TSTP Solution File: SYN143-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN143-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 : Thu Jul 21 08:59:59 EDT 2022
% Result : Unsatisfiable 0.37s 0.56s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 29
% Syntax : Number of clauses : 118 ( 52 unt; 0 nHn; 79 RR)
% Number of literals : 221 ( 0 equ; 104 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 124 ( 54 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1,axiom,
s0(d) ).
cnf(axiom_5,axiom,
s0(b) ).
cnf(axiom_14,axiom,
p0(b,X) ).
cnf(axiom_17,axiom,
q0(X,d) ).
cnf(axiom_19,axiom,
m0(X,d,Y) ).
cnf(axiom_20,axiom,
l0(a) ).
cnf(axiom_28,axiom,
k0(e) ).
cnf(axiom_32,axiom,
k0(b) ).
cnf(axiom_34,axiom,
n0(c,d) ).
cnf(axiom_36,axiom,
q0(a,b) ).
cnf(axiom_37,axiom,
n0(b,a) ).
cnf(rule_002,axiom,
( l1(G,G)
| ~ n0(H,G) ) ).
cnf(rule_050,axiom,
( n1(D,E,D)
| ~ s0(b)
| ~ l0(D)
| ~ p0(b,E) ) ).
cnf(rule_054,axiom,
( n1(E,F,F)
| ~ l0(G)
| ~ l1(G,E)
| ~ n1(E,F,E) ) ).
cnf(rule_072,axiom,
( p1(F,F,F)
| ~ s0(G)
| ~ s0(F) ) ).
cnf(rule_085,axiom,
( p1(B,B,B)
| ~ p0(C,B) ) ).
cnf(rule_125,axiom,
( s1(I)
| ~ p0(I,I) ) ).
cnf(rule_126,axiom,
( s1(F)
| ~ q0(F,G)
| ~ s1(H) ) ).
cnf(rule_133,axiom,
( l2(J,J)
| ~ p0(A,A)
| ~ s1(B)
| ~ m0(C,B,J) ) ).
cnf(rule_137,axiom,
( n2(A)
| ~ p1(B,C,A) ) ).
cnf(rule_177,axiom,
( q2(E,F,F)
| ~ k0(F)
| ~ p1(E,E,E) ) ).
cnf(rule_182,axiom,
( q2(F,G,F)
| ~ p1(F,F,H)
| ~ n1(G,F,H)
| ~ q2(G,H,F) ) ).
cnf(rule_189,axiom,
( s2(H)
| ~ q2(b,H,b)
| ~ s1(b) ) ).
cnf(rule_244,axiom,
( p3(H,H,H)
| ~ n2(H) ) ).
cnf(rule_273,axiom,
( s3(I,J)
| ~ q2(A,I,A)
| ~ s2(I)
| ~ m0(A,B,J) ) ).
cnf(rule_279,axiom,
( m4(E,F)
| ~ l2(G,F)
| ~ s3(a,E) ) ).
cnf(rule_299,axiom,
( s4(A)
| ~ p3(B,C,D)
| ~ l1(A,C) ) ).
cnf(rule_305,axiom,
( m5(B,B)
| ~ s4(B)
| ~ m4(e,e) ) ).
cnf(prove_this,negated_conjecture,
~ m5(d,d) ).
cnf(refute_0_0,plain,
( ~ n0(c,d)
| l1(d,d) ),
inference(subst,[],[rule_002:[bind(G,$fot(d)),bind(H,$fot(c))]]) ).
cnf(refute_0_1,plain,
l1(d,d),
inference(resolve,[$cnf( n0(c,d) )],[axiom_34,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ n2(d)
| p3(d,d,d) ),
inference(subst,[],[rule_244:[bind(H,$fot(d))]]) ).
cnf(refute_0_3,plain,
( ~ s0(d)
| p1(d,d,d) ),
inference(subst,[],[rule_072:[bind(F,$fot(d)),bind(G,$fot(d))]]) ).
