TSTP Solution File: SYN190-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN190-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 09:00:19 EDT 2022
% Result : Unsatisfiable 0.40s 0.56s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 32
% Syntax : Number of clauses : 127 ( 51 unt; 0 nHn; 107 RR)
% Number of literals : 248 ( 0 equ; 123 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 22 ( 21 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 108 ( 39 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1,axiom,
s0(d) ).
cnf(axiom_9,axiom,
r0(b) ).
cnf(axiom_14,axiom,
p0(b,X) ).
cnf(axiom_15,axiom,
n0(a,b) ).
cnf(axiom_17,axiom,
q0(X,d) ).
cnf(axiom_19,axiom,
m0(X,d,Y) ).
cnf(axiom_20,axiom,
l0(a) ).
cnf(axiom_24,axiom,
l0(c) ).
cnf(axiom_32,axiom,
k0(b) ).
cnf(axiom_35,axiom,
m0(d,e,c) ).
cnf(axiom_36,axiom,
q0(a,b) ).
cnf(axiom_37,axiom,
n0(b,a) ).
cnf(rule_001,axiom,
( k1(I)
| ~ n0(J,I) ) ).
cnf(rule_002,axiom,
( l1(G,G)
| ~ n0(H,G) ) ).
cnf(rule_021,axiom,
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) ).
cnf(rule_107,axiom,
( q1(e,A,A)
| ~ m0(A,d,A)
| ~ m0(e,d,A) ) ).
cnf(rule_110,axiom,
( q1(B,B,B)
| ~ m0(C,D,B) ) ).
cnf(rule_120,axiom,
( q1(b,b,b)
| ~ r0(b) ) ).
cnf(rule_124,axiom,
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) ) ).
cnf(rule_125,axiom,
( s1(I)
| ~ p0(I,I) ) ).
cnf(rule_126,axiom,
( s1(F)
| ~ q0(F,G)
| ~ s1(H) ) ).
cnf(rule_127,axiom,
( k2(C,D)
| ~ m1(E,D,C)
| ~ k1(F)
| ~ k2(F,D) ) ).
cnf(rule_129,axiom,
( k2(J,J)
| ~ q1(A,J,J) ) ).
cnf(rule_133,axiom,
( l2(J,J)
| ~ p0(A,A)
| ~ s1(B)
| ~ m0(C,B,J) ) ).
cnf(rule_135,axiom,
( m2(F)
| ~ s0(F)
| ~ l1(G,H) ) ).
cnf(rule_188,axiom,
( r2(G)
| ~ r1(G)
| ~ l0(G) ) ).
cnf(rule_190,axiom,
( s2(d)
| ~ s1(a)
| ~ s0(d) ) ).
cnf(rule_231,axiom,
( m3(H,I,H)
| ~ r2(H)
| ~ k2(c,I) ) ).
cnf(rule_260,axiom,
( r3(G,H,H)
| ~ s2(H)
| ~ l2(c,G) ) ).
cnf(rule_268,axiom,
( r3(H,H,I)
| ~ m2(I)
| ~ m3(J,b,H)
| ~ r3(I,A,A) ) ).
cnf(rule_272,axiom,
( r3(J,A,B)
| ~ k2(A,B)
| ~ r2(B)
| ~ r3(B,J,J) ) ).
cnf(prove_this,negated_conjecture,
~ r3(a,X,d) ).
cnf(refute_0_0,plain,
( ~ l0(X_193)
| ~ r1(X_193)
| r2(X_193) ),
inference(subst,[],[rule_188:[bind(G,$fot(X_193))]]) ).
cnf(refute_0_1,plain,
q0(X_191,d),
inference(subst,[],[axiom_17:[bind(X,$fot(X_191))]]) ).
cnf(refute_0_2,plain,
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ),
inference(resolve,[$cnf( s0(d) )],[axiom_1,rule_124]) ).
cnf(refute_0_3,plain,
( ~ q0(X_191,d)
| ~ q1(d,d,d)
| r1(X_191) ),
inference(subst,[],[refute_0_2:[bind(D,$fot(X_191)),bind(E,$fot(d))]]) ).
