TSTP Solution File: SYN156-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN156-1 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 09:00:04 EDT 2022
% Result : Unsatisfiable 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of clauses : 109 ( 46 unt; 0 nHn; 85 RR)
% Number of literals : 200 ( 0 equ; 92 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 : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 98 ( 37 sgn)
% Comments :
%------------------------------------------------------------------------------
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_20,axiom,
l0(a) ).
cnf(axiom_28,axiom,
k0(e) ).
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_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_085,axiom,
( p1(B,B,B)
| ~ p0(C,B) ) ).
cnf(rule_113,axiom,
( q1(H,H,I)
| ~ r0(J)
| ~ m1(H,I,I) ) ).
cnf(rule_137,axiom,
( n2(A)
| ~ p1(B,C,A) ) ).
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_236,axiom,
( m3(A,A,A)
| ~ n2(A) ) ).
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(prove_this,negated_conjecture,
~ n4(a,e) ).
cnf(refute_0_0,plain,
( ~ n4(X_448,X_448)
| ~ p3(X_448,A,A)
| n4(X_448,A) ),
inference(subst,[],[rule_281:[bind(J,$fot(X_448))]]) ).
cnf(refute_0_1,plain,
( ~ n2(X_112)
| m3(X_112,X_112,X_112) ),
inference(subst,[],[rule_236:[bind(A,$fot(X_112))]]) ).
cnf(refute_0_2,plain,
p0(b,X_68),
inference(subst,[],[axiom_14:[bind(X,$fot(X_68))]]) ).
cnf(refute_0_3,plain,
( ~ p0(b,X_68)
| p1(X_68,X_68,X_68) ),
inference(subst,[],[rule_085:[bind(B,$fot(X_68)),bind(C,$fot(b))]]) ).
cnf(refute_0_4,plain,
p1(X_68,X_68,X_68),
inference(resolve,[$cnf( p0(b,X_68) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
p1(X_109,X_109,X_109),
inference(subst,[],[refute_0_4:[bind(X_68,$fot(X_109))]]) ).
cnf(refute_0_6,plain,
( ~ p1(X_109,X_109,X_109)
| n2(X_109) ),
inference(subst,[],[rule_137:[bind(A,$fot(X_109)),bind(B,$fot(X_109)),bind(C,$fot(X_109))]]) ).
cnf(refute_0_7,plain,
n2(X_109),
inference(resolve,[$cnf( p1(X_109,X_109,X_109) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
n2(X_112),
inference(subst,[],[refute_0_7:[bind(X_109,$fot(X_112))]]) ).
cnf(refute_0_9,plain,
m3(X_112,X_112,X_112),
inference(resolve,[$cnf( n2(X_112) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
m3(H,H,H),
inference(subst,[],[refute_0_9:[bind(X_112,$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_189,b)
| p2(X_189,b,X_189) ),
inference(subst,[],[rule_176:[bind(D,$fot(X_189)),bind(E,$fot(b))]]) ).
cnf(refute_0_17,plain,
p0(b,X_188),
inference(subst,[],[axiom_14:[bind(X,$fot(X_188))]]) ).
cnf(refute_0_18,plain,
( ~ p0(b,X_188)
| ~ s0(b)
| m1(b,X_188,b) ),
inference(subst,[],[rule_029:[bind(H,$fot(b)),bind(I,$fot(X_188))]]) ).
cnf(refute_0_19,plain,
( ~ s0(b)
| m1(b,X_188,b) ),
inference(resolve,[$cnf( p0(b,X_188) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
m1(b,X_188,b),
inference(resolve,[$cnf( s0(b) )],[axiom_5,refute_0_19]) ).
cnf(refute_0_21,plain,
m1(b,X_189,b),
inference(subst,[],[refute_0_20:[bind(X_188,$fot(X_189))]]) ).
cnf(refute_0_22,plain,
p2(X_189,b,X_189),
inference(resolve,[$cnf( m1(b,X_189,b) )],[refute_0_21,refute_0_16]) ).
cnf(refute_0_23,plain,
p2(e,b,e),
inference(subst,[],[refute_0_22:[bind(X_189,$fot(e))]]) ).
cnf(refute_0_24,plain,
( ~ k1(X_325)
| ~ p2(e,b,e)
| p2(b,e,e) ),
inference(subst,[],[rule_155:[bind(H,$fot(b)),bind(I,$fot(e)),bind(J,$fot(X_325))]]) ).
cnf(refute_0_25,plain,
( ~ k1(X_325)
| p2(b,e,e) ),
inference(resolve,[$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_325,$fot(a))]]) ).
cnf(refute_0_27,plain,
p2(b,e,e),
inference(resolve,[$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_68,$fot(E))]]) ).
cnf(refute_0_32,plain,
( ~ k0(F)
| q2(E,F,F) ),
inference(resolve,[$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,[$cnf( k0(b) )],[axiom_32,refute_0_33]) ).
cnf(refute_0_35,plain,
q2(X_334,b,b),
inference(subst,[],[refute_0_34:[bind(X_230,$fot(X_334))]]) ).
