TSTP Solution File: PUZ039-10 by CSE

TSTP Solution File: PUZ039-10 by CSE_E---1.5

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : PUZ039-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 : Thu Aug 31 13:12:19 EDT 2023

% Result   : Unsatisfiable 20.43s 20.47s
% Output   : CNFRefutation 20.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   63
%            Number of leaves      :   49
% Syntax   : Number of formulae    :  143 ( 126 unt;  17 typ;   0 def)
%            Number of atoms       :  126 ( 125 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   41 (  15   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   2 con; 0-12 aty)
%            Number of variables   :  720 (  24 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ifeq: ( $i * $i * $i * $i ) > $i ).

tff(decl_23,type,
    s1: ( $i * $i ) > $i ).

tff(decl_24,type,
    s: $i > $i ).

tff(decl_25,type,
    e1: ( $i * $i ) > $i ).

tff(decl_26,type,
    state: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).

tff(decl_27,type,
    true: $i ).

tff(decl_28,type,
    s2: ( $i * $i ) > $i ).

tff(decl_29,type,
    s3: ( $i * $i ) > $i ).

tff(decl_30,type,
    s4: ( $i * $i ) > $i ).

tff(decl_31,type,
    v1: ( $i * $i ) > $i ).

tff(decl_32,type,
    e2: ( $i * $i ) > $i ).

tff(decl_33,type,
    v2: ( $i * $i ) > $i ).

tff(decl_34,type,
    v3: ( $i * $i ) > $i ).

tff(decl_35,type,
    v4: ( $i * $i ) > $i ).

tff(decl_36,type,
    h: ( $i * $i ) > $i ).

tff(decl_37,type,
    bb: ( $i * $i ) > $i ).

tff(decl_38,type,
    o: $i ).

cnf(swap_blanks,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X11,X12),e2(X13,X14)),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X13,X14),e2(X11,X12)),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',swap_blanks) ).

cnf(initial_state,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_state) ).

cnf(ifeq_axiom,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

cnf(v4_down,axiom,
    ifeq(state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true,state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_down) ).

cnf(v2_down,axiom,
    ifeq(state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true,state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_down) ).

cnf(v3_down,axiom,
    ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true,state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_down) ).

cnf(v1_down,axiom,
    ifeq(state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true,state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_down) ).

cnf(v2_up,axiom,
    ifeq(state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true,state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v2_up) ).

cnf(h_right,axiom,
    ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true,state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_right) ).

cnf(s1_up,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_up) ).

cnf(s3_up,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_up) ).

cnf(v1_up,axiom,
    ifeq(state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true,state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_up) ).

cnf(s1_left,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_left) ).

cnf(v3_right,axiom,
    ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true,state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_right) ).

cnf(s1_down,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_down) ).

cnf(s3_left,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_left) ).

cnf(s3_down,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_down) ).

cnf(h_left,axiom,
    ifeq(state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true,state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_left) ).

cnf(s2_up,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(s(X8),X9),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(s(X8),X9),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_up) ).

cnf(s4_up,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_up) ).

cnf(s2_right,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_right) ).

cnf(s1_right,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_right) ).

cnf(h_down,axiom,
    ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(s(X6),X7),e2(s(X6),s(X7))),true,state(X1,X2,X3,X4,X5,h(s(X6),X7),X8,X9,X10,X11,e1(X6,X7),e2(X6,s(X7))),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_down) ).

cnf(s4_left,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,s(X11)),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(X10,s(X11)),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_left) ).

cnf(s2_left,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_left) ).

cnf(v3_up,axiom,
    ifeq(state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_up) ).

cnf(s3_right,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_right) ).

cnf(v4_up,axiom,
    ifeq(state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_up) ).

cnf(s4_down,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s4_down) ).

cnf(v3_left,axiom,
    ifeq(state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v3_left) ).

cnf(v4_left,axiom,
    ifeq(state(X1,X2,X3,X4,v4(X5,s(X6)),X7,X8,X9,X10,X11,e1(X5,X6),e2(s(X5),X6)),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(X5,s(X6)),e2(s(X5),s(X6))),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',v4_left) ).

cnf(goal_state,negated_conjecture,
    state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11) != true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_state) ).