cnf(refute_0_4,plain,
( ~ q1(d,d,d)
| r1(X_191) ),
inference(resolve,[$cnf( q0(X_191,d) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
m0(X_164,d,X_163),
inference(subst,[],[axiom_19:[bind(X,$fot(X_164)),bind(Y,$fot(X_163))]]) ).
cnf(refute_0_6,plain,
( ~ m0(X_164,d,X_163)
| q1(X_163,X_163,X_163) ),
inference(subst,[],[rule_110:[bind(B,$fot(X_163)),bind(C,$fot(X_164)),bind(D,$fot(d))]]) ).
cnf(refute_0_7,plain,
q1(X_163,X_163,X_163),
inference(resolve,[$cnf( m0(X_164,d,X_163) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
q1(d,d,d),
inference(subst,[],[refute_0_7:[bind(X_163,$fot(d))]]) ).
cnf(refute_0_9,plain,
r1(X_191),
inference(resolve,[$cnf( q1(d,d,d) )],[refute_0_8,refute_0_4]) ).
cnf(refute_0_10,plain,
r1(X_193),
inference(subst,[],[refute_0_9:[bind(X_191,$fot(X_193))]]) ).
cnf(refute_0_11,plain,
( ~ l0(X_193)
| r2(X_193) ),
inference(resolve,[$cnf( r1(X_193) )],[refute_0_10,refute_0_0]) ).
cnf(refute_0_12,plain,
( ~ l0(a)
| r2(a) ),
inference(subst,[],[refute_0_11:[bind(X_193,$fot(a))]]) ).
cnf(refute_0_13,plain,
r2(a),
inference(resolve,[$cnf( l0(a) )],[axiom_20,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ k2(c,b)
| ~ r2(H)
| m3(H,b,H) ),
inference(subst,[],[rule_231:[bind(I,$fot(b))]]) ).
cnf(refute_0_15,plain,
q1(b,b,b),
inference(resolve,[$cnf( r0(b) )],[axiom_9,rule_120]) ).
cnf(refute_0_16,plain,
( ~ q1(b,b,b)
| k2(b,b) ),
inference(subst,[],[rule_129:[bind(A,$fot(b)),bind(J,$fot(b))]]) ).
cnf(refute_0_17,plain,
k2(b,b),
inference(resolve,[$cnf( q1(b,b,b) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ k0(X_173)
| ~ l0(a)
| m1(a,X_173,a) ),
inference(subst,[],[rule_021:[bind(I,$fot(a)),bind(J,$fot(X_173))]]) ).
cnf(refute_0_19,plain,
( ~ k0(X_173)
| m1(a,X_173,a) ),
inference(resolve,[$cnf( l0(a) )],[axiom_20,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ k0(b)
| m1(a,b,a) ),
inference(subst,[],[refute_0_19:[bind(X_173,$fot(b))]]) ).
cnf(refute_0_21,plain,
m1(a,b,a),
inference(resolve,[$cnf( k0(b) )],[axiom_32,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ k1(X_723)
| ~ k2(X_723,b)
| ~ m1(a,b,a)
| k2(a,b) ),
inference(subst,[],[rule_127:[bind(C,$fot(a)),bind(D,$fot(b)),bind(E,$fot(a)),bind(F,$fot(X_723))]]) ).
cnf(refute_0_23,plain,
( ~ k1(X_723)
| ~ k2(X_723,b)
| k2(a,b) ),
inference(resolve,[$cnf( m1(a,b,a) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ k1(b)
| ~ k2(b,b)
| k2(a,b) ),
inference(subst,[],[refute_0_23:[bind(X_723,$fot(b))]]) ).
cnf(refute_0_25,plain,
( ~ k1(b)
| k2(a,b) ),
inference(resolve,[$cnf( k2(b,b) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ n0(a,b)
| k1(b) ),
inference(subst,[],[rule_001:[bind(I,$fot(b)),bind(J,$fot(a))]]) ).
