TSTP Solution File: GEO049-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO049-2 : 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 : n008.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 22:45:46 EDT 2023
% Result : Unsatisfiable 142.40s 142.50s
% Output : CNFRefutation 142.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 30
% Syntax : Number of formulae : 95 ( 40 unt; 16 typ; 0 def)
% Number of atoms : 160 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 146 ( 65 ~; 81 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 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 : 14 ( 14 usr; 9 con; 0-6 aty)
% Number of variables : 211 ( 22 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,
u1: $i ).
tff(decl_35,type,
v1: $i ).
tff(decl_36,type,
w: $i ).
tff(decl_37,type,
w1: $i ).
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(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(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(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(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_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO002-0.ax',identity_for_betweeness) ).
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(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(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
cnf(prove_v1_between_u1_and_w1,negated_conjecture,
~ between(u1,v1,w1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_v1_between_u1_and_w1) ).
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,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_17,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_18,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2 ).
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_14,c_0_15]) ).
cnf(c_0_21,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1 ).
cnf(c_0_23,plain,
( between(X1,inner_pasch(X2,X3,extension(X4,X1,X5,X6),X1,X4),X2)
| ~ between(X2,X3,extension(X4,X1,X5,X6)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,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_26,plain,
equidistant(X1,X2,extension(X3,X4,X1,X2),X4),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_27,plain,
( between(X1,inner_pasch(X2,X1,extension(X3,X4,X5,X6),X4,X3),X3)
| ~ between(X2,X1,extension(X3,X4,X5,X6)) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_28,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_29,plain,
between(X1,inner_pasch(X2,extension(X3,X1,X4,X5),extension(X3,X1,X4,X5),X1,X3),X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,hypothesis,
equidistant(v,w,v1,w1),
v_to_w_equals_v1_to_w1 ).
cnf(c_0_31,plain,
( X1 = X2
| equidistant(X3,extension(X4,X2,X5,X6),X7,X6)
| ~ between(X8,X5,X7)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,extension(X4,X2,X5,X6),X8,X6)
| ~ equidistant(X2,X3,X5,X7)
| ~ equidistant(X1,X2,X8,X5) ),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_32,plain,
equidistant(X1,X1,X2,X2),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_33,plain,
equidistant(extension(X1,X2,X3,X4),X2,X4,X3),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_34,plain,
between(extension(X1,X2,X3,X4),inner_pasch(X5,extension(X1,X2,X3,X4),extension(X1,X2,X3,X4),X2,X1),X1),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_35,plain,
inner_pasch(X1,extension(X2,X1,X3,X4),extension(X2,X1,X3,X4),X1,X2) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,hypothesis,
equidistant(v1,w1,w,v),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_37,plain,
( extension(X1,X2,X3,X4) = X2
| equidistant(X5,extension(X1,X2,X3,X4),X6,X4)
| ~ between(extension(X1,X2,X3,X4),X2,X5)
| ~ between(X4,X3,X6)
| ~ equidistant(X2,X5,X3,X6) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]) ).
cnf(c_0_38,plain,
between(extension(X1,X2,X3,X4),X2,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,hypothesis,
equidistant(w,v,w1,v1),
inference(spm,[status(thm)],[c_0_21,c_0_36]) ).
cnf(c_0_40,plain,
equidistant(X1,X2,X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_41,hypothesis,
equidistant(u,w,u1,w1),
u_to_w_equals_u1_to_w1 ).
cnf(c_0_42,plain,
( extension(X1,X2,X3,X4) = X2
| equidistant(X1,extension(X1,X2,X3,X4),X5,X4)
| ~ between(X4,X3,X5)
| ~ equidistant(X2,X1,X3,X5) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,hypothesis,
equidistant(w1,v1,v,w),
inference(spm,[status(thm)],[c_0_21,c_0_39]) ).
cnf(c_0_44,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1 ).
cnf(c_0_45,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X3,X4,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_40]) ).
cnf(c_0_46,hypothesis,
( equidistant(X1,X2,u1,w1)
| ~ equidistant(u,w,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_41]) ).
cnf(c_0_47,hypothesis,
( extension(v1,w1,v,X1) = w1
| equidistant(v1,extension(v1,w1,v,X1),w,X1)
| ~ between(X1,v,w) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_49,hypothesis,
( equidistant(X1,X2,u1,v1)
| ~ equidistant(u,v,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_44]) ).
cnf(c_0_50,plain,
( X1 = X2
| equidistant(X3,X4,X5,X2)
| ~ between(X6,X4,X5)
| ~ between(X1,X2,X3)
| ~ equidistant(X2,X3,X4,X5)
| ~ equidistant(X1,X4,X6,X2)
| ~ equidistant(X1,X2,X6,X4) ),
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_51,plain,
equidistant(X1,X2,X3,extension(X4,X3,X1,X2)),
inference(spm,[status(thm)],[c_0_45,c_0_15]) ).
cnf(c_0_52,hypothesis,
equidistant(w,u,u1,w1),
inference(spm,[status(thm)],[c_0_46,c_0_17]) ).
