TSTP Solution File: SYN170-10 by Metis---2.4

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN170-10 : TPTP v8.1.0. Released v7.5.0.
% 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 09:00:10 EDT 2022

% Result   : Unsatisfiable 0.93s 1.11s
% Output   : CNFRefutation 0.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   25
% Syntax   : Number of clauses     :   73 (  41 unt;   0 nHn;  38 RR)
%            Number of literals    :  122 ( 121 equ;  52 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    :   10 (  10 usr;   4 con; 0-4 aty)
%            Number of variables   :   79 (   7 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
    ifeq(A,A,B,C) = B ).

cnf(axiom_19,axiom,
    m0(X,d,Y) = true ).

cnf(rule_107,axiom,
    ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = true ).

cnf(rule_129,axiom,
    ifeq(q1(A,J,J),true,k2(J,J),true) = true ).

cnf(rule_194,axiom,
    ifeq(k2(G,F),true,k3(F,F,G),true) = true ).

cnf(rule_287,axiom,
    ifeq(k3(B,B,C),true,p4(B,C,B),true) = true ).

cnf(prove_this,negated_conjecture,
    p4(X,c,Y) != true ).

cnf(refute_0_0,plain,
    p4(c,c,c) != true,
    inference(subst,[],[prove_this:[bind(X,$fot(c)),bind(Y,$fot(c))]]) ).

cnf(refute_0_1,plain,
    ifeq(k3(X_146,X_146,X_146),true,p4(X_146,X_146,X_146),true) = true,
    inference(subst,[],[rule_287:[bind(B,$fot(X_146)),bind(C,$fot(X_146))]]) ).

cnf(refute_0_2,plain,
    ifeq(k2(X_122,X_122),true,k3(X_122,X_122,X_122),true) = true,
    inference(subst,[],[rule_194:[bind(F,$fot(X_122)),bind(G,$fot(X_122))]]) ).

cnf(refute_0_3,plain,
    ifeq(q1(e,X_92,X_92),true,k2(X_92,X_92),true) = true,
    inference(subst,[],[rule_129:[bind(A,$fot(e)),bind(J,$fot(X_92))]]) ).

cnf(refute_0_4,plain,
    ifeq(true,true,q1(e,A,A),true) = q1(e,A,A),
    inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(q1(e,A,A))),bind(C,$fot(true))]]) ).

cnf(refute_0_5,plain,
    m0(A,d,A) = true,
    inference(subst,[],[axiom_19:[bind(X,$fot(A)),bind(Y,$fot(A))]]) ).

cnf(refute_0_6,plain,
    ifeq(m0(A,d,A),true,q1(e,A,A),true) = ifeq(m0(A,d,A),true,q1(e,A,A),true),
    introduced(tautology,[refl,[$fot(ifeq(m0(A,d,A),true,q1(e,A,A),true))]]) ).

cnf(refute_0_7,plain,
    ( ifeq(m0(A,d,A),true,q1(e,A,A),true) != ifeq(m0(A,d,A),true,q1(e,A,A),true)
    | m0(A,d,A) != true
    | ifeq(m0(A,d,A),true,q1(e,A,A),true) = ifeq(true,true,q1(e,A,A),true) ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(m0(A,d,A),true,q1(e,A,A),true),ifeq(m0(A,d,A),true,q1(e,A,A),true)) ),[1,0],$fot(true)]]) ).

cnf(refute_0_8,plain,
    ( m0(A,d,A) != true
    | ifeq(m0(A,d,A),true,q1(e,A,A),true) = ifeq(true,true,q1(e,A,A),true) ),
    inference(resolve,[$cnf( $equal(ifeq(m0(A,d,A),true,q1(e,A,A),true),ifeq(m0(A,d,A),true,q1(e,A,A),true)) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    ifeq(m0(A,d,A),true,q1(e,A,A),true) = ifeq(true,true,q1(e,A,A),true),
    inference(resolve,[$cnf( $equal(m0(A,d,A),true) )],[refute_0_5,refute_0_8]) ).

