TSTP Solution File: SYN163-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN163-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 09:00:07 EDT 2022
% Result : Unsatisfiable 0.45s 0.61s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 49
% Syntax : Number of clauses : 220 ( 98 unt; 0 nHn; 140 RR)
% Number of literals : 411 ( 0 equ; 192 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 273 ( 100 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1,axiom,
s0(d) ).
cnf(axiom_5,axiom,
s0(b) ).
cnf(axiom_9,axiom,
r0(b) ).
cnf(axiom_12,axiom,
m0(a,X,a) ).
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_32,axiom,
k0(b) ).
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_016,axiom,
( m1(H,I,I)
| ~ m1(J,I,H)
| ~ m1(J,A,I) ) ).
cnf(rule_021,axiom,
( m1(I,J,I)
| ~ l0(I)
| ~ k0(J) ) ).
cnf(rule_024,axiom,
( m1(F,a,G)
| ~ m0(a,H,a)
| ~ q0(F,G)
| ~ m1(G,c,G) ) ).
cnf(rule_029,axiom,
( m1(H,I,H)
| ~ p0(H,I)
| ~ s0(H) ) ).
cnf(rule_072,axiom,
( p1(F,F,F)
| ~ s0(G)
| ~ s0(F) ) ).
cnf(rule_075,axiom,
( p1(a,a,a)
| ~ p0(b,a) ) ).
cnf(rule_082,axiom,
( p1(H,I,J)
| ~ m0(J,H,A)
| ~ p1(J,H,A) ) ).
cnf(rule_085,axiom,
( p1(B,B,B)
| ~ p0(C,B) ) ).
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_112,axiom,
( q1(A,A,A)
| ~ k1(A)
| ~ s0(b) ) ).
cnf(rule_113,axiom,
( q1(H,H,I)
| ~ r0(J)
| ~ m1(H,I,I) ) ).
cnf(rule_124,axiom,
( r1(D)
| ~ q0(D,E)
| ~ s0(d)
| ~ q1(d,E,d) ) ).
cnf(rule_129,axiom,
( k2(J,J)
| ~ q1(A,J,J) ) ).
cnf(rule_137,axiom,
( n2(A)
| ~ p1(B,C,A) ) ).
cnf(rule_146,axiom,
( p2(C,D,D)
| ~ p1(C,E,F)
| ~ l1(E,F)
| ~ p2(C,D,C) ) ).
cnf(rule_155,axiom,
( p2(H,I,I)
| ~ k1(J)
| ~ p2(e,H,I) ) ).
cnf(rule_176,axiom,
( p2(D,E,D)
| ~ m1(E,D,E) ) ).
cnf(rule_177,axiom,
( q2(E,F,F)
| ~ k0(F)
| ~ p1(E,E,E) ) ).
cnf(rule_181,axiom,
( q2(I,I,I)
| ~ p1(I,I,I) ) ).
cnf(rule_187,axiom,
( q2(C,D,C)
| ~ r1(D)
| ~ m0(E,F,C)
| ~ k0(D)
| ~ q2(D,D,D) ) ).
cnf(rule_194,axiom,
( k3(F,F,G)
| ~ k2(G,F) ) ).
cnf(rule_236,axiom,
( m3(A,A,A)
| ~ n2(A) ) ).
cnf(rule_241,axiom,
( p3(C,D,E)
| ~ q2(F,d,C)
| ~ k2(D,E) ) ).
cnf(rule_251,axiom,
( p3(A,B,B)
| ~ m3(B,C,D)
| ~ p2(A,B,D) ) ).
cnf(rule_255,axiom,
( q3(G,H)
| ~ q2(I,G,H)
| ~ n0(I,G) ) ).
cnf(rule_267,axiom,
( r3(B,C,B)
| ~ p2(B,D,C) ) ).
cnf(rule_276,axiom,
( k4(e)
| ~ q3(C,C)
| ~ q1(a,a,D)
| ~ r3(C,e,D) ) ).
cnf(rule_281,axiom,
( n4(J,A)
| ~ p3(J,A,A)
| ~ n4(J,J) ) ).
cnf(rule_284,axiom,
( n4(H,H)
| ~ k4(I)
| ~ m3(H,H,H) ) ).
cnf(rule_287,axiom,
( p4(B,C,B)
| ~ k3(B,B,C) ) ).
cnf(rule_295,axiom,
( q4(B,C)
| ~ k3(D,D,B)
| ~ q2(E,C,B)
| ~ m3(E,F,E) ) ).
cnf(rule_307,axiom,
( n5(B,C)
| ~ q4(D,E)
| ~ n4(B,E)
| ~ p4(F,F,C)
| ~ n5(F,C) ) ).
cnf(rule_309,axiom,
( n5(H,H)
| ~ n4(I,H) ) ).
