TSTP Solution File: GEO126-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO126-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 05:24:30 EDT 2022
% Result : Unsatisfiable 53.44s 53.60s
% Output : CNFRefutation 53.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 54 ( 24 unt; 8 nHn; 39 RR)
% Number of literals : 94 ( 27 equ; 35 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(end_point_defn_13,axiom,
( ~ end_point(A,B)
| incident_c(A,B) ) ).
cnf(open_defn_33,axiom,
( ~ open(A)
| end_point(ax0_sk7(A),A) ) ).
cnf(c6_41,axiom,
( ~ end_point(A,B)
| end_point(ax0_sk11(A,B),B) ) ).
cnf(c6_42,axiom,
( ~ end_point(A,B)
| A != ax0_sk11(A,B) ) ).
cnf(start_point_defn_8,axiom,
( ~ start_point(A,B)
| A = C
| ~ incident_o(C,B)
| ordered_by(B,A,C) ) ).
cnf(o2_19,axiom,
open(ax2_sk3(A)) ).
cnf(o2_21,axiom,
( ~ incident_c(A,ax2_sk3(B))
| incident_o(A,B) ) ).
cnf(o4_29,axiom,
start_point(ax2_sk6(A),A) ).
cnf(theorem_4_11_133,negated_conjecture,
( ~ ordered_by(sk25,A,B)
| A = B ) ).
cnf(refute_0_0,plain,
( ~ ordered_by(sk25,ax2_sk6(sk25),ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)))
| ax2_sk6(sk25) = ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)) ),
inference(subst,[],[theorem_4_11_133:[bind(A,$fot(ax2_sk6(sk25))),bind(B,$fot(ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))))]]) ).
cnf(refute_0_1,plain,
start_point(ax2_sk6(X_9840),X_9840),
inference(subst,[],[o4_29:[bind(A,$fot(X_9840))]]) ).
cnf(refute_0_2,plain,
( ~ incident_o(X_9841,X_9840)
| ~ start_point(ax2_sk6(X_9840),X_9840)
| ax2_sk6(X_9840) = X_9841
| ordered_by(X_9840,ax2_sk6(X_9840),X_9841) ),
inference(subst,[],[start_point_defn_8:[bind(A,$fot(ax2_sk6(X_9840))),bind(B,$fot(X_9840)),bind(C,$fot(X_9841))]]) ).
cnf(refute_0_3,plain,
( ~ incident_o(X_9841,X_9840)
| ax2_sk6(X_9840) = X_9841
| ordered_by(X_9840,ax2_sk6(X_9840),X_9841) ),
inference(resolve,[$cnf( start_point(ax2_sk6(X_9840),X_9840) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ incident_o(ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)),sk25)
| ax2_sk6(sk25) = ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))
| ordered_by(sk25,ax2_sk6(sk25),ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))) ),
inference(subst,[],[refute_0_3:[bind(X_9840,$fot(sk25)),bind(X_9841,$fot(ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))))]]) ).
cnf(refute_0_5,plain,
( ~ incident_c(ax0_sk11(ax0_sk7(ax2_sk3(X_110)),ax2_sk3(X_110)),ax2_sk3(X_110))
| incident_o(ax0_sk11(ax0_sk7(ax2_sk3(X_110)),ax2_sk3(X_110)),X_110) ),
inference(subst,[],[o2_21:[bind(A,$fot(ax0_sk11(ax0_sk7(ax2_sk3(X_110)),ax2_sk3(X_110)))),bind(B,$fot(X_110))]]) ).
cnf(refute_0_6,plain,
( ~ end_point(ax0_sk11(ax0_sk7(ax2_sk3(X_109)),ax2_sk3(X_109)),ax2_sk3(X_109))
| incident_c(ax0_sk11(ax0_sk7(ax2_sk3(X_109)),ax2_sk3(X_109)),ax2_sk3(X_109)) ),
inference(subst,[],[end_point_defn_13:[bind(A,$fot(ax0_sk11(ax0_sk7(ax2_sk3(X_109)),ax2_sk3(X_109)))),bind(B,$fot(ax2_sk3(X_109)))]]) ).
cnf(refute_0_7,plain,
( ~ open(ax2_sk3(A))
| end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)) ),
inference(subst,[],[open_defn_33:[bind(A,$fot(ax2_sk3(A)))]]) ).
cnf(refute_0_8,plain,
end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),
inference(resolve,[$cnf( open(ax2_sk3(A)) )],[o2_19,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A))
| end_point(ax0_sk11(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),ax2_sk3(A)) ),
inference(subst,[],[c6_41:[bind(A,$fot(ax0_sk7(ax2_sk3(A)))),bind(B,$fot(ax2_sk3(A)))]]) ).
