TSTP Solution File: ANA022-2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ANA022-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n004.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 : Mon May 20 18:41:07 EDT 2024

% Result   : Unsatisfiable 64.09s 9.51s
% Output   : Refutation 64.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   99 (  59 unt;   0 def)
%            Number of atoms       :  157 (  51 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  109 (  51   ~;  58   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-3 aty)
%            Number of variables   :  144 ( 144   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f184483,plain,
    $false,
    inference(subsumption_resolution,[],[f184482,f53]) ).

fof(f53,plain,
    ! [X0] : c_lessequals(X0,X0,t_b),
    inference(factoring,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( c_lessequals(X0,X1,t_b)
      | c_lessequals(X1,X0,t_b) ),
    inference(subsumption_resolution,[],[f51,f34]) ).

fof(f34,plain,
    class_Orderings_Oorder(t_b),
    inference(unit_resulting_resolution,[],[f32,f20]) ).

fof(f20,axiom,
    ! [X9] :
      ( ~ class_LOrder_Ojoin__semilorder(X9)
      | class_Orderings_Oorder(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

fof(f32,plain,
    class_LOrder_Ojoin__semilorder(t_b),
    inference(unit_resulting_resolution,[],[f3,f25]) ).

fof(f25,axiom,
    ! [X9] :
      ( ~ class_Ring__and__Field_Oordered__idom(X9)
      | class_LOrder_Ojoin__semilorder(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

fof(f3,axiom,
    class_Ring__and__Field_Oordered__idom(t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(t_b)
      | c_lessequals(X0,X1,t_b)
      | c_lessequals(X1,X0,t_b) ),
    inference(resolution,[],[f19,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( c_less(X0,X1,t_b)
      | c_lessequals(X1,X0,t_b) ),
    inference(resolution,[],[f16,f30]) ).

fof(f30,plain,
    class_Orderings_Olinorder(t_b),
    inference(unit_resulting_resolution,[],[f3,f24]) ).

fof(f24,axiom,
    ! [X9] :
      ( ~ class_Ring__and__Field_Oordered__idom(X9)
      | class_Orderings_Olinorder(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).

fof(f16,axiom,
    ! [X1,X6,X5] :
      ( ~ class_Orderings_Olinorder(X1)
      | c_less(X5,X6,X1)
      | c_lessequals(X6,X5,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).

fof(f19,axiom,
    ! [X1,X6,X5] :
      ( ~ c_less(X6,X5,X1)
      | ~ class_Orderings_Oorder(X1)
      | c_lessequals(X6,X5,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).

fof(f184482,plain,
    ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(forward_demodulation,[],[f184281,f52161]) ).

fof(f52161,plain,
    c_minus(v_f(v_x),v_g(v_x),t_b) = c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
    inference(unit_resulting_resolution,[],[f53,f49457,f365]) ).

fof(f365,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_0,X0,t_b)
      | c_HOL_Oabs(X1,t_b) = X1
      | c_lessequals(X1,X0,t_b) ),
    inference(forward_demodulation,[],[f364,f279]) ).

fof(f279,plain,
    ! [X0] : c_uminus(c_uminus(X0,t_b),t_b) = X0,
    inference(forward_demodulation,[],[f278,f46]) ).

fof(f46,plain,
    ! [X0] : c_plus(c_0,X0,t_b) = X0,
    inference(unit_resulting_resolution,[],[f28,f8]) ).

fof(f8,axiom,
    ! [X1,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
      | c_plus(c_0,X5,X1) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).

fof(f28,plain,
    class_OrderedGroup_Ocomm__monoid__add(t_b),
    inference(unit_resulting_resolution,[],[f3,f23]) ).

fof(f23,axiom,
    ! [X9] :
      ( ~ class_Ring__and__Field_Oordered__idom(X9)
      | class_OrderedGroup_Ocomm__monoid__add(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).

fof(f278,plain,
    ! [X0] : c_plus(c_0,X0,t_b) = c_uminus(c_uminus(X0,t_b),t_b),
    inference(forward_demodulation,[],[f270,f115]) ).

fof(f115,plain,
    ! [X0,X1] : c_plus(X0,X1,t_b) = c_minus(X0,c_uminus(X1,t_b),t_b),
    inference(unit_resulting_resolution,[],[f36,f13]) ).

fof(f13,axiom,
    ! [X2,X1,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_plus(X2,X4,X1) = c_minus(X2,c_uminus(X4,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).