cnf(c_0_32,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X11,X12),e2(X13,X14)),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,e1(X13,X14),e2(X11,X12)),true) = true,
    swap_blanks ).

cnf(c_0_33,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
    initial_state ).

cnf(c_0_34,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    ifeq_axiom ).

cnf(c_0_35,axiom,
    ifeq(state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true,state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true) = true,
    v4_down ).

cnf(c_0_36,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).

cnf(c_0_37,axiom,
    ifeq(state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true,state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true) = true,
    v2_down ).

cnf(c_0_38,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_34]) ).

cnf(c_0_39,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]) ).

cnf(c_0_40,axiom,
    ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true,state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true) = true,
    v3_down ).

cnf(c_0_41,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_34]) ).

cnf(c_0_42,axiom,
    ifeq(state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true,state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true) = true,
    v1_down ).

cnf(c_0_43,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_34]) ).

cnf(c_0_44,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_34]) ).

cnf(c_0_45,axiom,
    ifeq(state(X1,X2,v2(s(X3),X4),X5,X6,X7,X8,X9,X10,X11,e1(X3,X4),X12),true,state(X1,X2,v2(X3,X4),X5,X6,X7,X8,X9,X10,X11,e1(s(s(X3)),X4),X12),true) = true,
    v2_up ).

cnf(c_0_46,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,s(s(s(o)))),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_44]),c_0_34]) ).

cnf(c_0_47,axiom,
    ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true,state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true) = true,
    h_right ).

cnf(c_0_48,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_34]) ).

cnf(c_0_49,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true) = true,
    s1_up ).

cnf(c_0_50,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_34]) ).

cnf(c_0_51,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true) = true,
    s3_up ).

cnf(c_0_52,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_34]) ).

cnf(c_0_53,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),s(o)),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_34]) ).

cnf(c_0_54,axiom,
    ifeq(state(X1,v1(s(X2),X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(X2,X3),X12),true,state(X1,v1(X2,X3),X4,X5,X6,X7,X8,X9,X10,X11,e1(s(s(X2)),X3),X12),true) = true,
    v1_up ).

cnf(c_0_55,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(s(s(o)))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_53]),c_0_34]) ).

cnf(c_0_56,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true) = true,
    s1_left ).

cnf(c_0_57,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),s(o)),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_34]) ).

cnf(c_0_58,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(s(o)))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_34]) ).

cnf(c_0_59,axiom,
    ifeq(state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true,state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true) = true,
    v3_right ).

cnf(c_0_60,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(o)),e2(s(s(s(s(o)))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_58]),c_0_34]) ).

cnf(c_0_61,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(s(X7),X8),X12),true,state(X1,X2,X3,X4,X5,X6,s1(s(X7),X8),X9,X10,X11,e1(X7,X8),X12),true) = true,
    s1_down ).

cnf(c_0_62,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(o)),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_34]) ).

cnf(c_0_63,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true) = true,
    s3_left ).

cnf(c_0_64,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),s(o)),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_34]) ).

cnf(c_0_65,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_34]) ).

cnf(c_0_66,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(o))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(o)),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_65]),c_0_34]) ).

cnf(c_0_67,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(s(X9),X10),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(s(X9),X10),X11,e1(X9,X10),X12),true) = true,
    s3_down ).

cnf(c_0_68,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(o)),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),o),e2(s(s(o)),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_66]),c_0_34]) ).

cnf(c_0_69,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(s(s(o)),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_34]) ).

cnf(c_0_70,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(s(s(o)),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_69]),c_0_34]) ).

cnf(c_0_71,axiom,
    ifeq(state(X1,X2,X3,X4,X5,h(X6,s(X7)),X8,X9,X10,X11,e1(X6,X7),X12),true,state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(X6,s(s(X7))),X12),true) = true,
    h_left ).

cnf(c_0_72,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(s(o))),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_70]),c_0_34]) ).

cnf(c_0_73,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_34]) ).

cnf(c_0_74,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,s(s(s(o)))),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_73]),c_0_34]) ).

cnf(c_0_75,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(o,o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_74]),c_0_34]) ).

cnf(c_0_76,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),s(o)),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_75]),c_0_34]) ).

