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E---3.5.1.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SET837-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:15:32 PM UTC 2026

% Result   : Unsatisfiable 173.96s 26.27s
% Output   : CNFRefutation 173.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   13
% Syntax   : Number of clauses     :   81 (  16 unt;  22 nHn;  59 RR)
%            Number of literals    :  186 (  30 equ;  87 neg)
%            Maximal clause size   :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-3 aty)
%            Number of variables   :  124 (  13 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(cls_Set_OUnCI_0,axiom,
    ( ~ c_in(X1,X2,X3)
    | c_in(X1,c_union(X4,X2,X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Set_OUnCI_0) ).

cnf(cls_Set_OsubsetD_0,axiom,
    ( ~ c_lessequals(X2,X4,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | c_in(X1,X4,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetD_0) ).

cnf(cls_Set_OUnCI_1,axiom,
    ( ~ c_in(X1,X2,X3)
    | c_in(X1,c_union(X2,X4,X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Set_OUnCI_1) ).

cnf(cls_Set_OsubsetI_1,axiom,
    ( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_1) ).

cnf(cls_conjecture_1,negated_conjecture,
    ( c_lessequals(v_Z,v_X,tc_set(t_a))
    | v_X = c_union(v_Y,v_Z,t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_conjecture_0,negated_conjecture,
    ( c_lessequals(v_Y,v_X,tc_set(t_a))
    | v_X = c_union(v_Y,v_Z,t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Set_OsubsetI_0,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_OsubsetI_0) ).

cnf(cls_Set_OUnE_0,axiom,
    ( ~ c_in(X1,c_union(X2,X3,X4),X4)
    | c_in(X1,X2,X4)
    | c_in(X1,X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-2.ax',cls_Set_OUnE_0) ).

cnf(cls_conjecture_5,negated_conjecture,
    ( ~ c_lessequals(v_Y,X1,tc_set(t_a))
    | ~ c_lessequals(v_Z,X1,tc_set(t_a))
    | c_lessequals(v_X,X1,tc_set(t_a))
    | v_X = c_union(v_Y,v_Z,t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

cnf(cls_Set_Osubset__antisym_0,axiom,
    ( ~ c_lessequals(X2,X1,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | X2 = X1 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',cls_Set_Osubset__antisym_0) ).

cnf(cls_conjecture_2,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | c_lessequals(v_Y,v_x,tc_set(t_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_conjecture_3,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | c_lessequals(v_Z,v_x,tc_set(t_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_4,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(c_0_13,plain,
    ( ~ c_in(X1,X2,X3)
    | c_in(X1,c_union(X4,X2,X3),X3) ),
    inference(fof_simplification,[status(thm)],[cls_Set_OUnCI_0]) ).

cnf(c_0_14,plain,
    ( ~ c_lessequals(X2,X4,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | c_in(X1,X4,X3) ),
    inference(fof_simplification,[status(thm)],[cls_Set_OsubsetD_0]) ).

cnf(c_0_15,plain,
    ( ~ c_in(X1,X2,X3)
    | c_in(X1,c_union(X2,X4,X3),X3) ),
    inference(fof_simplification,[status(thm)],[cls_Set_OUnCI_1]) ).

cnf(c_0_16,plain,
    ( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    inference(fof_simplification,[status(thm)],[cls_Set_OsubsetI_1]) ).

cnf(c_0_17,plain,
    ( ~ c_in(X1,X2,X3)
    | c_in(X1,c_union(X4,X2,X3),X3) ),
    c_0_13 ).

cnf(c_0_18,negated_conjecture,
    ( c_lessequals(v_Z,v_X,tc_set(t_a))
    | v_X = c_union(v_Y,v_Z,t_a) ),
    cls_conjecture_1 ).

cnf(c_0_19,plain,
    ( ~ c_lessequals(X2,X4,tc_set(X3))
    | ~ c_in(X1,X2,X3)
    | c_in(X1,X4,X3) ),
    c_0_14 ).

