%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ANA020-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n011.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 : Wed Aug 31 15:44:58 EDT 2022

% Result   : Unsatisfiable 0.19s 0.48s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   40 (  27 unt;   0 def)
%            Number of atoms       :   59 (  14 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   41 (  22   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-3 aty)
%            Number of variables   :   24 (  24   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f118,plain,
    $false,
    inference(subsumption_resolution,[],[f117,f32]) ).

fof(f32,plain,
    ~ c_lessequals(v_x,sF4,t_a),
    inference(backward_demodulation,[],[f24,f31]) ).

fof(f31,plain,
    v_x = sF1,
    inference(backward_demodulation,[],[f25,f30]) ).

fof(f30,plain,
    v_x = c_HOL_Oabs(v_x,t_a),
    inference(resolution,[],[f16,f29]) ).

fof(f29,plain,
    class_OrderedGroup_Olordered__ab__group__abs(t_a),
    inference(resolution,[],[f12,f5]) ).

fof(f5,axiom,
    class_Ring__and__Field_Oordered__idom(t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

fof(f12,axiom,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | class_OrderedGroup_Olordered__ab__group__abs(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

fof(f16,plain,
    ! [X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
      | v_x = c_HOL_Oabs(v_x,X0) ),
    inference(definition_unfolding,[],[f6,f3,f3]) ).

fof(f3,axiom,
    c_0 = v_x,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f6,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
      | c_0 = c_HOL_Oabs(c_0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).

fof(f25,plain,
    c_HOL_Oabs(v_x,t_a) = sF1,
    inference(backward_demodulation,[],[f20,f19]) ).

fof(f19,plain,
    v_x = sF0,
    inference(definition_folding,[],[f14,f18]) ).

fof(f18,plain,
    v_f(v_x) = sF0,
    introduced(function_definition,[]) ).

fof(f14,plain,
    v_x = v_f(v_x),
    inference(definition_unfolding,[],[f1,f3,f3]) ).

fof(f1,axiom,
    c_0 = v_f(c_0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f20,plain,
    c_HOL_Oabs(sF0,t_a) = sF1,
    introduced(function_definition,[]) ).

fof(f24,plain,
    ~ c_lessequals(sF1,sF4,t_a),
    inference(definition_folding,[],[f4,f23,f22,f21,f20,f18]) ).

fof(f21,plain,
    v_h(v_x) = sF2,
    introduced(function_definition,[]) ).

fof(f22,plain,
    c_HOL_Oabs(sF2,t_a) = sF3,
    introduced(function_definition,[]) ).

fof(f23,plain,
    sF4 = c_times(v_c,sF3,t_a),
    introduced(function_definition,[]) ).

fof(f4,axiom,
    ~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f117,plain,
    c_lessequals(v_x,sF4,t_a),
    inference(forward_demodulation,[],[f115,f23]) ).

fof(f115,plain,
    c_lessequals(v_x,c_times(v_c,sF3,t_a),t_a),
    inference(superposition,[],[f92,f22]) ).

fof(f92,plain,
    ! [X0] : c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(X0,t_a),t_a),t_a),
    inference(resolution,[],[f38,f41]) ).

fof(f41,plain,
    c_lessequals(v_x,v_c,t_a),
    inference(subsumption_resolution,[],[f40,f28]) ).

fof(f28,plain,
    class_Orderings_Oorder(t_a),
    inference(resolution,[],[f11,f5]) ).

fof(f11,axiom,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | class_Orderings_Oorder(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).

fof(f40,plain,
    ( c_lessequals(v_x,v_c,t_a)
    | ~ class_Orderings_Oorder(t_a) ),
    inference(resolution,[],[f8,f17]) ).

fof(f17,plain,
    c_less(v_x,v_c,t_a),
    inference(definition_unfolding,[],[f2,f3]) ).

fof(f2,axiom,
    c_less(c_0,v_c,t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f8,axiom,
    ! [X2,X3,X0] :
      ( ~ c_less(X2,X3,X0)
      | c_lessequals(X2,X3,X0)
      | ~ class_Orderings_Oorder(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(v_x,X0,t_a)
      | c_lessequals(v_x,c_times(X0,c_HOL_Oabs(X1,t_a),t_a),t_a) ),
    inference(subsumption_resolution,[],[f36,f27]) ).

fof(f27,plain,
    class_Ring__and__Field_Opordered__cancel__semiring(t_a),
    inference(resolution,[],[f10,f5]) ).

fof(f10,axiom,
    ! [X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X5)
      | class_Ring__and__Field_Opordered__cancel__semiring(X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(v_x,X0,t_a)
      | ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
      | c_lessequals(v_x,c_times(X0,c_HOL_Oabs(X1,t_a),t_a),t_a) ),
    inference(resolution,[],[f15,f33]) ).

fof(f33,plain,
    ! [X0] : c_lessequals(v_x,c_HOL_Oabs(X0,t_a),t_a),
    inference(resolution,[],[f13,f29]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
      | c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0) ),
    inference(definition_unfolding,[],[f7,f3]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
      | c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

fof(f15,plain,
    ! [X0,X1,X4] :
      ( ~ c_lessequals(v_x,X4,X0)
      | ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(v_x,X1,X0)
      | c_lessequals(v_x,c_times(X1,X4,X0),X0) ),
    inference(definition_unfolding,[],[f9,f3,f3,f3]) ).

fof(f9,axiom,
    ! [X0,X1,X4] :
      ( c_lessequals(c_0,c_times(X1,X4,X0),X0)
      | ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
      | ~ c_lessequals(c_0,X1,X0)
      | ~ c_lessequals(c_0,X4,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : ANA020-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 29 15:10:24 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.46  % (13325)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.47  % (13341)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.19/0.47  % (13325)First to succeed.
% 0.19/0.48  % (13335)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.48  % (13325)Refutation found. Thanks to Tanya!
% 0.19/0.48  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.48  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.48  % (13325)------------------------------
% 0.19/0.48  % (13325)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.48  % (13325)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.48  % (13325)Termination reason: Refutation
% 0.19/0.48  
% 0.19/0.48  % (13325)Memory used [KB]: 5500
% 0.19/0.48  % (13325)Time elapsed: 0.107 s
% 0.19/0.48  % (13325)Instructions burned: 5 (million)
% 0.19/0.48  % (13325)------------------------------
% 0.19/0.48  % (13325)------------------------------
% 0.19/0.48  % (13320)Success in time 0.142 s
%------------------------------------------------------------------------------