cnf(prove_this,negated_conjecture,
~ n5(e,a) ).
cnf(refute_0_0,plain,
( ~ n4(X_454,X_454)
| ~ p3(X_454,A,A)
| n4(X_454,A) ),
inference(subst,[],[rule_281:[bind(J,$fot(X_454))]]) ).
cnf(refute_0_1,plain,
( ~ n2(X_111)
| m3(X_111,X_111,X_111) ),
inference(subst,[],[rule_236:[bind(A,$fot(X_111))]]) ).
cnf(refute_0_2,plain,
p0(b,X_66),
inference(subst,[],[axiom_14:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_3,plain,
( ~ p0(b,X_66)
| p1(X_66,X_66,X_66) ),
inference(subst,[],[rule_085:[bind(B,$fot(X_66)),bind(C,$fot(b))]]) ).
cnf(refute_0_4,plain,
p1(X_66,X_66,X_66),
inference(resolve,[$cnf( p0(b,X_66) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
p1(X_108,X_108,X_108),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(X_108))]]) ).
cnf(refute_0_6,plain,
( ~ p1(X_108,X_108,X_108)
| n2(X_108) ),
inference(subst,[],[rule_137:[bind(A,$fot(X_108)),bind(B,$fot(X_108)),bind(C,$fot(X_108))]]) ).
cnf(refute_0_7,plain,
n2(X_108),
inference(resolve,[$cnf( p1(X_108,X_108,X_108) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
n2(X_111),
inference(subst,[],[refute_0_7:[bind(X_108,$fot(X_111))]]) ).
cnf(refute_0_9,plain,
m3(X_111,X_111,X_111),
inference(resolve,[$cnf( n2(X_111) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
m3(H,H,H),
inference(subst,[],[refute_0_9:[bind(X_111,$fot(H))]]) ).
cnf(refute_0_11,plain,
( ~ k4(I)
| n4(H,H) ),
inference(resolve,[$cnf( m3(H,H,H) )],[refute_0_10,rule_284]) ).
cnf(refute_0_12,plain,
( ~ k4(e)
| n4(H,H) ),
inference(subst,[],[refute_0_11:[bind(I,$fot(e))]]) ).
cnf(refute_0_13,plain,
( ~ p2(b,e,e)
| r3(b,e,b) ),
inference(subst,[],[rule_267:[bind(B,$fot(b)),bind(C,$fot(e)),bind(D,$fot(e))]]) ).
cnf(refute_0_14,plain,
( ~ n0(b,a)
| k1(a) ),
inference(subst,[],[rule_001:[bind(I,$fot(a)),bind(J,$fot(b))]]) ).
cnf(refute_0_15,plain,
k1(a),
inference(resolve,[$cnf( n0(b,a) )],[axiom_37,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ m1(b,X_178,b)
| p2(X_178,b,X_178) ),
inference(subst,[],[rule_176:[bind(D,$fot(X_178)),bind(E,$fot(b))]]) ).
cnf(refute_0_17,plain,
p0(b,X_177),
inference(subst,[],[axiom_14:[bind(X,$fot(X_177))]]) ).
cnf(refute_0_18,plain,
( ~ p0(b,X_177)
| ~ s0(b)
| m1(b,X_177,b) ),
inference(subst,[],[rule_029:[bind(H,$fot(b)),bind(I,$fot(X_177))]]) ).
cnf(refute_0_19,plain,
( ~ s0(b)
| m1(b,X_177,b) ),
inference(resolve,[$cnf( p0(b,X_177) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
m1(b,X_177,b),
inference(resolve,[$cnf( s0(b) )],[axiom_5,refute_0_19]) ).
cnf(refute_0_21,plain,
m1(b,X_178,b),
inference(subst,[],[refute_0_20:[bind(X_177,$fot(X_178))]]) ).
cnf(refute_0_22,plain,
p2(X_178,b,X_178),
inference(resolve,[$cnf( m1(b,X_178,b) )],[refute_0_21,refute_0_16]) ).
cnf(refute_0_23,plain,
p2(e,b,e),
inference(subst,[],[refute_0_22:[bind(X_178,$fot(e))]]) ).
cnf(refute_0_24,plain,
( ~ k1(X_315)
| ~ p2(e,b,e)
| p2(b,e,e) ),
inference(subst,[],[rule_155:[bind(H,$fot(b)),bind(I,$fot(e)),bind(J,$fot(X_315))]]) ).
cnf(refute_0_25,plain,
( ~ k1(X_315)
| p2(b,e,e) ),
inference(resolve,[$cnf( p2(e,b,e) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ k1(a)
| p2(b,e,e) ),
inference(subst,[],[refute_0_25:[bind(X_315,$fot(a))]]) ).
