TSTP Solution File: GEO007-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO007-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n006.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 22:45:26 EDT 2023
% Result : Unsatisfiable 0.52s 0.68s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 68 ( 26 unt; 14 typ; 0 def)
% Number of atoms : 102 ( 27 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 87 ( 39 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 12 ( 12 usr; 7 con; 0-6 aty)
% Number of variables : 79 ( 8 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
between: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
equidistant: ( $i * $i * $i * $i ) > $o ).
tff(decl_24,type,
outer_pasch: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_25,type,
euclid1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_26,type,
euclid2: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_27,type,
extension: ( $i * $i * $i * $i ) > $i ).
tff(decl_28,type,
lower_dimension_point_1: $i ).
tff(decl_29,type,
lower_dimension_point_2: $i ).
tff(decl_30,type,
lower_dimension_point_3: $i ).
tff(decl_31,type,
continuous: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_32,type,
a: $i ).
tff(decl_33,type,
c: $i ).
tff(decl_34,type,
d: $i ).
tff(decl_35,type,
e: $i ).
cnf(identity_for_betweeness,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_betweeness) ).
cnf(outer_pasch1,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch1) ).
cnf(identity_for_equidistance,axiom,
( X1 = X2
| ~ equidistant(X1,X2,X3,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',identity_for_equidistance) ).
cnf(segment_construction2,axiom,
equidistant(X1,extension(X2,X1,X3,X4),X3,X4),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction2) ).
cnf(a_between_a_and_e,hypothesis,
between(e,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_between_a_and_e) ).
cnf(segment_construction1,axiom,
between(X1,X2,extension(X1,X2,X3,X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',segment_construction1) ).
cnf(a_between_a_and_c,hypothesis,
between(d,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_between_a_and_c) ).
cnf(outer_pasch2,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',outer_pasch2) ).
cnf(connectivity_for_betweeness,axiom,
( X1 = X2
| between(X1,X3,X4)
| between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',connectivity_for_betweeness) ).
cnf(a_not_c,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
cnf(transitivity_for_betweeness,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO001-0.ax',transitivity_for_betweeness) ).
cnf(e_not_between_d_and_a,hypothesis,
~ between(d,e,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_not_between_d_and_a) ).
cnf(prove_d_between_e_and_a,negated_conjecture,
~ between(e,d,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_between_e_and_a) ).
cnf(c_0_13,axiom,
( X1 = X2
| ~ between(X1,X2,X1) ),
identity_for_betweeness ).
cnf(c_0_14,axiom,
( between(X1,outer_pasch(X2,X1,X4,X5,X3),X4)
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch1 ).
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,
( outer_pasch(X1,X2,X2,X3,X4) = X2
| ~ between(X2,X4,X3)
| ~ between(X2,X1,X4) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,hypothesis,
between(e,a,c),
a_between_a_and_e ).
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,hypothesis,
( outer_pasch(X1,e,e,c,a) = e
| ~ between(e,X1,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
between(X1,X2,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,hypothesis,
between(d,a,c),
a_between_a_and_c ).
cnf(c_0_24,axiom,
( between(X5,X2,outer_pasch(X2,X1,X4,X5,X3))
| ~ between(X1,X2,X3)
| ~ between(X4,X3,X5) ),
outer_pasch2 ).
cnf(c_0_25,hypothesis,
outer_pasch(a,e,e,c,a) = e,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,hypothesis,
( outer_pasch(X1,d,d,c,a) = d
| ~ between(d,X1,a) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_27,axiom,
( X1 = X2
| between(X1,X3,X4)
| between(X1,X4,X3)
| ~ between(X1,X2,X3)
| ~ between(X1,X2,X4) ),
connectivity_for_betweeness ).
cnf(c_0_28,hypothesis,
between(c,a,e),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_18]),c_0_22])]) ).
cnf(c_0_29,hypothesis,
a != c,
a_not_c ).
cnf(c_0_30,hypothesis,
outer_pasch(a,d,d,c,a) = d,
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_31,hypothesis,
( between(c,e,X1)
| between(c,X1,e)
| ~ between(c,a,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,hypothesis,
between(c,a,d),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_23]),c_0_22])]) ).
cnf(c_0_33,hypothesis,
( between(c,d,e)
| between(c,e,d) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,hypothesis,
( outer_pasch(X1,c,c,d,e) = c
| between(c,d,e)
| ~ between(c,X1,e) ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_35,hypothesis,
( outer_pasch(e,c,c,d,e) = c
| between(c,d,e) ),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_36,hypothesis,
( outer_pasch(e,c,c,d,e) = c
| outer_pasch(X1,c,c,e,d) = c
| ~ between(c,X1,d) ),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_37,hypothesis,
( outer_pasch(d,c,c,e,d) = c
| outer_pasch(e,c,c,d,e) = c ),
inference(spm,[status(thm)],[c_0_36,c_0_22]) ).
cnf(c_0_38,hypothesis,
( outer_pasch(d,c,c,e,d) = c
| between(d,e,c)
| ~ between(c,e,d) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_37]),c_0_22])]) ).
cnf(c_0_39,hypothesis,
( outer_pasch(d,c,c,e,d) = c
| between(c,d,e)
| between(d,e,c) ),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_40,axiom,
( between(X1,X2,X4)
| ~ between(X1,X2,X3)
| ~ between(X2,X4,X3) ),
transitivity_for_betweeness ).
cnf(c_0_41,hypothesis,
( outer_pasch(d,c,c,e,d) = c
| outer_pasch(X1,c,c,e,d) = c
| between(d,e,c)
| ~ between(c,X1,d) ),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_42,hypothesis,
( between(X1,e,a)
| ~ between(X1,e,c) ),
inference(spm,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_43,hypothesis,
( outer_pasch(d,c,c,e,d) = c
| between(d,e,c) ),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_44,hypothesis,
~ between(d,e,a),
e_not_between_d_and_a ).
cnf(c_0_45,hypothesis,
outer_pasch(d,c,c,e,d) = c,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_46,hypothesis,
( between(X1,d,a)
| ~ between(X1,d,c) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_47,hypothesis,
( between(e,d,c)
| ~ between(c,d,e) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_45]),c_0_22])]) ).
cnf(c_0_48,negated_conjecture,
~ between(e,d,a),
prove_d_between_e_and_a ).
cnf(c_0_49,hypothesis,
~ between(c,d,e),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_50,hypothesis,
outer_pasch(e,c,c,d,e) = c,
inference(sr,[status(thm)],[c_0_35,c_0_49]) ).
cnf(c_0_51,hypothesis,
between(c,e,d),
inference(sr,[status(thm)],[c_0_33,c_0_49]) ).
cnf(c_0_52,hypothesis,
between(d,e,c),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_50]),c_0_22])]),c_0_51])]) ).
cnf(c_0_53,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_52]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO007-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 20:58:51 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.52/0.68 % Version : CSE_E---1.5
% 0.52/0.68 % Problem : theBenchmark.p
% 0.52/0.68 % Proof found
% 0.52/0.68 % SZS status Theorem for theBenchmark.p
% 0.52/0.68 % SZS output start Proof
% See solution above
% 0.52/0.69 % Total time : 0.117000 s
% 0.52/0.69 % SZS output end Proof
% 0.52/0.69 % Total time : 0.120000 s
%------------------------------------------------------------------------------