%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO111-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 : 600s
% DateTime : Sat Jul 16 05:24:22 EDT 2022
% Result : Unsatisfiable 4.91s 5.08s
% Output : CNFRefutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of clauses : 73 ( 23 unt; 11 nHn; 71 RR)
% Number of literals : 147 ( 54 equ; 64 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 43 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(part_of_defn_1,axiom,
( ~ part_of(A,B)
| ~ incident_c(C,A)
| incident_c(C,B) ) ).
cnf(end_point_defn_13,axiom,
( ~ end_point(A,B)
| incident_c(A,B) ) ).
cnf(inner_point_defn_21,axiom,
( ~ inner_point(A,B)
| incident_c(A,B) ) ).
cnf(inner_point_defn_22,axiom,
( ~ inner_point(A,B)
| ~ end_point(A,B) ) ).
cnf(between_c_defn_1,axiom,
( ~ between_c(A,B,C,D)
| B != D ) ).
cnf(between_c_defn_2,axiom,
( ~ between_c(A,B,C,D)
| part_of(ax1_sk1(D,C,B,A),A) ) ).
cnf(between_c_defn_3,axiom,
( ~ between_c(A,B,C,D)
| end_point(B,ax1_sk1(D,C,B,A)) ) ).
cnf(between_c_defn_4,axiom,
( ~ between_c(A,B,C,D)
| end_point(D,ax1_sk1(D,C,B,A)) ) ).
cnf(between_c_defn_5,axiom,
( ~ between_c(A,B,C,D)
| inner_point(C,ax1_sk1(D,C,B,A)) ) ).
cnf(theorem_3_8_1_77,negated_conjecture,
between_c(sk15,sk16,sk17,sk18) ).
cnf(theorem_3_8_1_78,negated_conjecture,
( ~ incident_c(sk16,sk15)
| ~ incident_c(sk17,sk15)
| ~ incident_c(sk18,sk15)
| sk16 = sk17
| sk17 = sk18
| sk16 = sk18 ) ).
cnf(refute_0_0,plain,
( ~ end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(subst,[],[inner_point_defn_22:[bind(A,$fot(sk17)),bind(B,$fot(ax1_sk1(sk18,sk17,sk16,sk15)))]]) ).
cnf(refute_0_1,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(subst,[],[between_c_defn_5:[bind(A,$fot(sk15)),bind(B,$fot(sk16)),bind(C,$fot(sk17)),bind(D,$fot(sk18))]]) ).
cnf(refute_0_2,plain,
inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[$cnf( between_c(sk15,sk16,sk17,sk18) )],[theorem_3_8_1_77,refute_0_1]) ).
cnf(refute_0_3,plain,
~ end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[$cnf( inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_2,refute_0_0]) ).
cnf(refute_0_4,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(subst,[],[between_c_defn_4:[bind(A,$fot(sk15)),bind(B,$fot(sk16)),bind(C,$fot(sk17)),bind(D,$fot(sk18))]]) ).
cnf(refute_0_5,plain,
end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[$cnf( between_c(sk15,sk16,sk17,sk18) )],[theorem_3_8_1_77,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(subst,[],[end_point_defn_13:[bind(A,$fot(sk16)),bind(B,$fot(ax1_sk1(sk18,sk17,sk16,sk15)))]]) ).
cnf(refute_0_7,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(subst,[],[between_c_defn_3:[bind(A,$fot(sk15)),bind(B,$fot(sk16)),bind(C,$fot(sk17)),bind(D,$fot(sk18))]]) ).
cnf(refute_0_8,plain,
end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[$cnf( between_c(sk15,sk16,sk17,sk18) )],[theorem_3_8_1_77,refute_0_7]) ).
cnf(refute_0_9,plain,
incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[$cnf( end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_8,refute_0_6]) ).
cnf(refute_0_10,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) ),
inference(subst,[],[between_c_defn_2:[bind(A,$fot(sk15)),bind(B,$fot(sk16)),bind(C,$fot(sk17)),bind(D,$fot(sk18))]]) ).
cnf(refute_0_11,plain,
part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15),
inference(resolve,[$cnf( between_c(sk15,sk16,sk17,sk18) )],[theorem_3_8_1_77,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ incident_c(X_718,ax1_sk1(sk18,sk17,sk16,sk15))
| ~ part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15)
| incident_c(X_718,sk15) ),
inference(subst,[],[part_of_defn_1:[bind(A,$fot(ax1_sk1(sk18,sk17,sk16,sk15))),bind(B,$fot(sk15)),bind(C,$fot(X_718))]]) ).