cnf(refute_0_27,plain,
p2(b,e,e),
inference(resolve,[$cnf( k1(a) )],[refute_0_15,refute_0_26]) ).
cnf(refute_0_28,plain,
r3(b,e,b),
inference(resolve,[$cnf( p2(b,e,e) )],[refute_0_27,refute_0_13]) ).
cnf(refute_0_29,plain,
( ~ q1(a,a,b)
| ~ q3(b,b)
| ~ r3(b,e,b)
| k4(e) ),
inference(subst,[],[rule_276:[bind(C,$fot(b)),bind(D,$fot(b))]]) ).
cnf(refute_0_30,plain,
( ~ q1(a,a,b)
| ~ q3(b,b)
| k4(e) ),
inference(resolve,[$cnf( r3(b,e,b) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
p1(E,E,E),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(E))]]) ).
cnf(refute_0_32,plain,
( ~ k0(F)
| q2(E,F,F) ),
inference(resolve,[$cnf( p1(E,E,E) )],[refute_0_31,rule_177]) ).
cnf(refute_0_33,plain,
( ~ k0(b)
| q2(X_230,b,b) ),
inference(subst,[],[refute_0_32:[bind(E,$fot(X_230)),bind(F,$fot(b))]]) ).
cnf(refute_0_34,plain,
q2(X_230,b,b),
inference(resolve,[$cnf( k0(b) )],[axiom_32,refute_0_33]) ).
cnf(refute_0_35,plain,
q2(X_325,b,b),
inference(subst,[],[refute_0_34:[bind(X_230,$fot(X_325))]]) ).
cnf(refute_0_36,plain,
( ~ n0(X_325,b)
| ~ q2(X_325,b,b)
| q3(b,b) ),
inference(subst,[],[rule_255:[bind(G,$fot(b)),bind(H,$fot(b)),bind(I,$fot(X_325))]]) ).
cnf(refute_0_37,plain,
( ~ n0(X_325,b)
| q3(b,b) ),
inference(resolve,[$cnf( q2(X_325,b,b) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ n0(a,b)
| q3(b,b) ),
inference(subst,[],[refute_0_37:[bind(X_325,$fot(a))]]) ).
cnf(refute_0_39,plain,
q3(b,b),
inference(resolve,[$cnf( n0(a,b) )],[axiom_15,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ q1(a,a,b)
| k4(e) ),
inference(resolve,[$cnf( q3(b,b) )],[refute_0_39,refute_0_30]) ).
cnf(refute_0_41,plain,
( ~ m1(a,b,b)
| ~ r0(J)
| q1(a,a,b) ),
inference(subst,[],[rule_113:[bind(H,$fot(a)),bind(I,$fot(b))]]) ).
cnf(refute_0_42,plain,
m1(b,c,b),
inference(subst,[],[refute_0_20:[bind(X_177,$fot(c))]]) ).
cnf(refute_0_43,plain,
m0(a,H,a),
inference(subst,[],[axiom_12:[bind(X,$fot(H))]]) ).
cnf(refute_0_44,plain,
( ~ m1(G,c,G)
| ~ q0(F,G)
| m1(F,a,G) ),
inference(resolve,[$cnf( m0(a,H,a) )],[refute_0_43,rule_024]) ).
cnf(refute_0_45,plain,
( ~ m1(b,c,b)
| ~ q0(X_258,b)
| m1(X_258,a,b) ),
inference(subst,[],[refute_0_44:[bind(F,$fot(X_258)),bind(G,$fot(b))]]) ).
cnf(refute_0_46,plain,
( ~ q0(X_258,b)
| m1(X_258,a,b) ),
inference(resolve,[$cnf( m1(b,c,b) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ q0(a,b)
| m1(a,a,b) ),
inference(subst,[],[refute_0_46:[bind(X_258,$fot(a))]]) ).
cnf(refute_0_48,plain,
m1(a,a,b),
inference(resolve,[$cnf( q0(a,b) )],[axiom_36,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ k0(X_166)
| ~ l0(a)
| m1(a,X_166,a) ),
inference(subst,[],[rule_021:[bind(I,$fot(a)),bind(J,$fot(X_166))]]) ).
cnf(refute_0_50,plain,
( ~ k0(X_166)
| m1(a,X_166,a) ),
inference(resolve,[$cnf( l0(a) )],[axiom_20,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ k0(b)
| m1(a,b,a) ),
inference(subst,[],[refute_0_50:[bind(X_166,$fot(b))]]) ).
cnf(refute_0_52,plain,
m1(a,b,a),
inference(resolve,[$cnf( k0(b) )],[axiom_32,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ m1(a,X_438,b)
| ~ m1(a,b,a)
| m1(a,b,b) ),
inference(subst,[],[rule_016:[bind(A,$fot(X_438)),bind(H,$fot(a)),bind(I,$fot(b)),bind(J,$fot(a))]]) ).