cnf(c_0_53,hypothesis,
( extension(v1,w1,v,u) = w1
| equidistant(v1,extension(v1,w1,v,u),w,u) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,hypothesis,
equidistant(v,u,u1,v1),
inference(spm,[status(thm)],[c_0_49,c_0_17]) ).
cnf(c_0_55,plain,
( X1 = X2
| equidistant(X3,X4,extension(X5,X4,X2,X3),X2)
| ~ between(X6,X4,extension(X5,X4,X2,X3))
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X4,X6,X2)
| ~ equidistant(X1,X2,X6,X4) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,hypothesis,
( equidistant(X1,X2,u1,w1)
| ~ equidistant(w,u,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_52]) ).
cnf(c_0_57,hypothesis,
( extension(v1,w1,v,u) = w1
| equidistant(w,u,extension(v1,w1,v,u),v1) ),
inference(spm,[status(thm)],[c_0_21,c_0_53]) ).
cnf(c_0_58,hypothesis,
( equidistant(X1,X2,u1,v1)
| ~ equidistant(v,u,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_54]) ).
cnf(c_0_59,plain,
( X1 = X2
| equidistant(X3,X4,extension(X5,X4,X2,X3),X2)
| ~ between(X1,X2,X3)
| ~ equidistant(X1,X4,X5,X2)
| ~ equidistant(X1,X2,X5,X4) ),
inference(spm,[status(thm)],[c_0_55,c_0_19]) ).
cnf(c_0_60,hypothesis,
( extension(v1,w1,v,u) = w1
| equidistant(extension(v1,w1,v,u),v1,u1,w1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_61,hypothesis,
equidistant(extension(X1,X2,v,u),X2,u1,v1),
inference(spm,[status(thm)],[c_0_58,c_0_26]) ).
cnf(c_0_62,hypothesis,
( extension(v1,w1,v,u) = w1
| equidistant(X1,v1,extension(u1,v1,w1,X1),w1)
| ~ between(extension(v1,w1,v,u),w1,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61])]) ).
cnf(c_0_63,hypothesis,
( extension(v1,w1,v,u) = w1
| equidistant(v1,v1,extension(u1,v1,w1,v1),w1) ),
inference(spm,[status(thm)],[c_0_62,c_0_38]) ).
cnf(c_0_64,plain,
( equidistant(X1,X2,extension(X3,X4,X5,X6),X4)
| ~ equidistant(X5,X6,X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_65,hypothesis,
( extension(v1,w1,v,u) = w1
| equidistant(extension(u1,v1,w1,v1),w1,v1,v1) ),
inference(spm,[status(thm)],[c_0_21,c_0_63]) ).
cnf(c_0_66,hypothesis,
equidistant(u1,v1,extension(X1,X2,v,u),X2),
inference(spm,[status(thm)],[c_0_64,c_0_54]) ).
cnf(c_0_67,hypothesis,
( extension(v1,w1,v,u) = w1
| extension(u1,v1,w1,v1) = w1 ),
inference(spm,[status(thm)],[c_0_14,c_0_65]) ).
cnf(c_0_68,plain,
( between(X1,inner_pasch(X2,X3,X1,X1,X4),X2)
| ~ between(X2,X3,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_69,hypothesis,
( extension(u1,v1,w1,v1) = w1
| equidistant(u1,v1,w1,w1) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,plain,
( between(X1,inner_pasch(X2,X1,X3,X3,X4),X4)
| ~ between(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_71,plain,
between(X1,inner_pasch(X2,X1,X1,X1,X3),X2),
inference(spm,[status(thm)],[c_0_68,c_0_24]) ).
cnf(c_0_72,hypothesis,
( extension(u1,v1,w1,v1) = w1
| v1 = u1 ),
inference(spm,[status(thm)],[c_0_14,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
~ between(u1,v1,w1),
prove_v1_between_u1_and_w1 ).
cnf(c_0_74,plain,
between(X1,inner_pasch(X2,X1,X1,X1,X3),X3),
inference(spm,[status(thm)],[c_0_70,c_0_24]) ).
cnf(c_0_75,plain,
inner_pasch(X1,X1,X1,X1,X2) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_71]) ).
cnf(c_0_76,hypothesis,
v1 = u1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_72]),c_0_73]) ).
cnf(c_0_77,plain,
between(X1,X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_76]),c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GEO049-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.19/0.35 % Computer : n008.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Tue Aug 29 22:35:47 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 142.40/142.50 % Version : CSE_E---1.5
% 142.40/142.50 % Problem : theBenchmark.p
% 142.40/142.50 % Proof found
% 142.40/142.50 % SZS status Theorem for theBenchmark.p
% 142.40/142.50 % SZS output start Proof
% See solution above
% 142.40/142.50 % Total time : 141.774000 s
% 142.40/142.50 % SZS output end Proof
% 142.40/142.50 % Total time : 141.785000 s
%------------------------------------------------------------------------------