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FindProof---0.1.UNS-Prf.s

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%------------------------------------------------------------------------------
% File     : FindProof---0.1
% Problem  : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300

% Computer : n005.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 : Fri Sep 25 12:55:09 PM UTC 2026

% Result   : Unsatisfiable 10.42s 1.92s
% Output   : Proof 10.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   98 (  62 unt;   0 def)
%            Number of atoms       :  150 (  52 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  110 (  58   ~;  52   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-4 aty)
%            Number of variables   :  129 (   2 sgn  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
cnf(f6,axiom,
    ( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
    | ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).

fof(f6_nnf,plain,
    ! [T_a,V_a,V_b,V_c] :
      ( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
      | ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
      | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    inference(nnf_transformation,[status(thm)],[f6]) ).

fof(f6_sk,plain,
    ! [T_a,V_a,V_b,V_c] :
      ( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
      | ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
      | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    inference(skolemisation,[status(esa)],[f6_nnf]) ).

cnf(c6,plain,
    ( c_lessequals(X1,c_minus(X3,X2,X0),X0)
    | ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
    inference(cnf_transformation,[status(esa)],[f6_sk]) ).

cnf(t18,plain,
    ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
    inference(equality_encoding,[status(esa)],[c6]) ).

cnf(t28,plain,
    ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
    inference(orient,[status(thm)],[t18]) ).

cnf(f12,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(T)
    | ~ class_Ring__and__Field_Oordered__idom(T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

fof(f12_nnf,plain,
    ! [T] :
      ( class_OrderedGroup_Olordered__ab__group__abs(T)
      | ~ class_Ring__and__Field_Oordered__idom(T) ),
    inference(nnf_transformation,[status(thm)],[f12]) ).

fof(f12_sk,plain,
    ! [T] :
      ( class_OrderedGroup_Olordered__ab__group__abs(T)
      | ~ class_Ring__and__Field_Oordered__idom(T) ),
    inference(skolemisation,[status(esa)],[f12_nnf]) ).

cnf(c12,plain,
    ( class_OrderedGroup_Olordered__ab__group__abs(X0)
    | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(cnf_transformation,[status(esa)],[f12_sk]) ).

cnf(hi11,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c12]) ).

cnf(f3,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).

fof(f3_nnf,plain,
    class_Ring__and__Field_Oordered__idom(t_b),
    inference(nnf_transformation,[status(thm)],[f3]) ).

cnf(c3,plain,
    class_Ring__and__Field_Oordered__idom(t_b),
    inference(cnf_transformation,[status(esa)],[f3_nnf]) ).

cnf(hi2,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b) = true,
    inference(equality_encoding,[status(esa)],[c3]) ).

cnf(h0,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
    inference(hyper_resolution,[status(thm)],[hi11,hi2]) ).

cnf(f9,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(T)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

fof(f9_nnf,plain,
    ! [T] :
      ( class_OrderedGroup_Opordered__ab__group__add(T)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
    inference(nnf_transformation,[status(thm)],[f9]) ).

fof(f9_sk,plain,
    ! [T] :
      ( class_OrderedGroup_Opordered__ab__group__add(T)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
    inference(skolemisation,[status(esa)],[f9_nnf]) ).

cnf(c9,plain,
    ( class_OrderedGroup_Opordered__ab__group__add(X0)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
    inference(cnf_transformation,[status(esa)],[f9_sk]) ).

cnf(hi8,axiom,
    ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c9]) ).

cnf(t3,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
    inference(hyper_resolution,[status(thm)],[hi8,h0]) ).

cnf(t52,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
    inference(orient,[status(thm)],[t3]) ).

cnf(t54,plain,
    true = ifeq(true,true,ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true),true),
    inference(cp,[status(thm)],[t28,t52]) ).

cnf(t7,plain,
    ifeq(X1,X1,X2,X3) = X2,
    introduced(definition) ).

cnf(t20,plain,
    ifeq(X1,X1,X2,X3) = X2,
    inference(orient,[status(thm)],[t7]) ).

cnf(t137,plain,
    true = ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true),
    inference(step,[status(thm)],[t54,t20]) ).

cnf(t71,plain,
    ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true) = true,
    inference(orient,[status(thm)],[t137]) ).

