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CSE_E---1.7.UNS-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GRP771-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n021.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 04:27:15 PM UTC 2026

% Result   : Unsatisfiable 96.55s 80.14s
% Output   : CNFRefutation 98.22s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_26)

% Comments : 
%------------------------------------------------------------------------------
cnf(sos12,axiom,
    eta(X1) = product(i(X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).

cnf(sos09,axiom,
    i(X1) = difference(X1,one),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).

cnf(sos20,axiom,
    t(eta(X1),product(X2,X3)) = product(t(eta(X1),X2),t(eta(X1),X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos20) ).

cnf(sos19,axiom,
    t(X1,X2) = quotient(product(X1,X2),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos19) ).

cnf(sos18,axiom,
    product(product(product(quotient(j(X1),X1),product(X1,X1)),X2),X3) = product(product(quotient(j(X1),X1),product(X1,X1)),product(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos18) ).

cnf(sos10,axiom,
    j(X1) = quotient(one,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).

cnf(sos16,axiom,
    product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).

cnf(sos15,axiom,
    product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos15) ).

cnf(sos14,axiom,
    product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).

cnf(sos13,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).

cnf(sos22,axiom,
    product(j(j(X1)),j(product(X2,X1))) = j(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos22) ).

cnf(sos21,axiom,
    product(i(product(X1,X2)),i(i(X1))) = i(X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos21) ).

cnf(sos17,axiom,
    quotient(j(X1),X1) = product(j(X1),i(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).

cnf(sos11,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).

cnf(sos08,axiom,
    difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).

cnf(sos23,axiom,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos23) ).

cnf(goals,negated_conjecture,
    product(product(x0,x1),c(x2,x3)) != product(x0,product(x1,c(x2,x3))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

cnf(sos07,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).

cnf(sos24,axiom,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos24) ).

cnf(sos05,axiom,
    quotient(product(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).

cnf(sos06,axiom,
    product(quotient(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).

cnf(sos04,axiom,
    difference(X1,product(X1,X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).

cnf(sos03,axiom,
    product(X1,difference(X1,X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).

cnf(sos02,axiom,
    product(one,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).

cnf(sos01,axiom,
    product(X1,one) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).

cnf(i_0_25,axiom,
    eta(X1) = product(i(X1),X1),
    sos12 ).

cnf(i_0_26,axiom,
    i(X1) = difference(X1,one),
    sos09 ).

cnf(i_0_27,axiom,
    t(eta(X1),product(X2,X3)) = product(t(eta(X1),X2),t(eta(X1),X3)),
    sos20 ).

cnf(i_0_28,plain,
    eta(X1) = product(difference(X1,one),X1),
    inference(rw,[status(thm)],[i_0_25,c_0_26]) ).

cnf(i_0_29,axiom,
    t(X1,X2) = quotient(product(X1,X2),X1),
    sos19 ).

cnf(i_0_30,axiom,
    product(product(product(quotient(j(X1),X1),product(X1,X1)),X2),X3) = product(product(quotient(j(X1),X1),product(X1,X1)),product(X2,X3)),
    sos18 ).

cnf(i_0_31,axiom,
    j(X1) = quotient(one,X1),
    sos10 ).

cnf(i_0_32,axiom,
    product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
    sos16 ).

cnf(i_0_33,axiom,
    product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
    sos15 ).

cnf(i_0_34,axiom,
    product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
    sos14 ).

cnf(i_0_35,axiom,
    product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
    sos13 ).

cnf(i_0_36,axiom,
    product(j(j(X1)),j(product(X2,X1))) = j(X2),
    sos22 ).

cnf(i_0_37,axiom,
    product(i(product(X1,X2)),i(i(X1))) = i(X2),
    sos21 ).

cnf(i_0_38,axiom,
    quotient(j(X1),X1) = product(j(X1),i(X1)),
    sos17 ).

cnf(i_0_39,axiom,
    product(i(X1),X1) = product(X1,j(X1)),
    sos11 ).

