1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_101,hypothesis,
( inner_pasch(v,w,u,u,w) = w
| extension(v,u,w,u) = w
| v = u
| between(u,v,w) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_102,hypothesis,
( inner_pasch(u,v,v,u,w) = u
| w1 = u1
| v1 = u1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_100]),c_0_71]) ).
cnf(c_0_103,hypothesis,
( inner_pasch(v,w,u,u,w) = w
| extension(v,u,w,u) = w
| extension(u1,v1,v1,w1) = w1
| v = u
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_63,c_0_101]) ).
cnf(c_0_104,negated_conjecture,
( inner_pasch(u,v,v,u,w) = u
| v1 = u1 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_102]),c_0_54])]) ).
cnf(c_0_105,hypothesis,
( inner_pasch(v,w,u,u,w) = w
| extension(v,u,w,u) = w
| v1 = u1
| v = u ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_103]),c_0_71]) ).
cnf(c_0_106,negated_conjecture,
inner_pasch(u,v,v,u,w) = u,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_104]),c_0_54])]) ).
cnf(c_0_107,negated_conjecture,
( inner_pasch(v,w,u,u,w) = w
| extension(v,u,w,u) = w
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_105]),c_0_54])]) ).
cnf(c_0_108,negated_conjecture,
( between(v,u,w)
| ~ between(w,u,v) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_106]),c_0_54])]) ).
cnf(c_0_109,hypothesis,
equidistant(u1,w1,w,u),
inference(spm,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_110,negated_conjecture,
( extension(v,u,w,u) = w
| v = u
| between(u,w,v)
| ~ between(v,w,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_107]),c_0_54])]) ).
cnf(c_0_111,hypothesis,
( between(v,w,u)
| between(u,v,w)
| between(v,u,w) ),
inference(spm,[status(thm)],[c_0_108,c_0_51]) ).
cnf(c_0_112,hypothesis,
equidistant(w,u,w1,u1),
inference(spm,[status(thm)],[c_0_22,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
( extension(v,u,w,u) = w
| v = u
| between(u,v,w)
| between(u,w,v) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_98]) ).
cnf(c_0_114,hypothesis,
equidistant(w1,u1,u,w),
inference(spm,[status(thm)],[c_0_22,c_0_112]) ).
cnf(c_0_115,hypothesis,
( extension(v,u,w,u) = w
| extension(u1,w1,v1,w1) = v1
| v = u
| w1 = u1
| between(u,v,w) ),
inference(spm,[status(thm)],[c_0_86,c_0_113]) ).
cnf(c_0_116,hypothesis,
( equidistant(X1,X2,u,w)
| ~ equidistant(w1,u1,X1,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_114]) ).
cnf(c_0_117,hypothesis,
( extension(u1,w1,v1,w1) = v1
| extension(v,u,w,u) = w
| extension(u1,v1,v1,w1) = w1
| w1 = u1
| v = u
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_63,c_0_115]) ).
cnf(c_0_118,hypothesis,
( X1 = u1
| equidistant(X2,w1,X3,w)
| ~ between(X4,u,X3)
| ~ between(X1,u1,X2)
| ~ equidistant(u1,X2,u,X3)
| ~ equidistant(X1,w1,X4,w)
| ~ equidistant(X1,u1,X4,u) ),
inference(spm,[status(thm)],[c_0_30,c_0_45]) ).
cnf(c_0_119,hypothesis,
equidistant(X1,extension(X2,X1,w1,u1),u,w),
inference(spm,[status(thm)],[c_0_116,c_0_32]) ).
cnf(c_0_120,hypothesis,
equidistant(u,v,v1,u1),
inference(spm,[status(thm)],[c_0_22,c_0_46]) ).
cnf(c_0_121,hypothesis,
( extension(u1,v1,v1,w1) = w1
| extension(v,u,w,u) = w
| v1 = u1
| v = u
| w1 = u1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_117]),c_0_97]) ).
cnf(c_0_122,hypothesis,
( X1 = u1
| equidistant(extension(X2,u1,w1,u1),w1,w,w)
| ~ between(X1,u1,extension(X2,u1,w1,u1))
| ~ between(X3,u,w)
| ~ equidistant(X1,w1,X3,w)
| ~ equidistant(X1,u1,X3,u) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,hypothesis,
equidistant(v1,u1,v,u),
inference(spm,[status(thm)],[c_0_22,c_0_120]) ).
cnf(c_0_124,hypothesis,
( extension(v,u,w,u) = w
| w1 = u1
| v = u
| v1 = u1 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_121]),c_0_71]) ).
cnf(c_0_125,hypothesis,
( v1 = u1
| equidistant(extension(X1,u1,w1,u1),w1,w,w)
| ~ between(v1,u1,extension(X1,u1,w1,u1))
| ~ between(v,u,w) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_25]),c_0_123])]) ).
cnf(c_0_126,negated_conjecture,
( extension(v,u,w,u) = w
| v1 = u1
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_124]),c_0_54])]) ).
cnf(c_0_127,hypothesis,
( extension(X1,u1,w1,u1) = w1
| v1 = u1
| ~ between(v1,u1,extension(X1,u1,w1,u1))
| ~ between(v,u,w) ),
inference(spm,[status(thm)],[c_0_39,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
( extension(v,u,w,u) = w
| v = u ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_126]),c_0_54])]) ).
cnf(c_0_129,hypothesis,
( extension(v1,u1,w1,u1) = w1
| v1 = u1
| ~ between(v,u,w) ),
inference(spm,[status(thm)],[c_0_127,c_0_48]) ).
cnf(c_0_130,negated_conjecture,
( v = u
| between(v,u,w) ),
inference(spm,[status(thm)],[c_0_48,c_0_128]) ).
cnf(c_0_131,negated_conjecture,
( extension(v1,u1,w1,u1) = w1
| v = u
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_132,negated_conjecture,
( v1 = u1
| v = u ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_131]),c_0_74]) ).
cnf(c_0_133,negated_conjecture,
v = u,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_132]),c_0_54])]) ).
cnf(c_0_134,plain,
( inner_pasch(X1,X2,X1,X1,X3) = X1
| ~ between(X1,X2,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_54]) ).
cnf(c_0_135,hypothesis,
equidistant(v1,u1,u,u),
inference(rw,[status(thm)],[c_0_123,c_0_133]) ).
cnf(c_0_136,plain,
inner_pasch(X1,X1,X1,X1,X2) = X1,
inference(spm,[status(thm)],[c_0_134,c_0_54]) ).
cnf(c_0_137,hypothesis,
v1 = u1,
inference(spm,[status(thm)],[c_0_39,c_0_135]) ).
cnf(c_0_138,plain,
between(X1,X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_136]),c_0_54]),c_0_54])]) ).
cnf(c_0_139,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_137]),c_0_138])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO068-2 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n019.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 21:07:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 99.10/99.25 % Version : CSE_E---1.5
% 99.10/99.25 % Problem : theBenchmark.p
% 99.10/99.25 % Proof found
% 99.10/99.25 % SZS status Theorem for theBenchmark.p
% 99.10/99.25 % SZS output start Proof
% See solution above
% 99.10/99.25 % Total time : 98.572000 s
% 99.10/99.25 % SZS output end Proof
% 99.10/99.25 % Total time : 98.580000 s
%------------------------------------------------------------------------------