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E---3.5.1.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n019.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 12:37:29 PM UTC 2026

% Result   : Unsatisfiable 0.15s 0.61s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   38
%            Number of leaves      :   28
% Syntax   : Number of clauses     :  116 (  59 unt;  48 nHn; 116 RR)
%            Number of literals    :  261 ( 171 equ;  41 neg)
%            Maximal clause size   :    7 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;  11 con; 0-1 aty)
%            Number of variables   :   34 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(all_of_group1,hypothesis,
    ( ~ group_member(X1,g1)
    | X1 = c
    | X1 = b
    | X1 = a ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_of_group1) ).

cnf(prove_product_holds_in_group2,negated_conjecture,
    ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).

cnf(d3_in_group1,hypothesis,
    group_member(d3,g1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_in_group1) ).

cnf(a_maps_to_f,hypothesis,
    an_isomorphism(a) = f,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_f) ).

cnf(d2_in_group1,hypothesis,
    group_member(d2,g1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_in_group1) ).

cnf(d1_in_group1,hypothesis,
    group_member(d1,g1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_in_group1) ).

cnf(d1_times_d2_is_d3,hypothesis,
    product(g1,d1,d2,d3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).

cnf(f_times_f_is_f,hypothesis,
    product(g2,f,f,f),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_f_is_f) ).

cnf(total_function2,axiom,
    ( ~ product(X1,X2,X3,X5)
    | ~ product(X1,X2,X3,X4)
    | X5 = X4 ),
    file('/export/starexec/sandbox/benchmark/Axioms/GRP006-0.ax',total_function2) ).

cnf(a_times_a_is_a,hypothesis,
    product(g1,a,a,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).

cnf(c_maps_to_h,hypothesis,
    an_isomorphism(c) = h,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_maps_to_h) ).

cnf(a_times_c_is_c,hypothesis,
    product(g1,a,c,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_c) ).

cnf(f_times_h_is_h,hypothesis,
    product(g2,f,h,h),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_h_is_h) ).

cnf(b_maps_to_g,hypothesis,
    an_isomorphism(b) = g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_g) ).

cnf(a_times_b_is_b,hypothesis,
    product(g1,a,b,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_b) ).

cnf(f_times_g_is_g,hypothesis,
    product(g2,f,g,g),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_times_g_is_g) ).

cnf(c_times_a_is_c,hypothesis,
    product(g1,c,a,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_a_is_c) ).

cnf(h_times_f_is_h,hypothesis,
    product(g2,h,f,h),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_f_is_h) ).

cnf(c_times_c_is_b,hypothesis,
    product(g1,c,c,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_b) ).

cnf(h_times_h_is_g,hypothesis,
    product(g2,h,h,g),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_h_is_g) ).

cnf(c_times_b_is_a,hypothesis,
    product(g1,c,b,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_b_is_a) ).

cnf(h_times_g_is_f,hypothesis,
    product(g2,h,g,f),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_g_is_f) ).

cnf(b_times_a_is_b,hypothesis,
    product(g1,b,a,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_is_b) ).

cnf(g_times_f_is_g,hypothesis,
    product(g2,g,f,g),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_f_is_g) ).

cnf(b_times_c_is_a,hypothesis,
    product(g1,b,c,a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_c_is_a) ).

cnf(g_times_h_is_f,hypothesis,
    product(g2,g,h,f),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_h_is_f) ).

cnf(b_times_b_is_c,hypothesis,
    product(g1,b,b,c),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_b_is_c) ).

cnf(g_times_g_is_h,hypothesis,
    product(g2,g,g,h),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',g_times_g_is_h) ).

cnf(c_0_28,hypothesis,
    ( ~ group_member(X1,g1)
    | X1 = c
    | X1 = b
    | X1 = a ),
    inference(fof_simplification,[status(thm)],[all_of_group1]) ).

cnf(c_0_29,negated_conjecture,
    ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
    inference(fof_simplification,[status(thm)],[prove_product_holds_in_group2]) ).