cnf(f11,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(T)
    | ~ class_Ring__and__Field_Oordered__idom(T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

fof(f11_nnf,plain,
    ! [T] :
      ( class_OrderedGroup_Ocomm__monoid__add(T)
      | ~ class_Ring__and__Field_Oordered__idom(T) ),
    inference(nnf_transformation,[status(thm)],[f11]) ).

fof(f11_sk,plain,
    ! [T] :
      ( class_OrderedGroup_Ocomm__monoid__add(T)
      | ~ class_Ring__and__Field_Oordered__idom(T) ),
    inference(skolemisation,[status(esa)],[f11_nnf]) ).

cnf(c11,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(X0)
    | ~ class_Ring__and__Field_Oordered__idom(X0) ),
    inference(cnf_transformation,[status(esa)],[f11_sk]) ).

cnf(hi10,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c11]) ).

cnf(h1,plain,
    class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
    inference(hyper_resolution,[status(thm)],[hi10,hi2]) ).

cnf(f4,axiom,
    ( c_plus(c_0,V_y,T_a) = V_y
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).

fof(f4_nnf,plain,
    ! [T_a,V_y] :
      ( c_plus(c_0,V_y,T_a) = V_y
      | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    inference(nnf_transformation,[status(thm)],[f4]) ).

fof(f4_sk,plain,
    ! [T_a,V_y] :
      ( c_plus(c_0,V_y,T_a) = V_y
      | ~ class_OrderedGroup_Ocomm__monoid__add(T_a) ),
    inference(skolemisation,[status(esa)],[f4_nnf]) ).

cnf(c4,plain,
    ( c_plus(c_0,X1,X0) = X1
    | ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
    inference(cnf_transformation,[status(esa)],[f4_sk]) ).

cnf(hi3,axiom,
    ifeq(class_OrderedGroup_Ocomm__monoid__add(X0),true,c_plus(c_0,X1,X0),X1) = X1,
    inference(equality_encoding,[status(esa)],[c4]) ).

cnf(t6,plain,
    c_plus(c_0,X1,t_b) = X1,
    inference(hyper_resolution,[status(thm)],[hi3,h1]) ).

cnf(t22,plain,
    c_plus(c_0,X1,t_b) = X1,
    inference(orient,[status(thm)],[t6]) ).

cnf(t72,plain,
    true = ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_0,c_minus(X2,X1,t_b),t_b),true),
    inference(cp,[status(thm)],[t71,t22]) ).

cnf(t73,plain,
    ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_0,c_minus(X2,X1,t_b),t_b),true) = true,
    inference(orient,[status(thm)],[t72]) ).

cnf(f7,axiom,
    ( c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ class_Orderings_Oorder(T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).

fof(f7_nnf,plain,
    ! [T_a,V_y,V_z,V_x] :
      ( c_lessequals(V_x,V_z,T_a)
      | ~ c_lessequals(V_x,V_y,T_a)
      | ~ c_lessequals(V_y,V_z,T_a)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(nnf_transformation,[status(thm)],[f7]) ).

fof(f7_sk,plain,
    ! [T_a,V_y,V_z,V_x] :
      ( c_lessequals(V_x,V_z,T_a)
      | ~ c_lessequals(V_x,V_y,T_a)
      | ~ c_lessequals(V_y,V_z,T_a)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(skolemisation,[status(esa)],[f7_nnf]) ).

cnf(c7,plain,
    ( c_lessequals(X3,X2,X0)
    | ~ c_lessequals(X3,X1,X0)
    | ~ c_lessequals(X1,X2,X0)
    | ~ class_Orderings_Oorder(X0) ),
    inference(cnf_transformation,[status(esa)],[f7_sk]) ).

cnf(t19,plain,
    ifeq(class_Orderings_Oorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X4,X2,X1),true,c_lessequals(X4,X3,X1),true),true),true) = true,
    inference(equality_encoding,[status(esa)],[c7]) ).

cnf(t33,plain,
    ifeq(class_Orderings_Oorder(X1),true,ifeq(c_lessequals(X2,X3,X1),true,ifeq(c_lessequals(X4,X2,X1),true,c_lessequals(X4,X3,X1),true),true),true) = true,
    inference(orient,[status(thm)],[t19]) ).