cnf(refute_0_10,plain,
end_point(ax0_sk11(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),ax2_sk3(A)),
inference(resolve,[$cnf( end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
end_point(ax0_sk11(ax0_sk7(ax2_sk3(X_109)),ax2_sk3(X_109)),ax2_sk3(X_109)),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_109))]]) ).
cnf(refute_0_12,plain,
incident_c(ax0_sk11(ax0_sk7(ax2_sk3(X_109)),ax2_sk3(X_109)),ax2_sk3(X_109)),
inference(resolve,[$cnf( end_point(ax0_sk11(ax0_sk7(ax2_sk3(X_109)),ax2_sk3(X_109)),ax2_sk3(X_109)) )],[refute_0_11,refute_0_6]) ).
cnf(refute_0_13,plain,
incident_c(ax0_sk11(ax0_sk7(ax2_sk3(X_110)),ax2_sk3(X_110)),ax2_sk3(X_110)),
inference(subst,[],[refute_0_12:[bind(X_109,$fot(X_110))]]) ).
cnf(refute_0_14,plain,
incident_o(ax0_sk11(ax0_sk7(ax2_sk3(X_110)),ax2_sk3(X_110)),X_110),
inference(resolve,[$cnf( incident_c(ax0_sk11(ax0_sk7(ax2_sk3(X_110)),ax2_sk3(X_110)),ax2_sk3(X_110)) )],[refute_0_13,refute_0_5]) ).
cnf(refute_0_15,plain,
incident_o(ax0_sk11(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)),sk25),
inference(subst,[],[refute_0_14:[bind(X_110,$fot(sk25))]]) ).
cnf(refute_0_16,plain,
( ~ ordered_by(sk25,ax2_sk6(sk25),ax0_sk7(ax2_sk3(sk25)))
| ax2_sk6(sk25) = ax0_sk7(ax2_sk3(sk25)) ),
inference(subst,[],[theorem_4_11_133:[bind(A,$fot(ax2_sk6(sk25))),bind(B,$fot(ax0_sk7(ax2_sk3(sk25))))]]) ).
cnf(refute_0_17,plain,
( ~ incident_c(ax0_sk7(ax2_sk3(X_20)),ax2_sk3(X_20))
| incident_o(ax0_sk7(ax2_sk3(X_20)),X_20) ),
inference(subst,[],[o2_21:[bind(A,$fot(ax0_sk7(ax2_sk3(X_20)))),bind(B,$fot(X_20))]]) ).
cnf(refute_0_18,plain,
( ~ end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A))
| incident_c(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)) ),
inference(subst,[],[end_point_defn_13:[bind(A,$fot(ax0_sk7(ax2_sk3(A)))),bind(B,$fot(ax2_sk3(A)))]]) ).
cnf(refute_0_19,plain,
incident_c(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)),
inference(resolve,[$cnf( end_point(ax0_sk7(ax2_sk3(A)),ax2_sk3(A)) )],[refute_0_8,refute_0_18]) ).
cnf(refute_0_20,plain,
incident_c(ax0_sk7(ax2_sk3(X_20)),ax2_sk3(X_20)),
inference(subst,[],[refute_0_19:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_21,plain,
incident_o(ax0_sk7(ax2_sk3(X_20)),X_20),
inference(resolve,[$cnf( incident_c(ax0_sk7(ax2_sk3(X_20)),ax2_sk3(X_20)) )],[refute_0_20,refute_0_17]) ).
cnf(refute_0_22,plain,
incident_o(ax0_sk7(ax2_sk3(X_9842)),X_9842),
inference(subst,[],[refute_0_21:[bind(X_20,$fot(X_9842))]]) ).
cnf(refute_0_23,plain,
( ~ incident_o(ax0_sk7(ax2_sk3(X_9842)),X_9842)
| ax2_sk6(X_9842) = ax0_sk7(ax2_sk3(X_9842))
| ordered_by(X_9842,ax2_sk6(X_9842),ax0_sk7(ax2_sk3(X_9842))) ),
inference(subst,[],[refute_0_3:[bind(X_9840,$fot(X_9842)),bind(X_9841,$fot(ax0_sk7(ax2_sk3(X_9842))))]]) ).
cnf(refute_0_24,plain,
( ax2_sk6(X_9842) = ax0_sk7(ax2_sk3(X_9842))
| ordered_by(X_9842,ax2_sk6(X_9842),ax0_sk7(ax2_sk3(X_9842))) ),
inference(resolve,[$cnf( incident_o(ax0_sk7(ax2_sk3(X_9842)),X_9842) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ax2_sk6(sk25) = ax0_sk7(ax2_sk3(sk25))
| ordered_by(sk25,ax2_sk6(sk25),ax0_sk7(ax2_sk3(sk25))) ),
inference(subst,[],[refute_0_24:[bind(X_9842,$fot(sk25))]]) ).
cnf(refute_0_26,plain,
ax2_sk6(sk25) = ax0_sk7(ax2_sk3(sk25)),
inference(resolve,[$cnf( ordered_by(sk25,ax2_sk6(sk25),ax0_sk7(ax2_sk3(sk25))) )],[refute_0_25,refute_0_16]) ).