cnf(refute_0_13,plain,
( ~ incident_c(X_718,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(X_718,sk15) ),
inference(resolve,[$cnf( part_of(ax1_sk1(sk18,sk17,sk16,sk15),sk15) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk16,sk15) ),
inference(subst,[],[refute_0_13:[bind(X_718,$fot(sk16))]]) ).
cnf(refute_0_15,plain,
incident_c(sk16,sk15),
inference(resolve,[$cnf( incident_c(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ incident_c(sk17,sk15)
| ~ incident_c(sk18,sk15)
| sk16 = sk17
| sk16 = sk18
| sk17 = sk18 ),
inference(resolve,[$cnf( incident_c(sk16,sk15) )],[refute_0_15,theorem_3_8_1_78]) ).
cnf(refute_0_17,plain,
( ~ incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk17,sk15) ),
inference(subst,[],[refute_0_13:[bind(X_718,$fot(sk17))]]) ).
cnf(refute_0_18,plain,
( ~ inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(subst,[],[inner_point_defn_21:[bind(A,$fot(sk17)),bind(B,$fot(ax1_sk1(sk18,sk17,sk16,sk15)))]]) ).
cnf(refute_0_19,plain,
incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[$cnf( inner_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_2,refute_0_18]) ).
cnf(refute_0_20,plain,
incident_c(sk17,sk15),
inference(resolve,[$cnf( incident_c(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_19,refute_0_17]) ).
cnf(refute_0_21,plain,
( ~ incident_c(sk18,sk15)
| sk16 = sk17
| sk16 = sk18
| sk17 = sk18 ),
inference(resolve,[$cnf( incident_c(sk17,sk15) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
( ~ incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk18,sk15) ),
inference(subst,[],[refute_0_13:[bind(X_718,$fot(sk18))]]) ).
cnf(refute_0_23,plain,
( ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(subst,[],[end_point_defn_13:[bind(A,$fot(sk18)),bind(B,$fot(ax1_sk1(sk18,sk17,sk16,sk15)))]]) ).
cnf(refute_0_24,plain,
incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15)),
inference(resolve,[$cnf( end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_5,refute_0_23]) ).
cnf(refute_0_25,plain,
incident_c(sk18,sk15),
inference(resolve,[$cnf( incident_c(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_24,refute_0_22]) ).
cnf(refute_0_26,plain,
( sk16 = sk17
| sk16 = sk18
| sk17 = sk18 ),
inference(resolve,[$cnf( incident_c(sk18,sk15) )],[refute_0_25,refute_0_21]) ).
cnf(refute_0_27,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_28,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_29,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( sk16 != sk18
| sk18 = sk16 ),
inference(subst,[],[refute_0_29:[bind(X,$fot(sk16)),bind(Y,$fot(sk18))]]) ).
cnf(refute_0_31,plain,
( sk16 = sk17
| sk17 = sk18
| sk18 = sk16 ),
inference(resolve,[$cnf( $equal(sk16,sk18) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( sk18 != sk16
| ~ between_c(sk15,sk16,sk17,sk18)
| between_c(sk15,sk16,sk17,sk16) ),
introduced(tautology,[equality,[$cnf( between_c(sk15,sk16,sk17,sk18) ),[3],$fot(sk16)]]) ).
cnf(refute_0_33,plain,
( ~ between_c(sk15,sk16,sk17,sk18)
| sk16 = sk17
| sk17 = sk18
| between_c(sk15,sk16,sk17,sk16) ),
inference(resolve,[$cnf( $equal(sk18,sk16) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( sk16 = sk17
| sk17 = sk18
| between_c(sk15,sk16,sk17,sk16) ),
inference(resolve,[$cnf( between_c(sk15,sk16,sk17,sk18) )],[theorem_3_8_1_77,refute_0_33]) ).
cnf(refute_0_35,plain,
( D != D
| ~ between_c(A,D,C,D) ),
inference(subst,[],[between_c_defn_1:[bind(B,$fot(D))]]) ).
cnf(refute_0_36,plain,
D = D,
introduced(tautology,[refl,[$fot(D)]]) ).
cnf(refute_0_37,plain,
~ between_c(A,D,C,D),
inference(resolve,[$cnf( $equal(D,D) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
~ between_c(sk15,sk16,sk17,sk16),
inference(subst,[],[refute_0_37:[bind(A,$fot(sk15)),bind(C,$fot(sk17)),bind(D,$fot(sk16))]]) ).
