TSTP Solution File: PUZ039-10 by Drodi---3.5.1

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : PUZ039-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 May 31 12:31:53 EDT 2023

% Result   : Unsatisfiable 5.84s 1.14s
% Output   : CNFRefutation 6.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   41 (  41 unt;   0 def)
%            Number of atoms       :   41 (  40 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    8 (   2 avg)
%            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   :  222 (; 222   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B,C] : ifeq(A,A,B,C) = B,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [B,V1,V2,V3,V4,H,S1,X,Y,S3,S4,E2] : ifeq(state(B,V1,V2,V3,V4,H,S1,s2(X,Y),S3,S4,e1(s(X),Y),E2),true,state(B,V1,V2,V3,V4,H,S1,s2(s(X),Y),S3,S4,e1(X,Y),E2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,axiom,
    ! [B,V1,V2,V3,V4,H,S1,S2,S3,X,Y,E2] : ifeq(state(B,V1,V2,V3,V4,H,S1,S2,S3,s4(X,Y),e1(X,s(Y)),E2),true,state(B,V1,V2,V3,V4,H,S1,S2,S3,s4(X,s(Y)),e1(X,Y),E2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [B,X,Y,V2,V3,V4,H,S1,S2,S3,S4,E2] : ifeq(state(B,v1(X,Y),V2,V3,V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2),true,state(B,v1(s(X),Y),V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),E2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [B,X,Y,V2,V3,V4,H,S1,S2,S3,S4,E2] : ifeq(state(B,v1(s(X),Y),V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),E2),true,state(B,v1(X,Y),V2,V3,V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [B,V1,V2,X,Y,V4,H,S1,S2,S3,S4,E2] : ifeq(state(B,V1,V2,v3(X,Y),V4,H,S1,S2,S3,S4,e1(s(s(X)),Y),E2),true,state(B,V1,V2,v3(s(X),Y),V4,H,S1,S2,S3,S4,e1(X,Y),E2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,axiom,
    ! [B,V1,V2,V3,X,Y,H,S1,S2,S3,S4] : ifeq(state(B,V1,V2,V3,v4(X,s(Y)),H,S1,S2,S3,S4,e1(X,Y),e2(s(X),Y)),true,state(B,V1,V2,V3,v4(X,Y),H,S1,S2,S3,S4,e1(X,s(Y)),e2(s(X),s(Y))),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f35,axiom,
    ! [B,V1,V2,V3,V4,X,Y,S1,S2,S3,S4,E2] : ifeq(state(B,V1,V2,V3,V4,h(X,s(Y)),S1,S2,S3,S4,e1(X,Y),E2),true,state(B,V1,V2,V3,V4,h(X,Y),S1,S2,S3,S4,e1(X,s(s(Y))),E2),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f42,axiom,
    ! [B,V1,V2,V3,V4,H,S1,S2,S3,S4,X,Y,Q,W] : ifeq(state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(X,Y),e2(Q,W)),true,state(B,V1,V2,V3,V4,H,S1,S2,S3,S4,e1(Q,W),e2(X,Y)),true) = true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f43,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/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,negated_conjecture,
    ! [B,V1,V2,V3,H,S1,S2,S3,S4,E1,E2] : state(B,V1,V2,V3,v4(s(s(o)),s(s(o))),H,S1,S2,S3,S4,E1,E2) != true,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,plain,
    ! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,X3,X4,X5,X6,s2(X7,X8),X9,X10,e1(s(X7),X8),X11),true,state(X0,X1,X2,X3,X4,X5,X6,s2(s(X7),X8),X9,X10,e1(X7,X8),X11),true) = true,
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f58,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,X10),e1(X9,s(X10)),X11),true,state(X0,X1,X2,X3,X4,X5,X6,X7,X8,s4(X9,s(X10)),e1(X9,X10),X11),true) = true,
    inference(cnf_transformation,[status(esa)],[f14]) ).

fof(f64,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11),true,state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11),true) = true,
    inference(cnf_transformation,[status(esa)],[f20]) ).

fof(f65,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,v1(s(X1),X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(X1,X2),X11),true,state(X0,v1(X1,X2),X3,X4,X5,X6,X7,X8,X9,X10,e1(s(s(X1)),X2),X11),true) = true,
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f72,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,v3(X3,X4),X5,X6,X7,X8,X9,X10,e1(s(s(X3)),X4),X11),true,state(X0,X1,X2,v3(s(X3),X4),X5,X6,X7,X8,X9,X10,e1(X3,X4),X11),true) = true,
    inference(cnf_transformation,[status(esa)],[f28]) ).

