TSTP Solution File: SYN116-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN116-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 08:59:47 EDT 2022
% Result : Unsatisfiable 1.62s 1.80s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 50
% Syntax : Number of clauses : 142 ( 78 unt; 0 nHn; 81 RR)
% Number of literals : 239 ( 238 equ; 99 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 148 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
cnf(axiom_3,axiom,
n0(d,e) = true ).
cnf(axiom_14,axiom,
p0(b,X) = true ).
cnf(axiom_15,axiom,
n0(a,b) = true ).
cnf(rule_001,axiom,
ifeq(n0(J,I),true,k1(I),true) = true ).
cnf(rule_002,axiom,
ifeq(n0(H,G),true,l1(G,G),true) = true ).
cnf(rule_085,axiom,
ifeq(p0(C,B),true,p1(B,B,B),true) = true ).
cnf(rule_137,axiom,
ifeq(p1(B,C,A),true,n2(A),true) = true ).
cnf(rule_174,axiom,
ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) = true ).
cnf(rule_244,axiom,
ifeq(n2(H),true,p3(H,H,H),true) = true ).
cnf(rule_267,axiom,
ifeq(p2(B,D,C),true,r3(B,C,B),true) = true ).
cnf(rule_299,axiom,
ifeq(p3(B,C,D),true,ifeq(l1(A,C),true,s4(A),true),true) = true ).
cnf(rule_300,axiom,
ifeq(s4(F),true,ifeq(r3(G,E,E),true,k5(E),true),true) = true ).
cnf(prove_this,negated_conjecture,
k5(b) != true ).
cnf(refute_0_0,plain,
ifeq(s4(X_363),true,ifeq(r3(X_362,X_362,X_362),true,k5(X_362),true),true) = true,
inference(subst,[],[rule_300:[bind(E,$fot(X_362)),bind(F,$fot(X_363)),bind(G,$fot(X_362))]]) ).
cnf(refute_0_1,plain,
ifeq(p2(X_324,X_324,X_324),true,r3(X_324,X_324,X_324),true) = true,
inference(subst,[],[rule_267:[bind(B,$fot(X_324)),bind(C,$fot(X_324)),bind(D,$fot(X_324))]]) ).
cnf(refute_0_2,plain,
ifeq(true,true,p2(H,H,H),true) = p2(H,H,H),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(p2(H,H,H))),bind(C,$fot(true))]]) ).
cnf(refute_0_3,plain,
ifeq(n0(d,e),true,k1(e),true) = true,
inference(subst,[],[rule_001:[bind(I,$fot(e)),bind(J,$fot(d))]]) ).
cnf(refute_0_4,plain,
( ifeq(n0(d,e),true,k1(e),true) != true
| n0(d,e) != true
| ifeq(true,true,k1(e),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n0(d,e),true,k1(e),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_5,plain,
( ifeq(n0(d,e),true,k1(e),true) != true
| ifeq(true,true,k1(e),true) = true ),
inference(resolve,[$cnf( $equal(n0(d,e),true) )],[axiom_3,refute_0_4]) ).
cnf(refute_0_6,plain,
ifeq(true,true,k1(e),true) = true,
inference(resolve,[$cnf( $equal(ifeq(n0(d,e),true,k1(e),true),true) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
ifeq(true,true,k1(e),true) = k1(e),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(k1(e))),bind(C,$fot(true))]]) ).
cnf(refute_0_8,plain,
( ifeq(true,true,k1(e),true) != k1(e)
| ifeq(true,true,k1(e),true) != true
| k1(e) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,k1(e),true),true) ),[0],$fot(k1(e))]]) ).
cnf(refute_0_9,plain,
( ifeq(true,true,k1(e),true) != true
| k1(e) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,k1(e),true),k1(e)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
k1(e) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,k1(e),true),true) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
ifeq(k1(e),true,p2(H,H,H),true) = ifeq(k1(e),true,p2(H,H,H),true),
introduced(tautology,[refl,[$fot(ifeq(k1(e),true,p2(H,H,H),true))]]) ).