cnf(refute_0_4,plain,
p1(d,d,d),
inference(resolve,[$cnf( s0(d) )],[axiom_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ p1(d,d,d)
| n2(d) ),
inference(subst,[],[rule_137:[bind(A,$fot(d)),bind(B,$fot(d)),bind(C,$fot(d))]]) ).
cnf(refute_0_6,plain,
n2(d),
inference(resolve,[$cnf( p1(d,d,d) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
p3(d,d,d),
inference(resolve,[$cnf( n2(d) )],[refute_0_6,refute_0_2]) ).
cnf(refute_0_8,plain,
( ~ l1(X_347,d)
| ~ p3(d,d,d)
| s4(X_347) ),
inference(subst,[],[rule_299:[bind(A,$fot(X_347)),bind(B,$fot(d)),bind(C,$fot(d)),bind(D,$fot(d))]]) ).
cnf(refute_0_9,plain,
( ~ l1(X_347,d)
| s4(X_347) ),
inference(resolve,[$cnf( p3(d,d,d) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ l1(d,d)
| s4(d) ),
inference(subst,[],[refute_0_9:[bind(X_347,$fot(d))]]) ).
cnf(refute_0_11,plain,
s4(d),
inference(resolve,[$cnf( l1(d,d) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ l2(X_766,X_766)
| ~ s3(a,E)
| m4(E,X_766) ),
inference(subst,[],[rule_279:[bind(F,$fot(X_766)),bind(G,$fot(X_766))]]) ).
cnf(refute_0_13,plain,
p0(b,b),
inference(subst,[],[axiom_14:[bind(X,$fot(b))]]) ).
cnf(refute_0_14,plain,
m0(X_756,d,X_757),
inference(subst,[],[axiom_19:[bind(X,$fot(X_756)),bind(Y,$fot(X_757))]]) ).
cnf(refute_0_15,plain,
( ~ p0(b,b)
| s1(b) ),
inference(subst,[],[rule_125:[bind(I,$fot(b))]]) ).
cnf(refute_0_16,plain,
s1(b),
inference(resolve,[$cnf( p0(b,b) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ q0(a,b)
| ~ s1(X_216)
| s1(a) ),
inference(subst,[],[rule_126:[bind(F,$fot(a)),bind(G,$fot(b)),bind(H,$fot(X_216))]]) ).
cnf(refute_0_18,plain,
( ~ s1(X_216)
| s1(a) ),
inference(resolve,[$cnf( q0(a,b) )],[axiom_36,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ s1(b)
| s1(a) ),
inference(subst,[],[refute_0_18:[bind(X_216,$fot(b))]]) ).
cnf(refute_0_20,plain,
s1(a),
inference(resolve,[$cnf( s1(b) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
q0(X_214,d),
inference(subst,[],[axiom_17:[bind(X,$fot(X_214))]]) ).
cnf(refute_0_22,plain,
( ~ q0(X_214,d)
| ~ s1(X_216)
| s1(X_214) ),
inference(subst,[],[rule_126:[bind(F,$fot(X_214)),bind(G,$fot(d)),bind(H,$fot(X_216))]]) ).
cnf(refute_0_23,plain,
( ~ s1(X_216)
| s1(X_214) ),
inference(resolve,[$cnf( q0(X_214,d) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ s1(a)
| s1(X_220) ),
inference(subst,[],[refute_0_23:[bind(X_214,$fot(X_220)),bind(X_216,$fot(a))]]) ).
cnf(refute_0_25,plain,
s1(X_220),
inference(resolve,[$cnf( s1(a) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
s1(B),
inference(subst,[],[refute_0_25:[bind(X_220,$fot(B))]]) ).
cnf(refute_0_27,plain,
( ~ m0(C,B,J)
| ~ p0(A,A)
| l2(J,J) ),
inference(resolve,[$cnf( s1(B) )],[refute_0_26,rule_133]) ).