cnf(refute_0_36,plain,
( ~ n0(X_334,b)
| ~ q2(X_334,b,b)
| q3(b,b) ),
inference(subst,[],[rule_255:[bind(G,$fot(b)),bind(H,$fot(b)),bind(I,$fot(X_334))]]) ).
cnf(refute_0_37,plain,
( ~ n0(X_334,b)
| q3(b,b) ),
inference(resolve,[$cnf( q2(X_334,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_334,$fot(a))]]) ).
cnf(refute_0_39,plain,
q3(b,b),
inference(resolve,[$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,$fot(b))]]) ).
cnf(refute_0_42,plain,
m1(b,c,b),
inference(subst,[],[refute_0_20:[bind(X_188,$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,[$cnf( q0(a,b) )],[axiom_36,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ k0(X_170)
| ~ l0(a)
| m1(a,X_170,a) ),
inference(subst,[],[rule_021:[bind(I,$fot(a)),bind(J,$fot(X_170))]]) ).
cnf(refute_0_50,plain,
( ~ k0(X_170)
| m1(a,X_170,a) ),
inference(resolve,[$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_170,$fot(b))]]) ).
cnf(refute_0_52,plain,
m1(a,b,a),
inference(resolve,[$cnf( k0(b) )],[axiom_32,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ m1(a,X_440,b)
| ~ m1(a,b,a)
| m1(a,b,b) ),
inference(subst,[],[rule_016:[bind(A,$fot(X_440)),bind(H,$fot(a)),bind(I,$fot(b)),bind(J,$fot(a))]]) ).
cnf(refute_0_54,plain,
( ~ m1(a,X_440,b)
| m1(a,b,b) ),
inference(resolve,[$cnf( m1(a,b,a) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ m1(a,a,b)
| m1(a,b,b) ),
inference(subst,[],[refute_0_54:[bind(X_440,$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_448,X_448),
inference(subst,[],[refute_0_61:[bind(H,$fot(X_448))]]) ).
cnf(refute_0_63,plain,
( ~ p3(X_448,A,A)
| n4(X_448,A) ),
inference(resolve,[$cnf( n4(X_448,X_448) )],[refute_0_62,refute_0_0]) ).
cnf(refute_0_64,plain,
( ~ p3(a,e,e)
| n4(a,e) ),
inference(subst,[],[refute_0_63:[bind(A,$fot(e)),bind(X_448,$fot(a))]]) ).
cnf(refute_0_65,plain,
m3(e,e,e),
inference(subst,[],[refute_0_9:[bind(X_112,$fot(e))]]) ).
cnf(refute_0_66,plain,
( ~ m1(a,e,a)
| p2(e,a,e) ),
inference(subst,[],[rule_176:[bind(D,$fot(e)),bind(E,$fot(a))]]) ).
cnf(refute_0_67,plain,
( ~ k0(e)
| m1(a,e,a) ),
inference(subst,[],[refute_0_50:[bind(X_170,$fot(e))]]) ).
cnf(refute_0_68,plain,
m1(a,e,a),
inference(resolve,[$cnf( k0(e) )],[axiom_28,refute_0_67]) ).
cnf(refute_0_69,plain,
p2(e,a,e),
inference(resolve,[$cnf( m1(a,e,a) )],[refute_0_68,refute_0_66]) ).
cnf(refute_0_70,plain,
( ~ k1(X_325)
| ~ p2(e,a,e)
| p2(a,e,e) ),
inference(subst,[],[rule_155:[bind(H,$fot(a)),bind(I,$fot(e)),bind(J,$fot(X_325))]]) ).
cnf(refute_0_71,plain,
( ~ k1(X_325)
| p2(a,e,e) ),
inference(resolve,[$cnf( p2(e,a,e) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ k1(a)
| p2(a,e,e) ),
inference(subst,[],[refute_0_71:[bind(X_325,$fot(a))]]) ).
cnf(refute_0_73,plain,
p2(a,e,e),
inference(resolve,[$cnf( k1(a) )],[refute_0_15,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ m3(e,X_562,e)
| ~ p2(a,e,e)
| p3(a,e,e) ),
inference(subst,[],[rule_251:[bind(A,$fot(a)),bind(B,$fot(e)),bind(C,$fot(X_562)),bind(D,$fot(e))]]) ).
cnf(refute_0_75,plain,
( ~ m3(e,X_562,e)
| p3(a,e,e) ),
inference(resolve,[$cnf( p2(a,e,e) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ m3(e,e,e)
| p3(a,e,e) ),
inference(subst,[],[refute_0_75:[bind(X_562,$fot(e))]]) ).
cnf(refute_0_77,plain,
p3(a,e,e),
inference(resolve,[$cnf( m3(e,e,e) )],[refute_0_65,refute_0_76]) ).
cnf(refute_0_78,plain,
n4(a,e),
inference(resolve,[$cnf( p3(a,e,e) )],[refute_0_77,refute_0_64]) ).
cnf(refute_0_79,plain,
$false,
inference(resolve,[$cnf( n4(a,e) )],[refute_0_78,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN156-1 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n005.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 : Mon Jul 11 20:20:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53
% 0.19/0.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.54
%------------------------------------------------------------------------------