cnf(refute_0_12,plain,
( ifeq(k1(e),true,p2(H,H,H),true) != ifeq(k1(e),true,p2(H,H,H),true)
| k1(e) != true
| ifeq(k1(e),true,p2(H,H,H),true) = ifeq(true,true,p2(H,H,H),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(k1(e),true,p2(H,H,H),true),ifeq(k1(e),true,p2(H,H,H),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_13,plain,
( k1(e) != true
| ifeq(k1(e),true,p2(H,H,H),true) = ifeq(true,true,p2(H,H,H),true) ),
inference(resolve,[$cnf( $equal(ifeq(k1(e),true,p2(H,H,H),true),ifeq(k1(e),true,p2(H,H,H),true)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
ifeq(k1(e),true,p2(H,H,H),true) = ifeq(true,true,p2(H,H,H),true),
inference(resolve,[$cnf( $equal(k1(e),true) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_17,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ifeq(k1(e),true,p2(H,H,H),true) != ifeq(true,true,p2(H,H,H),true)
| ifeq(true,true,p2(H,H,H),true) != p2(H,H,H)
| ifeq(k1(e),true,p2(H,H,H),true) = p2(H,H,H) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(ifeq(k1(e),true,p2(H,H,H),true))),bind(Y,$fot(ifeq(true,true,p2(H,H,H),true))),bind(Z,$fot(p2(H,H,H)))]]) ).
cnf(refute_0_21,plain,
( ifeq(true,true,p2(H,H,H),true) != p2(H,H,H)
| ifeq(k1(e),true,p2(H,H,H),true) = p2(H,H,H) ),
inference(resolve,[$cnf( $equal(ifeq(k1(e),true,p2(H,H,H),true),ifeq(true,true,p2(H,H,H),true)) )],[refute_0_14,refute_0_20]) ).
cnf(refute_0_22,plain,
ifeq(k1(e),true,p2(H,H,H),true) = p2(H,H,H),
inference(resolve,[$cnf( $equal(ifeq(true,true,p2(H,H,H),true),p2(H,H,H)) )],[refute_0_2,refute_0_21]) ).
cnf(refute_0_23,plain,
ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) = ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true),
introduced(tautology,[refl,[$fot(ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true))]]) ).
cnf(refute_0_24,plain,
( ifeq(k1(e),true,p2(H,H,H),true) != p2(H,H,H)
| ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) != ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true)
| ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) = ifeq(n2(H),true,p2(H,H,H),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true),ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true)) ),[1,2],$fot(p2(H,H,H))]]) ).
cnf(refute_0_25,plain,
( ifeq(k1(e),true,p2(H,H,H),true) != p2(H,H,H)
| ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) = ifeq(n2(H),true,p2(H,H,H),true) ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true),ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) = ifeq(n2(H),true,p2(H,H,H),true),
inference(resolve,[$cnf( $equal(ifeq(k1(e),true,p2(H,H,H),true),p2(H,H,H)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
( ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) != ifeq(n2(H),true,p2(H,H,H),true)
| ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) != true
| ifeq(n2(H),true,p2(H,H,H),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true),true) ),[0],$fot(ifeq(n2(H),true,p2(H,H,H),true))]]) ).
cnf(refute_0_28,plain,
( ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true) != true
| ifeq(n2(H),true,p2(H,H,H),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true),ifeq(n2(H),true,p2(H,H,H),true)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
ifeq(n2(H),true,p2(H,H,H),true) = true,
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,ifeq(k1(e),true,p2(H,H,H),true),true),true) )],[rule_174,refute_0_28]) ).
cnf(refute_0_30,plain,
ifeq(p1(X_203,X_203,X_203),true,n2(X_203),true) = true,
inference(subst,[],[rule_137:[bind(A,$fot(X_203)),bind(B,$fot(X_203)),bind(C,$fot(X_203))]]) ).
cnf(refute_0_31,plain,
ifeq(p0(b,X_80),true,p1(X_80,X_80,X_80),true) = true,
inference(subst,[],[rule_085:[bind(B,$fot(X_80)),bind(C,$fot(b))]]) ).
cnf(refute_0_32,plain,
p0(b,X_80) = true,
inference(subst,[],[axiom_14:[bind(X,$fot(X_80))]]) ).