cnf(refute_0_54,plain,
( ~ m1(a,X_438,b)
| m1(a,b,b) ),
inference(resolve,[$cnf( m1(a,b,a) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ m1(a,a,b)
| m1(a,b,b) ),
inference(subst,[],[refute_0_54:[bind(X_438,$fot(a))]]) ).
cnf(refute_0_56,plain,
m1(a,b,b),
inference(resolve,[$cnf( m1(a,a,b) )],[refute_0_48,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ r0(J)
| q1(a,a,b) ),
inference(resolve,[$cnf( m1(a,b,b) )],[refute_0_56,refute_0_41]) ).
cnf(refute_0_58,plain,
( ~ r0(b)
| q1(a,a,b) ),
inference(subst,[],[refute_0_57:[bind(J,$fot(b))]]) ).
cnf(refute_0_59,plain,
q1(a,a,b),
inference(resolve,[$cnf( r0(b) )],[axiom_9,refute_0_58]) ).
cnf(refute_0_60,plain,
k4(e),
inference(resolve,[$cnf( q1(a,a,b) )],[refute_0_59,refute_0_40]) ).
cnf(refute_0_61,plain,
n4(H,H),
inference(resolve,[$cnf( k4(e) )],[refute_0_60,refute_0_12]) ).
cnf(refute_0_62,plain,
n4(X_454,X_454),
inference(subst,[],[refute_0_61:[bind(H,$fot(X_454))]]) ).
cnf(refute_0_63,plain,
( ~ p3(X_454,A,A)
| n4(X_454,A) ),
inference(resolve,[$cnf( n4(X_454,X_454) )],[refute_0_62,refute_0_0]) ).
cnf(refute_0_64,plain,
( ~ p3(X_957,b,b)
| n4(X_957,b) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(b)),bind(X_454,$fot(X_957))]]) ).
cnf(refute_0_65,plain,
m3(X_560,X_560,X_560),
inference(subst,[],[refute_0_9:[bind(X_111,$fot(X_560))]]) ).
cnf(refute_0_66,plain,
( ~ m3(X_560,X_560,X_560)
| ~ p2(X_557,X_560,X_560)
| p3(X_557,X_560,X_560) ),
inference(subst,[],[rule_251:[bind(A,$fot(X_557)),bind(B,$fot(X_560)),bind(C,$fot(X_560)),bind(D,$fot(X_560))]]) ).
cnf(refute_0_67,plain,
( ~ p2(X_557,X_560,X_560)
| p3(X_557,X_560,X_560) ),
inference(resolve,[$cnf( m3(X_560,X_560,X_560) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ p2(X_956,b,b)
| p3(X_956,b,b) ),
inference(subst,[],[refute_0_67:[bind(X_557,$fot(X_956)),bind(X_560,$fot(b))]]) ).
cnf(refute_0_69,plain,
( ~ n0(b,a)
| l1(a,a) ),
inference(subst,[],[rule_002:[bind(G,$fot(a)),bind(H,$fot(b))]]) ).
cnf(refute_0_70,plain,
l1(a,a),
inference(resolve,[$cnf( n0(b,a) )],[axiom_37,refute_0_69]) ).
cnf(refute_0_71,plain,
p2(X_951,b,X_951),
inference(subst,[],[refute_0_22:[bind(X_178,$fot(X_951))]]) ).
cnf(refute_0_72,plain,
( ~ m0(a,X_497,a)
| ~ p1(a,X_497,a)
| p1(X_497,I,a) ),
inference(subst,[],[rule_082:[bind(A,$fot(a)),bind(H,$fot(X_497)),bind(J,$fot(a))]]) ).
cnf(refute_0_73,plain,
p0(b,a),
inference(subst,[],[axiom_14:[bind(X,$fot(a))]]) ).
cnf(refute_0_74,plain,
p1(a,a,a),
inference(resolve,[$cnf( p0(b,a) )],[refute_0_73,rule_075]) ).
cnf(refute_0_75,plain,
( ~ m0(a,a,a)
| ~ p1(a,a,a)
| p1(a,X_495,a) ),
inference(subst,[],[rule_082:[bind(A,$fot(a)),bind(H,$fot(a)),bind(I,$fot(X_495)),bind(J,$fot(a))]]) ).
cnf(refute_0_76,plain,
( ~ m0(a,a,a)
| p1(a,X_495,a) ),
inference(resolve,[$cnf( p1(a,a,a) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
m0(a,a,a),
inference(subst,[],[axiom_12:[bind(X,$fot(a))]]) ).