cnf(h3,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
    inference(hyper_resolution,[status(thm)],[hi8,h0]) ).

cnf(f5,axiom,
    ( c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
    | ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
    | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).

fof(f5_nnf,plain,
    ! [T_a,V_a,V_c,V_b] :
      ( c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
      | ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
      | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    inference(nnf_transformation,[status(thm)],[f5]) ).

fof(f5_sk,plain,
    ! [T_a,V_a,V_c,V_b] :
      ( c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
      | ~ c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
      | ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
    inference(skolemisation,[status(esa)],[f5_nnf]) ).

cnf(c5,plain,
    ( c_lessequals(c_plus(X1,X3,X0),X2,X0)
    | ~ c_lessequals(X1,c_minus(X2,X3,X0),X0)
    | ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
    inference(cnf_transformation,[status(esa)],[f5_sk]) ).

cnf(hi4,axiom,
    ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(X1,c_minus(X2,X3,X0),X0),true,c_lessequals(c_plus(X1,X3,X0),X2,X0),true),true) = true,
    inference(equality_encoding,[status(esa)],[c5]) ).

cnf(f0,negated_conjecture,
    c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f0_nnf,plain,
    c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
    inference(nnf_transformation,[status(thm)],[f0]) ).

cnf(c0,plain,
    c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
    inference(cnf_transformation,[status(esa)],[f0_nnf]) ).

cnf(hi0,negated_conjecture,
    c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) = true,
    inference(equality_encoding,[status(esa)],[c0]) ).

cnf(t15,plain,
    c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b) = true,
    inference(hyper_resolution,[status(thm)],[hi4,h3,hi0]) ).

cnf(t133,plain,
    c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
    inference(step,[status(thm)],[t15,t22]) ).

cnf(t34,plain,
    c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
    inference(orient,[status(thm)],[t133]) ).

cnf(t35,plain,
    true = ifeq(class_Orderings_Oorder(t_b),true,ifeq(true,true,ifeq(c_lessequals(X1,v_k(v_x),t_b),true,c_lessequals(X1,v_f(v_x),t_b),true),true),true),
    inference(cp,[status(thm)],[t33,t34]) ).

cnf(f10,axiom,
    ( class_LOrder_Ojoin__semilorder(T)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).

fof(f10_nnf,plain,
    ! [T] :
      ( class_LOrder_Ojoin__semilorder(T)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
    inference(nnf_transformation,[status(thm)],[f10]) ).

fof(f10_sk,plain,
    ! [T] :
      ( class_LOrder_Ojoin__semilorder(T)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
    inference(skolemisation,[status(esa)],[f10_nnf]) ).

cnf(c10,plain,
    ( class_LOrder_Ojoin__semilorder(X0)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
    inference(cnf_transformation,[status(esa)],[f10_sk]) ).

cnf(hi9,axiom,
    ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_LOrder_Ojoin__semilorder(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c10]) ).

cnf(h2,plain,
    class_LOrder_Ojoin__semilorder(t_b) = true,
    inference(hyper_resolution,[status(thm)],[hi9,h0]) ).

cnf(f8,axiom,
    ( class_Orderings_Oorder(T)
    | ~ class_LOrder_Ojoin__semilorder(T) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

fof(f8_nnf,plain,
    ! [T] :
      ( class_Orderings_Oorder(T)
      | ~ class_LOrder_Ojoin__semilorder(T) ),
    inference(nnf_transformation,[status(thm)],[f8]) ).

fof(f8_sk,plain,
    ! [T] :
      ( class_Orderings_Oorder(T)
      | ~ class_LOrder_Ojoin__semilorder(T) ),
    inference(skolemisation,[status(esa)],[f8_nnf]) ).

cnf(c8,plain,
    ( class_Orderings_Oorder(X0)
    | ~ class_LOrder_Ojoin__semilorder(X0) ),
    inference(cnf_transformation,[status(esa)],[f8_sk]) ).

cnf(hi7,axiom,
    ifeq(class_LOrder_Ojoin__semilorder(X0),true,class_Orderings_Oorder(X0),true) = true,
    inference(equality_encoding,[status(esa)],[c8]) ).

