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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : COL066-2 : TPTP v9.2.1. Bugfixed v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n026.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  : 300s
% DateTime : Tue May  5 04:12:14 PM UTC 2026

% Result   : Unsatisfiable 0.57s 1.61s
% Output   : CNFRefutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   14
% Syntax   : Number of clauses     :  102 (  94 unt;   0 nHn;  58 RR)
%            Number of literals    :  112 ( 111 equ;  63 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    9 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :  133 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(prove_p_combinator,negated_conjecture,
    apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p_combinator) ).

cnf(q_definition,axiom,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_definition) ).

cnf(b_definition,axiom,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).

cnf(w_definition,axiom,
    apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).

cnf(i_0_4,negated_conjecture,
    apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
    prove_p_combinator,
    [final] ).

cnf(i_0_5,axiom,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    q_definition,
    [final] ).

cnf(i_0_6,axiom,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    b_definition,
    [final] ).

cnf(i_0_7,axiom,
    apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
    w_definition,
    [final] ).

cnf(i_0_8,axiom,
    X1 = X1 ).

cnf(i_0_9,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_10,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_11,axiom,
    ( X1 != X2
    | apply(X1,X3) = apply(X2,X3) ) ).

cnf(i_0_12,axiom,
    ( X1 != X2
    | apply(X3,X1) = apply(X3,X2) ) ).

cnf(i_0_8_001,axiom,
    X1 = X1 ).

cnf(i_0_9_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_10_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_11_004,axiom,
    ( X1 != X2
    | apply(X1,X3) = apply(X2,X3) ) ).

cnf(i_0_12_005,axiom,
    ( X1 != X2
    | apply(X3,X1) = apply(X3,X2) ) ).

cnf(i_0_13,plain,
    apply(apply(X1,X2),X2) = apply(apply(w,X1),X2),
    inference(scs_inference,[],[i_0_7,i_0_9]) ).

cnf(i_0_14,plain,
    apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(apply(q,apply(x,y)),apply(x,y)),z),
    inference(scs_inference,[],[i_0_4,i_0_7,i_0_5,i_0_9,i_0_10]) ).

cnf(i_0_15,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_16,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(q,apply(x,y)),apply(x,y)),
    inference(scs_inference,[],[i_0_4,i_0_7,i_0_5,i_0_9,i_0_10,i_0_11]) ).

cnf(i_0_17,plain,
    apply(X1,apply(X2,X3)) = apply(apply(apply(b,X1),X2),X3),
    inference(scs_inference,[],[i_0_6,i_0_9]) ).

cnf(i_0_18,plain,
    apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(apply(b,apply(x,y)),apply(x,y)),z),
    inference(scs_inference,[],[i_0_4,i_0_6,i_0_9,i_0_10]) ).

cnf(i_0_19,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_20,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(b,apply(x,y)),apply(x,y)),
    inference(scs_inference,[],[i_0_4,i_0_6,i_0_9,i_0_10,i_0_11]) ).

cnf(i_0_21,plain,
    apply(X1,apply(X2,X3)) = apply(apply(apply(q,X2),X1),X3),
    inference(scs_inference,[],[i_0_5,i_0_9]) ).

cnf(i_0_22,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(w,q),apply(x,y)),
    inference(scs_inference,[],[i_0_16,i_0_7,i_0_5,i_0_9,i_0_10]) ).

cnf(i_0_23,plain,
    apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
    inference(rename_variables,[],[i_0_7]) ).

cnf(i_0_24,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(w,b),apply(x,y)),
    inference(scs_inference,[],[i_0_20,i_0_7,i_0_10]) ).

cnf(i_0_25,plain,
    apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
    inference(rename_variables,[],[i_0_7]) ).

cnf(i_0_26,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(q,x),apply(q,apply(x,y))),y),
    inference(scs_inference,[],[i_0_16,i_0_5,i_0_10]) ).

cnf(i_0_27,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_28,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(q,x),apply(q,apply(x,y))),
    inference(scs_inference,[],[i_0_16,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_29,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(b,apply(q,apply(x,y))),x),y),
    inference(scs_inference,[],[i_0_16,i_0_6,i_0_10]) ).