cnf(i_0_40,plain,
    quotient(product(product(difference(X1,one),X1),product(X2,X3)),product(difference(X1,one),X1)) = product(quotient(product(product(difference(X1,one),X1),X2),product(difference(X1,one),X1)),quotient(product(product(difference(X1,one),X1),X3),product(difference(X1,one),X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_27,c_0_28]),c_0_28]),c_0_28]),c_0_29]),c_0_29]),c_0_29]),
    [final] ).

cnf(i_0_41,plain,
    product(product(product(quotient(quotient(one,X1),X1),product(X1,X1)),X2),X3) = product(product(quotient(quotient(one,X1),X1),product(X1,X1)),product(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_30,c_0_31]),c_0_31]),
    [final] ).

cnf(i_0_42,axiom,
    difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
    sos08,
    [final] ).

cnf(i_0_43,plain,
    product(product(difference(X1,one),X1),product(X2,X3)) = product(product(product(difference(X1,one),X1),X2),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_32,c_0_28]),c_0_28]),
    [final] ).

cnf(i_0_44,plain,
    product(X1,product(X2,product(difference(X1,one),X1))) = product(product(X1,X2),product(difference(X1,one),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_33,c_0_28]),c_0_28]),
    [final] ).

cnf(i_0_45,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_34,c_0_31]),c_0_31]),c_0_28]),
    [final] ).

cnf(i_0_46,axiom,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    sos23,
    [final] ).

cnf(i_0_47,negated_conjecture,
    product(product(x0,x1),c(x2,x3)) != product(x0,product(x1,c(x2,x3))),
    goals,
    [final] ).

cnf(i_0_48,plain,
    product(difference(difference(X1,one),one),X2) = product(product(difference(X1,one),X1),product(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_35,c_0_26]),c_0_26]),c_0_28]),
    [final] ).

cnf(i_0_49,axiom,
    difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
    sos07,
    [final] ).

cnf(i_0_50,plain,
    product(quotient(one,quotient(one,X1)),quotient(one,product(X2,X1))) = quotient(one,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_36,c_0_31]),c_0_31]),c_0_31]),c_0_31]),
    [final] ).

cnf(i_0_51,plain,
    product(difference(product(X1,X2),one),difference(difference(X1,one),one)) = difference(X2,one),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_37,c_0_26]),c_0_26]),c_0_26]),c_0_26]),
    [final] ).

cnf(i_0_52,plain,
    quotient(quotient(one,X1),X1) = product(quotient(one,X1),difference(X1,one)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_38,c_0_26]),c_0_31]),c_0_31]),
    [final] ).

cnf(i_0_53,axiom,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    sos24,
    [final] ).

cnf(i_0_54,plain,
    product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_39,c_0_26]),c_0_31]),
    [final] ).

cnf(i_0_55,axiom,
    quotient(product(X1,X2),X2) = X1,
    sos05,
    [final] ).

cnf(i_0_56,axiom,
    product(quotient(X1,X2),X2) = X1,
    sos06,
    [final] ).

cnf(i_0_57,axiom,
    difference(X1,product(X1,X2)) = X2,
    sos04,
    [final] ).

cnf(i_0_58,axiom,
    product(X1,difference(X1,X2)) = X2,
    sos03,
    [final] ).

cnf(i_0_59,axiom,
    product(one,X1) = X1,
    sos02,
    [final] ).

cnf(i_0_60,axiom,
    product(X1,one) = X1,
    sos01,
    [final] ).

cnf(i_0_61,axiom,
    X1 = X1 ).

cnf(i_0_62,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_63,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_64,axiom,
    ( X1 != X2
    | quotient(X1,X3) = quotient(X2,X3) ) ).

cnf(i_0_65,axiom,
    ( X1 != X2
    | quotient(X3,X1) = quotient(X3,X2) ) ).

cnf(i_0_66,axiom,
    ( X1 != X2
    | product(X1,X3) = product(X2,X3) ) ).

cnf(i_0_67,axiom,
    ( X1 != X2
    | product(X3,X1) = product(X3,X2) ) ).