cnf(refute_0_33,plain,
( ifeq(p0(b,X_80),true,p1(X_80,X_80,X_80),true) != true
| p0(b,X_80) != true
| ifeq(true,true,p1(X_80,X_80,X_80),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(p0(b,X_80),true,p1(X_80,X_80,X_80),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_34,plain,
( ifeq(p0(b,X_80),true,p1(X_80,X_80,X_80),true) != true
| ifeq(true,true,p1(X_80,X_80,X_80),true) = true ),
inference(resolve,[$cnf( $equal(p0(b,X_80),true) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
ifeq(true,true,p1(X_80,X_80,X_80),true) = true,
inference(resolve,[$cnf( $equal(ifeq(p0(b,X_80),true,p1(X_80,X_80,X_80),true),true) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
ifeq(true,true,p1(X_80,X_80,X_80),true) = p1(X_80,X_80,X_80),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(p1(X_80,X_80,X_80))),bind(C,$fot(true))]]) ).
cnf(refute_0_37,plain,
( ifeq(true,true,p1(X_80,X_80,X_80),true) != p1(X_80,X_80,X_80)
| ifeq(true,true,p1(X_80,X_80,X_80),true) != true
| p1(X_80,X_80,X_80) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,p1(X_80,X_80,X_80),true),true) ),[0],$fot(p1(X_80,X_80,X_80))]]) ).
cnf(refute_0_38,plain,
( ifeq(true,true,p1(X_80,X_80,X_80),true) != true
| p1(X_80,X_80,X_80) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,p1(X_80,X_80,X_80),true),p1(X_80,X_80,X_80)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
p1(X_80,X_80,X_80) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,p1(X_80,X_80,X_80),true),true) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
p1(X_203,X_203,X_203) = true,
inference(subst,[],[refute_0_39:[bind(X_80,$fot(X_203))]]) ).
cnf(refute_0_41,plain,
( ifeq(p1(X_203,X_203,X_203),true,n2(X_203),true) != true
| p1(X_203,X_203,X_203) != true
| ifeq(true,true,n2(X_203),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(p1(X_203,X_203,X_203),true,n2(X_203),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_42,plain,
( ifeq(p1(X_203,X_203,X_203),true,n2(X_203),true) != true
| ifeq(true,true,n2(X_203),true) = true ),
inference(resolve,[$cnf( $equal(p1(X_203,X_203,X_203),true) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
ifeq(true,true,n2(X_203),true) = true,
inference(resolve,[$cnf( $equal(ifeq(p1(X_203,X_203,X_203),true,n2(X_203),true),true) )],[refute_0_30,refute_0_42]) ).
cnf(refute_0_44,plain,
ifeq(true,true,n2(X_203),true) = n2(X_203),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(n2(X_203))),bind(C,$fot(true))]]) ).
cnf(refute_0_45,plain,
( ifeq(true,true,n2(X_203),true) != n2(X_203)
| ifeq(true,true,n2(X_203),true) != true
| n2(X_203) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,n2(X_203),true),true) ),[0],$fot(n2(X_203))]]) ).
cnf(refute_0_46,plain,
( ifeq(true,true,n2(X_203),true) != true
| n2(X_203) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,n2(X_203),true),n2(X_203)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
n2(X_203) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,n2(X_203),true),true) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
n2(H) = true,
inference(subst,[],[refute_0_47:[bind(X_203,$fot(H))]]) ).
cnf(refute_0_49,plain,
ifeq(n2(H),true,p2(H,H,H),true) = ifeq(n2(H),true,p2(H,H,H),true),
introduced(tautology,[refl,[$fot(ifeq(n2(H),true,p2(H,H,H),true))]]) ).