cnf(refute_0_28,plain,
( ~ m0(X_756,d,X_757)
| ~ p0(X_754,X_754)
| l2(X_757,X_757) ),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_754)),bind(B,$fot(d)),bind(C,$fot(X_756)),bind(J,$fot(X_757))]]) ).
cnf(refute_0_29,plain,
( ~ p0(X_754,X_754)
| l2(X_757,X_757) ),
inference(resolve,[$cnf( m0(X_756,d,X_757) )],[refute_0_14,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ p0(b,b)
| l2(X_765,X_765) ),
inference(subst,[],[refute_0_29:[bind(X_754,$fot(b)),bind(X_757,$fot(X_765))]]) ).
cnf(refute_0_31,plain,
l2(X_765,X_765),
inference(resolve,[$cnf( p0(b,b) )],[refute_0_13,refute_0_30]) ).
cnf(refute_0_32,plain,
l2(X_766,X_766),
inference(subst,[],[refute_0_31:[bind(X_765,$fot(X_766))]]) ).
cnf(refute_0_33,plain,
( ~ s3(a,E)
| m4(E,X_766) ),
inference(resolve,[$cnf( l2(X_766,X_766) )],[refute_0_32,refute_0_12]) ).
cnf(refute_0_34,plain,
( ~ s3(a,X_881)
| m4(X_881,X_766) ),
inference(subst,[],[refute_0_33:[bind(E,$fot(X_881))]]) ).
cnf(refute_0_35,plain,
m0(e,d,X_880),
inference(subst,[],[axiom_19:[bind(X,$fot(e)),bind(Y,$fot(X_880))]]) ).
cnf(refute_0_36,plain,
( ~ n0(b,a)
| l1(a,a) ),
inference(subst,[],[rule_002:[bind(G,$fot(a)),bind(H,$fot(b))]]) ).
cnf(refute_0_37,plain,
l1(a,a),
inference(resolve,[$cnf( n0(b,a) )],[axiom_37,refute_0_36]) ).
cnf(refute_0_38,plain,
p0(b,E),
inference(subst,[],[axiom_14:[bind(X,$fot(E))]]) ).
cnf(refute_0_39,plain,
( ~ l0(D)
| ~ s0(b)
| n1(D,E,D) ),
inference(resolve,[$cnf( p0(b,E) )],[refute_0_38,rule_050]) ).
cnf(refute_0_40,plain,
( ~ l0(D)
| n1(D,E,D) ),
inference(resolve,[$cnf( s0(b) )],[axiom_5,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ l0(a)
| n1(a,X_50,a) ),
inference(subst,[],[refute_0_40:[bind(D,$fot(a)),bind(E,$fot(X_50))]]) ).
cnf(refute_0_42,plain,
n1(a,X_50,a),
inference(resolve,[$cnf( l0(a) )],[axiom_20,refute_0_41]) ).
cnf(refute_0_43,plain,
n1(a,X_636,a),
inference(subst,[],[refute_0_42:[bind(X_50,$fot(X_636))]]) ).
cnf(refute_0_44,plain,
( ~ l0(X_637)
| ~ l1(X_637,a)
| ~ n1(a,X_636,a)
| n1(a,X_636,X_636) ),
inference(subst,[],[rule_054:[bind(E,$fot(a)),bind(F,$fot(X_636)),bind(G,$fot(X_637))]]) ).
cnf(refute_0_45,plain,
( ~ l0(X_637)
| ~ l1(X_637,a)
| n1(a,X_636,X_636) ),
inference(resolve,[$cnf( n1(a,X_636,a) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ l0(a)
| ~ l1(a,a)
| n1(a,X_643,X_643) ),
inference(subst,[],[refute_0_45:[bind(X_636,$fot(X_643)),bind(X_637,$fot(a))]]) ).
cnf(refute_0_47,plain,
( ~ l0(a)
| n1(a,X_643,X_643) ),
inference(resolve,[$cnf( l1(a,a) )],[refute_0_37,refute_0_46]) ).