cnf(c_0_30,hypothesis,
    ( ~ group_member(X1,g1)
    | X1 = c
    | X1 = b
    | X1 = a ),
    c_0_28 ).

cnf(c_0_31,hypothesis,
    group_member(d3,g1),
    d3_in_group1 ).

cnf(c_0_32,negated_conjecture,
    ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
    c_0_29 ).

cnf(c_0_33,hypothesis,
    ( d3 = a
    | d3 = b
    | d3 = c ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,hypothesis,
    an_isomorphism(a) = f,
    a_maps_to_f ).

cnf(c_0_35,hypothesis,
    group_member(d2,g1),
    d2_in_group1 ).

cnf(c_0_36,negated_conjecture,
    ( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),f)
    | d3 = c
    | d3 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_37,hypothesis,
    ( d2 = a
    | d2 = b
    | d2 = c ),
    inference(spm,[status(thm)],[c_0_30,c_0_35]) ).

cnf(c_0_38,hypothesis,
    group_member(d1,g1),
    d1_in_group1 ).

cnf(c_0_39,hypothesis,
    product(g1,d1,d2,d3),
    d1_times_d2_is_d3 ).

cnf(c_0_40,hypothesis,
    ( ~ product(g2,an_isomorphism(d1),f,f)
    | d3 = b
    | d3 = c
    | d2 = c
    | d2 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_34]) ).

cnf(c_0_41,hypothesis,
    ( d1 = a
    | d1 = b
    | d1 = c ),
    inference(spm,[status(thm)],[c_0_30,c_0_38]) ).

cnf(c_0_42,hypothesis,
    product(g2,f,f,f),
    f_times_f_is_f ).

cnf(c_0_43,plain,
    ( ~ product(X1,X2,X3,X5)
    | ~ product(X1,X2,X3,X4)
    | X5 = X4 ),
    inference(fof_simplification,[status(thm)],[total_function2]) ).

cnf(c_0_44,hypothesis,
    ( product(g1,d1,a,d3)
    | d2 = c
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_39,c_0_37]) ).

cnf(c_0_45,hypothesis,
    ( d2 = b
    | d2 = c
    | d3 = c
    | d3 = b
    | d1 = c
    | d1 = b ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_34]),c_0_42])]) ).

cnf(c_0_46,plain,
    ( ~ product(X1,X2,X3,X5)
    | ~ product(X1,X2,X3,X4)
    | X5 = X4 ),
    c_0_43 ).

cnf(c_0_47,hypothesis,
    ( product(g1,d1,a,c)
    | d2 = b
    | d2 = c
    | d1 = b
    | d1 = c
    | d3 = b ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_48,hypothesis,
    ( ~ product(g1,d1,a,X1)
    | X1 = c
    | d3 = b
    | d1 = c
    | d1 = b
    | d2 = c
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_49,hypothesis,
    ( a != c
    | d1 = c
    | d1 = b ),
    inference(ef,[status(thm)],[c_0_41]) ).

cnf(c_0_50,hypothesis,
    ( a != b
    | d1 = c
    | d1 = b ),
    inference(ef,[status(thm)],[c_0_41]) ).

cnf(c_0_51,hypothesis,
    ( ~ product(g1,a,a,X1)
    | X1 = c
    | d2 = b
    | d2 = c
    | d3 = b
    | d1 = c
    | d1 = b ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_41]),c_0_49]),c_0_50]) ).

cnf(c_0_52,hypothesis,
    product(g1,a,a,a),
    a_times_a_is_a ).

cnf(c_0_53,hypothesis,
    ( d1 = b
    | d1 = c
    | d3 = b
    | d2 = c
    | d2 = b ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_49]) ).

cnf(c_0_54,hypothesis,
    ( product(g1,d1,a,b)
    | d2 = b
    | d2 = c
    | d1 = c
    | d1 = b ),
    inference(spm,[status(thm)],[c_0_44,c_0_53]) ).