cnf(refute_0_10,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_11,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_12,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( Y0 != X0
    | Y0 != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_14,plain,
    ( X0 != Y0
    | Y0 != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( ifeq(m0(A,d,A),true,q1(e,A,A),true) != ifeq(true,true,q1(e,A,A),true)
    | ifeq(true,true,q1(e,A,A),true) != q1(e,A,A)
    | ifeq(m0(A,d,A),true,q1(e,A,A),true) = q1(e,A,A) ),
    inference(subst,[],[refute_0_14:[bind(X0,$fot(ifeq(m0(A,d,A),true,q1(e,A,A),true))),bind(Y0,$fot(ifeq(true,true,q1(e,A,A),true))),bind(Z,$fot(q1(e,A,A)))]]) ).

cnf(refute_0_16,plain,
    ( ifeq(true,true,q1(e,A,A),true) != q1(e,A,A)
    | ifeq(m0(A,d,A),true,q1(e,A,A),true) = q1(e,A,A) ),
    inference(resolve,[$cnf( $equal(ifeq(m0(A,d,A),true,q1(e,A,A),true),ifeq(true,true,q1(e,A,A),true)) )],[refute_0_9,refute_0_15]) ).

cnf(refute_0_17,plain,
    ifeq(m0(A,d,A),true,q1(e,A,A),true) = q1(e,A,A),
    inference(resolve,[$cnf( $equal(ifeq(true,true,q1(e,A,A),true),q1(e,A,A)) )],[refute_0_4,refute_0_16]) ).

cnf(refute_0_18,plain,
    ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),
    introduced(tautology,[refl,[$fot(ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true))]]) ).

cnf(refute_0_19,plain,
    ( ifeq(m0(A,d,A),true,q1(e,A,A),true) != q1(e,A,A)
    | ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)
    | ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,q1(e,A,A),true) ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)) ),[1,2],$fot(q1(e,A,A))]]) ).

cnf(refute_0_20,plain,
    ( ifeq(m0(A,d,A),true,q1(e,A,A),true) != q1(e,A,A)
    | ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,q1(e,A,A),true) ),
    inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,q1(e,A,A),true),
    inference(resolve,[$cnf( $equal(ifeq(m0(A,d,A),true,q1(e,A,A),true),q1(e,A,A)) )],[refute_0_17,refute_0_20]) ).

cnf(refute_0_22,plain,
    m0(e,d,A) = true,
    inference(subst,[],[axiom_19:[bind(X,$fot(e)),bind(Y,$fot(A))]]) ).

cnf(refute_0_23,plain,
    ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),
    introduced(tautology,[refl,[$fot(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true))]]) ).

cnf(refute_0_24,plain,
    ( ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)
    | m0(e,d,A) != true
    | ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)) ),[1,0],$fot(true)]]) ).

cnf(refute_0_25,plain,
    ( m0(e,d,A) != true
    | ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) ),
    inference(resolve,[$cnf( $equal(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),
    inference(resolve,[$cnf( $equal(m0(e,d,A),true) )],[refute_0_22,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)
    | ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != ifeq(true,true,q1(e,A,A),true)
    | ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,q1(e,A,A),true) ),
    inference(subst,[],[refute_0_14:[bind(X0,$fot(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true))),bind(Y0,$fot(ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true))),bind(Z,$fot(ifeq(true,true,q1(e,A,A),true)))]]) ).

cnf(refute_0_28,plain,
    ( ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != ifeq(true,true,q1(e,A,A),true)
    | ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,q1(e,A,A),true) ),
    inference(resolve,[$cnf( $equal(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true)) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = ifeq(true,true,q1(e,A,A),true),
    inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),ifeq(true,true,q1(e,A,A),true)) )],[refute_0_21,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != ifeq(true,true,q1(e,A,A),true)
    | ifeq(true,true,q1(e,A,A),true) != q1(e,A,A)
    | ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = q1(e,A,A) ),
    inference(subst,[],[refute_0_14:[bind(X0,$fot(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true))),bind(Y0,$fot(ifeq(true,true,q1(e,A,A),true))),bind(Z,$fot(q1(e,A,A)))]]) ).

cnf(refute_0_31,plain,
    ( ifeq(true,true,q1(e,A,A),true) != q1(e,A,A)
    | ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = q1(e,A,A) ),
    inference(resolve,[$cnf( $equal(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),ifeq(true,true,q1(e,A,A),true)) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) = q1(e,A,A),
    inference(resolve,[$cnf( $equal(ifeq(true,true,q1(e,A,A),true),q1(e,A,A)) )],[refute_0_4,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != q1(e,A,A)
    | ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != true
    | q1(e,A,A) = true ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),true) ),[0],$fot(q1(e,A,A))]]) ).