fof(f36,plain,
    class_OrderedGroup_Oab__group__add(t_b),
    inference(unit_resulting_resolution,[],[f3,f26]) ).

fof(f26,axiom,
    ! [X9] :
      ( ~ class_Ring__and__Field_Oordered__idom(X9)
      | class_OrderedGroup_Oab__group__add(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).

fof(f270,plain,
    ! [X0] : c_minus(c_0,c_uminus(X0,t_b),t_b) = c_uminus(c_uminus(X0,t_b),t_b),
    inference(superposition,[],[f164,f252]) ).

fof(f252,plain,
    ! [X0] : c_uminus(X0,t_b) = c_minus(c_uminus(X0,t_b),c_0,t_b),
    inference(superposition,[],[f239,f179]) ).

fof(f179,plain,
    ! [X0] : c_plus(X0,c_0,t_b) = c_minus(X0,c_0,t_b),
    inference(superposition,[],[f115,f166]) ).

fof(f166,plain,
    c_0 = c_uminus(c_0,t_b),
    inference(superposition,[],[f164,f48]) ).

fof(f48,plain,
    ! [X0] : c_0 = c_minus(X0,X0,t_b),
    inference(unit_resulting_resolution,[],[f36,f14]) ).

fof(f14,axiom,
    ! [X2,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_0 = c_minus(X2,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).

fof(f239,plain,
    ! [X0] : c_uminus(X0,t_b) = c_plus(c_uminus(X0,t_b),c_0,t_b),
    inference(forward_demodulation,[],[f238,f46]) ).

fof(f238,plain,
    ! [X0] : c_plus(c_uminus(X0,t_b),c_0,t_b) = c_uminus(c_plus(c_0,X0,t_b),t_b),
    inference(forward_demodulation,[],[f225,f174]) ).

fof(f174,plain,
    c_0 = c_HOL_Oabs(c_0,t_b),
    inference(superposition,[],[f166,f57]) ).

fof(f57,plain,
    c_HOL_Oabs(c_0,t_b) = c_uminus(c_0,t_b),
    inference(unit_resulting_resolution,[],[f38,f53,f6]) ).

fof(f6,axiom,
    ! [X2,X1] :
      ( ~ c_lessequals(X2,c_0,X1)
      | ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_HOL_Oabs(X2,X1) = c_uminus(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).

fof(f38,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_b),
    inference(unit_resulting_resolution,[],[f3,f27]) ).

fof(f27,axiom,
    ! [X9] :
      ( ~ class_Ring__and__Field_Oordered__idom(X9)
      | class_OrderedGroup_Olordered__ab__group__abs(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

fof(f225,plain,
    ! [X0] : c_plus(c_uminus(X0,t_b),c_0,t_b) = c_uminus(c_plus(c_HOL_Oabs(c_0,t_b),X0,t_b),t_b),
    inference(superposition,[],[f167,f117]) ).

fof(f117,plain,
    ! [X0] : c_plus(X0,c_0,t_b) = c_minus(X0,c_HOL_Oabs(c_0,t_b),t_b),
    inference(superposition,[],[f115,f57]) ).

fof(f167,plain,
    ! [X0,X1] : c_uminus(c_plus(X0,X1,t_b),t_b) = c_minus(c_uminus(X1,t_b),X0,t_b),
    inference(superposition,[],[f164,f115]) ).

fof(f164,plain,
    ! [X0,X1] : c_minus(X0,X1,t_b) = c_uminus(c_minus(X1,X0,t_b),t_b),
    inference(unit_resulting_resolution,[],[f36,f15]) ).

fof(f15,axiom,
    ! [X2,X1,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_uminus(c_minus(X2,X4,X1),X1) = c_minus(X4,X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).

fof(f364,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(c_0,X0,t_b)
      | c_lessequals(X1,X0,t_b)
      | c_HOL_Oabs(X1,t_b) = c_uminus(c_uminus(X1,t_b),t_b) ),
    inference(subsumption_resolution,[],[f344,f34]) ).

fof(f344,plain,
    ! [X0,X1] :
      ( ~ class_Orderings_Oorder(t_b)
      | ~ c_lessequals(c_0,X0,t_b)
      | c_lessequals(X1,X0,t_b)
      | c_HOL_Oabs(X1,t_b) = c_uminus(c_uminus(X1,t_b),t_b) ),
    inference(resolution,[],[f18,f124]) ).

