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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SET018-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 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 05:06:52 PM UTC 2026

% Result   : Unsatisfiable 1.67s 1.86s
% Output   : CNFRefutation 1.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   19
% Syntax   : Number of clauses     :  103 (  33 unt;  37 nHn;  77 RR)
%            Number of literals    :  198 (  93 equ;  61 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   7 con; 0-2 aty)
%            Number of variables   :  104 (  25 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(ordered_pair,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).

cnf(singleton_set,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).

cnf(prove_ordered_pair_determines_components2_1,negated_conjecture,
    ordered_pair(w,x) = ordered_pair(y,z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_1) ).

cnf(unordered_pair3,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).

cnf(unordered_pairs_in_universal,axiom,
    member(unordered_pair(X1,X2),universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pairs_in_universal) ).

cnf(unordered_pair_member,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).

cnf(subclass_members,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).

cnf(class_elements_are_sets,axiom,
    subclass(X1,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).

cnf(regularity1,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity1) ).

cnf(unordered_pair2,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).

cnf(prove_ordered_pair_determines_components2_3,negated_conjecture,
    x != z,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_3) ).

cnf(complement1,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).

cnf(cartesian_product2,axiom,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product2) ).

cnf(cartesian_product3,axiom,
    ( member(ordered_pair(X1,X3),cross_product(X2,X4))
    | ~ member(X1,X2)
    | ~ member(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',cartesian_product3) ).

cnf(prove_ordered_pair_determines_components2_2,negated_conjecture,
    member(x,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components2_2) ).

cnf(intersection3,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).

cnf(regularity2,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).

cnf(inductive1,axiom,
    ( member(null_class,X1)
    | ~ inductive(X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).

cnf(omega_is_inductive1,axiom,
    inductive(omega),
    file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).

cnf(c_0_19,axiom,
    unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
    ordered_pair ).

cnf(c_0_20,axiom,
    unordered_pair(X1,X1) = singleton(X1),
    singleton_set ).

cnf(c_0_21,negated_conjecture,
    ordered_pair(w,x) = ordered_pair(y,z),
    prove_ordered_pair_determines_components2_1 ).

cnf(c_0_22,plain,
    unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).

cnf(c_0_23,axiom,
    ( member(X1,unordered_pair(X2,X1))
    | ~ member(X1,universal_class) ),
    unordered_pair3 ).

cnf(c_0_24,negated_conjecture,
    unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).

cnf(c_0_25,axiom,
    member(unordered_pair(X1,X2),universal_class),
    unordered_pairs_in_universal ).

cnf(c_0_26,axiom,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    unordered_pair_member ).

cnf(c_0_27,negated_conjecture,
    member(unordered_pair(w,unordered_pair(x,x)),unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).

cnf(c_0_28,negated_conjecture,
    ( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,unordered_pair(z,z))
    | unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_29,negated_conjecture,
    ( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y)
    | member(unordered_pair(x,x),unordered_pair(y,unordered_pair(z,z))) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_25])]) ).

cnf(c_0_30,negated_conjecture,
    ( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y)
    | unordered_pair(z,z) = unordered_pair(x,x)
    | unordered_pair(x,x) = y ),
    inference(spm,[status(thm)],[c_0_26,c_0_29]) ).

cnf(c_0_31,negated_conjecture,
    ( unordered_pair(z,z) = unordered_pair(x,x)
    | unordered_pair(x,x) = y
    | member(unordered_pair(x,x),unordered_pair(y,y)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_30]),c_0_25])]) ).

cnf(c_0_32,axiom,
    ( member(X3,X2)
    | ~ subclass(X1,X2)
    | ~ member(X3,X1) ),
    subclass_members ).

cnf(c_0_33,axiom,
    subclass(X1,universal_class),
    class_elements_are_sets ).

cnf(c_0_34,axiom,
    ( X1 = null_class
    | member(regular(X1),X1) ),
    regularity1 ).

cnf(c_0_35,axiom,
    ( member(X1,unordered_pair(X1,X2))
    | ~ member(X1,universal_class) ),
    unordered_pair2 ).

cnf(c_0_36,negated_conjecture,
    ( unordered_pair(z,z) = unordered_pair(x,x)
    | unordered_pair(x,x) = y ),
    inference(spm,[status(thm)],[c_0_26,c_0_31]) ).

cnf(c_0_37,plain,
    ( member(X1,universal_class)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_38,plain,
    ( regular(unordered_pair(X1,X2)) = X1
    | regular(unordered_pair(X1,X2)) = X2
    | unordered_pair(X1,X2) = null_class ),
    inference(spm,[status(thm)],[c_0_26,c_0_34]) ).

cnf(c_0_39,negated_conjecture,
    member(unordered_pair(w,w),unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_24]),c_0_25])]) ).

cnf(c_0_40,negated_conjecture,
    ( unordered_pair(x,x) = y
    | member(z,unordered_pair(x,x))
    | ~ member(z,universal_class) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,negated_conjecture,
    x != z,
    prove_ordered_pair_determines_components2_3 ).