cnf(c_0_55,hypothesis,
    ( ~ product(g1,d1,a,X1)
    | X1 = b
    | d1 = b
    | d1 = c
    | d2 = c
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_46,c_0_54]) ).

cnf(c_0_56,hypothesis,
    ( ~ product(g1,d1,d2,X1)
    | X1 = d3 ),
    inference(spm,[status(thm)],[c_0_46,c_0_39]) ).

cnf(c_0_57,hypothesis,
    ( ~ product(g1,a,a,X1)
    | X1 = b
    | d2 = b
    | d2 = c
    | d1 = c
    | d1 = b ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_41]),c_0_50]),c_0_49]) ).

cnf(c_0_58,hypothesis,
    ( ~ product(g1,a,d2,X1)
    | X1 = d3
    | d1 = c
    | d1 = b ),
    inference(spm,[status(thm)],[c_0_56,c_0_41]) ).

cnf(c_0_59,hypothesis,
    ( d1 = b
    | d1 = c
    | d2 = c
    | d2 = b ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_52]),c_0_50]) ).

cnf(c_0_60,negated_conjecture,
    ( ~ product(g2,f,an_isomorphism(d2),an_isomorphism(d3))
    | d1 = c
    | d1 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_34]) ).

cnf(c_0_61,hypothesis,
    an_isomorphism(c) = h,
    c_maps_to_h ).

cnf(c_0_62,hypothesis,
    ( ~ product(g1,a,c,X1)
    | X1 = d3
    | d1 = b
    | d1 = c
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_63,hypothesis,
    product(g1,a,c,c),
    a_times_c_is_c ).

cnf(c_0_64,negated_conjecture,
    ( ~ product(g2,f,h,an_isomorphism(d3))
    | d1 = b
    | d1 = c
    | d2 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_59]),c_0_61]) ).

cnf(c_0_65,hypothesis,
    ( d2 = b
    | d1 = c
    | d1 = b
    | d3 = c ),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_66,hypothesis,
    product(g2,f,h,h),
    f_times_h_is_h ).

cnf(c_0_67,negated_conjecture,
    ( d2 = b
    | d1 = c
    | d1 = b ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_61]),c_0_66])]) ).

cnf(c_0_68,hypothesis,
    an_isomorphism(b) = g,
    b_maps_to_g ).

cnf(c_0_69,hypothesis,
    ( ~ product(g1,a,b,X1)
    | X1 = d3
    | d1 = b
    | d1 = c ),
    inference(spm,[status(thm)],[c_0_58,c_0_67]) ).

cnf(c_0_70,hypothesis,
    product(g1,a,b,b),
    a_times_b_is_b ).

cnf(c_0_71,negated_conjecture,
    ( ~ product(g2,f,g,an_isomorphism(d3))
    | d1 = b
    | d1 = c ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_67]),c_0_68]) ).

cnf(c_0_72,hypothesis,
    ( d1 = c
    | d1 = b
    | d3 = b ),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_73,hypothesis,
    product(g2,f,g,g),
    f_times_g_is_g ).

cnf(c_0_74,hypothesis,
    ( ~ product(g1,d1,a,X1)
    | X1 = d3
    | d2 = c
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_56,c_0_37]) ).

cnf(c_0_75,negated_conjecture,
    ( d1 = c
    | d1 = b ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_68]),c_0_73])]) ).

cnf(c_0_76,negated_conjecture,
    ( ~ product(g2,an_isomorphism(d1),f,an_isomorphism(d3))
    | d2 = c
    | d2 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_34]) ).

cnf(c_0_77,hypothesis,
    ( ~ product(g1,c,a,X1)
    | X1 = d3
    | d2 = b
    | d2 = c
    | d1 = b ),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_78,hypothesis,
    product(g1,c,a,c),
    c_times_a_is_c ).