fof(f124,plain,
    ! [X0] :
      ( c_lessequals(X0,c_0,t_b)
      | c_HOL_Oabs(X0,t_b) = c_uminus(c_uminus(X0,t_b),t_b) ),
    inference(forward_demodulation,[],[f123,f54]) ).

fof(f54,plain,
    ! [X0] : c_HOL_Oabs(X0,t_b) = c_HOL_Oabs(c_uminus(X0,t_b),t_b),
    inference(unit_resulting_resolution,[],[f38,f5]) ).

fof(f5,axiom,
    ! [X2,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_HOL_Oabs(X2,X1) = c_HOL_Oabs(c_uminus(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).

fof(f123,plain,
    ! [X0] :
      ( c_lessequals(X0,c_0,t_b)
      | c_HOL_Oabs(c_uminus(X0,t_b),t_b) = c_uminus(c_uminus(X0,t_b),t_b) ),
    inference(forward_demodulation,[],[f122,f46]) ).

fof(f122,plain,
    ! [X0] :
      ( c_lessequals(c_plus(c_0,X0,t_b),c_0,t_b)
      | c_HOL_Oabs(c_uminus(X0,t_b),t_b) = c_uminus(c_uminus(X0,t_b),t_b) ),
    inference(superposition,[],[f76,f115]) ).

fof(f76,plain,
    ! [X0] :
      ( c_lessequals(c_minus(c_0,X0,t_b),c_0,t_b)
      | c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b) ),
    inference(subsumption_resolution,[],[f71,f41]) ).

fof(f41,plain,
    class_OrderedGroup_Opordered__ab__group__add(t_b),
    inference(unit_resulting_resolution,[],[f38,f21]) ).

fof(f21,axiom,
    ! [X9] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X9)
      | class_OrderedGroup_Opordered__ab__group__add(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).

fof(f71,plain,
    ! [X0] :
      ( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
      | c_lessequals(c_minus(c_0,X0,t_b),c_0,t_b)
      | c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b) ),
    inference(resolution,[],[f12,f61]) ).

fof(f61,plain,
    ! [X0] :
      ( c_lessequals(c_0,X0,t_b)
      | c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b) ),
    inference(subsumption_resolution,[],[f58,f38]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
      | c_HOL_Oabs(X0,t_b) = c_uminus(X0,t_b)
      | c_lessequals(c_0,X0,t_b) ),
    inference(resolution,[],[f6,f52]) ).

fof(f12,axiom,
    ! [X2,X1,X4] :
      ( ~ c_lessequals(X2,X4,X1)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_lessequals(c_minus(X2,X4,X1),c_0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).

fof(f18,axiom,
    ! [X1,X8,X6,X5] :
      ( ~ c_lessequals(X6,X5,X1)
      | ~ class_Orderings_Oorder(X1)
      | ~ c_lessequals(X5,X8,X1)
      | c_lessequals(X6,X8,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).

fof(f49457,plain,
    ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b),
    inference(unit_resulting_resolution,[],[f34,f15804,f48880,f18]) ).

fof(f48880,plain,
    ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
    inference(unit_resulting_resolution,[],[f30,f53,f48804,f17]) ).

fof(f17,axiom,
    ! [X8,X6,X7,X5] :
      ( ~ c_lessequals(X6,X8,X7)
      | ~ class_Orderings_Olinorder(X7)
      | ~ c_lessequals(X5,X8,X7)
      | c_lessequals(c_Orderings_Omax(X6,X5,X7),X8,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).

fof(f48804,plain,
    ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_0,t_b),
    inference(unit_resulting_resolution,[],[f34,f44,f2,f18]) ).

fof(f2,axiom,
    ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

fof(f44,plain,
    ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
    inference(unit_resulting_resolution,[],[f38,f4]) ).

fof(f4,axiom,
    ! [X2,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
      | c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

fof(f15804,plain,
    ! [X0,X1] : c_lessequals(c_minus(v_k(X0),X1,t_b),c_minus(v_f(X0),X1,t_b),t_b),
    inference(forward_demodulation,[],[f15738,f284]) ).

fof(f284,plain,
    ! [X0,X1] : c_minus(X1,X0,t_b) = c_plus(X1,c_uminus(X0,t_b),t_b),
    inference(superposition,[],[f115,f279]) ).

fof(f15738,plain,
    ! [X0,X1] : c_lessequals(c_minus(v_k(X0),X1,t_b),c_plus(v_f(X0),c_uminus(X1,t_b),t_b),t_b),
    inference(superposition,[],[f15498,f284]) ).