cnf(refute_0_50,plain,
( ifeq(n2(H),true,p2(H,H,H),true) != ifeq(n2(H),true,p2(H,H,H),true)
| n2(H) != true
| ifeq(n2(H),true,p2(H,H,H),true) = ifeq(true,true,p2(H,H,H),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n2(H),true,p2(H,H,H),true),ifeq(n2(H),true,p2(H,H,H),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_51,plain,
( n2(H) != true
| ifeq(n2(H),true,p2(H,H,H),true) = ifeq(true,true,p2(H,H,H),true) ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p2(H,H,H),true),ifeq(n2(H),true,p2(H,H,H),true)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
ifeq(n2(H),true,p2(H,H,H),true) = ifeq(true,true,p2(H,H,H),true),
inference(resolve,[$cnf( $equal(n2(H),true) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
( ifeq(n2(H),true,p2(H,H,H),true) != ifeq(true,true,p2(H,H,H),true)
| ifeq(true,true,p2(H,H,H),true) != p2(H,H,H)
| ifeq(n2(H),true,p2(H,H,H),true) = p2(H,H,H) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(ifeq(n2(H),true,p2(H,H,H),true))),bind(Y,$fot(ifeq(true,true,p2(H,H,H),true))),bind(Z,$fot(p2(H,H,H)))]]) ).
cnf(refute_0_54,plain,
( ifeq(true,true,p2(H,H,H),true) != p2(H,H,H)
| ifeq(n2(H),true,p2(H,H,H),true) = p2(H,H,H) ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p2(H,H,H),true),ifeq(true,true,p2(H,H,H),true)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
ifeq(n2(H),true,p2(H,H,H),true) = p2(H,H,H),
inference(resolve,[$cnf( $equal(ifeq(true,true,p2(H,H,H),true),p2(H,H,H)) )],[refute_0_2,refute_0_54]) ).
cnf(refute_0_56,plain,
( ifeq(n2(H),true,p2(H,H,H),true) != p2(H,H,H)
| ifeq(n2(H),true,p2(H,H,H),true) != true
| p2(H,H,H) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n2(H),true,p2(H,H,H),true),true) ),[0],$fot(p2(H,H,H))]]) ).
cnf(refute_0_57,plain,
( ifeq(n2(H),true,p2(H,H,H),true) != true
| p2(H,H,H) = true ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p2(H,H,H),true),p2(H,H,H)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
p2(H,H,H) = true,
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p2(H,H,H),true),true) )],[refute_0_29,refute_0_57]) ).
cnf(refute_0_59,plain,
p2(X_324,X_324,X_324) = true,
inference(subst,[],[refute_0_58:[bind(H,$fot(X_324))]]) ).
cnf(refute_0_60,plain,
( ifeq(p2(X_324,X_324,X_324),true,r3(X_324,X_324,X_324),true) != true
| p2(X_324,X_324,X_324) != true
| ifeq(true,true,r3(X_324,X_324,X_324),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(p2(X_324,X_324,X_324),true,r3(X_324,X_324,X_324),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_61,plain,
( ifeq(p2(X_324,X_324,X_324),true,r3(X_324,X_324,X_324),true) != true
| ifeq(true,true,r3(X_324,X_324,X_324),true) = true ),
inference(resolve,[$cnf( $equal(p2(X_324,X_324,X_324),true) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
ifeq(true,true,r3(X_324,X_324,X_324),true) = true,
inference(resolve,[$cnf( $equal(ifeq(p2(X_324,X_324,X_324),true,r3(X_324,X_324,X_324),true),true) )],[refute_0_1,refute_0_61]) ).
cnf(refute_0_63,plain,
ifeq(true,true,r3(X_324,X_324,X_324),true) = r3(X_324,X_324,X_324),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(r3(X_324,X_324,X_324))),bind(C,$fot(true))]]) ).
cnf(refute_0_64,plain,
( ifeq(true,true,r3(X_324,X_324,X_324),true) != r3(X_324,X_324,X_324)
| ifeq(true,true,r3(X_324,X_324,X_324),true) != true
| r3(X_324,X_324,X_324) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,r3(X_324,X_324,X_324),true),true) ),[0],$fot(r3(X_324,X_324,X_324))]]) ).
cnf(refute_0_65,plain,
( ifeq(true,true,r3(X_324,X_324,X_324),true) != true
| r3(X_324,X_324,X_324) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,r3(X_324,X_324,X_324),true),r3(X_324,X_324,X_324)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
r3(X_324,X_324,X_324) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,r3(X_324,X_324,X_324),true),true) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
r3(X_362,X_362,X_362) = true,
inference(subst,[],[refute_0_66:[bind(X_324,$fot(X_362))]]) ).