cnf(refute_0_78,plain,
p1(a,X_495,a),
inference(resolve,[$cnf( m0(a,a,a) )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
p1(a,X_497,a),
inference(subst,[],[refute_0_78:[bind(X_495,$fot(X_497))]]) ).
cnf(refute_0_80,plain,
( ~ m0(a,X_497,a)
| p1(X_497,I,a) ),
inference(resolve,[$cnf( p1(a,X_497,a) )],[refute_0_79,refute_0_72]) ).
cnf(refute_0_81,plain,
m0(a,X_497,a),
inference(subst,[],[axiom_12:[bind(X,$fot(X_497))]]) ).
cnf(refute_0_82,plain,
p1(X_497,I,a),
inference(resolve,[$cnf( m0(a,X_497,a) )],[refute_0_81,refute_0_80]) ).
cnf(refute_0_83,plain,
p1(X_930,X_932,a),
inference(subst,[],[refute_0_82:[bind(I,$fot(X_932)),bind(X_497,$fot(X_930))]]) ).
cnf(refute_0_84,plain,
( ~ l1(X_932,a)
| ~ p1(X_930,X_932,a)
| ~ p2(X_930,X_931,X_930)
| p2(X_930,X_931,X_931) ),
inference(subst,[],[rule_146:[bind(C,$fot(X_930)),bind(D,$fot(X_931)),bind(E,$fot(X_932)),bind(F,$fot(a))]]) ).
cnf(refute_0_85,plain,
( ~ l1(X_932,a)
| ~ p2(X_930,X_931,X_930)
| p2(X_930,X_931,X_931) ),
inference(resolve,[$cnf( p1(X_930,X_932,a) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( ~ l1(X_953,a)
| ~ p2(X_951,b,X_951)
| p2(X_951,b,b) ),
inference(subst,[],[refute_0_85:[bind(X_930,$fot(X_951)),bind(X_931,$fot(b)),bind(X_932,$fot(X_953))]]) ).
cnf(refute_0_87,plain,
( ~ l1(X_953,a)
| p2(X_951,b,b) ),
inference(resolve,[$cnf( p2(X_951,b,X_951) )],[refute_0_71,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ l1(a,a)
| p2(X_954,b,b) ),
inference(subst,[],[refute_0_87:[bind(X_951,$fot(X_954)),bind(X_953,$fot(a))]]) ).
cnf(refute_0_89,plain,
p2(X_954,b,b),
inference(resolve,[$cnf( l1(a,a) )],[refute_0_70,refute_0_88]) ).
cnf(refute_0_90,plain,
p2(X_956,b,b),
inference(subst,[],[refute_0_89:[bind(X_954,$fot(X_956))]]) ).
cnf(refute_0_91,plain,
p3(X_956,b,b),
inference(resolve,[$cnf( p2(X_956,b,b) )],[refute_0_90,refute_0_68]) ).
cnf(refute_0_92,plain,
p3(X_957,b,b),
inference(subst,[],[refute_0_91:[bind(X_956,$fot(X_957))]]) ).
cnf(refute_0_93,plain,
n4(X_957,b),
inference(resolve,[$cnf( p3(X_957,b,b) )],[refute_0_92,refute_0_64]) ).
cnf(refute_0_94,plain,
n4(X_1128,b),
inference(subst,[],[refute_0_93:[bind(X_957,$fot(X_1128))]]) ).
cnf(refute_0_95,plain,
( ~ k1(A)
| q1(A,A,A) ),
inference(resolve,[$cnf( s0(b) )],[axiom_5,rule_112]) ).
cnf(refute_0_96,plain,
( ~ k1(a)
| q1(a,a,a) ),
inference(subst,[],[refute_0_95:[bind(A,$fot(a))]]) ).
cnf(refute_0_97,plain,
q1(a,a,a),
inference(resolve,[$cnf( k1(a) )],[refute_0_15,refute_0_96]) ).
cnf(refute_0_98,plain,
( ~ q1(a,a,a)
| k2(a,a) ),
inference(subst,[],[rule_129:[bind(A,$fot(a)),bind(J,$fot(a))]]) ).
cnf(refute_0_99,plain,
k2(a,a),
inference(resolve,[$cnf( q1(a,a,a) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( ~ k2(a,a)
| k3(a,a,a) ),
inference(subst,[],[rule_194:[bind(F,$fot(a)),bind(G,$fot(a))]]) ).
cnf(refute_0_101,plain,
k3(a,a,a),
inference(resolve,[$cnf( k2(a,a) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
( ~ k3(a,a,a)
| p4(a,a,a) ),
inference(subst,[],[rule_287:[bind(B,$fot(a)),bind(C,$fot(a))]]) ).