cnf(refute_0_34,plain,
    ( ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true) != true
    | q1(e,A,A) = true ),
    inference(resolve,[$cnf( $equal(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),q1(e,A,A)) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    q1(e,A,A) = true,
    inference(resolve,[$cnf( $equal(ifeq(m0(e,d,A),true,ifeq(m0(A,d,A),true,q1(e,A,A),true),true),true) )],[rule_107,refute_0_34]) ).

cnf(refute_0_36,plain,
    q1(e,X_92,X_92) = true,
    inference(subst,[],[refute_0_35:[bind(A,$fot(X_92))]]) ).

cnf(refute_0_37,plain,
    ( ifeq(q1(e,X_92,X_92),true,k2(X_92,X_92),true) != true
    | q1(e,X_92,X_92) != true
    | ifeq(true,true,k2(X_92,X_92),true) = true ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(q1(e,X_92,X_92),true,k2(X_92,X_92),true),true) ),[0,0],$fot(true)]]) ).

cnf(refute_0_38,plain,
    ( ifeq(q1(e,X_92,X_92),true,k2(X_92,X_92),true) != true
    | ifeq(true,true,k2(X_92,X_92),true) = true ),
    inference(resolve,[$cnf( $equal(q1(e,X_92,X_92),true) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    ifeq(true,true,k2(X_92,X_92),true) = true,
    inference(resolve,[$cnf( $equal(ifeq(q1(e,X_92,X_92),true,k2(X_92,X_92),true),true) )],[refute_0_3,refute_0_38]) ).

cnf(refute_0_40,plain,
    ifeq(true,true,k2(X_92,X_92),true) = k2(X_92,X_92),
    inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(k2(X_92,X_92))),bind(C,$fot(true))]]) ).

cnf(refute_0_41,plain,
    ( ifeq(true,true,k2(X_92,X_92),true) != k2(X_92,X_92)
    | ifeq(true,true,k2(X_92,X_92),true) != true
    | k2(X_92,X_92) = true ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,k2(X_92,X_92),true),true) ),[0],$fot(k2(X_92,X_92))]]) ).

cnf(refute_0_42,plain,
    ( ifeq(true,true,k2(X_92,X_92),true) != true
    | k2(X_92,X_92) = true ),
    inference(resolve,[$cnf( $equal(ifeq(true,true,k2(X_92,X_92),true),k2(X_92,X_92)) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    k2(X_92,X_92) = true,
    inference(resolve,[$cnf( $equal(ifeq(true,true,k2(X_92,X_92),true),true) )],[refute_0_39,refute_0_42]) ).

cnf(refute_0_44,plain,
    k2(X_122,X_122) = true,
    inference(subst,[],[refute_0_43:[bind(X_92,$fot(X_122))]]) ).

cnf(refute_0_45,plain,
    ( ifeq(k2(X_122,X_122),true,k3(X_122,X_122,X_122),true) != true
    | k2(X_122,X_122) != true
    | ifeq(true,true,k3(X_122,X_122,X_122),true) = true ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(k2(X_122,X_122),true,k3(X_122,X_122,X_122),true),true) ),[0,0],$fot(true)]]) ).

cnf(refute_0_46,plain,
    ( ifeq(k2(X_122,X_122),true,k3(X_122,X_122,X_122),true) != true
    | ifeq(true,true,k3(X_122,X_122,X_122),true) = true ),
    inference(resolve,[$cnf( $equal(k2(X_122,X_122),true) )],[refute_0_44,refute_0_45]) ).

cnf(refute_0_47,plain,
    ifeq(true,true,k3(X_122,X_122,X_122),true) = true,
    inference(resolve,[$cnf( $equal(ifeq(k2(X_122,X_122),true,k3(X_122,X_122,X_122),true),true) )],[refute_0_2,refute_0_46]) ).

cnf(refute_0_48,plain,
    ifeq(true,true,k3(X_122,X_122,X_122),true) = k3(X_122,X_122,X_122),
    inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(k3(X_122,X_122,X_122))),bind(C,$fot(true))]]) ).

cnf(refute_0_49,plain,
    ( ifeq(true,true,k3(X_122,X_122,X_122),true) != k3(X_122,X_122,X_122)
    | ifeq(true,true,k3(X_122,X_122,X_122),true) != true
    | k3(X_122,X_122,X_122) = true ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,k3(X_122,X_122,X_122),true),true) ),[0],$fot(k3(X_122,X_122,X_122))]]) ).