cnf(refute_0_27,plain,
k1(b),
inference(resolve,[$cnf( n0(a,b) )],[axiom_15,refute_0_26]) ).
cnf(refute_0_28,plain,
k2(a,b),
inference(resolve,[$cnf( k1(b) )],[refute_0_27,refute_0_25]) ).
cnf(refute_0_29,plain,
( ~ k0(X_173)
| ~ l0(c)
| m1(c,X_173,c) ),
inference(subst,[],[rule_021:[bind(I,$fot(c)),bind(J,$fot(X_173))]]) ).
cnf(refute_0_30,plain,
( ~ k0(X_173)
| m1(c,X_173,c) ),
inference(resolve,[$cnf( l0(c) )],[axiom_24,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ k0(b)
| m1(c,b,c) ),
inference(subst,[],[refute_0_30:[bind(X_173,$fot(b))]]) ).
cnf(refute_0_32,plain,
m1(c,b,c),
inference(resolve,[$cnf( k0(b) )],[axiom_32,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ k1(X_723)
| ~ k2(X_723,b)
| ~ m1(c,b,c)
| k2(c,b) ),
inference(subst,[],[rule_127:[bind(C,$fot(c)),bind(D,$fot(b)),bind(E,$fot(c)),bind(F,$fot(X_723))]]) ).
cnf(refute_0_34,plain,
( ~ k1(X_723)
| ~ k2(X_723,b)
| k2(c,b) ),
inference(resolve,[$cnf( m1(c,b,c) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ k1(a)
| ~ k2(a,b)
| k2(c,b) ),
inference(subst,[],[refute_0_34:[bind(X_723,$fot(a))]]) ).
cnf(refute_0_36,plain,
( ~ k1(a)
| k2(c,b) ),
inference(resolve,[$cnf( k2(a,b) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ n0(b,a)
| k1(a) ),
inference(subst,[],[rule_001:[bind(I,$fot(a)),bind(J,$fot(b))]]) ).
cnf(refute_0_38,plain,
k1(a),
inference(resolve,[$cnf( n0(b,a) )],[axiom_37,refute_0_37]) ).
cnf(refute_0_39,plain,
k2(c,b),
inference(resolve,[$cnf( k1(a) )],[refute_0_38,refute_0_36]) ).
cnf(refute_0_40,plain,
( ~ r2(H)
| m3(H,b,H) ),
inference(resolve,[$cnf( k2(c,b) )],[refute_0_39,refute_0_14]) ).
cnf(refute_0_41,plain,
( ~ r2(a)
| m3(a,b,a) ),
inference(subst,[],[refute_0_40:[bind(H,$fot(a))]]) ).
cnf(refute_0_42,plain,
m3(a,b,a),
inference(resolve,[$cnf( r2(a) )],[refute_0_13,refute_0_41]) ).
cnf(refute_0_43,plain,
m0(A,d,A),
inference(subst,[],[axiom_19:[bind(X,$fot(A)),bind(Y,$fot(A))]]) ).
cnf(refute_0_44,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[$cnf( m0(A,d,A) )],[refute_0_43,rule_107]) ).
cnf(refute_0_45,plain,
m0(e,d,A),
inference(subst,[],[axiom_19:[bind(X,$fot(e)),bind(Y,$fot(A))]]) ).
cnf(refute_0_46,plain,
q1(e,A,A),
inference(resolve,[$cnf( m0(e,d,A) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
q1(e,X_83,X_83),
inference(subst,[],[refute_0_46:[bind(A,$fot(X_83))]]) ).
cnf(refute_0_48,plain,
( ~ q1(e,X_83,X_83)
| k2(X_83,X_83) ),
inference(subst,[],[rule_129:[bind(A,$fot(e)),bind(J,$fot(X_83))]]) ).
cnf(refute_0_49,plain,
k2(X_83,X_83),
inference(resolve,[$cnf( q1(e,X_83,X_83) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
k2(X_655,X_655),
inference(subst,[],[refute_0_49:[bind(X_83,$fot(X_655))]]) ).