cnf(c_0_79,negated_conjecture,
    ( ~ product(g2,h,f,an_isomorphism(d3))
    | d2 = b
    | d2 = c
    | d1 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_61]) ).

cnf(c_0_80,hypothesis,
    ( d1 = b
    | d2 = c
    | d2 = b
    | d3 = c ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_81,hypothesis,
    product(g2,h,f,h),
    h_times_f_is_h ).

cnf(c_0_82,hypothesis,
    ( ~ product(g1,c,d2,X1)
    | X1 = d3
    | d1 = b ),
    inference(spm,[status(thm)],[c_0_56,c_0_75]) ).

cnf(c_0_83,negated_conjecture,
    ( d1 = b
    | d2 = c
    | d2 = b ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_61]),c_0_81])]) ).

cnf(c_0_84,negated_conjecture,
    ( ~ product(g2,h,an_isomorphism(d2),an_isomorphism(d3))
    | d1 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_75]),c_0_61]) ).

cnf(c_0_85,hypothesis,
    ( ~ product(g1,c,c,X1)
    | X1 = d3
    | d1 = b
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_86,hypothesis,
    product(g1,c,c,b),
    c_times_c_is_b ).

cnf(c_0_87,negated_conjecture,
    ( ~ product(g2,h,h,an_isomorphism(d3))
    | d1 = b
    | d2 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_61]) ).

cnf(c_0_88,hypothesis,
    ( d2 = b
    | d1 = b
    | d3 = b ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_89,hypothesis,
    product(g2,h,h,g),
    h_times_h_is_g ).

cnf(c_0_90,negated_conjecture,
    ( d2 = b
    | d1 = b ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_68]),c_0_89])]) ).

cnf(c_0_91,hypothesis,
    ( ~ product(g1,c,b,X1)
    | X1 = d3
    | d1 = b ),
    inference(spm,[status(thm)],[c_0_82,c_0_90]) ).

cnf(c_0_92,hypothesis,
    product(g1,c,b,a),
    c_times_b_is_a ).

cnf(c_0_93,negated_conjecture,
    ( ~ product(g2,h,g,an_isomorphism(d3))
    | d1 = b ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_90]),c_0_68]) ).

cnf(c_0_94,hypothesis,
    ( d1 = b
    | d3 = a ),
    inference(spm,[status(thm)],[c_0_91,c_0_92]) ).

cnf(c_0_95,hypothesis,
    product(g2,h,g,f),
    h_times_g_is_f ).

cnf(c_0_96,negated_conjecture,
    d1 = b,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_34]),c_0_95])]) ).

cnf(c_0_97,hypothesis,
    ( ~ product(g1,b,a,X1)
    | X1 = d3
    | d2 = b
    | d2 = c ),
    inference(rw,[status(thm)],[c_0_74,c_0_96]) ).

cnf(c_0_98,hypothesis,
    product(g1,b,a,b),
    b_times_a_is_b ).

cnf(c_0_99,hypothesis,
    ( d2 = c
    | d2 = b
    | d3 = b ),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_100,hypothesis,
    product(g2,g,f,g),
    g_times_f_is_g ).

cnf(c_0_101,hypothesis,
    product(g1,b,c,a),
    b_times_c_is_a ).

cnf(c_0_102,hypothesis,
    product(g1,b,d2,d3),
    inference(rw,[status(thm)],[c_0_39,c_0_96]) ).

cnf(c_0_103,negated_conjecture,
    ( d2 = b
    | d2 = c ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_99]),c_0_96]),c_0_68]),c_0_68]),c_0_100])]) ).

cnf(c_0_104,hypothesis,
    ( ~ product(g1,b,c,X1)
    | X1 = a ),
    inference(spm,[status(thm)],[c_0_46,c_0_101]) ).

cnf(c_0_105,hypothesis,
    ( product(g1,b,c,d3)
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_106,negated_conjecture,
    ( ~ product(g2,g,h,an_isomorphism(d3))
    | d2 = b ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_103]),c_0_96]),c_0_68]),c_0_61]) ).