cnf(refute_0_50,plain,
    ( ifeq(true,true,k3(X_122,X_122,X_122),true) != true
    | k3(X_122,X_122,X_122) = true ),
    inference(resolve,[$cnf( $equal(ifeq(true,true,k3(X_122,X_122,X_122),true),k3(X_122,X_122,X_122)) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    k3(X_122,X_122,X_122) = true,
    inference(resolve,[$cnf( $equal(ifeq(true,true,k3(X_122,X_122,X_122),true),true) )],[refute_0_47,refute_0_50]) ).

cnf(refute_0_52,plain,
    k3(X_146,X_146,X_146) = true,
    inference(subst,[],[refute_0_51:[bind(X_122,$fot(X_146))]]) ).

cnf(refute_0_53,plain,
    ( ifeq(k3(X_146,X_146,X_146),true,p4(X_146,X_146,X_146),true) != true
    | k3(X_146,X_146,X_146) != true
    | ifeq(true,true,p4(X_146,X_146,X_146),true) = true ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(k3(X_146,X_146,X_146),true,p4(X_146,X_146,X_146),true),true) ),[0,0],$fot(true)]]) ).

cnf(refute_0_54,plain,
    ( ifeq(k3(X_146,X_146,X_146),true,p4(X_146,X_146,X_146),true) != true
    | ifeq(true,true,p4(X_146,X_146,X_146),true) = true ),
    inference(resolve,[$cnf( $equal(k3(X_146,X_146,X_146),true) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    ifeq(true,true,p4(X_146,X_146,X_146),true) = true,
    inference(resolve,[$cnf( $equal(ifeq(k3(X_146,X_146,X_146),true,p4(X_146,X_146,X_146),true),true) )],[refute_0_1,refute_0_54]) ).

cnf(refute_0_56,plain,
    ifeq(true,true,p4(X_146,X_146,X_146),true) = p4(X_146,X_146,X_146),
    inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(p4(X_146,X_146,X_146))),bind(C,$fot(true))]]) ).

cnf(refute_0_57,plain,
    ( ifeq(true,true,p4(X_146,X_146,X_146),true) != p4(X_146,X_146,X_146)
    | ifeq(true,true,p4(X_146,X_146,X_146),true) != true
    | p4(X_146,X_146,X_146) = true ),
    introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,p4(X_146,X_146,X_146),true),true) ),[0],$fot(p4(X_146,X_146,X_146))]]) ).

cnf(refute_0_58,plain,
    ( ifeq(true,true,p4(X_146,X_146,X_146),true) != true
    | p4(X_146,X_146,X_146) = true ),
    inference(resolve,[$cnf( $equal(ifeq(true,true,p4(X_146,X_146,X_146),true),p4(X_146,X_146,X_146)) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    p4(X_146,X_146,X_146) = true,
    inference(resolve,[$cnf( $equal(ifeq(true,true,p4(X_146,X_146,X_146),true),true) )],[refute_0_55,refute_0_58]) ).

cnf(refute_0_60,plain,
    p4(c,c,c) = true,
    inference(subst,[],[refute_0_59:[bind(X_146,$fot(c))]]) ).

cnf(refute_0_61,plain,
    ( p4(c,c,c) != true
    | true != true
    | p4(c,c,c) = true ),
    introduced(tautology,[equality,[$cnf( ~ $equal(p4(c,c,c),true) ),[0],$fot(true)]]) ).

cnf(refute_0_62,plain,
    ( true != true
    | p4(c,c,c) = true ),
    inference(resolve,[$cnf( $equal(p4(c,c,c),true) )],[refute_0_60,refute_0_61]) ).

cnf(refute_0_63,plain,
    true != true,
    inference(resolve,[$cnf( $equal(p4(c,c,c),true) )],[refute_0_62,refute_0_0]) ).

cnf(refute_0_64,plain,
    true = true,
    introduced(tautology,[refl,[$fot(true)]]) ).

cnf(refute_0_65,plain,
    $false,
    inference(resolve,[$cnf( $equal(true,true) )],[refute_0_64,refute_0_63]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SYN170-10 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n028.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 19:01:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.93/1.11  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/1.11  
% 0.93/1.11  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.93/1.12  
%------------------------------------------------------------------------------