fof(f15498,plain,
    ! [X0,X1] : c_lessequals(c_plus(v_k(X0),X1,t_b),c_plus(v_f(X0),X1,t_b),t_b),
    inference(unit_resulting_resolution,[],[f4273,f10122]) ).

fof(f10122,plain,
    ! [X2,X0,X1] :
      ( ~ c_lessequals(c_minus(X2,X1,t_b),X0,t_b)
      | c_lessequals(X2,c_plus(X0,X1,t_b),t_b) ),
    inference(superposition,[],[f1900,f10032]) ).

fof(f10032,plain,
    ! [X0,X1] : c_minus(c_plus(X1,X0,t_b),X0,t_b) = X1,
    inference(forward_demodulation,[],[f9956,f279]) ).

fof(f9956,plain,
    ! [X0,X1] : c_uminus(c_uminus(X1,t_b),t_b) = c_minus(c_plus(X1,X0,t_b),X0,t_b),
    inference(superposition,[],[f164,f9842]) ).

fof(f9842,plain,
    ! [X0,X1] : c_uminus(X1,t_b) = c_minus(X0,c_plus(X1,X0,t_b),t_b),
    inference(forward_demodulation,[],[f9841,f307]) ).

fof(f307,plain,
    ! [X0] : c_uminus(X0,t_b) = c_minus(c_0,X0,t_b),
    inference(superposition,[],[f164,f290]) ).

fof(f290,plain,
    ! [X0] : c_minus(X0,c_0,t_b) = X0,
    inference(superposition,[],[f252,f279]) ).

fof(f9841,plain,
    ! [X0,X1] : c_minus(c_0,X1,t_b) = c_minus(X0,c_plus(X1,X0,t_b),t_b),
    inference(forward_demodulation,[],[f9840,f115]) ).

fof(f9840,plain,
    ! [X0,X1] : c_minus(c_0,X1,t_b) = c_minus(X0,c_minus(X1,c_uminus(X0,t_b),t_b),t_b),
    inference(forward_demodulation,[],[f9759,f307]) ).

fof(f9759,plain,
    ! [X0,X1] : c_minus(c_0,X1,t_b) = c_minus(X0,c_minus(X1,c_minus(c_0,X0,t_b),t_b),t_b),
    inference(superposition,[],[f9441,f306]) ).

fof(f306,plain,
    ! [X0] : c_0 = c_plus(X0,c_minus(c_0,X0,t_b),t_b),
    inference(superposition,[],[f171,f290]) ).

fof(f171,plain,
    ! [X0,X1] : c_0 = c_plus(c_minus(X1,X0,t_b),c_minus(X0,X1,t_b),t_b),
    inference(superposition,[],[f118,f164]) ).

fof(f118,plain,
    ! [X0] : c_0 = c_plus(c_uminus(X0,t_b),X0,t_b),
    inference(superposition,[],[f115,f48]) ).

fof(f9441,plain,
    ! [X2,X0,X1] : c_minus(X0,c_minus(X2,X1,t_b),t_b) = c_minus(c_plus(X0,X1,t_b),X2,t_b),
    inference(forward_demodulation,[],[f9439,f172]) ).

fof(f172,plain,
    ! [X2,X0,X1] : c_plus(X2,c_minus(X0,X1,t_b),t_b) = c_minus(X2,c_minus(X1,X0,t_b),t_b),
    inference(superposition,[],[f115,f164]) ).

fof(f9439,plain,
    ! [X2,X0,X1] : c_plus(X0,c_minus(X1,X2,t_b),t_b) = c_minus(c_plus(X0,X1,t_b),X2,t_b),
    inference(unit_resulting_resolution,[],[f36,f9]) ).

fof(f9,axiom,
    ! [X2,X3,X1,X4] :
      ( ~ class_OrderedGroup_Oab__group__add(X1)
      | c_plus(X2,c_minus(X4,X3,X1),X1) = c_minus(c_plus(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).

fof(f1900,plain,
    ! [X2,X0,X1] :
      ( ~ c_lessequals(c_minus(X0,X1,t_b),c_minus(X2,X1,t_b),t_b)
      | c_lessequals(X0,X2,t_b) ),
    inference(forward_demodulation,[],[f1899,f284]) ).