cnf(i_0_30,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_31,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(b,apply(q,apply(x,y))),x),
    inference(scs_inference,[],[i_0_16,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_32,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(q,x),apply(b,apply(x,y))),y),
    inference(scs_inference,[],[i_0_20,i_0_5,i_0_10]) ).

cnf(i_0_33,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_34,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(q,x),apply(b,apply(x,y))),
    inference(scs_inference,[],[i_0_20,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_35,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(b,apply(b,apply(x,y))),x),y),
    inference(scs_inference,[],[i_0_20,i_0_6,i_0_10]) ).

cnf(i_0_36,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_37,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(b,apply(b,apply(x,y))),x),
    inference(scs_inference,[],[i_0_20,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_38,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(q,x),apply(w,q)),y),
    inference(scs_inference,[],[i_0_22,i_0_5,i_0_10]) ).

cnf(i_0_39,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_40,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(q,x),apply(w,q)),
    inference(scs_inference,[],[i_0_22,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_41,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(b,apply(w,q)),x),y),
    inference(scs_inference,[],[i_0_22,i_0_6,i_0_10]) ).

cnf(i_0_42,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_43,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(b,apply(w,q)),x),
    inference(scs_inference,[],[i_0_22,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_44,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(q,x),apply(w,b)),y),
    inference(scs_inference,[],[i_0_24,i_0_5,i_0_10]) ).

cnf(i_0_45,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_46,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(q,x),apply(w,b)),
    inference(scs_inference,[],[i_0_24,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_47,plain,
    apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y) != apply(apply(apply(b,apply(w,b)),x),y),
    inference(scs_inference,[],[i_0_24,i_0_6,i_0_10]) ).

cnf(i_0_48,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_49,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(b,apply(w,b)),x),
    inference(scs_inference,[],[i_0_24,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_50,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,q),apply(q,x)),apply(x,y)),
    inference(scs_inference,[],[i_0_28,i_0_5,i_0_10]) ).

cnf(i_0_51,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_52,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(q,x)),q),apply(x,y)),
    inference(scs_inference,[],[i_0_28,i_0_6,i_0_10]) ).

cnf(i_0_53,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_54,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,b),apply(q,x)),apply(x,y)),
    inference(scs_inference,[],[i_0_34,i_0_5,i_0_10]) ).

cnf(i_0_55,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_56,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(q,x)),b),apply(x,y)),
    inference(scs_inference,[],[i_0_34,i_0_6,i_0_10]) ).

cnf(i_0_57,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_58,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,w),apply(q,x)),q),
    inference(scs_inference,[],[i_0_40,i_0_5,i_0_10]) ).

cnf(i_0_59,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_60,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(q,x)),w),q),
    inference(scs_inference,[],[i_0_40,i_0_6,i_0_10]) ).

cnf(i_0_61,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_62,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,w),apply(q,x)),b),
    inference(scs_inference,[],[i_0_46,i_0_5,i_0_10]) ).

cnf(i_0_63,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_64,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(q,x)),w),b),
    inference(scs_inference,[],[i_0_46,i_0_6,i_0_10]) ).

cnf(i_0_65,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_66,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,x),apply(apply(q,q),apply(q,x))),y),
    inference(scs_inference,[],[i_0_50,i_0_5,i_0_10]) ).

cnf(i_0_67,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_68,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(q,x),apply(apply(q,q),apply(q,x))),
    inference(scs_inference,[],[i_0_50,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_69,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(apply(q,q),apply(q,x))),x),y),
    inference(scs_inference,[],[i_0_50,i_0_6,i_0_10]) ).

cnf(i_0_70,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_71,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(b,apply(apply(q,q),apply(q,x))),x),
    inference(scs_inference,[],[i_0_50,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_72,plain,
    apply(apply(q,q),apply(w,apply(q,apply(q,q)))) != apply(b,apply(apply(q,q),apply(q,x))),
    inference(scs_inference,[],[i_0_71,i_0_11]) ).

cnf(i_0_73,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,x),apply(apply(b,apply(q,x)),q)),y),
    inference(scs_inference,[],[i_0_52,i_0_5,i_0_10]) ).