cnf(c_0_107,hypothesis,
    ( d3 = a
    | d2 = b ),
    inference(spm,[status(thm)],[c_0_104,c_0_105]) ).

cnf(c_0_108,hypothesis,
    product(g2,g,h,f),
    g_times_h_is_f ).

cnf(c_0_109,hypothesis,
    product(g1,b,b,c),
    b_times_b_is_c ).

cnf(c_0_110,negated_conjecture,
    d2 = b,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_34]),c_0_108])]) ).

cnf(c_0_111,hypothesis,
    ( ~ product(g1,b,b,X1)
    | X1 = c ),
    inference(spm,[status(thm)],[c_0_46,c_0_109]) ).

cnf(c_0_112,hypothesis,
    product(g1,b,b,d3),
    inference(rw,[status(thm)],[c_0_102,c_0_110]) ).

cnf(c_0_113,hypothesis,
    d3 = c,
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_114,hypothesis,
    product(g2,g,g,h),
    g_times_g_is_h ).

cnf(c_0_115,negated_conjecture,
    $false,
    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)],[inference(spm,[status(thm)],[c_0_32,c_0_113]),c_0_96]),c_0_68]),c_0_110]),c_0_68]),c_0_61]),c_0_114])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% 0.00/0.04  % Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.52  % Computer : n019.cluster.edu
% 0.11/0.52  % Model    : x86_64 x86_64
% 0.11/0.52  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52  % Memory   : 8046.5625MB
% 0.11/0.52  % OS       : Linux 6.8.0-71-generic
% 0.11/0.52  % CPULimit : 300
% 0.11/0.52  % WCLimit  : 300
% 0.11/0.52  % DateTime : Sun Sep 20 19:54:21 UTC 2026
% 0.11/0.52  % CPUTime  : 
% 0.11/0.52  Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.56  Running first-order theorem proving
% 0.11/0.56  Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 0.15/0.61  % Version: 3.5.1
% 0.15/0.61  % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.15/0.61  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.61  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.15/0.61  % Starting new_bool_3 with 300s (1) cores
% 0.15/0.61  % Starting new_bool_1 with 300s (1) cores
% 0.15/0.61  % Starting sh5l with 300s (1) cores
% 0.15/0.61  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 783599 completed with status 0
% 0.15/0.61  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.15/0.61  % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.15/0.61  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.61  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.15/0.61  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.61  % No SInE strategy applied
% 0.15/0.61  % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.15/0.61  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.61  % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.61  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.15/0.61  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.61  % Starting new_bool_3 with 136s (1) cores
% 0.15/0.61  % Starting new_bool_1 with 136s (1) cores
% 0.15/0.61  % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with pid 783605 completed with status 0
% 0.15/0.61  % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI
% 0.15/0.61  % Preprocessing class: FSMSSMSMSSSNFFN.
% 0.15/0.61  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.61  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 1500s (5) cores
% 0.15/0.61  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.61  % No SInE strategy applied
% 0.15/0.61  % Search class: FGUSM-FFMM31-SFFFFFNN
% 0.15/0.61  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.61  % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.61  % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S2SI with 151s (1) cores
% 0.15/0.61  % Preprocessing time       : 0.002 s
% 0.15/0.61  % Presaturation interreduction done
% 0.15/0.61  
% 0.15/0.61  % Proof found!
% 0.15/0.61  % SZS status Unsatisfiable
% 0.15/0.61  % SZS output start CNFRefutation
% See solution above
% 0.15/0.61  % Parsed axioms                        : 45