cnf(refute_0_51,plain,
( ~ k2(X_655,X_655)
| ~ r2(X_655)
| ~ r3(X_655,X_656,X_656)
| r3(X_656,X_655,X_655) ),
inference(subst,[],[rule_272:[bind(A,$fot(X_655)),bind(B,$fot(X_655)),bind(J,$fot(X_656))]]) ).
cnf(refute_0_52,plain,
( ~ r2(X_655)
| ~ r3(X_655,X_656,X_656)
| r3(X_656,X_655,X_655) ),
inference(resolve,[$cnf( k2(X_655,X_655) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ r2(c)
| ~ r3(c,d,d)
| r3(d,c,c) ),
inference(subst,[],[refute_0_52:[bind(X_655,$fot(c)),bind(X_656,$fot(d))]]) ).
cnf(refute_0_54,plain,
( ~ s1(a)
| s2(d) ),
inference(resolve,[$cnf( s0(d) )],[axiom_1,rule_190]) ).
cnf(refute_0_55,plain,
p0(b,b),
inference(subst,[],[axiom_14:[bind(X,$fot(b))]]) ).
cnf(refute_0_56,plain,
( ~ p0(b,b)
| s1(b) ),
inference(subst,[],[rule_125:[bind(I,$fot(b))]]) ).
cnf(refute_0_57,plain,
s1(b),
inference(resolve,[$cnf( p0(b,b) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ q0(a,b)
| ~ s1(X_212)
| s1(a) ),
inference(subst,[],[rule_126:[bind(F,$fot(a)),bind(G,$fot(b)),bind(H,$fot(X_212))]]) ).
cnf(refute_0_59,plain,
( ~ s1(X_212)
| s1(a) ),
inference(resolve,[$cnf( q0(a,b) )],[axiom_36,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ s1(b)
| s1(a) ),
inference(subst,[],[refute_0_59:[bind(X_212,$fot(b))]]) ).
cnf(refute_0_61,plain,
s1(a),
inference(resolve,[$cnf( s1(b) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
s2(d),
inference(resolve,[$cnf( s1(a) )],[refute_0_61,refute_0_54]) ).
cnf(refute_0_63,plain,
( ~ l2(c,c)
| ~ s2(H)
| r3(c,H,H) ),
inference(subst,[],[rule_260:[bind(G,$fot(c))]]) ).
cnf(refute_0_64,plain,
q0(X_210,d),
inference(subst,[],[axiom_17:[bind(X,$fot(X_210))]]) ).
cnf(refute_0_65,plain,
( ~ q0(X_210,d)
| ~ s1(X_212)
| s1(X_210) ),
inference(subst,[],[rule_126:[bind(F,$fot(X_210)),bind(G,$fot(d)),bind(H,$fot(X_212))]]) ).
cnf(refute_0_66,plain,
( ~ s1(X_212)
| s1(X_210) ),
inference(resolve,[$cnf( q0(X_210,d) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ s1(a)
| s1(X_216) ),
inference(subst,[],[refute_0_66:[bind(X_210,$fot(X_216)),bind(X_212,$fot(a))]]) ).
cnf(refute_0_68,plain,
s1(X_216),
inference(resolve,[$cnf( s1(a) )],[refute_0_61,refute_0_67]) ).
cnf(refute_0_69,plain,
s1(B),
inference(subst,[],[refute_0_68:[bind(X_216,$fot(B))]]) ).
cnf(refute_0_70,plain,
( ~ m0(C,B,J)
| ~ p0(A,A)
| l2(J,J) ),
inference(resolve,[$cnf( s1(B) )],[refute_0_69,rule_133]) ).
cnf(refute_0_71,plain,
( ~ m0(d,e,c)
| ~ p0(X_759,X_759)
| l2(c,c) ),
inference(subst,[],[refute_0_70:[bind(A,$fot(X_759)),bind(B,$fot(e)),bind(C,$fot(d)),bind(J,$fot(c))]]) ).
cnf(refute_0_72,plain,
( ~ p0(X_759,X_759)
| l2(c,c) ),
inference(resolve,[$cnf( m0(d,e,c) )],[axiom_35,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ p0(b,b)
| l2(c,c) ),
inference(subst,[],[refute_0_72:[bind(X_759,$fot(b))]]) ).