cnf(i_0_74,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_75,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(q,x),apply(apply(b,apply(q,x)),q)),
    inference(scs_inference,[],[i_0_52,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_76,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(apply(b,apply(q,x)),q)),x),y),
    inference(scs_inference,[],[i_0_52,i_0_6,i_0_10]) ).

cnf(i_0_77,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_78,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(b,apply(apply(b,apply(q,x)),q)),x),
    inference(scs_inference,[],[i_0_52,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_79,plain,
    apply(apply(q,q),apply(w,apply(q,apply(q,q)))) != apply(b,apply(apply(b,apply(q,x)),q)),
    inference(scs_inference,[],[i_0_78,i_0_11]) ).

cnf(i_0_80,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,x),apply(apply(q,b),apply(q,x))),y),
    inference(scs_inference,[],[i_0_54,i_0_5,i_0_10]) ).

cnf(i_0_81,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_82,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(q,x),apply(apply(q,b),apply(q,x))),
    inference(scs_inference,[],[i_0_54,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_83,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(apply(q,b),apply(q,x))),x),y),
    inference(scs_inference,[],[i_0_54,i_0_6,i_0_10]) ).

cnf(i_0_84,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_85,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(b,apply(apply(q,b),apply(q,x))),x),
    inference(scs_inference,[],[i_0_54,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_86,plain,
    apply(apply(q,q),apply(w,apply(q,apply(q,q)))) != apply(b,apply(apply(q,b),apply(q,x))),
    inference(scs_inference,[],[i_0_85,i_0_11]) ).

cnf(i_0_87,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(q,x),apply(apply(b,apply(q,x)),b)),y),
    inference(scs_inference,[],[i_0_56,i_0_5,i_0_10]) ).

cnf(i_0_88,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_89,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(q,x),apply(apply(b,apply(q,x)),b)),
    inference(scs_inference,[],[i_0_56,i_0_5,i_0_10,i_0_11]) ).

cnf(i_0_90,plain,
    apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y) != apply(apply(apply(b,apply(apply(b,apply(q,x)),b)),x),y),
    inference(scs_inference,[],[i_0_56,i_0_6,i_0_10]) ).

cnf(i_0_91,plain,
    apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
    inference(rename_variables,[],[i_0_6]) ).

cnf(i_0_92,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(b,apply(apply(b,apply(q,x)),b)),x),
    inference(scs_inference,[],[i_0_56,i_0_6,i_0_10,i_0_11]) ).

cnf(i_0_93,plain,
    apply(apply(q,q),apply(w,apply(q,apply(q,q)))) != apply(b,apply(apply(b,apply(q,x)),b)),
    inference(scs_inference,[],[i_0_92,i_0_11]) ).

cnf(i_0_94,plain,
    apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x) != apply(apply(apply(q,apply(q,q)),apply(q,x)),apply(q,x)),
    inference(scs_inference,[],[i_0_68,i_0_5,i_0_10]) ).

cnf(i_0_95,plain,
    apply(apply(apply(q,X1),X2),X3) = apply(X2,apply(X1,X3)),
    inference(rename_variables,[],[i_0_5]) ).

cnf(i_0_96,plain,
    $false,
    inference(scs_inference,[],[i_0_94,i_0_7,i_0_5,i_0_10]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : COL066-2 : TPTP v9.2.1. Bugfixed v1.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33  % Computer : n026.cluster.edu
% 0.15/0.33  % Model    : x86_64 x86_64
% 0.15/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33  % Memory   : 8042.1875MB
% 0.15/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33  % CPULimit   : 300
% 0.15/0.33  % WCLimit    : 300
% 0.15/0.33  % DateTime   : Mon May  4 16:16:53 EDT 2026
% 0.15/0.33  % CPUTime    : 
% 0.15/0.34  % start to proof: theBenchmark
% 0.57/1.61  % Version  : CSE_E---1.7
% 0.57/1.61  % Problem  : theBenchmark.p
% 0.57/1.61  % SZS status Unsatisfiable for theBenchmark.p
% 0.57/1.61  % SZS output start CNFRefutation
% See solution above
% 0.67/1.74  % Total time : 1.271s
%------------------------------------------------------------------------------