cnf(refute_0_103,plain,
p4(a,a,a),
inference(resolve,[$cnf( k3(a,a,a) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ n4(X_1115,X_1118)
| ~ n5(a,a)
| ~ p4(a,a,a)
| ~ q4(X_1117,X_1118)
| n5(X_1115,a) ),
inference(subst,[],[rule_307:[bind(B,$fot(X_1115)),bind(C,$fot(a)),bind(D,$fot(X_1117)),bind(E,$fot(X_1118)),bind(F,$fot(a))]]) ).
cnf(refute_0_105,plain,
( ~ n4(X_1115,X_1118)
| ~ n5(a,a)
| ~ q4(X_1117,X_1118)
| n5(X_1115,a) ),
inference(resolve,[$cnf( p4(a,a,a) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( ~ n4(d,X_455)
| n5(X_455,X_455) ),
inference(subst,[],[rule_309:[bind(H,$fot(X_455)),bind(I,$fot(d))]]) ).
cnf(refute_0_107,plain,
( ~ n4(d,d)
| ~ p3(d,X_420,X_420)
| n4(d,X_420) ),
inference(subst,[],[rule_281:[bind(A,$fot(X_420)),bind(J,$fot(d))]]) ).
cnf(refute_0_108,plain,
m0(A,d,A),
inference(subst,[],[axiom_19:[bind(X,$fot(A)),bind(Y,$fot(A))]]) ).
cnf(refute_0_109,plain,
( ~ m0(e,d,A)
| q1(e,A,A) ),
inference(resolve,[$cnf( m0(A,d,A) )],[refute_0_108,rule_107]) ).
cnf(refute_0_110,plain,
m0(e,d,A),
inference(subst,[],[axiom_19:[bind(X,$fot(e)),bind(Y,$fot(A))]]) ).
cnf(refute_0_111,plain,
q1(e,A,A),
inference(resolve,[$cnf( m0(e,d,A) )],[refute_0_110,refute_0_109]) ).
cnf(refute_0_112,plain,
q1(e,X_78,X_78),
inference(subst,[],[refute_0_111:[bind(A,$fot(X_78))]]) ).
cnf(refute_0_113,plain,
( ~ q1(e,X_78,X_78)
| k2(X_78,X_78) ),
inference(subst,[],[rule_129:[bind(A,$fot(e)),bind(J,$fot(X_78))]]) ).
cnf(refute_0_114,plain,
k2(X_78,X_78),
inference(resolve,[$cnf( q1(e,X_78,X_78) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
k2(X_419,X_419),
inference(subst,[],[refute_0_114:[bind(X_78,$fot(X_419))]]) ).
cnf(refute_0_116,plain,
( ~ s0(d)
| p1(d,d,d) ),
inference(subst,[],[rule_072:[bind(F,$fot(d)),bind(G,$fot(d))]]) ).
cnf(refute_0_117,plain,
p1(d,d,d),
inference(resolve,[$cnf( s0(d) )],[axiom_1,refute_0_116]) ).
cnf(refute_0_118,plain,
( ~ p1(d,d,d)
| q2(d,d,d) ),
inference(subst,[],[rule_181:[bind(I,$fot(d))]]) ).
cnf(refute_0_119,plain,
q2(d,d,d),
inference(resolve,[$cnf( p1(d,d,d) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( ~ k2(X_415,X_416)
| ~ q2(d,d,d)
| p3(d,X_415,X_416) ),
inference(subst,[],[rule_241:[bind(C,$fot(d)),bind(D,$fot(X_415)),bind(E,$fot(X_416)),bind(F,$fot(d))]]) ).
cnf(refute_0_121,plain,
( ~ k2(X_415,X_416)
| p3(d,X_415,X_416) ),
inference(resolve,[$cnf( q2(d,d,d) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( ~ k2(X_419,X_419)
| p3(d,X_419,X_419) ),
inference(subst,[],[refute_0_121:[bind(X_415,$fot(X_419)),bind(X_416,$fot(X_419))]]) ).
cnf(refute_0_123,plain,
p3(d,X_419,X_419),
inference(resolve,[$cnf( k2(X_419,X_419) )],[refute_0_115,refute_0_122]) ).
cnf(refute_0_124,plain,
p3(d,X_420,X_420),
inference(subst,[],[refute_0_123:[bind(X_419,$fot(X_420))]]) ).
cnf(refute_0_125,plain,
( ~ n4(d,d)
| n4(d,X_420) ),
inference(resolve,[$cnf( p3(d,X_420,X_420) )],[refute_0_124,refute_0_107]) ).
cnf(refute_0_126,plain,
n4(d,d),
inference(subst,[],[refute_0_61:[bind(H,$fot(d))]]) ).
cnf(refute_0_127,plain,
n4(d,X_420),
inference(resolve,[$cnf( n4(d,d) )],[refute_0_126,refute_0_125]) ).