fof(f75,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : ifeq(state(X0,X1,X2,X3,v4(X4,s(X5)),X6,X7,X8,X9,X10,e1(X4,X5),e2(s(X4),X5)),true,state(X0,X1,X2,X3,v4(X4,X5),X6,X7,X8,X9,X10,e1(X4,s(X5)),e2(s(X4),s(X5))),true) = true,
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f79,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] : ifeq(state(X0,X1,X2,X3,X4,h(X5,s(X6)),X7,X8,X9,X10,e1(X5,X6),X11),true,state(X0,X1,X2,X3,X4,h(X5,X6),X7,X8,X9,X10,e1(X5,s(s(X6))),X11),true) = true,
    inference(cnf_transformation,[status(esa)],[f35]) ).

fof(f86,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13] : ifeq(state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X10,X11),e2(X12,X13)),true,state(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,e1(X12,X13),e2(X10,X11)),true) = true,
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f87,plain,
    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,
    inference(cnf_transformation,[status(esa)],[f43]) ).

fof(f88,plain,
    ! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : state(X0,X1,X2,X3,v4(s(s(o)),s(s(o))),X4,X5,X6,X7,X8,X9,X10) != true,
    inference(cnf_transformation,[status(esa)],[f44]) ).

fof(f90,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(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(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))),true) = true,
    inference(paramodulation,[status(thm)],[f87,f72]) ).

fof(f91,plain,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(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(o)),o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
    inference(forward_demodulation,[status(thm)],[f45,f90]) ).

fof(f102,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(o,o),e2(s(s(s(s(o)))),s(s(s(o))))),true) = true,
    inference(paramodulation,[status(thm)],[f91,f64]) ).

fof(f103,plain,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(o,o),e2(s(s(s(s(o)))),s(s(s(o))))) = true,
    inference(forward_demodulation,[status(thm)],[f45,f102]) ).

fof(f122,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(o,o)),true) = true,
    inference(paramodulation,[status(thm)],[f103,f86]) ).

fof(f123,plain,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(o,o)) = true,
    inference(forward_demodulation,[status(thm)],[f45,f122]) ).

fof(f129,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),e1(s(s(s(s(o)))),s(s(o))),e2(o,o)),true) = true,
    inference(paramodulation,[status(thm)],[f123,f58]) ).

fof(f130,plain,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),e1(s(s(s(s(o)))),s(s(o))),e2(o,o)) = true,
    inference(forward_demodulation,[status(thm)],[f45,f129]) ).

fof(f214,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(o))),s(s(o))),e2(o,o)),true) = true,
    inference(paramodulation,[status(thm)],[f130,f52]) ).

fof(f215,plain,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(s(o))),s(s(o))),e2(o,o)) = true,
    inference(forward_demodulation,[status(thm)],[f45,f214]) ).

fof(f237,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(o,o),e2(s(s(s(o))),s(s(o)))),true) = true,
    inference(paramodulation,[status(thm)],[f215,f86]) ).

fof(f238,plain,
    state(bb(o,s(o)),v1(s(o),o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(o,o),e2(s(s(s(o))),s(s(o)))) = true,
    inference(forward_demodulation,[status(thm)],[f45,f237]) ).

fof(f273,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),o),e2(s(s(s(o))),s(s(o)))),true) = true,
    inference(paramodulation,[status(thm)],[f238,f65]) ).

fof(f274,plain,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(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(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),o),e2(s(s(s(o))),s(s(o)))) = true,
    inference(forward_demodulation,[status(thm)],[f45,f273]) ).

fof(f1109,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))),true) = true,
    inference(paramodulation,[status(thm)],[f274,f79]) ).

fof(f1110,plain,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(s(o)))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(o))),e2(s(s(s(o))),s(s(o)))) = true,
    inference(forward_demodulation,[status(thm)],[f45,f1109]) ).

fof(f2161,plain,
    ifeq(true,true,state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(o))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(o))),s(s(s(o))))),true) = true,
    inference(paramodulation,[status(thm)],[f1110,f75]) ).

fof(f2162,plain,
    state(bb(o,s(o)),v1(o,o),v2(o,s(s(s(o)))),v3(s(s(s(o))),o),v4(s(s(o)),s(s(o))),h(s(s(o)),o),s1(s(s(s(o))),s(o)),s2(s(s(s(s(o)))),s(s(o))),s3(s(s(s(s(o)))),s(o)),s4(s(s(s(s(o)))),s(s(s(o)))),e1(s(s(o)),s(s(s(o)))),e2(s(s(s(o))),s(s(s(o))))) = true,
    inference(forward_demodulation,[status(thm)],[f45,f2161]) ).

fof(f2163,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f2162,f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : PUZ039-10 : TPTP v8.1.2. Released v7.5.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n019.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 : Tue May 30 10:33:10 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 5.84/1.14  % Refutation found
% 5.84/1.14  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.84/1.14  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 6.78/1.24  % Elapsed time: 0.882510 seconds
% 6.78/1.24  % CPU time: 6.641157 seconds
% 6.78/1.24  % Memory used: 210.023 MB
%------------------------------------------------------------------------------