cnf(refute_0_68,plain,
( ifeq(s4(X_363),true,ifeq(r3(X_362,X_362,X_362),true,k5(X_362),true),true) != true
| r3(X_362,X_362,X_362) != true
| ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(s4(X_363),true,ifeq(r3(X_362,X_362,X_362),true,k5(X_362),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_69,plain,
( ifeq(s4(X_363),true,ifeq(r3(X_362,X_362,X_362),true,k5(X_362),true),true) != true
| ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) = true ),
inference(resolve,[$cnf( $equal(r3(X_362,X_362,X_362),true) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(s4(X_363),true,ifeq(r3(X_362,X_362,X_362),true,k5(X_362),true),true),true) )],[refute_0_0,refute_0_69]) ).
cnf(refute_0_71,plain,
ifeq(true,true,k5(X_362),true) = k5(X_362),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(k5(X_362))),bind(C,$fot(true))]]) ).
cnf(refute_0_72,plain,
ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) = ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true),
introduced(tautology,[refl,[$fot(ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true))]]) ).
cnf(refute_0_73,plain,
( ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) != ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true)
| ifeq(true,true,k5(X_362),true) != k5(X_362)
| ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) = ifeq(s4(X_363),true,k5(X_362),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true),ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true)) ),[1,2],$fot(k5(X_362))]]) ).
cnf(refute_0_74,plain,
( ifeq(true,true,k5(X_362),true) != k5(X_362)
| ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) = ifeq(s4(X_363),true,k5(X_362),true) ),
inference(resolve,[$cnf( $equal(ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true),ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) = ifeq(s4(X_363),true,k5(X_362),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,k5(X_362),true),k5(X_362)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) != ifeq(s4(X_363),true,k5(X_362),true)
| ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) != true
| ifeq(s4(X_363),true,k5(X_362),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true),true) ),[0],$fot(ifeq(s4(X_363),true,k5(X_362),true))]]) ).
cnf(refute_0_77,plain,
( ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true) != true
| ifeq(s4(X_363),true,k5(X_362),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true),ifeq(s4(X_363),true,k5(X_362),true)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
ifeq(s4(X_363),true,k5(X_362),true) = true,
inference(resolve,[$cnf( $equal(ifeq(s4(X_363),true,ifeq(true,true,k5(X_362),true),true),true) )],[refute_0_70,refute_0_77]) ).
cnf(refute_0_79,plain,
ifeq(s4(b),true,k5(X_362),true) = true,
inference(subst,[],[refute_0_78:[bind(X_363,$fot(b))]]) ).
cnf(refute_0_80,plain,
ifeq(p3(X_536,X_536,X_536),true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) = true,
inference(subst,[],[rule_299:[bind(A,$fot(X_533)),bind(B,$fot(X_536)),bind(C,$fot(X_536)),bind(D,$fot(X_536))]]) ).
cnf(refute_0_81,plain,
ifeq(true,true,p3(H,H,H),true) = p3(H,H,H),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(p3(H,H,H))),bind(C,$fot(true))]]) ).
cnf(refute_0_82,plain,
ifeq(n2(H),true,p3(H,H,H),true) = ifeq(n2(H),true,p3(H,H,H),true),
introduced(tautology,[refl,[$fot(ifeq(n2(H),true,p3(H,H,H),true))]]) ).
cnf(refute_0_83,plain,
( ifeq(n2(H),true,p3(H,H,H),true) != ifeq(n2(H),true,p3(H,H,H),true)
| n2(H) != true
| ifeq(n2(H),true,p3(H,H,H),true) = ifeq(true,true,p3(H,H,H),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n2(H),true,p3(H,H,H),true),ifeq(n2(H),true,p3(H,H,H),true)) ),[1,0],$fot(true)]]) ).
cnf(refute_0_84,plain,
( n2(H) != true
| ifeq(n2(H),true,p3(H,H,H),true) = ifeq(true,true,p3(H,H,H),true) ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p3(H,H,H),true),ifeq(n2(H),true,p3(H,H,H),true)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
ifeq(n2(H),true,p3(H,H,H),true) = ifeq(true,true,p3(H,H,H),true),
inference(resolve,[$cnf( $equal(n2(H),true) )],[refute_0_48,refute_0_84]) ).