cnf(c_0_42,plain,
    ( X1 = null_class
    | member(regular(X1),universal_class) ),
    inference(spm,[status(thm)],[c_0_37,c_0_34]) ).

cnf(c_0_43,plain,
    ( regular(unordered_pair(X1,X1)) = X1
    | unordered_pair(X1,X1) = null_class ),
    inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_38])]) ).

cnf(c_0_44,negated_conjecture,
    ( unordered_pair(y,unordered_pair(z,z)) = unordered_pair(w,w)
    | unordered_pair(w,w) = unordered_pair(y,y) ),
    inference(spm,[status(thm)],[c_0_26,c_0_39]) ).

cnf(c_0_45,negated_conjecture,
    ( unordered_pair(x,x) = y
    | ~ member(z,universal_class) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_40]),c_0_41]) ).

cnf(c_0_46,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,universal_class) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_47,axiom,
    ( ~ member(X1,complement(X2))
    | ~ member(X1,X2) ),
    complement1 ).

cnf(c_0_48,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | member(y,unordered_pair(w,w))
    | ~ member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_35,c_0_44]) ).

cnf(c_0_49,axiom,
    ( member(X2,X4)
    | ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
    cartesian_product2 ).

cnf(c_0_50,negated_conjecture,
    ( unordered_pair(z,z) = null_class
    | unordered_pair(x,x) = y ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

cnf(c_0_51,plain,
    ( complement(X1) = null_class
    | ~ member(regular(complement(X1)),X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_34]) ).

cnf(c_0_52,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | w = y
    | ~ member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_26,c_0_48]) ).

cnf(c_0_53,plain,
    ( member(X2,X4)
    | ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
    inference(rw,[status(thm)],[c_0_49,c_0_22]) ).

cnf(c_0_54,axiom,
    ( member(ordered_pair(X1,X3),cross_product(X2,X4))
    | ~ member(X1,X2)
    | ~ member(X3,X4) ),
    cartesian_product3 ).

cnf(c_0_55,negated_conjecture,
    ( unordered_pair(x,x) = y
    | unordered_pair(x,x) = null_class ),
    inference(spm,[status(thm)],[c_0_36,c_0_50]) ).

cnf(c_0_56,plain,
    complement(universal_class) = null_class,
    inference(spm,[status(thm)],[c_0_51,c_0_42]) ).

cnf(c_0_57,plain,
    ( unordered_pair(X1,X1) = null_class
    | member(X1,unordered_pair(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_34,c_0_43]) ).

cnf(c_0_58,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | unordered_pair(y,y) = null_class
    | w = y ),
    inference(spm,[status(thm)],[c_0_52,c_0_46]) ).

cnf(c_0_59,negated_conjecture,
    ( member(x,X1)
    | ~ member(unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))),cross_product(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_53,c_0_24]) ).

cnf(c_0_60,plain,
    ( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X3,X3))),cross_product(X2,X4))
    | ~ member(X3,X4)
    | ~ member(X1,X2) ),
    inference(rw,[status(thm)],[c_0_54,c_0_22]) ).

cnf(c_0_61,negated_conjecture,
    ( unordered_pair(x,x) = y
    | X1 = z
    | ~ member(X1,unordered_pair(x,x)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_36]) ).

cnf(c_0_62,negated_conjecture,
    member(x,universal_class),
    prove_ordered_pair_determines_components2_2 ).

cnf(c_0_63,negated_conjecture,
    ( unordered_pair(x,x) = null_class
    | y != null_class ),
    inference(ef,[status(thm)],[c_0_55]) ).

cnf(c_0_64,plain,
    ~ member(X1,null_class),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_56]),c_0_37]) ).

cnf(c_0_65,negated_conjecture,
    ( unordered_pair(y,y) = null_class
    | w = y
    | member(w,unordered_pair(y,y)) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_66,negated_conjecture,
    ( member(x,X1)
    | ~ member(z,X1)
    | ~ member(y,X2) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_67,negated_conjecture,
    ( unordered_pair(x,x) = null_class
    | member(y,universal_class) ),
    inference(spm,[status(thm)],[c_0_25,c_0_55]) ).

cnf(c_0_68,negated_conjecture,
    unordered_pair(x,x) = y,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_35]),c_0_62])]),c_0_41]) ).

cnf(c_0_69,negated_conjecture,
    y != null_class,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_63]),c_0_62])]),c_0_64]) ).

cnf(c_0_70,negated_conjecture,
    ( unordered_pair(x,x) = null_class
    | X1 = x
    | ~ member(X1,y) ),
    inference(spm,[status(thm)],[c_0_26,c_0_55]) ).

cnf(c_0_71,negated_conjecture,
    ( unordered_pair(y,y) = null_class
    | w = y ),
    inference(spm,[status(thm)],[c_0_26,c_0_65]) ).

cnf(c_0_72,negated_conjecture,
    ( member(x,unordered_pair(X1,z))
    | ~ member(z,universal_class)
    | ~ member(y,X2) ),
    inference(spm,[status(thm)],[c_0_66,c_0_23]) ).

cnf(c_0_73,negated_conjecture,
    member(y,universal_class),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68]),c_0_69]) ).