cnf(refute_0_48,plain,
n1(a,X_643,X_643),
inference(resolve,[$cnf( l0(a) )],[axiom_20,refute_0_47]) ).
cnf(refute_0_49,plain,
n1(a,e,e),
inference(subst,[],[refute_0_48:[bind(X_643,$fot(e))]]) ).
cnf(refute_0_50,plain,
p0(b,X_69),
inference(subst,[],[axiom_14:[bind(X,$fot(X_69))]]) ).
cnf(refute_0_51,plain,
( ~ p0(b,X_69)
| p1(X_69,X_69,X_69) ),
inference(subst,[],[rule_085:[bind(B,$fot(X_69)),bind(C,$fot(b))]]) ).
cnf(refute_0_52,plain,
p1(X_69,X_69,X_69),
inference(resolve,[$cnf( p0(b,X_69) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
p1(E,E,E),
inference(subst,[],[refute_0_52:[bind(X_69,$fot(E))]]) ).
cnf(refute_0_54,plain,
( ~ k0(F)
| q2(E,F,F) ),
inference(resolve,[$cnf( p1(E,E,E) )],[refute_0_53,rule_177]) ).
cnf(refute_0_55,plain,
( ~ k0(e)
| q2(X_174,e,e) ),
inference(subst,[],[refute_0_54:[bind(E,$fot(X_174)),bind(F,$fot(e))]]) ).
cnf(refute_0_56,plain,
q2(X_174,e,e),
inference(resolve,[$cnf( k0(e) )],[axiom_28,refute_0_55]) ).
cnf(refute_0_57,plain,
q2(X_824,e,e),
inference(subst,[],[refute_0_56:[bind(X_174,$fot(X_824))]]) ).
cnf(refute_0_58,plain,
( ~ n1(X_824,e,e)
| ~ p1(e,e,e)
| ~ q2(X_824,e,e)
| q2(e,X_824,e) ),
inference(subst,[],[rule_182:[bind(F,$fot(e)),bind(G,$fot(X_824)),bind(H,$fot(e))]]) ).
cnf(refute_0_59,plain,
( ~ n1(X_824,e,e)
| ~ p1(e,e,e)
| q2(e,X_824,e) ),
inference(resolve,[$cnf( q2(X_824,e,e) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
p1(e,e,e),
inference(subst,[],[refute_0_52:[bind(X_69,$fot(e))]]) ).
cnf(refute_0_61,plain,
( ~ n1(X_824,e,e)
| q2(e,X_824,e) ),
inference(resolve,[$cnf( p1(e,e,e) )],[refute_0_60,refute_0_59]) ).
cnf(refute_0_62,plain,
( ~ n1(a,e,e)
| q2(e,a,e) ),
inference(subst,[],[refute_0_61:[bind(X_824,$fot(a))]]) ).
cnf(refute_0_63,plain,
q2(e,a,e),
inference(resolve,[$cnf( n1(a,e,e) )],[refute_0_49,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ m0(e,X_876,X_878)
| ~ q2(e,a,e)
| ~ s2(a)
| s3(a,X_878) ),
inference(subst,[],[rule_273:[bind(A,$fot(e)),bind(B,$fot(X_876)),bind(I,$fot(a)),bind(J,$fot(X_878))]]) ).
cnf(refute_0_65,plain,
( ~ m0(e,X_876,X_878)
| ~ s2(a)
| s3(a,X_878) ),
inference(resolve,[$cnf( q2(e,a,e) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ q2(b,H,b)
| s2(H) ),
inference(resolve,[$cnf( s1(b) )],[refute_0_16,rule_189]) ).
cnf(refute_0_67,plain,
( ~ q2(b,a,b)
| s2(a) ),
inference(subst,[],[refute_0_66:[bind(H,$fot(a))]]) ).
cnf(refute_0_68,plain,
n1(a,b,b),
inference(subst,[],[refute_0_48:[bind(X_643,$fot(b))]]) ).