cnf(c_0_20,plain,
    ( ~ c_in(X1,X2,X3)
    | c_in(X1,c_union(X2,X4,X3),X3) ),
    c_0_15 ).

cnf(c_0_21,negated_conjecture,
    ( c_lessequals(v_Y,v_X,tc_set(t_a))
    | v_X = c_union(v_Y,v_Z,t_a) ),
    cls_conjecture_0 ).

cnf(c_0_22,plain,
    ( ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3)
    | c_lessequals(X1,X2,tc_set(X3)) ),
    c_0_16 ).

cnf(c_0_23,negated_conjecture,
    ( ~ c_in(X1,v_Z,t_a)
    | c_in(X1,v_X,t_a) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

cnf(c_0_24,axiom,
    ( c_lessequals(X1,X2,tc_set(X3))
    | c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3) ),
    cls_Set_OsubsetI_0 ).

cnf(c_0_25,plain,
    ( ~ c_in(X1,c_union(X2,X3,X4),X4)
    | c_in(X1,X2,X4)
    | c_in(X1,X3,X4) ),
    inference(fof_simplification,[status(thm)],[cls_Set_OUnE_0]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ c_in(X1,v_Y,t_a)
    | c_in(X1,v_X,t_a) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).

cnf(c_0_27,plain,
    ( ~ c_in(c_Main_OsubsetI__1(X1,c_union(X2,X3,X4),X4),X3,X4)
    | c_lessequals(X1,c_union(X2,X3,X4),tc_set(X4)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_17]) ).

cnf(c_0_28,negated_conjecture,
    ( c_in(c_Main_OsubsetI__1(v_Z,X1,t_a),v_X,t_a)
    | c_lessequals(v_Z,X1,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    ( ~ c_in(X1,c_union(X2,X3,X4),X4)
    | c_in(X1,X2,X4)
    | c_in(X1,X3,X4) ),
    c_0_25 ).

cnf(c_0_30,negated_conjecture,
    ( ~ c_lessequals(v_Y,X1,tc_set(t_a))
    | ~ c_lessequals(v_Z,X1,tc_set(t_a))
    | c_lessequals(v_X,X1,tc_set(t_a))
    | v_X = c_union(v_Y,v_Z,t_a) ),
    inference(fof_simplification,[status(thm)],[cls_conjecture_5]) ).

cnf(c_0_31,plain,
    ( ~ c_in(c_Main_OsubsetI__1(X1,c_union(X2,X3,X4),X4),X2,X4)
    | c_lessequals(X1,c_union(X2,X3,X4),tc_set(X4)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_20]) ).

cnf(c_0_32,negated_conjecture,
    ( c_in(c_Main_OsubsetI__1(v_Y,X1,t_a),v_X,t_a)
    | c_lessequals(v_Y,X1,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_24]) ).

cnf(c_0_33,negated_conjecture,
    c_lessequals(v_Z,c_union(X1,v_X,t_a),tc_set(t_a)),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,plain,
    ( c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X4,X3),X2,X3)
    | c_in(c_Main_OsubsetI__1(c_union(X1,X2,X3),X4,X3),X1,X3)
    | c_lessequals(c_union(X1,X2,X3),X4,tc_set(X3)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_24]) ).

cnf(c_0_35,negated_conjecture,
    ( ~ c_lessequals(v_Y,X1,tc_set(t_a))
    | ~ c_lessequals(v_Z,X1,tc_set(t_a))
    | c_lessequals(v_X,X1,tc_set(t_a))
    | v_X = c_union(v_Y,v_Z,t_a) ),
    c_0_30 ).

cnf(c_0_36,plain,
    c_lessequals(X1,c_union(X1,X2,X3),tc_set(X3)),
    inference(spm,[status(thm)],[c_0_31,c_0_24]) ).

cnf(c_0_37,negated_conjecture,
    c_lessequals(v_Y,c_union(v_X,X1,t_a),tc_set(t_a)),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_38,negated_conjecture,
    ( ~ c_in(X1,v_Z,t_a)
    | c_in(X1,c_union(X2,v_X,t_a),t_a) ),
    inference(spm,[status(thm)],[c_0_19,c_0_33]) ).