cnf(i_0_68,axiom,
    ( X1 != X2
    | difference(X1,X3) = difference(X2,X3) ) ).

cnf(i_0_69,axiom,
    ( X1 != X2
    | difference(X3,X1) = difference(X3,X2) ) ).

cnf(i_0_70,plain,
    X1 = product(one,X1),
    inference(scs_inference,[],[i_0_59,i_0_62]) ).

cnf(i_0_71,plain,
    product(product(X1,X2),c(X3,X4)) != product(one,product(X1,product(X2,c(X3,X4)))),
    inference(scs_inference,[],[i_0_47,i_0_59,i_0_62,i_0_63]) ).

cnf(i_0_72,plain,
    product(one,X1) = X1,
    inference(rename_variables,[],[i_0_59]) ).

cnf(i_0_73,plain,
    X1 = product(X1,one),
    inference(scs_inference,[],[i_0_60,i_0_62]) ).

cnf(i_0_74,plain,
    product(product(X1,X2),c(X3,X4)) != product(product(X1,product(X2,c(X3,X4))),one),
    inference(scs_inference,[],[i_0_47,i_0_60,i_0_62,i_0_63]) ).

cnf(i_0_75,plain,
    product(X1,one) = X1,
    inference(rename_variables,[],[i_0_60]) ).

cnf(i_0_76,plain,
    product(product(X1,X2),X3) = product(product(X1,product(X2,X3)),a(X1,X2,X3)),
    inference(scs_inference,[],[i_0_46,i_0_62]) ).

cnf(i_0_78,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_79,plain,
    product(X1,X2) = product(product(X2,X1),c(X1,X2)),
    inference(scs_inference,[],[i_0_53,i_0_62]) ).

cnf(i_0_81,plain,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_82,plain,
    X1 = quotient(product(X1,X2),X2),
    inference(scs_inference,[],[i_0_55,i_0_62]) ).

cnf(i_0_83,plain,
    product(product(X1,X2),c(X3,X4)) != quotient(product(product(X1,product(X2,c(X3,X4))),X5),X5),
    inference(scs_inference,[],[i_0_47,i_0_55,i_0_62,i_0_63]) ).

cnf(i_0_84,plain,
    quotient(product(X1,X2),X2) = X1,
    inference(rename_variables,[],[i_0_55]) ).

cnf(i_0_85,plain,
    X1 = product(quotient(X1,X2),X2),
    inference(scs_inference,[],[i_0_56,i_0_62]) ).

cnf(i_0_86,plain,
    product(product(X1,X2),c(X3,X4)) != product(quotient(product(X1,product(X2,c(X3,X4))),X5),X5),
    inference(scs_inference,[],[i_0_47,i_0_56,i_0_62,i_0_63]) ).

cnf(i_0_87,plain,
    product(quotient(X1,X2),X2) = X1,
    inference(rename_variables,[],[i_0_56]) ).

cnf(i_0_88,plain,
    product(X1,X2) != quotient(product(X1,product(X2,c(X3,X4))),c(X3,X4)),
    inference(scs_inference,[],[i_0_47,i_0_56,i_0_62,i_0_63,i_0_66]) ).

cnf(i_0_89,plain,
    X1 = difference(X2,product(X2,X1)),
    inference(scs_inference,[],[i_0_57,i_0_62]) ).

cnf(i_0_93,plain,
    X1 = product(X2,difference(X2,X1)),
    inference(scs_inference,[],[i_0_58,i_0_62]) ).

cnf(i_0_106,plain,
    product(X1,quotient(one,X1)) = product(difference(X1,one),X1),
    inference(scs_inference,[],[i_0_54,i_0_62]) ).

cnf(i_0_147,plain,
    product(quotient(one,X1),difference(X1,one)) = quotient(quotient(one,X1),X1),
    inference(scs_inference,[],[i_0_52,i_0_62]) ).

cnf(i_0_176,plain,
    quotient(product(X1,product(X2,X3)),X3) = difference(X3,product(product(X3,X1),X2)),
    inference(scs_inference,[],[i_0_49,i_0_62]) ).