cnf(refute_0_86,plain,
( ifeq(n2(H),true,p3(H,H,H),true) != ifeq(true,true,p3(H,H,H),true)
| ifeq(true,true,p3(H,H,H),true) != p3(H,H,H)
| ifeq(n2(H),true,p3(H,H,H),true) = p3(H,H,H) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(ifeq(n2(H),true,p3(H,H,H),true))),bind(Y,$fot(ifeq(true,true,p3(H,H,H),true))),bind(Z,$fot(p3(H,H,H)))]]) ).
cnf(refute_0_87,plain,
( ifeq(true,true,p3(H,H,H),true) != p3(H,H,H)
| ifeq(n2(H),true,p3(H,H,H),true) = p3(H,H,H) ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p3(H,H,H),true),ifeq(true,true,p3(H,H,H),true)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
ifeq(n2(H),true,p3(H,H,H),true) = p3(H,H,H),
inference(resolve,[$cnf( $equal(ifeq(true,true,p3(H,H,H),true),p3(H,H,H)) )],[refute_0_81,refute_0_87]) ).
cnf(refute_0_89,plain,
( ifeq(n2(H),true,p3(H,H,H),true) != p3(H,H,H)
| ifeq(n2(H),true,p3(H,H,H),true) != true
| p3(H,H,H) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n2(H),true,p3(H,H,H),true),true) ),[0],$fot(p3(H,H,H))]]) ).
cnf(refute_0_90,plain,
( ifeq(n2(H),true,p3(H,H,H),true) != true
| p3(H,H,H) = true ),
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p3(H,H,H),true),p3(H,H,H)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
p3(H,H,H) = true,
inference(resolve,[$cnf( $equal(ifeq(n2(H),true,p3(H,H,H),true),true) )],[rule_244,refute_0_90]) ).
cnf(refute_0_92,plain,
p3(X_536,X_536,X_536) = true,
inference(subst,[],[refute_0_91:[bind(H,$fot(X_536))]]) ).
cnf(refute_0_93,plain,
( ifeq(p3(X_536,X_536,X_536),true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) != true
| p3(X_536,X_536,X_536) != true
| ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(p3(X_536,X_536,X_536),true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_94,plain,
( ifeq(p3(X_536,X_536,X_536),true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) != true
| ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) = true ),
inference(resolve,[$cnf( $equal(p3(X_536,X_536,X_536),true) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(p3(X_536,X_536,X_536),true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true),true) )],[refute_0_80,refute_0_94]) ).
cnf(refute_0_96,plain,
ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) = ifeq(l1(X_533,X_536),true,s4(X_533),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(l1(X_533,X_536),true,s4(X_533),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_97,plain,
( ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) != ifeq(l1(X_533,X_536),true,s4(X_533),true)
| ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) != true
| ifeq(l1(X_533,X_536),true,s4(X_533),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true),true) ),[0],$fot(ifeq(l1(X_533,X_536),true,s4(X_533),true))]]) ).
cnf(refute_0_98,plain,
( ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true) != true
| ifeq(l1(X_533,X_536),true,s4(X_533),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true),ifeq(l1(X_533,X_536),true,s4(X_533),true)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
ifeq(l1(X_533,X_536),true,s4(X_533),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(l1(X_533,X_536),true,s4(X_533),true),true),true) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
ifeq(l1(b,b),true,s4(b),true) = true,
inference(subst,[],[refute_0_99:[bind(X_533,$fot(b)),bind(X_536,$fot(b))]]) ).
cnf(refute_0_101,plain,
ifeq(n0(a,b),true,l1(b,b),true) = true,
inference(subst,[],[rule_002:[bind(G,$fot(b)),bind(H,$fot(a))]]) ).
cnf(refute_0_102,plain,
( ifeq(n0(a,b),true,l1(b,b),true) != true
| n0(a,b) != true
| ifeq(true,true,l1(b,b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(n0(a,b),true,l1(b,b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_103,plain,
( ifeq(n0(a,b),true,l1(b,b),true) != true
| ifeq(true,true,l1(b,b),true) = true ),
inference(resolve,[$cnf( $equal(n0(a,b),true) )],[axiom_15,refute_0_102]) ).