cnf(c_0_39,plain,
    ( ~ c_lessequals(X2,X1,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | X2 = X1 ),
    inference(fof_simplification,[status(thm)],[cls_Set_Osubset__antisym_0]) ).

cnf(c_0_40,plain,
    ( c_in(c_Main_OsubsetI__1(c_union(X1,X1,X2),X3,X2),X1,X2)
    | c_lessequals(c_union(X1,X1,X2),X3,tc_set(X2)) ),
    inference(ef,[status(thm)],[c_0_34]) ).

cnf(c_0_41,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | c_lessequals(v_Y,v_x,tc_set(t_a)) ),
    inference(fof_simplification,[status(thm)],[cls_conjecture_2]) ).

cnf(c_0_42,negated_conjecture,
    ( ~ c_lessequals(v_Z,c_union(v_Y,X1,t_a),tc_set(t_a))
    | c_lessequals(v_X,c_union(v_Y,X1,t_a),tc_set(t_a))
    | c_union(v_Y,v_Z,t_a) = v_X ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_43,plain,
    c_lessequals(X1,c_union(X2,X1,X3),tc_set(X3)),
    inference(spm,[status(thm)],[c_0_27,c_0_24]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ c_in(X1,v_Y,t_a)
    | c_in(X1,c_union(v_X,X2,t_a),t_a) ),
    inference(spm,[status(thm)],[c_0_19,c_0_37]) ).

cnf(c_0_45,negated_conjecture,
    ( ~ c_in(c_Main_OsubsetI__1(X1,c_union(X2,v_X,t_a),t_a),v_Z,t_a)
    | c_lessequals(X1,c_union(X2,v_X,t_a),tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_38]) ).

cnf(c_0_46,plain,
    ( ~ c_lessequals(X2,X1,tc_set(X3))
    | ~ c_lessequals(X1,X2,tc_set(X3))
    | X2 = X1 ),
    c_0_39 ).

cnf(c_0_47,plain,
    c_lessequals(c_union(X1,X1,X2),X1,tc_set(X2)),
    inference(spm,[status(thm)],[c_0_22,c_0_40]) ).

cnf(c_0_48,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | c_lessequals(v_Y,v_x,tc_set(t_a)) ),
    c_0_41 ).

cnf(c_0_49,negated_conjecture,
    c_lessequals(v_Z,v_X,tc_set(t_a)),
    inference(spm,[status(thm)],[c_0_22,c_0_28]) ).

cnf(c_0_50,negated_conjecture,
    ( c_lessequals(v_X,c_union(v_Y,v_Z,t_a),tc_set(t_a))
    | c_union(v_Y,v_Z,t_a) = v_X ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_51,negated_conjecture,
    ( ~ c_in(c_Main_OsubsetI__1(X1,c_union(v_X,X2,t_a),t_a),v_Y,t_a)
    | c_lessequals(X1,c_union(v_X,X2,t_a),tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_44]) ).

cnf(c_0_52,negated_conjecture,
    ( c_in(c_Main_OsubsetI__1(c_union(X1,v_Z,t_a),c_union(X2,v_X,t_a),t_a),X1,t_a)
    | c_lessequals(c_union(X1,v_Z,t_a),c_union(X2,v_X,t_a),tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_45,c_0_34]) ).

cnf(c_0_53,plain,
    c_union(X1,X1,X2) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_36])]) ).

cnf(c_0_54,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | c_lessequals(v_Z,v_x,tc_set(t_a)) ),
    inference(fof_simplification,[status(thm)],[cls_conjecture_3]) ).

cnf(c_0_55,negated_conjecture,
    ( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | c_union(v_Y,v_Z,t_a) != v_X
    | c_lessequals(v_Y,v_x,tc_set(t_a)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).