cnf(refute_0_74,plain,
l2(c,c),
inference(resolve,[$cnf( p0(b,b) )],[refute_0_55,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ s2(H)
| r3(c,H,H) ),
inference(resolve,[$cnf( l2(c,c) )],[refute_0_74,refute_0_63]) ).
cnf(refute_0_76,plain,
( ~ s2(d)
| r3(c,d,d) ),
inference(subst,[],[refute_0_75:[bind(H,$fot(d))]]) ).
cnf(refute_0_77,plain,
r3(c,d,d),
inference(resolve,[$cnf( s2(d) )],[refute_0_62,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ r2(c)
| r3(d,c,c) ),
inference(resolve,[$cnf( r3(c,d,d) )],[refute_0_77,refute_0_53]) ).
cnf(refute_0_79,plain,
( ~ l0(c)
| r2(c) ),
inference(subst,[],[refute_0_11:[bind(X_193,$fot(c))]]) ).
cnf(refute_0_80,plain,
r2(c),
inference(resolve,[$cnf( l0(c) )],[axiom_24,refute_0_79]) ).
cnf(refute_0_81,plain,
r3(d,c,c),
inference(resolve,[$cnf( r2(c) )],[refute_0_80,refute_0_78]) ).
cnf(refute_0_82,plain,
( ~ m2(d)
| ~ m3(X_920,b,X_918)
| ~ r3(d,c,c)
| r3(X_918,X_918,d) ),
inference(subst,[],[rule_268:[bind(A,$fot(c)),bind(H,$fot(X_918)),bind(I,$fot(d)),bind(J,$fot(X_920))]]) ).
cnf(refute_0_83,plain,
( ~ m2(d)
| ~ m3(X_920,b,X_918)
| r3(X_918,X_918,d) ),
inference(resolve,[$cnf( r3(d,c,c) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ n0(b,a)
| l1(a,a) ),
inference(subst,[],[rule_002:[bind(G,$fot(a)),bind(H,$fot(b))]]) ).
cnf(refute_0_85,plain,
l1(a,a),
inference(resolve,[$cnf( n0(b,a) )],[axiom_37,refute_0_84]) ).
cnf(refute_0_86,plain,
( ~ l1(a,a)
| ~ s0(X_220)
| m2(X_220) ),
inference(subst,[],[rule_135:[bind(F,$fot(X_220)),bind(G,$fot(a)),bind(H,$fot(a))]]) ).
cnf(refute_0_87,plain,
( ~ s0(X_220)
| m2(X_220) ),
inference(resolve,[$cnf( l1(a,a) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ s0(d)
| m2(d) ),
inference(subst,[],[refute_0_87:[bind(X_220,$fot(d))]]) ).
cnf(refute_0_89,plain,
m2(d),
inference(resolve,[$cnf( s0(d) )],[axiom_1,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ m3(X_920,b,X_918)
| r3(X_918,X_918,d) ),
inference(resolve,[$cnf( m2(d) )],[refute_0_89,refute_0_83]) ).
cnf(refute_0_91,plain,
( ~ m3(a,b,a)
| r3(a,a,d) ),
inference(subst,[],[refute_0_90:[bind(X_918,$fot(a)),bind(X_920,$fot(a))]]) ).
cnf(refute_0_92,plain,
r3(a,a,d),
inference(resolve,[$cnf( m3(a,b,a) )],[refute_0_42,refute_0_91]) ).
cnf(refute_0_93,plain,
~ r3(a,a,d),
inference(subst,[],[prove_this:[bind(X,$fot(a))]]) ).
cnf(refute_0_94,plain,
$false,
inference(resolve,[$cnf( r3(a,a,d) )],[refute_0_92,refute_0_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SYN190-1 : TPTP v8.1.0. Released v1.1.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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 : Mon Jul 11 20:07:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.56 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.56
% 0.40/0.56 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.40/0.57
%------------------------------------------------------------------------------