cnf(refute_0_104,plain,
ifeq(true,true,l1(b,b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(n0(a,b),true,l1(b,b),true),true) )],[refute_0_101,refute_0_103]) ).
cnf(refute_0_105,plain,
ifeq(true,true,l1(b,b),true) = l1(b,b),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(l1(b,b))),bind(C,$fot(true))]]) ).
cnf(refute_0_106,plain,
( ifeq(true,true,l1(b,b),true) != l1(b,b)
| ifeq(true,true,l1(b,b),true) != true
| l1(b,b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,l1(b,b),true),true) ),[0],$fot(l1(b,b))]]) ).
cnf(refute_0_107,plain,
( ifeq(true,true,l1(b,b),true) != true
| l1(b,b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,l1(b,b),true),l1(b,b)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
l1(b,b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,l1(b,b),true),true) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( ifeq(l1(b,b),true,s4(b),true) != true
| l1(b,b) != true
| ifeq(true,true,s4(b),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(l1(b,b),true,s4(b),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_110,plain,
( ifeq(l1(b,b),true,s4(b),true) != true
| ifeq(true,true,s4(b),true) = true ),
inference(resolve,[$cnf( $equal(l1(b,b),true) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
ifeq(true,true,s4(b),true) = true,
inference(resolve,[$cnf( $equal(ifeq(l1(b,b),true,s4(b),true),true) )],[refute_0_100,refute_0_110]) ).
cnf(refute_0_112,plain,
ifeq(true,true,s4(b),true) = s4(b),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(s4(b))),bind(C,$fot(true))]]) ).
cnf(refute_0_113,plain,
( ifeq(true,true,s4(b),true) != s4(b)
| ifeq(true,true,s4(b),true) != true
| s4(b) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,s4(b),true),true) ),[0],$fot(s4(b))]]) ).
cnf(refute_0_114,plain,
( ifeq(true,true,s4(b),true) != true
| s4(b) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,s4(b),true),s4(b)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
s4(b) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,s4(b),true),true) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
( ifeq(s4(b),true,k5(X_362),true) != true
| s4(b) != true
| ifeq(true,true,k5(X_362),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(s4(b),true,k5(X_362),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_117,plain,
( ifeq(s4(b),true,k5(X_362),true) != true
| ifeq(true,true,k5(X_362),true) = true ),
inference(resolve,[$cnf( $equal(s4(b),true) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
ifeq(true,true,k5(X_362),true) = true,
inference(resolve,[$cnf( $equal(ifeq(s4(b),true,k5(X_362),true),true) )],[refute_0_79,refute_0_117]) ).
cnf(refute_0_119,plain,
( ifeq(true,true,k5(X_362),true) != k5(X_362)
| ifeq(true,true,k5(X_362),true) != true
| k5(X_362) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,k5(X_362),true),true) ),[0],$fot(k5(X_362))]]) ).
cnf(refute_0_120,plain,
( ifeq(true,true,k5(X_362),true) != true
| k5(X_362) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,k5(X_362),true),k5(X_362)) )],[refute_0_71,refute_0_119]) ).
cnf(refute_0_121,plain,
k5(X_362) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,k5(X_362),true),true) )],[refute_0_118,refute_0_120]) ).
cnf(refute_0_122,plain,
k5(b) = true,
inference(subst,[],[refute_0_121:[bind(X_362,$fot(b))]]) ).
cnf(refute_0_123,plain,
( k5(b) != true
| true != true
| k5(b) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(k5(b),true) ),[0],$fot(true)]]) ).
cnf(refute_0_124,plain,
( true != true
| k5(b) = true ),
inference(resolve,[$cnf( $equal(k5(b),true) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
true != true,
inference(resolve,[$cnf( $equal(k5(b),true) )],[refute_0_124,prove_this]) ).
cnf(refute_0_126,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_127,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_126,refute_0_125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN116-10 : TPTP v8.1.0. Released v7.5.0.
% 0.00/0.09 % Command : metis --show proof --show saturation %s
% 0.09/0.29 % Computer : n024.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Mon Jul 11 19:48:28 EDT 2022
% 0.09/0.29 % CPUTime :
% 0.09/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.62/1.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.62/1.80
% 1.62/1.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.62/1.81
%------------------------------------------------------------------------------