TSTP Solution File: GEO047-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO047-2 : 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 : n023.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 22:45:45 EDT 2023
% Result : Unsatisfiable 2.37s 2.47s
% Output : CNFRefutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 26
% Syntax : Number of formulae : 66 ( 27 unt; 14 typ; 0 def)
% Number of atoms : 109 ( 26 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 109 ( 52 ~; 57 |; 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 : 132 ( 14 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(w_between_u_and_x,hypothesis,
between(u,w,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_between_u_and_x) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
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(prove_v_between_u_and_x,negated_conjecture,
~ between(u,v,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v_between_u_and_x) ).
cnf(c_0_12,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_13,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2 ).
cnf(c_0_14,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_15,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_16,plain,
( inner_pasch(X1,X2,X3,X1,X4) = X1
| ~ between(X4,X1,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,hypothesis,
between(u,w,x),
w_between_u_and_x ).
cnf(c_0_18,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_19,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
( inner_pasch(w,X1,x,w,u) = w
| ~ between(w,X1,x) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_23,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1 ).
cnf(c_0_24,hypothesis,
inner_pasch(w,x,x,w,u) = w,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
( inner_pasch(v,X1,w,v,u) = v
| ~ between(v,X1,w) ),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_26,hypothesis,
between(x,w,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_21])]) ).
cnf(c_0_27,hypothesis,
inner_pasch(v,w,w,v,u) = v,
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_28,hypothesis,
( inner_pasch(w,X1,u,w,x) = w
| ~ between(w,X1,u) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_29,hypothesis,
between(w,v,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_27]),c_0_22]),c_0_21])]) ).
cnf(c_0_30,plain,
( inner_pasch(X1,X2,X3,X4,X2) = X2
| ~ between(X2,X4,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_31,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_32,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_33,hypothesis,
inner_pasch(w,v,u,w,x) = w,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
( inner_pasch(X1,X2,X3,X3,X2) = X2
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_35,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,hypothesis,
between(v,w,x),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_33]),c_0_26]),c_0_29])]) ).
cnf(c_0_37,plain,
inner_pasch(X1,X2,extension(X1,X2,X3,X4),extension(X1,X2,X3,X4),X2) = X2,
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_38,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_39,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_40,hypothesis,
( inner_pasch(X1,v,x,w,v) = v
| ~ between(X1,v,x) ),
inference(spm,[status(thm)],[c_0_30,c_0_36]) ).
cnf(c_0_41,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_13,c_0_37]),c_0_21]),c_0_18])]) ).
cnf(c_0_42,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_38,c_0_39]) ).
cnf(c_0_43,hypothesis,
inner_pasch(extension(x,v,X1,X2),v,x,w,v) = v,
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
( X1 = X2
| equidistant(extension(X3,X2,X2,X4),X5,X4,X5)
| ~ between(X1,X2,extension(X3,X2,X2,X4))
| ~ between(X6,X2,X4)
| ~ equidistant(X1,X5,X6,X5)
| ~ equidistant(X1,X2,X6,X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_15]) ).
cnf(c_0_45,hypothesis,
between(w,v,extension(x,v,X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_43]),c_0_36]),c_0_41])]) ).
cnf(c_0_46,hypothesis,
( w = v
| equidistant(extension(x,v,v,X1),X2,X1,X2)
| ~ between(X3,v,X1)
| ~ equidistant(w,v,X3,v)
| ~ equidistant(w,X2,X3,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_47,hypothesis,
( w = v
| equidistant(extension(x,v,v,u),X1,u,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_29]),c_0_39]),c_0_39])]) ).
cnf(c_0_48,hypothesis,
( extension(x,v,v,u) = u
| w = v ),
inference(spm,[status(thm)],[c_0_14,c_0_47]) ).
cnf(c_0_49,negated_conjecture,
~ between(u,v,x),
prove_v_between_u_and_x ).
cnf(c_0_50,hypothesis,
w = v,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_48]),c_0_49]) ).
cnf(c_0_51,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_50]),c_0_49]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GEO047-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue Aug 29 21:13:09 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.18/0.56 start to proof: theBenchmark
% 2.37/2.47 % Version : CSE_E---1.5
% 2.37/2.47 % Problem : theBenchmark.p
% 2.37/2.47 % Proof found
% 2.37/2.47 % SZS status Theorem for theBenchmark.p
% 2.37/2.47 % SZS output start Proof
% See solution above
% 2.37/2.47 % Total time : 1.901000 s
% 2.37/2.47 % SZS output end Proof
% 2.37/2.47 % Total time : 1.904000 s
%------------------------------------------------------------------------------