fof(f1899,plain,
    ! [X2,X0,X1] :
      ( ~ c_lessequals(c_minus(X0,X1,t_b),c_plus(X2,c_uminus(X1,t_b),t_b),t_b)
      | c_lessequals(X0,X2,t_b) ),
    inference(subsumption_resolution,[],[f1847,f40]) ).

fof(f40,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
    inference(unit_resulting_resolution,[],[f38,f22]) ).

fof(f22,axiom,
    ! [X9] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X9)
      | class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).

fof(f1847,plain,
    ! [X2,X0,X1] :
      ( ~ c_lessequals(c_minus(X0,X1,t_b),c_plus(X2,c_uminus(X1,t_b),t_b),t_b)
      | c_lessequals(X0,X2,t_b)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
    inference(superposition,[],[f7,f284]) ).

fof(f7,axiom,
    ! [X2,X3,X1,X4] :
      ( ~ c_lessequals(c_plus(X2,X3,X1),c_plus(X4,X3,X1),X1)
      | c_lessequals(X2,X4,X1)
      | ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).

fof(f4273,plain,
    ! [X0,X1] : c_lessequals(c_minus(c_plus(v_k(X0),X1,t_b),X1,t_b),v_f(X0),t_b),
    inference(unit_resulting_resolution,[],[f34,f1,f4147,f18]) ).

fof(f4147,plain,
    ! [X0,X1] : c_lessequals(c_minus(c_plus(X0,X1,t_b),X1,t_b),X0,t_b),
    inference(unit_resulting_resolution,[],[f41,f53,f11]) ).

fof(f11,axiom,
    ! [X2,X3,X1,X4] :
      ( ~ c_lessequals(X2,c_plus(X3,X4,X1),X1)
      | ~ class_OrderedGroup_Opordered__ab__group__add(X1)
      | c_lessequals(c_minus(X2,X4,X1),X3,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).

fof(f1,axiom,
    ! [X0] : c_lessequals(v_k(X0),v_f(X0),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f184281,plain,
    ~ c_lessequals(c_minus(v_f(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    inference(unit_resulting_resolution,[],[f34,f15804,f48717,f18]) ).

fof(f48717,plain,
    ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
    inference(unit_resulting_resolution,[],[f30,f44,f2,f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : ANA022-2 : TPTP v8.2.0. Released v3.2.0.
% 0.10/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 07:54:53 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (1421)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39  % (1424)WARNING: value z3 for option sas not known
% 0.14/0.39  % (1423)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (1425)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  % (1422)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  % (1424)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39  % (1426)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39  % (1427)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39  % (1428)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.40  TRYING [3]
% 0.14/0.40  TRYING [1]
% 0.21/0.41  TRYING [2]
% 0.21/0.42  TRYING [4]
% 0.21/0.43  TRYING [3]
% 0.21/0.46  TRYING [5]
% 0.21/0.54  TRYING [4]
% 0.21/0.55  TRYING [6]
% 2.68/0.76  TRYING [7]
% 4.16/1.02  TRYING [5]
% 5.77/1.18  TRYING [8]
% 7.98/1.49  TRYING [1]
% 7.98/1.49  TRYING [2]
% 7.98/1.49  TRYING [3]
% 7.98/1.50  TRYING [4]
% 8.35/1.54  TRYING [5]
% 8.86/1.63  TRYING [6]
% 10.35/1.85  TRYING [7]
% 11.56/2.04  TRYING [9]
% 13.71/2.34  TRYING [8]
% 17.95/2.91  TRYING [6]
% 21.30/3.45  TRYING [9]
% 23.94/3.77  TRYING [10]
% 37.43/5.81  TRYING [10]
% 59.11/8.82  TRYING [11]
% 63.33/9.50  % (1428)First to succeed.
% 63.33/9.51  % (1428)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1421"
% 64.09/9.51  % (1428)Refutation found. Thanks to Tanya!
% 64.09/9.51  % SZS status Unsatisfiable for theBenchmark
% 64.09/9.51  % SZS output start Proof for theBenchmark
% See solution above
% 64.09/9.51  % (1428)------------------------------
% 64.09/9.51  % (1428)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 64.09/9.51  % (1428)Termination reason: Refutation
% 64.09/9.51  
% 64.09/9.51  % (1428)Memory used [KB]: 29067
% 64.09/9.51  % (1428)Time elapsed: 9.125 s
% 64.09/9.51  % (1428)Instructions burned: 18075 (million)
% 64.09/9.51  % (1421)Success in time 9.138 s
%------------------------------------------------------------------------------