% 0.15/0.61  % Removed by relevancy pruning/SinE    : 0
% 0.15/0.61  % Initial clauses                      : 45
% 0.15/0.61  % Removed in clause preprocessing      : 0
% 0.15/0.61  % Initial clauses in saturation        : 45
% 0.15/0.61  % Processed clauses                    : 332
% 0.15/0.61  % ...of these trivial                  : 0
% 0.15/0.61  % ...subsumed                          : 62
% 0.15/0.61  % ...remaining for further processing  : 270
% 0.15/0.61  % Other redundant clauses eliminated   : 0
% 0.15/0.61  % Clauses deleted for lack of memory   : 0
% 0.15/0.61  % Backward-subsumed                    : 73
% 0.15/0.61  % Backward-rewritten                   : 41
% 0.15/0.61  % Generated clauses                    : 868
% 0.15/0.61  % ...of the previous two non-redundant : 814
% 0.15/0.61  % ...aggressively subsumed             : 0
% 0.15/0.61  % Contextual simplify-reflections      : 6
% 0.15/0.61  % Paramodulations                      : 851
% 0.15/0.61  % Factorizations                       : 17
% 0.15/0.61  % NegExts                              : 0
% 0.15/0.61  % Equation resolutions                 : 0
% 0.15/0.61  % Disequality decompositions           : 0
% 0.15/0.61  % Total rewrite steps                  : 290
% 0.15/0.61  % ...of those cached                   : 258
% 0.15/0.61  % Propositional unsat checks           : 0
% 0.15/0.61  %    Propositional check models        : 0
% 0.15/0.61  %    Propositional check unsatisfiable : 0
% 0.15/0.61  %    Propositional clauses             : 0
% 0.15/0.61  %    Propositional clauses after purity: 0
% 0.15/0.61  %    Propositional unsat core size     : 0
% 0.15/0.61  %    Propositional preprocessing time  : 0.000
% 0.15/0.61  %    Propositional encoding time       : 0.000
% 0.15/0.61  %    Propositional solver time         : 0.000
% 0.15/0.61  %    Success case prop preproc time    : 0.000
% 0.15/0.61  %    Success case prop encoding time   : 0.000
% 0.15/0.61  %    Success case prop solver time     : 0.000
% 0.15/0.61  % Current number of processed clauses  : 111
% 0.15/0.61  %    Positive orientable unit clauses  : 65
% 0.15/0.61  %    Positive unorientable unit clauses: 0
% 0.15/0.61  %    Negative unit clauses             : 3
% 0.15/0.61  %    Non-unit-clauses                  : 43
% 0.15/0.61  % Current number of unprocessed clauses: 513
% 0.15/0.61  % ...number of literals in the above   : 1406
% 0.15/0.61  % Current number of archived formulas  : 0
% 0.15/0.61  % Current number of archived clauses   : 159
% 0.15/0.61  % Clause-clause subsumption calls (NU) : 4895
% 0.15/0.61  % Rec. Clause-clause subsumption calls : 1357
% 0.15/0.61  % Non-unit clause-clause subsumptions  : 139
% 0.15/0.61  % Unit Clause-clause subsumption calls : 59
% 0.15/0.61  % Rewrite failures with RHS unbound    : 0
% 0.15/0.61  % BW rewrite match attempts            : 153
% 0.15/0.61  % BW rewrite match successes           : 5
% 0.15/0.61  % Condensation attempts                : 0
% 0.15/0.61  % Condensation successes               : 0
% 0.15/0.61  % Termbank termtop insertions          : 11016
% 0.15/0.61  % Search garbage collected termcells   : 33
% 0.15/0.61  
% 0.15/0.61  % -------------------------------------------------
% 0.15/0.61  % User time                : 0.024 s
% 0.15/0.61  % System time              : 0.008 s
% 0.15/0.61  % Total time               : 0.032 s
% 0.15/0.61  % Maximum resident set size: 3656 pages
% 0.15/0.61  
% 0.15/0.61  % -------------------------------------------------
% 0.15/0.61  % User time                : 0.096 s
% 0.15/0.61  % System time              : 0.021 s
% 0.15/0.61  % Total time               : 0.117 s
% 0.15/0.61  % Maximum resident set size: 4608 pages
% 0.15/0.61  % E exiting
%------------------------------------------------------------------------------