TSTP Solution File: GEO126-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GEO126-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 22:46:15 EDT 2023
% Result : Unsatisfiable 1.76s 1.83s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 55
% Syntax : Number of formulae : 90 ( 13 unt; 40 typ; 0 def)
% Number of atoms : 101 ( 22 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 92 ( 41 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 39 >; 47 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 27 ( 27 usr; 1 con; 0-5 aty)
% Number of variables : 78 ( 5 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
part_of: ( $i * $i ) > $o ).
tff(decl_23,type,
incident_c: ( $i * $i ) > $o ).
tff(decl_24,type,
ax0_sk1: ( $i * $i ) > $i ).
tff(decl_25,type,
sum: ( $i * $i ) > $i ).
tff(decl_26,type,
ax0_sk2: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
end_point: ( $i * $i ) > $o ).
tff(decl_28,type,
ax0_sk3: ( $i * $i ) > $i ).
tff(decl_29,type,
ax0_sk4: ( $i * $i ) > $i ).
tff(decl_30,type,
inner_point: ( $i * $i ) > $o ).
tff(decl_31,type,
meet: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
ax0_sk5: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
closed: $i > $o ).
tff(decl_34,type,
ax0_sk6: $i > $i ).
tff(decl_35,type,
open: $i > $o ).
tff(decl_36,type,
ax0_sk7: $i > $i ).
tff(decl_37,type,
ax0_sk8: $i > $i ).
tff(decl_38,type,
ax0_sk9: ( $i * $i ) > $i ).
tff(decl_39,type,
ax0_sk10: ( $i * $i ) > $i ).
tff(decl_40,type,
ax0_sk11: ( $i * $i ) > $i ).
tff(decl_41,type,
ax0_sk12: ( $i * $i ) > $i ).
tff(decl_42,type,
ax0_sk13: ( $i * $i ) > $i ).
tff(decl_43,type,
between_c: ( $i * $i * $i * $i ) > $o ).
tff(decl_44,type,
ax1_sk1: ( $i * $i * $i * $i ) > $i ).
tff(decl_45,type,
between_o: ( $i * $i * $i * $i ) > $o ).
tff(decl_46,type,
ordered_by: ( $i * $i * $i ) > $o ).
tff(decl_47,type,
start_point: ( $i * $i ) > $o ).
tff(decl_48,type,
incident_o: ( $i * $i ) > $o ).
tff(decl_49,type,
ax2_sk1: ( $i * $i ) > $i ).
tff(decl_50,type,
finish_point: ( $i * $i ) > $o ).
tff(decl_51,type,
ax2_sk2: ( $i * $i ) > $i ).
tff(decl_52,type,
ax2_sk3: $i > $i ).
tff(decl_53,type,
ax2_sk4: ( $i * $i * $i * $i ) > $i ).
tff(decl_54,type,
ax2_sk5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_55,type,
ax2_sk6: $i > $i ).
tff(decl_56,type,
ax2_sk7: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
ax2_sk8: ( $i * $i ) > $i ).
tff(decl_58,type,
ax2_sk9: ( $i * $i ) > $i ).
tff(decl_59,type,
underlying_curve: $i > $i ).
tff(decl_60,type,
ax2_sk10: ( $i * $i ) > $i ).
tff(decl_61,type,
sk25: $i ).
cnf(open_defn_33,axiom,
( end_point(ax0_sk7(X1),X1)
| ~ open(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',open_defn_33) ).
cnf(o2_19,axiom,
open(ax2_sk3(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',o2_19) ).
cnf(end_point_defn_13,axiom,
( incident_c(X1,X2)
| ~ end_point(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',end_point_defn_13) ).
cnf(closed_defn_32,axiom,
( end_point(ax0_sk6(X1),X1)
| closed(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',closed_defn_32) ).
cnf(closed_defn_31,axiom,
( ~ closed(X1)
| ~ end_point(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',closed_defn_31) ).
cnf(o2_21,axiom,
( incident_o(X1,X2)
| ~ incident_c(X1,ax2_sk3(X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',o2_21) ).
cnf(start_point_defn_8,axiom,
( X1 = X3
| ordered_by(X2,X1,X3)
| ~ start_point(X1,X2)
| ~ incident_o(X3,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',start_point_defn_8) ).
cnf(underlying_curve_defn_39,axiom,
( incident_o(ax2_sk10(X1,X2),X1)
| incident_c(ax2_sk10(X1,X2),X2)
| X2 = underlying_curve(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',underlying_curve_defn_39) ).
cnf(o4_29,axiom,
start_point(ax2_sk6(X1),X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',o4_29) ).
cnf(underlying_curve_defn_38,axiom,
( incident_o(X3,X2)
| X1 != underlying_curve(X2)
| ~ incident_c(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',underlying_curve_defn_38) ).
cnf(c6_41,axiom,
( end_point(ax0_sk11(X1,X2),X2)
| ~ end_point(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',c6_41) ).
cnf(theorem_4_11_133,negated_conjecture,
( X1 = X2
| ~ ordered_by(sk25,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_11_133) ).
cnf(underlying_curve_defn_42,axiom,
( X2 = underlying_curve(X1)
| ~ incident_c(ax2_sk10(X1,X2),X2)
| ~ incident_o(ax2_sk10(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',underlying_curve_defn_42) ).
cnf(o2_20,axiom,
( incident_c(X1,ax2_sk3(X2))
| ~ incident_o(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-2.ax',o2_20) ).
cnf(c6_42,axiom,
( ~ end_point(X1,X2)
| X1 != ax0_sk11(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax',c6_42) ).
cnf(c_0_15,axiom,
( end_point(ax0_sk7(X1),X1)
| ~ open(X1) ),
open_defn_33 ).