cnf(refute_0_128,plain,
n4(d,X_455),
inference(subst,[],[refute_0_127:[bind(X_420,$fot(X_455))]]) ).
cnf(refute_0_129,plain,
n5(X_455,X_455),
inference(resolve,[$cnf( n4(d,X_455) )],[refute_0_128,refute_0_106]) ).
cnf(refute_0_130,plain,
n5(a,a),
inference(subst,[],[refute_0_129:[bind(X_455,$fot(a))]]) ).
cnf(refute_0_131,plain,
( ~ n4(X_1115,X_1118)
| ~ q4(X_1117,X_1118)
| n5(X_1115,a) ),
inference(resolve,[$cnf( n5(a,a) )],[refute_0_130,refute_0_105]) ).
cnf(refute_0_132,plain,
( ~ n4(X_1128,b)
| ~ q4(X_1129,b)
| n5(X_1128,a) ),
inference(subst,[],[refute_0_131:[bind(X_1115,$fot(X_1128)),bind(X_1117,$fot(X_1129)),bind(X_1118,$fot(b))]]) ).
cnf(refute_0_133,plain,
( ~ q4(X_1129,b)
| n5(X_1128,a) ),
inference(resolve,[$cnf( n4(X_1128,b) )],[refute_0_94,refute_0_132]) ).
cnf(refute_0_134,plain,
m3(X_1069,X_1069,X_1069),
inference(subst,[],[refute_0_9:[bind(X_111,$fot(X_1069))]]) ).
cnf(refute_0_135,plain,
k2(X_84,X_84),
inference(subst,[],[refute_0_114:[bind(X_78,$fot(X_84))]]) ).
cnf(refute_0_136,plain,
( ~ k2(X_84,X_84)
| k3(X_84,X_84,X_84) ),
inference(subst,[],[rule_194:[bind(F,$fot(X_84)),bind(G,$fot(X_84))]]) ).
cnf(refute_0_137,plain,
k3(X_84,X_84,X_84),
inference(resolve,[$cnf( k2(X_84,X_84) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
k3(X_1024,X_1024,X_1024),
inference(subst,[],[refute_0_137:[bind(X_84,$fot(X_1024))]]) ).
cnf(refute_0_139,plain,
( ~ k3(X_1024,X_1024,X_1024)
| ~ m3(X_1027,X_1028,X_1027)
| ~ q2(X_1027,X_1025,X_1024)
| q4(X_1024,X_1025) ),
inference(subst,[],[rule_295:[bind(B,$fot(X_1024)),bind(C,$fot(X_1025)),bind(D,$fot(X_1024)),bind(E,$fot(X_1027)),bind(F,$fot(X_1028))]]) ).
cnf(refute_0_140,plain,
( ~ m3(X_1027,X_1028,X_1027)
| ~ q2(X_1027,X_1025,X_1024)
| q4(X_1024,X_1025) ),
inference(resolve,[$cnf( k3(X_1024,X_1024,X_1024) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( ~ m3(X_1069,X_1069,X_1069)
| ~ q2(X_1069,X_1067,X_1066)
| q4(X_1066,X_1067) ),
inference(subst,[],[refute_0_140:[bind(X_1024,$fot(X_1066)),bind(X_1025,$fot(X_1067)),bind(X_1027,$fot(X_1069)),bind(X_1028,$fot(X_1069))]]) ).
cnf(refute_0_142,plain,
( ~ q2(X_1069,X_1067,X_1066)
| q4(X_1066,X_1067) ),
inference(resolve,[$cnf( m3(X_1069,X_1069,X_1069) )],[refute_0_134,refute_0_141]) ).
cnf(refute_0_143,plain,
( ~ q2(X_1082,b,X_1082)
| q4(X_1082,b) ),
inference(subst,[],[refute_0_142:[bind(X_1066,$fot(X_1082)),bind(X_1067,$fot(b)),bind(X_1069,$fot(X_1082))]]) ).
cnf(refute_0_144,plain,
m0(X_1075,d,X_1073),
inference(subst,[],[axiom_19:[bind(X,$fot(X_1075)),bind(Y,$fot(X_1073))]]) ).
cnf(refute_0_145,plain,
( ~ p1(X_68,X_68,X_68)
| q2(X_68,X_68,X_68) ),
inference(subst,[],[rule_181:[bind(I,$fot(X_68))]]) ).
cnf(refute_0_146,plain,
p1(X_68,X_68,X_68),
inference(subst,[],[refute_0_4:[bind(X_66,$fot(X_68))]]) ).
cnf(refute_0_147,plain,
q2(X_68,X_68,X_68),
inference(resolve,[$cnf( p1(X_68,X_68,X_68) )],[refute_0_146,refute_0_145]) ).