cnf(i_0_185,plain,
    quotient(one,X1) = product(quotient(one,quotient(one,X2)),quotient(one,product(X1,X2))),
    inference(scs_inference,[],[i_0_50,i_0_62]) ).

cnf(i_0_188,plain,
    difference(X1,one) = product(difference(product(X2,X1),one),difference(difference(X2,one),one)),
    inference(scs_inference,[],[i_0_51,i_0_62]) ).

cnf(i_0_257,plain,
    difference(X1,product(X1,X2)) = X2,
    inference(rename_variables,[],[i_0_57]) ).

cnf(i_0_264,plain,
    product(quotient(one,quotient(one,X1)),X2) = product(X1,product(product(difference(X1,one),X1),X2)),
    inference(scs_inference,[],[i_0_45,i_0_62]) ).

cnf(i_0_272,plain,
    product(X1,difference(X1,X2)) = X2,
    inference(rename_variables,[],[i_0_58]) ).

cnf(i_0_296,plain,
    product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_307,plain,
    product(difference(product(X1,X2),one),difference(difference(X1,one),one)) = difference(X2,one),
    inference(rename_variables,[],[i_0_51]) ).

cnf(i_0_310,plain,
    product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
    inference(rename_variables,[],[i_0_54]) ).

cnf(i_0_316,plain,
    product(difference(product(X1,X2),one),difference(difference(X1,one),one)) = difference(X2,one),
    inference(rename_variables,[],[i_0_51]) ).

cnf(i_0_346,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_353,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_357,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_361,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_370,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_378,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_384,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_390,plain,
    product(X1,product(product(difference(X1,one),X1),quotient(one,product(X2,X1)))) = quotient(one,X2),
    inference(scs_inference,[],[i_0_45,i_0_50,i_0_63]) ).

cnf(i_0_391,plain,
    product(quotient(one,quotient(one,X1)),quotient(one,product(X2,X1))) = quotient(one,X2),
    inference(rename_variables,[],[i_0_50]) ).

cnf(i_0_392,plain,
    product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
    inference(rename_variables,[],[i_0_45]) ).

cnf(i_0_393,plain,
    quotient(one,X1) = product(X2,product(product(difference(X2,one),X2),quotient(one,product(X1,X2)))),
    inference(scs_inference,[],[i_0_45,i_0_50,i_0_63,i_0_62]) ).

cnf(i_0_396,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_400,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_404,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_408,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_415,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_422,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_426,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_430,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_433,plain,
    product(product(X1,product(X2,X3)),a(X1,X2,X3)) = product(product(X1,X2),X3),
    inference(rename_variables,[],[i_0_46]) ).

cnf(i_0_540,plain,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_543,plain,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_549,plain,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_555,plain,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    inference(rename_variables,[],[i_0_53]) ).

cnf(i_0_561,plain,
    product(product(X1,X2),c(X2,X1)) = product(X2,X1),
    inference(rename_variables,[],[i_0_53]) ).

cnf(c_0_74,plain,
    product(product(X1,X2),c(X3,X4)) != product(one,product(X1,product(X2,c(X3,X4)))),
    i_0_71 ).

cnf(c_0_75,plain,
    X1 = product(one,X1),
    i_0_70 ).

cnf(c_0_76,plain,
    product(product(X1,X2),c(X3,X4)) != product(X1,product(X2,c(X3,X4))),
    inference(rw,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_77,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_75])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP771-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33  % Computer : n021.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Mon May  4 19:06:25 EDT 2026
% 0.16/0.33  % CPUTime    : 
% 0.16/0.34  % start to proof: theBenchmark
% 96.55/80.14  % Version  : CSE_E---1.7
% 96.55/80.14  % Problem  : theBenchmark.p
% 96.55/80.14  % SZS status Unsatisfiable for theBenchmark.p
% 96.55/80.14  % SZS output start CNFRefutation
% See solution above
% 98.22/81.82  % Total time : 79.798s
%------------------------------------------------------------------------------