cnf(t4,plain,
    class_Orderings_Oorder(t_b) = true,
    inference(hyper_resolution,[status(thm)],[hi7,h2]) ).

cnf(t60,plain,
    class_Orderings_Oorder(t_b) = true,
    inference(orient,[status(thm)],[t4]) ).

cnf(t151,plain,
    true = ifeq(true,true,ifeq(true,true,ifeq(c_lessequals(X1,v_k(v_x),t_b),true,c_lessequals(X1,v_f(v_x),t_b),true),true),true),
    inference(step,[status(thm)],[t35,t60]) ).

cnf(t152,plain,
    true = ifeq(true,true,ifeq(c_lessequals(X1,v_k(v_x),t_b),true,c_lessequals(X1,v_f(v_x),t_b),true),true),
    inference(step,[status(thm)],[t151,t20]) ).

cnf(t153,plain,
    true = ifeq(c_lessequals(X1,v_k(v_x),t_b),true,c_lessequals(X1,v_f(v_x),t_b),true),
    inference(step,[status(thm)],[t152,t20]) ).

cnf(t117,plain,
    ifeq(c_lessequals(X1,v_k(v_x),t_b),true,c_lessequals(X1,v_f(v_x),t_b),true) = true,
    inference(orient,[status(thm)],[t153]) ).

cnf(f1,negated_conjecture,
    c_lessequals(v_g(v_x),v_k(v_x),t_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f1_nnf,plain,
    c_lessequals(v_g(v_x),v_k(v_x),t_b),
    inference(nnf_transformation,[status(thm)],[f1]) ).

cnf(c1,plain,
    c_lessequals(v_g(v_x),v_k(v_x),t_b),
    inference(cnf_transformation,[status(esa)],[f1_nnf]) ).

cnf(t8,plain,
    c_lessequals(v_g(v_x),v_k(v_x),t_b) = true,
    inference(equality_encoding,[status(esa)],[c1]) ).

cnf(t44,plain,
    c_lessequals(v_g(v_x),v_k(v_x),t_b) = true,
    inference(orient,[status(thm)],[t8]) ).

cnf(t118,plain,
    true = ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true),
    inference(cp,[status(thm)],[t117,t44]) ).

cnf(t154,plain,
    true = c_lessequals(v_g(v_x),v_f(v_x),t_b),
    inference(step,[status(thm)],[t118,t20]) ).

cnf(t120,plain,
    c_lessequals(v_g(v_x),v_f(v_x),t_b) = true,
    inference(orient,[status(thm)],[t154]) ).

cnf(t121,plain,
    true = ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),
    inference(cp,[status(thm)],[t73,t120]) ).

cnf(t155,plain,
    true = c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(step,[status(thm)],[t121,t20]) ).

cnf(t126,plain,
    c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
    inference(orient,[status(thm)],[t155]) ).

cnf(f2,negated_conjecture,
    ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f2_nnf,plain,
    ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(nnf_transformation,[status(thm)],[f2]) ).

fof(f2_sk,plain,
    ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(skolemisation,[status(esa)],[f2_nnf]) ).

cnf(c2,plain,
    ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(cnf_transformation,[status(esa)],[f2_sk]) ).

cnf(goal_0,negated_conjecture,
    c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
    inference(equality_encoding,[status(esa)],[c2]) ).

cnf(g0_0,plain,
    true != true,
    inference(rw,[status(thm)],[goal_0,t126]) ).

cnf(contradiction_0,plain,
    $false,
    inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04  % Command  : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36  % Computer : n005.cluster.edu
% 0.09/0.36  % Model    : x86_64 x86_64
% 0.09/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36  % Memory   : 8046.5625MB
% 0.09/0.36  % OS       : Linux 6.8.0-71-generic
% 0.09/0.36  % CPULimit : 300
% 0.09/0.36  % WCLimit  : 300
% 0.09/0.36  % DateTime : Fri Sep 25 05:47:32 UTC 2026
% 0.09/0.36  % CPUTime  : 
% 0.09/0.36  Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.42/1.92  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.42/1.92  % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------