TSTP Solution File: GEO025-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO025-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 22:45:35 EDT 2023
% Result : Unsatisfiable 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 30
% Syntax : Number of formulae : 68 ( 32 unt; 16 typ; 0 def)
% Number of atoms : 100 ( 18 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 95 ( 47 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 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 : 101 ( 8 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(transitivity_for_equidistance,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',transitivity_for_equidistance) ).
cnf(reflexivity_for_equidistance,axiom,
equidistant(X1,X2,X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',reflexivity_for_equidistance) ).
cnf(u_to_v_equals_u1_to_v1,hypothesis,
equidistant(u,v,u1,v1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch2) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction2) ).
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/sandbox2/benchmark/Axioms/GEO002-0.ax',outer_five_segment) ).
cnf(v_to_w_equals_v1_to_w1,hypothesis,
equidistant(v,w,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
cnf(v1_between_u1_and_w1,hypothesis,
between(u1,v1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',segment_construction1) ).
cnf(prove_equal_sums,negated_conjecture,
~ equidistant(u,w,u1,w1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_sums) ).
cnf(v_between_u_and_w,hypothesis,
between(u,v,w),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GEO002-0.ax',inner_pasch1) ).
cnf(c_0_14,axiom,
( equidistant(X3,X4,X5,X6)
| ~ equidistant(X1,X2,X3,X4)
| ~ equidistant(X1,X2,X5,X6) ),
transitivity_for_equidistance ).
cnf(c_0_15,axiom,
equidistant(X1,X2,X2,X1),
reflexivity_for_equidistance ).
cnf(c_0_16,plain,
( equidistant(X1,X2,X3,X4)
| ~ equidistant(X4,X3,X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,hypothesis,
equidistant(u,v,u1,v1),
u_to_v_equals_u1_to_v1 ).
cnf(c_0_18,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_19,axiom,
( between(X5,inner_pasch(X1,X2,X3,X5,X4),X1)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch2 ).
cnf(c_0_20,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
identity_for_equidistance ).
cnf(c_0_21,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
segment_construction2 ).
cnf(c_0_22,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_23,hypothesis,
equidistant(v,w,v1,w1),
v_to_w_equals_v1_to_w1 ).
cnf(c_0_24,hypothesis,
equidistant(u1,v1,v,u),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
( inner_pasch(X1,X2,X3,X1,X4) = X1
| ~ between(X4,X1,X3)
| ~ between(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,hypothesis,
between(u1,v1,w1),
v1_between_u1_and_w1 ).
cnf(c_0_27,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
segment_construction1 ).
cnf(c_0_28,plain,
extension(X1,X2,X3,X3) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,hypothesis,
( X1 = v
| equidistant(X2,w,X3,w1)
| ~ between(X4,v1,X3)
| ~ between(X1,v,X2)
| ~ equidistant(v,X2,v1,X3)
| ~ equidistant(X1,w,X4,w1)
| ~ equidistant(X1,v,X4,v1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,hypothesis,
equidistant(v,u,v1,u1),
inference(spm,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_31,negated_conjecture,
~ equidistant(u,w,u1,w1),
prove_equal_sums ).
cnf(c_0_32,hypothesis,
equidistant(v1,w1,w,v),
inference(spm,[status(thm)],[c_0_16,c_0_23]) ).
cnf(c_0_33,hypothesis,
( inner_pasch(v1,X1,w1,v1,u1) = v1
| ~ between(v1,X1,w1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,hypothesis,
between(u,v,w),
v_between_u_and_w ).
cnf(c_0_36,hypothesis,
( X1 = v
| ~ between(X2,v1,u1)
| ~ between(X1,v,u)
| ~ equidistant(X1,w,X2,w1)
| ~ equidistant(X1,v,X2,v1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_37,plain,
equidistant(X1,X1,X2,X2),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_38,hypothesis,
equidistant(w,v,w1,v1),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_39,axiom,
( between(X2,inner_pasch(X1,X2,X3,X5,X4),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X5,X3) ),
inner_pasch1 ).
cnf(c_0_40,hypothesis,
inner_pasch(v1,w1,w1,v1,u1) = v1,
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,hypothesis,
( inner_pasch(v,X1,w,v,u) = v
| ~ between(v,X1,w) ),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_42,hypothesis,
( w = v
| ~ between(w1,v1,u1)
| ~ between(w,v,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38])]) ).
cnf(c_0_43,hypothesis,
between(w1,v1,u1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_26]),c_0_34])]) ).
cnf(c_0_44,hypothesis,
inner_pasch(v,w,w,v,u) = v,
inference(spm,[status(thm)],[c_0_41,c_0_34]) ).
cnf(c_0_45,hypothesis,
( w = v
| ~ between(w,v,u) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]) ).
cnf(c_0_46,hypothesis,
between(w,v,u),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_44]),c_0_35]),c_0_34])]) ).
cnf(c_0_47,hypothesis,
equidistant(w1,v1,v,w),
inference(spm,[status(thm)],[c_0_16,c_0_38]) ).
cnf(c_0_48,hypothesis,
w = v,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_49,hypothesis,
equidistant(w1,v1,v,v),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_50,hypothesis,
w1 = v1,
inference(spm,[status(thm)],[c_0_20,c_0_49]) ).
cnf(c_0_51,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_48]),c_0_50]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO025-2 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n024.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 23:14:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.62 % Total time : 0.036000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.039000 s
%------------------------------------------------------------------------------