cnf(c_0_56,negated_conjecture,
    c_lessequals(v_Y,v_X,tc_set(t_a)),
    inference(spm,[status(thm)],[c_0_22,c_0_32]) ).

cnf(c_0_57,negated_conjecture,
    ( ~ c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a))
    | c_union(v_Y,v_Z,t_a) = v_X ),
    inference(spm,[status(thm)],[c_0_46,c_0_50]) ).

cnf(c_0_58,negated_conjecture,
    c_lessequals(c_union(v_Y,v_Z,t_a),v_X,tc_set(t_a)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).

cnf(c_0_59,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
    inference(fof_simplification,[status(thm)],[cls_conjecture_4]) ).

cnf(c_0_60,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | c_lessequals(v_Z,v_x,tc_set(t_a)) ),
    c_0_54 ).

cnf(c_0_61,negated_conjecture,
    ( c_union(v_Y,v_Z,t_a) != v_X
    | c_lessequals(v_Y,v_x,tc_set(t_a)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]) ).

cnf(c_0_62,negated_conjecture,
    c_union(v_Y,v_Z,t_a) = v_X,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58])]) ).

cnf(c_0_63,negated_conjecture,
    ( v_X != c_union(v_Y,v_Z,t_a)
    | ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_Z,v_X,tc_set(t_a))
    | ~ c_lessequals(v_X,v_x,tc_set(t_a)) ),
    c_0_59 ).

cnf(c_0_64,negated_conjecture,
    ( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | c_union(v_Y,v_Z,t_a) != v_X
    | c_lessequals(v_Z,v_x,tc_set(t_a)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_49])]) ).

cnf(c_0_65,negated_conjecture,
    c_lessequals(v_Y,v_x,tc_set(t_a)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_62])]) ).

cnf(c_0_66,negated_conjecture,
    ( ~ c_lessequals(v_Y,v_X,tc_set(t_a))
    | ~ c_lessequals(v_X,v_x,tc_set(t_a))
    | c_union(v_Y,v_Z,t_a) != v_X ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_49])]) ).

cnf(c_0_67,negated_conjecture,
    ( c_union(v_Y,v_Z,t_a) != v_X
    | c_lessequals(v_Z,v_x,tc_set(t_a)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_56])]) ).

cnf(c_0_68,negated_conjecture,
    ( ~ c_in(X1,v_Y,t_a)
    | c_in(X1,v_x,t_a) ),
    inference(spm,[status(thm)],[c_0_19,c_0_65]) ).

cnf(c_0_69,negated_conjecture,
    ( ~ c_lessequals(v_X,v_x,tc_set(t_a))
    | c_union(v_Y,v_Z,t_a) != v_X ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_56])]) ).

cnf(c_0_70,negated_conjecture,
    c_lessequals(v_Z,v_x,tc_set(t_a)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_62])]) ).

cnf(c_0_71,negated_conjecture,
    ( ~ c_in(c_Main_OsubsetI__1(X1,v_x,t_a),v_Y,t_a)
    | c_lessequals(X1,v_x,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_68]) ).

cnf(c_0_72,negated_conjecture,
    ( c_in(c_Main_OsubsetI__1(c_union(X1,v_Z,t_a),X2,t_a),X1,t_a)
    | c_in(c_Main_OsubsetI__1(c_union(X1,v_Z,t_a),X2,t_a),v_X,t_a)
    | c_lessequals(c_union(X1,v_Z,t_a),X2,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_34]) ).

cnf(c_0_73,negated_conjecture,
    ~ c_lessequals(v_X,v_x,tc_set(t_a)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_62])]) ).

cnf(c_0_74,negated_conjecture,
    ( ~ c_in(X1,v_Z,t_a)
    | c_in(X1,v_x,t_a) ),
    inference(spm,[status(thm)],[c_0_19,c_0_70]) ).

cnf(c_0_75,negated_conjecture,
    ( ~ c_in(X1,v_X,t_a)
    | c_in(X1,v_Z,t_a)
    | c_in(X1,v_Y,t_a) ),
    inference(spm,[status(thm)],[c_0_29,c_0_62]) ).