cnf(c_0_16,axiom,
open(ax2_sk3(X1)),
o2_19 ).
cnf(c_0_17,axiom,
( incident_c(X1,X2)
| ~ end_point(X1,X2) ),
end_point_defn_13 ).
cnf(c_0_18,axiom,
( end_point(ax0_sk6(X1),X1)
| closed(X1) ),
closed_defn_32 ).
cnf(c_0_19,axiom,
( ~ closed(X1)
| ~ end_point(X2,X1) ),
closed_defn_31 ).
cnf(c_0_20,plain,
end_point(ax0_sk7(ax2_sk3(X1)),ax2_sk3(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,axiom,
( incident_o(X1,X2)
| ~ incident_c(X1,ax2_sk3(X2)) ),
o2_21 ).
cnf(c_0_22,plain,
( closed(X1)
| incident_c(ax0_sk6(X1),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
~ closed(ax2_sk3(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( X1 = X3
| ordered_by(X2,X1,X3)
| ~ start_point(X1,X2)
| ~ incident_o(X3,X2) ),
start_point_defn_8 ).
cnf(c_0_25,plain,
incident_o(ax0_sk6(ax2_sk3(X1)),X1),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_26,axiom,
( incident_o(ax2_sk10(X1,X2),X1)
| incident_c(ax2_sk10(X1,X2),X2)
| X2 = underlying_curve(X1) ),
underlying_curve_defn_39 ).
cnf(c_0_27,plain,
( X1 = ax0_sk6(ax2_sk3(X2))
| ordered_by(X2,X1,ax0_sk6(ax2_sk3(X2)))
| ~ start_point(X1,X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,axiom,
start_point(ax2_sk6(X1),X1),
o4_29 ).
cnf(c_0_29,plain,
( ax2_sk3(X1) = underlying_curve(X2)
| incident_o(ax2_sk10(X2,ax2_sk3(X1)),X2)
| incident_o(ax2_sk10(X2,ax2_sk3(X1)),X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_30,axiom,
( incident_o(X3,X2)
| X1 != underlying_curve(X2)
| ~ incident_c(X3,X1) ),
underlying_curve_defn_38 ).
cnf(c_0_31,axiom,
( end_point(ax0_sk11(X1,X2),X2)
| ~ end_point(X1,X2) ),
c6_41 ).
cnf(c_0_32,negated_conjecture,
( X1 = X2
| ~ ordered_by(sk25,X1,X2) ),
theorem_4_11_133 ).
cnf(c_0_33,plain,
( ax0_sk6(ax2_sk3(X1)) = ax2_sk6(X1)
| ordered_by(X1,ax2_sk6(X1),ax0_sk6(ax2_sk3(X1))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,axiom,
( X2 = underlying_curve(X1)
| ~ incident_c(ax2_sk10(X1,X2),X2)
| ~ incident_o(ax2_sk10(X1,X2),X1) ),
underlying_curve_defn_42 ).
cnf(c_0_35,plain,
( ax2_sk3(X1) = underlying_curve(X1)
| incident_o(ax2_sk10(X1,ax2_sk3(X1)),X1) ),
inference(ef,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( incident_o(X1,X2)
| ~ incident_c(X1,underlying_curve(X2)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
( incident_c(ax0_sk11(X1,X2),X2)
| ~ end_point(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_31]) ).
cnf(c_0_38,negated_conjecture,
ax0_sk6(ax2_sk3(sk25)) = ax2_sk6(sk25),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
( ax2_sk3(X1) = underlying_curve(X1)
| ~ incident_c(ax2_sk10(X1,ax2_sk3(X1)),ax2_sk3(X1)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,axiom,
( incident_c(X1,ax2_sk3(X2))
| ~ incident_o(X1,X2) ),
o2_20 ).
cnf(c_0_41,plain,
( incident_o(ax0_sk11(X1,underlying_curve(X2)),X2)
| ~ end_point(X1,underlying_curve(X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
end_point(ax2_sk6(sk25),ax2_sk3(sk25)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_38]),c_0_23]) ).
cnf(c_0_43,plain,
ax2_sk3(X1) = underlying_curve(X1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35]) ).
cnf(c_0_44,plain,
( X1 = ax0_sk11(X2,underlying_curve(X3))
| ordered_by(X3,X1,ax0_sk11(X2,underlying_curve(X3)))
| ~ start_point(X1,X3)
| ~ end_point(X2,underlying_curve(X3)) ),
inference(spm,[status(thm)],[c_0_24,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
end_point(ax2_sk6(sk25),underlying_curve(sk25)),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( X1 = ax0_sk11(ax2_sk6(sk25),underlying_curve(sk25))
| ~ start_point(X1,sk25) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_32]) ).
cnf(c_0_47,axiom,
( ~ end_point(X1,X2)
| X1 != ax0_sk11(X1,X2) ),
c6_42 ).
cnf(c_0_48,negated_conjecture,
ax0_sk11(ax2_sk6(sk25),underlying_curve(sk25)) = ax2_sk6(sk25),
inference(spm,[status(thm)],[c_0_46,c_0_28]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_45])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO126-1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.20/0.34 % DateTime : Tue Aug 29 21:18:31 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 1.76/1.83 % Version : CSE_E---1.5
% 1.76/1.83 % Problem : theBenchmark.p
% 1.76/1.83 % Proof found
% 1.76/1.83 % SZS status Theorem for theBenchmark.p
% 1.76/1.83 % SZS output start Proof
% See solution above
% 1.76/1.83 % Total time : 1.236000 s
% 1.76/1.83 % SZS output end Proof
% 1.76/1.83 % Total time : 1.239000 s
%------------------------------------------------------------------------------