cnf(c_0_77,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(s(X8),X9),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(s(X8),X9),X12),true) = true,
    s2_up ).

cnf(c_0_78,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(s(o))),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(o)),s(s(o))),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_76]),c_0_34]) ).

cnf(c_0_79,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true) = true,
    s4_up ).

cnf(c_0_80,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(s(o)))),s(s(o))),e1(s(s(s(o))),s(s(o))),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_34]) ).

cnf(c_0_81,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(s(s(s(s(o)))),s(s(o))),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_34]) ).

cnf(c_0_82,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(o,s(s(s(o)))),e2(s(s(s(s(o)))),s(s(o)))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_81]),c_0_34]) ).

cnf(c_0_83,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true) = true,
    s2_right ).

cnf(c_0_84,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(o))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(s(o)))),s(s(o)))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_82]),c_0_34]) ).

cnf(c_0_85,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(s(o))),s(s(o))),e1(s(s(o)),s(s(o))),e2(s(s(s(s(o)))),s(s(o)))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_34]) ).

cnf(c_0_86,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(o)),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(o))),s(s(o))),e2(s(s(s(s(o)))),s(s(o)))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_85]),c_0_34]) ).

cnf(c_0_87,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(o))),s(o)),e2(s(s(s(s(o)))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_86]),c_0_34]) ).

cnf(c_0_88,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,s1(X7,X8),X9,X10,X11,e1(X7,s(X8)),X12),true,state(X1,X2,X3,X4,X5,X6,s1(X7,s(X8)),X9,X10,X11,e1(X7,X8),X12),true) = true,
    s1_right ).

cnf(c_0_89,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),o),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(s(o)))),s(o)),e2(s(s(s(o))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_87]),c_0_34]) ).

cnf(c_0_90,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(o))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(s(o)))),o),e2(s(s(s(o))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_34]) ).

cnf(c_0_91,axiom,
    ifeq(state(X1,X2,X3,X4,X5,h(X6,X7),X8,X9,X10,X11,e1(s(X6),X7),e2(s(X6),s(X7))),true,state(X1,X2,X3,X4,X5,h(s(X6),X7),X8,X9,X10,X11,e1(X6,X7),e2(X6,s(X7))),true) = true,
    h_down ).

cnf(c_0_92,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(s(s(s(o))),o),e2(s(s(s(o))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_90]),c_0_34]) ).

cnf(c_0_93,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(s(s(o)),o),e2(s(s(o)),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_34]) ).

cnf(c_0_94,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(o,o),e2(s(s(o)),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_93]),c_0_34]) ).

cnf(c_0_95,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,s(X11)),e1(X10,X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(X10,s(X11)),X12),true) = true,
    s4_left ).

cnf(c_0_96,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(s(o))),e1(s(s(o)),s(o)),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_94]),c_0_34]) ).

cnf(c_0_97,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,s2(X8,s(X9)),X10,X11,e1(X8,X9),X12),true,state(X1,X2,X3,X4,X5,X6,X7,s2(X8,X9),X10,X11,e1(X8,s(X9)),X12),true) = true,
    s2_left ).

cnf(c_0_98,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(s(o)))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(s(s(o)),s(s(o))),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_34]) ).

cnf(c_0_99,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(s(s(o)),s(s(s(o)))),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_34]) ).

cnf(c_0_100,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(o,s(s(s(o)))),e2(o,o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_99]),c_0_34]) ).

cnf(c_0_101,hypothesis,
    state(bb(o,s(o)),v1(s(o),o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(o,o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_100]),c_0_34]) ).

cnf(c_0_102,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),s(o)),e1(s(s(o)),o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_101]),c_0_34]) ).

cnf(c_0_103,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(s(o))),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(o)),s(o)),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_102]),c_0_34]) ).

cnf(c_0_104,axiom,
    ifeq(state(X1,X2,X3,v3(s(X4),X5),X6,X7,X8,X9,X10,X11,e1(X4,X5),X12),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(s(s(X4)),X5),X12),true) = true,
    v3_up ).

cnf(c_0_105,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(s(o))),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(o)),s(s(o))),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_103]),c_0_34]) ).

cnf(c_0_106,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(o)),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(s(o))),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_34]) ).