cnf(c_0_76,negated_conjecture,
    c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_X,t_a),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_62]),c_0_62]),c_0_73]) ).

cnf(c_0_77,negated_conjecture,
    ( ~ c_in(c_Main_OsubsetI__1(X1,v_x,t_a),v_Z,t_a)
    | c_lessequals(X1,v_x,tc_set(t_a)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_74]) ).

cnf(c_0_78,negated_conjecture,
    ( c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Y,t_a)
    | c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Z,t_a) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_79,negated_conjecture,
    c_in(c_Main_OsubsetI__1(v_X,v_x,t_a),v_Y,t_a),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_73]) ).

cnf(c_0_80,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_79]),c_0_73]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SET837-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.57  % Computer : n026.cluster.edu
% 0.09/0.57  % Model    : x86_64 x86_64
% 0.09/0.57  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57  % Memory   : 8046.5625MB
% 0.09/0.57  % OS       : Linux 6.8.0-71-generic
% 0.09/0.57  % CPULimit : 300
% 0.09/0.57  % WCLimit  : 300
% 0.09/0.57  % DateTime : Mon Sep 21 05:43:08 UTC 2026
% 0.09/0.58  % CPUTime  : 
% 0.09/0.58  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.63  Running first-order theorem proving
% 0.14/0.63  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 173.96/26.27  % Version: 3.5.1
% 173.96/26.27  % Preprocessing class: FMLMSMSMSSSNFFN.
% 173.96/26.27  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 173.96/26.27  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 173.96/26.27  % Starting new_bool_3 with 300s (1) cores
% 173.96/26.27  % Starting new_bool_1 with 300s (1) cores
% 173.96/26.27  % Starting sh5l with 300s (1) cores
% 173.96/26.27  % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1482909 completed with status 0
% 173.96/26.27  % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 173.96/26.27  % Preprocessing class: FMLMSMSMSSSNFFN.
% 173.96/26.27  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 173.96/26.27  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 173.96/26.27  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 173.96/26.27  % No SInE strategy applied
% 173.96/26.27  % Search class: FGHSM-SSLM33-MFFFFFNN
% 173.96/26.27  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 173.96/26.27  % Starting SubtermCWHack with 136s (1) cores
% 173.96/26.27  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 173.96/26.27  % Starting G-E--_200_B02_F1_AE_CS_SP_PI_S2k with 136s (1) cores
% 173.96/26.27  % Starting new_bool_3 with 136s (1) cores
% 173.96/26.27  % Starting G-E--_200_B02_F1_SE_CS_SP_PI_S2k with 136s (1) cores
% 173.96/26.27  % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1482916 completed with status 0
% 173.96/26.27  % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 173.96/26.27  % Preprocessing class: FMLMSMSMSSSNFFN.
% 173.96/26.27  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 173.96/26.27  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 173.96/26.27  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 173.96/26.27  % No SInE strategy applied
% 173.96/26.27  % Search class: FGHSM-SSLM33-MFFFFFNN
% 173.96/26.27  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 173.96/26.27  % Starting SubtermCWHack with 136s (1) cores
% 173.96/26.27  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 173.96/26.27  % Preprocessing time       : 0.016 s
% 173.96/26.27  % Presaturation interreduction done
% 173.96/26.27  
% 173.96/26.27  % Proof found!
% 173.96/26.27  % SZS status Unsatisfiable
% 173.96/26.27  % SZS output start CNFRefutation
% See solution above
% 173.96/26.27  % Parsed axioms                        : 1363
% 173.96/26.27  % Removed by relevancy pruning/SinE    : 0
% 173.96/26.27  % Initial clauses                      : 1363