cnf(refute_0_69,plain,
( ~ k0(b)
| q2(X_174,b,b) ),
inference(subst,[],[refute_0_54:[bind(E,$fot(X_174)),bind(F,$fot(b))]]) ).
cnf(refute_0_70,plain,
q2(X_174,b,b),
inference(resolve,[$cnf( k0(b) )],[axiom_32,refute_0_69]) ).
cnf(refute_0_71,plain,
q2(X_824,b,b),
inference(subst,[],[refute_0_70:[bind(X_174,$fot(X_824))]]) ).
cnf(refute_0_72,plain,
( ~ n1(X_824,b,b)
| ~ p1(b,b,b)
| ~ q2(X_824,b,b)
| q2(b,X_824,b) ),
inference(subst,[],[rule_182:[bind(F,$fot(b)),bind(G,$fot(X_824)),bind(H,$fot(b))]]) ).
cnf(refute_0_73,plain,
( ~ n1(X_824,b,b)
| ~ p1(b,b,b)
| q2(b,X_824,b) ),
inference(resolve,[$cnf( q2(X_824,b,b) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
p1(b,b,b),
inference(subst,[],[refute_0_52:[bind(X_69,$fot(b))]]) ).
cnf(refute_0_75,plain,
( ~ n1(X_824,b,b)
| q2(b,X_824,b) ),
inference(resolve,[$cnf( p1(b,b,b) )],[refute_0_74,refute_0_73]) ).
cnf(refute_0_76,plain,
( ~ n1(a,b,b)
| q2(b,a,b) ),
inference(subst,[],[refute_0_75:[bind(X_824,$fot(a))]]) ).
cnf(refute_0_77,plain,
q2(b,a,b),
inference(resolve,[$cnf( n1(a,b,b) )],[refute_0_68,refute_0_76]) ).
cnf(refute_0_78,plain,
s2(a),
inference(resolve,[$cnf( q2(b,a,b) )],[refute_0_77,refute_0_67]) ).
cnf(refute_0_79,plain,
( ~ m0(e,X_876,X_878)
| s3(a,X_878) ),
inference(resolve,[$cnf( s2(a) )],[refute_0_78,refute_0_65]) ).
cnf(refute_0_80,plain,
( ~ m0(e,d,X_880)
| s3(a,X_880) ),
inference(subst,[],[refute_0_79:[bind(X_876,$fot(d)),bind(X_878,$fot(X_880))]]) ).
cnf(refute_0_81,plain,
s3(a,X_880),
inference(resolve,[$cnf( m0(e,d,X_880) )],[refute_0_35,refute_0_80]) ).
cnf(refute_0_82,plain,
s3(a,X_881),
inference(subst,[],[refute_0_81:[bind(X_880,$fot(X_881))]]) ).
cnf(refute_0_83,plain,
m4(X_881,X_766),
inference(resolve,[$cnf( s3(a,X_881) )],[refute_0_82,refute_0_34]) ).
cnf(refute_0_84,plain,
m4(e,e),
inference(subst,[],[refute_0_83:[bind(X_766,$fot(e)),bind(X_881,$fot(e))]]) ).
cnf(refute_0_85,plain,
( ~ s4(B)
| m5(B,B) ),
inference(resolve,[$cnf( m4(e,e) )],[refute_0_84,rule_305]) ).
cnf(refute_0_86,plain,
( ~ s4(d)
| m5(d,d) ),
inference(subst,[],[refute_0_85:[bind(B,$fot(d))]]) ).
cnf(refute_0_87,plain,
m5(d,d),
inference(resolve,[$cnf( s4(d) )],[refute_0_11,refute_0_86]) ).
cnf(refute_0_88,plain,
$false,
inference(resolve,[$cnf( m5(d,d) )],[refute_0_87,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN143-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jul 12 08:53:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.37/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.56
% 0.37/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.37/0.57
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