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( $equal(X,X) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ax2_sk6(sk25) != ax0_sk7(ax2_sk3(sk25))
| ax0_sk7(ax2_sk3(sk25)) = ax2_sk6(sk25) ),
inference(subst,[],[refute_0_29:[bind(X,$fot(ax2_sk6(sk25))),bind(Y,$fot(ax0_sk7(ax2_sk3(sk25))))]]) ).
cnf(refute_0_31,plain,
ax0_sk7(ax2_sk3(sk25)) = ax2_sk6(sk25),
inference(resolve,[$cnf( $equal(ax2_sk6(sk25),ax0_sk7(ax2_sk3(sk25))) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( ax0_sk7(ax2_sk3(sk25)) != ax2_sk6(sk25)
| ~ incident_o(ax0_sk11(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)),sk25)
| incident_o(ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)),sk25) ),
introduced(tautology,[equality,[$cnf( incident_o(ax0_sk11(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)),sk25) ),[0,0],$fot(ax2_sk6(sk25))]]) ).
cnf(refute_0_33,plain,
( ~ incident_o(ax0_sk11(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)),sk25)
| incident_o(ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)),sk25) ),
inference(resolve,[$cnf( $equal(ax0_sk7(ax2_sk3(sk25)),ax2_sk6(sk25)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
incident_o(ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)),sk25),
inference(resolve,[$cnf( incident_o(ax0_sk11(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)),sk25) )],[refute_0_15,refute_0_33]) ).
cnf(refute_0_35,plain,
( ax2_sk6(sk25) = ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))
| ordered_by(sk25,ax2_sk6(sk25),ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))) ),
inference(resolve,[$cnf( incident_o(ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)),sk25) )],[refute_0_34,refute_0_4]) ).
cnf(refute_0_36,plain,
( ax2_sk6(sk25) != ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))
| ~ end_point(ax2_sk6(sk25),ax2_sk3(sk25)) ),
inference(subst,[],[c6_42:[bind(A,$fot(ax2_sk6(sk25))),bind(B,$fot(ax2_sk3(sk25)))]]) ).
cnf(refute_0_37,plain,
end_point(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)),
inference(subst,[],[refute_0_8:[bind(A,$fot(sk25))]]) ).
cnf(refute_0_38,plain,
( ax0_sk7(ax2_sk3(sk25)) != ax2_sk6(sk25)
| ~ end_point(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25))
| end_point(ax2_sk6(sk25),ax2_sk3(sk25)) ),
introduced(tautology,[equality,[$cnf( end_point(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)) ),[0],$fot(ax2_sk6(sk25))]]) ).
cnf(refute_0_39,plain,
( ~ end_point(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25))
| end_point(ax2_sk6(sk25),ax2_sk3(sk25)) ),
inference(resolve,[$cnf( $equal(ax0_sk7(ax2_sk3(sk25)),ax2_sk6(sk25)) )],[refute_0_31,refute_0_38]) ).
cnf(refute_0_40,plain,
end_point(ax2_sk6(sk25),ax2_sk3(sk25)),
inference(resolve,[$cnf( end_point(ax0_sk7(ax2_sk3(sk25)),ax2_sk3(sk25)) )],[refute_0_37,refute_0_39]) ).
cnf(refute_0_41,plain,
ax2_sk6(sk25) != ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)),
inference(resolve,[$cnf( end_point(ax2_sk6(sk25),ax2_sk3(sk25)) )],[refute_0_40,refute_0_36]) ).
cnf(refute_0_42,plain,
ordered_by(sk25,ax2_sk6(sk25),ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))),
inference(resolve,[$cnf( $equal(ax2_sk6(sk25),ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))) )],[refute_0_35,refute_0_41]) ).
cnf(refute_0_43,plain,
ax2_sk6(sk25) = ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25)),
inference(resolve,[$cnf( ordered_by(sk25,ax2_sk6(sk25),ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))) )],[refute_0_42,refute_0_0]) ).
cnf(refute_0_44,plain,
$false,
inference(resolve,[$cnf( $equal(ax2_sk6(sk25),ax0_sk11(ax2_sk6(sk25),ax2_sk3(sk25))) )],[refute_0_43,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO126-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n009.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 : 600
% 0.12/0.33 % DateTime : Sat Jun 18 04:08:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 53.44/53.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.44/53.60
% 53.44/53.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 53.44/53.60
%------------------------------------------------------------------------------