cnf(c_0_107,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,X10),X11,e1(X9,s(X10)),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,s3(X9,s(X10)),X11,e1(X9,X10),X12),true) = true,
    s3_right ).

cnf(c_0_108,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),o),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(o)),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_106]),c_0_34]) ).

cnf(c_0_109,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(s(s(o)))),o),e2(o,s(s(s(o))))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_34]) ).

cnf(c_0_110,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(s(o),s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(o,s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_109]),c_0_34]) ).

cnf(c_0_111,axiom,
    ifeq(state(X1,X2,X3,X4,v4(s(X5),X6),X7,X8,X9,X10,X11,e1(X5,X6),X12),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(s(s(X5)),X6),X12),true) = true,
    v4_up ).

cnf(c_0_112,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(s(o))),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_110]),c_0_34]) ).

cnf(c_0_113,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(o))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(s(s(o)))),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_34]) ).

cnf(c_0_114,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(o)),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(s(o))),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_113]),c_0_34]) ).

cnf(c_0_115,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(o)),o),e1(s(s(s(s(o)))),s(o)),e2(s(s(s(s(o)))),o)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_114]),c_0_34]) ).

cnf(c_0_116,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(o))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(o)),o),e1(s(s(s(s(o)))),o),e2(s(s(s(s(o)))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_115]),c_0_34]) ).

cnf(c_0_117,axiom,
    ifeq(state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(X10,X11),e1(s(X10),X11),X12),true,state(X1,X2,X3,X4,X5,X6,X7,X8,X9,s4(s(X10),X11),e1(X10,X11),X12),true) = true,
    s4_down ).

cnf(c_0_118,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(o)),o),e1(s(s(s(o))),o),e2(s(s(s(o))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_116]),c_0_34]) ).

cnf(c_0_119,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),s(o)),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(s(o))),o),e1(s(s(o)),o),e2(s(s(s(o))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_34]) ).

cnf(c_0_120,axiom,
    ifeq(state(X1,X2,X3,v3(X4,s(X5)),X6,X7,X8,X9,X10,X11,e1(X4,X5),e2(s(X4),X5)),true,state(X1,X2,X3,v3(X4,X5),X6,X7,X8,X9,X10,X11,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true,
    v3_left ).

cnf(c_0_121,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(s(o))),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),o),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(s(o))),o),e1(s(s(o)),s(o)),e2(s(s(s(o))),s(o))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_119]),c_0_34]) ).

cnf(c_0_122,axiom,
    ifeq(state(X1,X2,X3,X4,v4(X5,s(X6)),X7,X8,X9,X10,X11,e1(X5,X6),e2(s(X5),X6)),true,state(X1,X2,X3,X4,v4(X5,X6),X7,X8,X9,X10,X11,e1(X5,s(X6)),e2(s(X5),s(X6))),true) = true,
    v4_left ).

cnf(c_0_123,hypothesis,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(o)),s(o)),v4(s(s(o)),s(s(s(o)))),h(s(s(s(s(o)))),o),s1(s(s(s(s(o)))),s(s(s(o)))),s2(s(s(o)),o),s3(s(s(s(s(o)))),s(s(o))),s4(s(s(s(o))),o),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_34]) ).

cnf(c_0_124,negated_conjecture,
    state(X1,X2,X3,X4,v4(s(s(o)),s(s(o))),X5,X6,X7,X8,X9,X10,X11) != true,
    goal_state ).

cnf(c_0_125,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_34]),c_0_124]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : PUZ039-10 : TPTP v8.1.2. Released v7.5.0.
% 0.12/0.15  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.37  % Computer : n003.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sat Aug 26 22:34:24 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.23/0.60  start to proof: theBenchmark
% 20.43/20.47  % Version  : CSE_E---1.5
% 20.43/20.47  % Problem  : theBenchmark.p
% 20.43/20.47  % Proof found
% 20.43/20.47  % SZS status Theorem for theBenchmark.p
% 20.43/20.47  % SZS output start Proof
% See solution above
% 20.43/20.49  % Total time : 19.868000 s
% 20.43/20.49  % SZS output end Proof
% 20.43/20.49  % Total time : 19.874000 s
%------------------------------------------------------------------------------