cnf(c_0_74,axiom,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    intersection3 ).

cnf(c_0_75,axiom,
    ( X1 = null_class
    | intersection(X1,regular(X1)) = null_class ),
    regularity2 ).

cnf(c_0_76,negated_conjecture,
    ( unordered_pair(x,x) = null_class
    | regular(y) = x ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_34]),c_0_69]) ).

cnf(c_0_77,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | member(unordered_pair(z,z),unordered_pair(w,w)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_44]),c_0_25])]) ).

cnf(c_0_78,negated_conjecture,
    ( w = y
    | ~ member(y,universal_class) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_71]),c_0_64]) ).

cnf(c_0_79,negated_conjecture,
    ( member(x,unordered_pair(X1,z))
    | ~ member(z,universal_class) ),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_80,plain,
    ( X1 = null_class
    | ~ member(X2,regular(X1))
    | ~ member(X2,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_64]) ).

cnf(c_0_81,negated_conjecture,
    regular(y) = x,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_76]),c_0_62])]),c_0_64]) ).

cnf(c_0_82,negated_conjecture,
    ( unordered_pair(w,w) = unordered_pair(y,y)
    | unordered_pair(z,z) = w ),
    inference(spm,[status(thm)],[c_0_26,c_0_77]) ).

cnf(c_0_83,negated_conjecture,
    ( unordered_pair(x,x) = null_class
    | w = y ),
    inference(spm,[status(thm)],[c_0_78,c_0_67]) ).

cnf(c_0_84,negated_conjecture,
    ( x = X1
    | ~ member(z,universal_class) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_79]),c_0_41]) ).

cnf(c_0_85,negated_conjecture,
    ( ~ member(X1,x)
    | ~ member(X1,y) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_69]) ).

cnf(c_0_86,negated_conjecture,
    member(x,y),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_81]),c_0_69]) ).

cnf(c_0_87,negated_conjecture,
    ( unordered_pair(z,z) = w
    | X1 = w
    | ~ member(X1,unordered_pair(y,y)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_82]) ).

cnf(c_0_88,negated_conjecture,
    w = y,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_83]),c_0_62])]),c_0_64]) ).

cnf(c_0_89,negated_conjecture,
    ( unordered_pair(z,z) = null_class
    | x = X1 ),
    inference(spm,[status(thm)],[c_0_84,c_0_46]) ).

cnf(c_0_90,negated_conjecture,
    ~ member(x,x),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_91,negated_conjecture,
    ( X1 = unordered_pair(w,unordered_pair(x,x))
    | X1 = unordered_pair(w,w)
    | ~ member(X1,unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z)))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_24]) ).

cnf(c_0_92,negated_conjecture,
    ( unordered_pair(z,z) = y
    | X1 = y
    | ~ member(X1,unordered_pair(y,y)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88]),c_0_88]) ).

cnf(c_0_93,negated_conjecture,
    unordered_pair(z,z) = null_class,
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_89]),c_0_90]),c_0_46]) ).

cnf(c_0_94,negated_conjecture,
    ( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,unordered_pair(z,z))
    | unordered_pair(y,unordered_pair(z,z)) = unordered_pair(w,w) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_23]),c_0_25])]) ).

cnf(c_0_95,axiom,
    ( member(null_class,X1)
    | ~ inductive(X1) ),
    inductive1 ).

cnf(c_0_96,negated_conjecture,
    ( X1 = y
    | ~ member(X1,unordered_pair(y,y)) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_69]) ).

cnf(c_0_97,negated_conjecture,
    unordered_pair(y,y) = unordered_pair(y,null_class),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_88]),c_0_88]),c_0_88]),c_0_93]),c_0_68]),c_0_93])]) ).

cnf(c_0_98,plain,
    ( member(null_class,universal_class)
    | ~ inductive(X1) ),
    inference(spm,[status(thm)],[c_0_37,c_0_95]) ).

cnf(c_0_99,axiom,
    inductive(omega),
    omega_is_inductive1 ).

cnf(c_0_100,negated_conjecture,
    ( X1 = y
    | ~ member(X1,unordered_pair(y,null_class)) ),
    inference(rw,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_101,plain,
    member(null_class,universal_class),
    inference(spm,[status(thm)],[c_0_98,c_0_99]) ).

cnf(c_0_102,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_23]),c_0_101])]),c_0_69]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET018-6 : TPTP v9.2.1. Bugfixed v2.1.0.
% 0.11/0.13  % 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
% 0.17/0.34  % Computer : n026.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit   : 300
% 0.17/0.34  % WCLimit    : 300
% 0.17/0.34  % DateTime   : Tue May  5 02:04:53 EDT 2026
% 0.17/0.34  % CPUTime    : 
% 0.17/0.35  % start to proof: theBenchmark
% 1.67/1.86  % Version  : CSE_E---1.7
% 1.67/1.86  % Problem  : theBenchmark.p
% 1.67/1.86  % SZS status Unsatisfiable for theBenchmark.p
% 1.67/1.86  % SZS output start CNFRefutation
% See solution above
% 1.67/1.86  % Total time : 1.369s
%------------------------------------------------------------------------------