cnf(refute_0_39,plain,
( sk16 = sk17
| sk17 = sk18 ),
inference(resolve,[$cnf( between_c(sk15,sk16,sk17,sk16) )],[refute_0_34,refute_0_38]) ).
cnf(refute_0_40,plain,
( sk17 != sk18
| sk18 = sk17 ),
inference(subst,[],[refute_0_29:[bind(X,$fot(sk17)),bind(Y,$fot(sk18))]]) ).
cnf(refute_0_41,plain,
( sk16 = sk17
| sk18 = sk17 ),
inference(resolve,[$cnf( $equal(sk17,sk18) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( sk18 != sk17
| ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
introduced(tautology,[equality,[$cnf( end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) ),[0],$fot(sk17)]]) ).
cnf(refute_0_43,plain,
( ~ end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15))
| sk16 = sk17
| end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(resolve,[$cnf( $equal(sk18,sk17) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( sk16 = sk17
| end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(resolve,[$cnf( end_point(sk18,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_5,refute_0_43]) ).
cnf(refute_0_45,plain,
sk16 = sk17,
inference(resolve,[$cnf( end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_44,refute_0_3]) ).
cnf(refute_0_46,plain,
( sk16 != sk17
| sk17 = sk16 ),
inference(subst,[],[refute_0_29:[bind(X,$fot(sk16)),bind(Y,$fot(sk17))]]) ).
cnf(refute_0_47,plain,
sk17 = sk16,
inference(resolve,[$cnf( $equal(sk16,sk17) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( sk17 != sk16
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
introduced(tautology,[equality,[$cnf( ~ end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),[0],$fot(sk16)]]) ).
cnf(refute_0_49,plain,
( ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(resolve,[$cnf( $equal(sk17,sk16) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk17,sk16,sk15),
introduced(tautology,[refl,[$fot(ax1_sk1(sk18,sk17,sk16,sk15))]]) ).
cnf(refute_0_51,plain,
( ax1_sk1(sk18,sk17,sk16,sk15) != ax1_sk1(sk18,sk17,sk16,sk15)
| sk17 != sk16
| ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk16,sk16,sk15) ),
introduced(tautology,[equality,[$cnf( $equal(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)) ),[1,1],$fot(sk16)]]) ).
cnf(refute_0_52,plain,
( sk17 != sk16
| ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk16,sk16,sk15) ),
inference(resolve,[$cnf( $equal(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
ax1_sk1(sk18,sk17,sk16,sk15) = ax1_sk1(sk18,sk16,sk16,sk15),
inference(resolve,[$cnf( $equal(sk17,sk16) )],[refute_0_47,refute_0_52]) ).
cnf(refute_0_54,plain,
( ax1_sk1(sk18,sk17,sk16,sk15) != ax1_sk1(sk18,sk16,sk16,sk15)
| ~ end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15))
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
introduced(tautology,[equality,[$cnf( ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),[1],$fot(ax1_sk1(sk18,sk16,sk16,sk15))]]) ).
cnf(refute_0_55,plain,
( ~ end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15))
| end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(resolve,[$cnf( $equal(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk16,sk16,sk15)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15))
| end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) ),
inference(resolve,[$cnf( end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_55,refute_0_49]) ).
cnf(refute_0_57,plain,
~ end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15)),
inference(resolve,[$cnf( end_point(sk17,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_56,refute_0_3]) ).
cnf(refute_0_58,plain,
( ax1_sk1(sk18,sk17,sk16,sk15) != ax1_sk1(sk18,sk16,sk16,sk15)
| ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15)) ),
introduced(tautology,[equality,[$cnf( end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) ),[1],$fot(ax1_sk1(sk18,sk16,sk16,sk15))]]) ).
cnf(refute_0_59,plain,
( ~ end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15))
| end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15)) ),
inference(resolve,[$cnf( $equal(ax1_sk1(sk18,sk17,sk16,sk15),ax1_sk1(sk18,sk16,sk16,sk15)) )],[refute_0_53,refute_0_58]) ).
cnf(refute_0_60,plain,
end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15)),
inference(resolve,[$cnf( end_point(sk16,ax1_sk1(sk18,sk17,sk16,sk15)) )],[refute_0_8,refute_0_59]) ).
cnf(refute_0_61,plain,
$false,
inference(resolve,[$cnf( end_point(sk16,ax1_sk1(sk18,sk16,sk16,sk15)) )],[refute_0_60,refute_0_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO111-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n025.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Fri Jun 17 20:34:42 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.91/5.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.91/5.08
% 4.91/5.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.91/5.09
%------------------------------------------------------------------------------