% 173.96/26.27  % Removed in clause preprocessing      : 1
% 173.96/26.27  % Initial clauses in saturation        : 1362
% 173.96/26.27  % Processed clauses                    : 43781
% 173.96/26.27  % ...of these trivial                  : 1021
% 173.96/26.27  % ...subsumed                          : 32908
% 173.96/26.27  % ...remaining for further processing  : 9852
% 173.96/26.27  % Other redundant clauses eliminated   : 240
% 173.96/26.27  % Clauses deleted for lack of memory   : 0
% 173.96/26.27  % Backward-subsumed                    : 1845
% 173.96/26.27  % Backward-rewritten                   : 824
% 173.96/26.27  % Generated clauses                    : 555596
% 173.96/26.27  % ...of the previous two non-redundant : 525349
% 173.96/26.27  % ...aggressively subsumed             : 0
% 173.96/26.27  % Contextual simplify-reflections      : 185
% 173.96/26.27  % Paramodulations                      : 555216
% 173.96/26.27  % Factorizations                       : 82
% 173.96/26.27  % NegExts                              : 0
% 173.96/26.27  % Equation resolutions                 : 295
% 173.96/26.27  % Disequality decompositions           : 0
% 173.96/26.27  % Total rewrite steps                  : 296782
% 173.96/26.27  % ...of those cached                   : 288910
% 173.96/26.27  % Propositional unsat checks           : 1
% 173.96/26.27  %    Propositional check models        : 0
% 173.96/26.27  %    Propositional check unsatisfiable : 0
% 173.96/26.27  %    Propositional clauses             : 0
% 173.96/26.27  %    Propositional clauses after purity: 0
% 173.96/26.27  %    Propositional unsat core size     : 0
% 173.96/26.27  %    Propositional preprocessing time  : 0.000
% 173.96/26.27  %    Propositional encoding time       : 0.595
% 173.96/26.27  %    Propositional solver time         : 0.285
% 173.96/26.27  %    Success case prop preproc time    : 0.000
% 173.96/26.27  %    Success case prop encoding time   : 0.000
% 173.96/26.27  %    Success case prop solver time     : 0.000
% 173.96/26.27  % Current number of processed clauses  : 5854
% 173.96/26.27  %    Positive orientable unit clauses  : 548
% 173.96/26.27  %    Positive unorientable unit clauses: 0
% 173.96/26.27  %    Negative unit clauses             : 328
% 173.96/26.27  %    Non-unit-clauses                  : 4978
% 173.96/26.27  % Current number of unprocessed clauses: 477326
% 173.96/26.27  % ...number of literals in the above   : 1608300
% 173.96/26.27  % Current number of archived formulas  : 0
% 173.96/26.27  % Current number of archived clauses   : 3998
% 173.96/26.27  % Clause-clause subsumption calls (NU) : 15402139
% 173.96/26.27  % Rec. Clause-clause subsumption calls : 11181574
% 173.96/26.27  % Non-unit clause-clause subsumptions  : 25085
% 173.96/26.27  % Unit Clause-clause subsumption calls : 292387
% 173.96/26.27  % Rewrite failures with RHS unbound    : 0
% 173.96/26.27  % BW rewrite match attempts            : 1079
% 173.96/26.27  % BW rewrite match successes           : 248
% 173.96/26.27  % Condensation attempts                : 0
% 173.96/26.27  % Condensation successes               : 0
% 173.96/26.27  % Termbank termtop insertions          : 28603937
% 173.96/26.27  % Search garbage collected termcells   : 1607
% 173.96/26.27  
% 173.96/26.27  % -------------------------------------------------
% 173.96/26.27  % User time                : 23.747 s
% 173.96/26.27  % System time              : 0.661 s
% 173.96/26.27  % Total time               : 24.409 s
% 173.96/26.27  % Maximum resident set size: 5576 pages
% 173.96/26.27  
% 173.96/26.27  % -------------------------------------------------
% 173.96/26.27  % User time                : 119.242 s
% 173.96/26.27  % System time              : 3.908 s
% 173.96/26.27  % Total time               : 123.151 s
% 173.96/26.27  % Maximum resident set size: 5376 pages
% 173.96/26.27  % E exiting
%------------------------------------------------------------------------------