cnf(refute_0_148,plain,
q2(D,D,D),
inference(subst,[],[refute_0_147:[bind(X_68,$fot(D))]]) ).
cnf(refute_0_149,plain,
( ~ k0(D)
| ~ m0(E,F,C)
| ~ r1(D)
| q2(C,D,C) ),
inference(resolve,[$cnf( q2(D,D,D) )],[refute_0_148,rule_187]) ).
cnf(refute_0_150,plain,
q0(X_188,d),
inference(subst,[],[axiom_17:[bind(X,$fot(X_188))]]) ).
cnf(refute_0_151,plain,
( ~ q0(D,E)
| ~ q1(d,E,d)
| r1(D) ),
inference(resolve,[$cnf( s0(d) )],[axiom_1,rule_124]) ).
cnf(refute_0_152,plain,
( ~ q0(X_188,d)
| ~ q1(d,d,d)
| r1(X_188) ),
inference(subst,[],[refute_0_151:[bind(D,$fot(X_188)),bind(E,$fot(d))]]) ).
cnf(refute_0_153,plain,
( ~ q1(d,d,d)
| r1(X_188) ),
inference(resolve,[$cnf( q0(X_188,d) )],[refute_0_150,refute_0_152]) ).
cnf(refute_0_154,plain,
m0(X_157,d,X_156),
inference(subst,[],[axiom_19:[bind(X,$fot(X_157)),bind(Y,$fot(X_156))]]) ).
cnf(refute_0_155,plain,
( ~ m0(X_157,d,X_156)
| q1(X_156,X_156,X_156) ),
inference(subst,[],[rule_110:[bind(B,$fot(X_156)),bind(C,$fot(X_157)),bind(D,$fot(d))]]) ).
cnf(refute_0_156,plain,
q1(X_156,X_156,X_156),
inference(resolve,[$cnf( m0(X_157,d,X_156) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
q1(d,d,d),
inference(subst,[],[refute_0_156:[bind(X_156,$fot(d))]]) ).
cnf(refute_0_158,plain,
r1(X_188),
inference(resolve,[$cnf( q1(d,d,d) )],[refute_0_157,refute_0_153]) ).
cnf(refute_0_159,plain,
r1(D),
inference(subst,[],[refute_0_158:[bind(X_188,$fot(D))]]) ).
cnf(refute_0_160,plain,
( ~ k0(D)
| ~ m0(E,F,C)
| q2(C,D,C) ),
inference(resolve,[$cnf( r1(D) )],[refute_0_159,refute_0_149]) ).
cnf(refute_0_161,plain,
( ~ k0(X_1074)
| ~ m0(X_1075,d,X_1073)
| q2(X_1073,X_1074,X_1073) ),
inference(subst,[],[refute_0_160:[bind(C,$fot(X_1073)),bind(D,$fot(X_1074)),bind(E,$fot(X_1075)),bind(F,$fot(d))]]) ).
cnf(refute_0_162,plain,
( ~ k0(X_1074)
| q2(X_1073,X_1074,X_1073) ),
inference(resolve,[$cnf( m0(X_1075,d,X_1073) )],[refute_0_144,refute_0_161]) ).
cnf(refute_0_163,plain,
( ~ k0(b)
| q2(X_1080,b,X_1080) ),
inference(subst,[],[refute_0_162:[bind(X_1073,$fot(X_1080)),bind(X_1074,$fot(b))]]) ).
cnf(refute_0_164,plain,
q2(X_1080,b,X_1080),
inference(resolve,[$cnf( k0(b) )],[axiom_32,refute_0_163]) ).
cnf(refute_0_165,plain,
q2(X_1082,b,X_1082),
inference(subst,[],[refute_0_164:[bind(X_1080,$fot(X_1082))]]) ).
cnf(refute_0_166,plain,
q4(X_1082,b),
inference(resolve,[$cnf( q2(X_1082,b,X_1082) )],[refute_0_165,refute_0_143]) ).
cnf(refute_0_167,plain,
q4(X_1129,b),
inference(subst,[],[refute_0_166:[bind(X_1082,$fot(X_1129))]]) ).
cnf(refute_0_168,plain,
n5(X_1128,a),
inference(resolve,[$cnf( q4(X_1129,b) )],[refute_0_167,refute_0_133]) ).
cnf(refute_0_169,plain,
n5(e,a),
inference(subst,[],[refute_0_168:[bind(X_1128,$fot(e))]]) ).
cnf(refute_0_170,plain,
$false,
inference(resolve,[$cnf( n5(e,a) )],[refute_0_169,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN163-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Tue Jul 12 04:09:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.45/0.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.61
% 0.45/0.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.45/0.63
%------------------------------------------------------------------------------