TSTP Solution File: NUM849+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM849+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n031.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 : Fri May  3 02:50:54 EDT 2024

% Result   : Theorem 3.92s 1.12s
% Output   : CNFRefutation 3.92s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f162)

% Comments : 
%------------------------------------------------------------------------------
fof(f157,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X0,X3) = X1
     => vplus(X0,sK2(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ? [X2] : vplus(X0,X2) = X1
     => vplus(X0,sK3(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X1,X3) = X0
     => vplus(X1,sK4(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

cnf(c_49,negated_conjecture,
    vmul(vmul(vd448,vd449),vplus(v1,sK0)) != vmul(vd448,vmul(vd449,vplus(v1,sK0))),
    inference(cnf_transformation,[],[f229]) ).

cnf(c_50,negated_conjecture,
    vmul(vmul(vd448,vd449),sK0) = vmul(vd448,vmul(vd449,sK0)),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_57,plain,
    vplus(vmul(X0,X1),vmul(X0,X2)) = vmul(X0,vplus(X1,X2)),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_58,plain,
    vmul(X0,X1) = vmul(X1,X0),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_59,plain,
    vplus(vmul(X0,X1),X1) = vmul(vplus(v1,X0),X1),
    inference(cnf_transformation,[],[f232]) ).

cnf(c_62,plain,
    vplus(vmul(X0,X1),X0) = vmul(X0,vplus(v1,X1)),
    inference(cnf_transformation,[],[f233]) ).

cnf(c_104,plain,
    vplus(X0,X1) = vplus(X1,X0),
    inference(cnf_transformation,[],[f218]) ).

cnf(c_460,plain,
    vmul(vd448,vmul(vd449,sK0)) = vmul(sK0,vmul(vd449,vd448)),
    inference(demodulation,[status(thm)],[c_50,c_58]) ).

cnf(c_5352,plain,
    vplus(vmul(X0,X1),vmul(X1,X2)) = vmul(X1,vplus(X0,X2)),
    inference(superposition,[status(thm)],[c_58,c_57]) ).

fof(f41,axiom,
    ! [X63,X64] :
      ( greater(X64,X63)
    <=> ? [X65] : vplus(X63,X65) = X64 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof(f248,plain,
    ! [X2,X0] : greater(vplus(X0,X2),X0),
    inference(equality_resolution,[],[f211]) ).

fof(f50,axiom,
    ! [X79] : vplus(v1,X79) = vsucc(X79),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).

fof(f228,plain,
    ! [X0] : vsucc(X0) != v1,
    inference(cnf_transformation,[],[f110]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
    <=> ? [X2] : vplus(X0,X2) = X1 ),
    inference(rectify,[],[f41]) ).

fof(f103,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(rectify,[],[f50]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( vsucc(X0) = vplus(X0,v1)
      & vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
    inference(rectify,[],[f52]) ).

fof(f106,plain,
    ! [X0] :
      ( v1 != X0
     => vsucc(vskolem2(X0)) = X0 ),
    inference(rectify,[],[f53]) ).

fof(f107,plain,
    ! [X0] : vsucc(X0) != X0,
    inference(rectify,[],[f54]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( X0 != X1
     => vsucc(X0) != vsucc(X1) ),
    inference(rectify,[],[f55]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( vsucc(X0) = vsucc(X1)
     => X0 = X1 ),
    inference(rectify,[],[f56]) ).

fof(f110,plain,
    ! [X0] : vsucc(X0) != v1,
    inference(rectify,[],[f57]) ).

fof(f142,plain,
    ! [X0] :
      ( vsucc(vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(ennf_transformation,[],[f106]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( vsucc(X0) != vsucc(X1)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f108]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( X0 = X1
      | vsucc(X0) != vsucc(X1) ),
    inference(ennf_transformation,[],[f109]) ).

fof(f155,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X2] : vplus(X0,X2) = X1
        | ~ greater(X1,X0) ) ),
    inference(nnf_transformation,[],[f94]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X3] : vplus(X0,X3) = X1
        | ~ greater(X1,X0) ) ),
    inference(rectify,[],[f155]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( vplus(X0,sK2(X0,X1)) = X1
        | ~ greater(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f156,f157]) ).

fof(f42,axiom,
    ! [X66,X67] :
      ( ? [X69] : vplus(X66,X69) = X67
      | ? [X68] : vplus(X67,X68) = X66
      | X66 = X67 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).

fof(f210,plain,
    ! [X0,X1] :
      ( vplus(X0,sK2(X0,X1)) = X1
      | ~ greater(X1,X0) ),
    inference(cnf_transformation,[],[f158]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ? [X2] : vplus(X0,X2) = X1
      | ? [X3] : vplus(X1,X3) = X0
      | X0 = X1 ),
    inference(rectify,[],[f42]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( vplus(X0,sK3(X0,X1)) = X1
      | vplus(X1,sK4(X0,X1)) = X0
      | X0 = X1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f95,f160,f159]) ).

fof(f43,axiom,
    ! [X66,X67] :
      ( ~ ? [X69] : vplus(X66,X69) = X67
      | X66 != X67 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).

fof(f212,plain,
    ! [X0,X1] :
      ( vplus(X0,sK3(X0,X1)) = X1
      | vplus(X1,sK4(X0,X1)) = X0
      | X0 = X1 ),
    inference(cnf_transformation,[],[f161]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X0,X2) = X1
      | X0 != X1 ),
    inference(rectify,[],[f43]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X0,X2) != X1
      | X0 != X1 ),
    inference(ennf_transformation,[],[f96]) ).

fof(f211,plain,
    ! [X2,X0,X1] :
      ( greater(X1,X0)
      | vplus(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f158]) ).

fof(f213,plain,
    ! [X2,X0,X1] :
      ( vplus(X0,X2) != X1
      | X0 != X1 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f44,axiom,
    ! [X66,X67] :
      ( ~ ? [X69] : vplus(X66,X69) = X67
      | ~ ? [X68] : vplus(X67,X68) = X66 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).

fof(f249,plain,
    ! [X2,X0] : vplus(X0,X2) != X0,
    inference(equality_resolution,[],[f213]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X0,X2) = X1
      | ~ ? [X3] : vplus(X1,X3) = X0 ),
    inference(rectify,[],[f44]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X0,X2) != X1
      | ! [X3] : vplus(X1,X3) != X0 ),
    inference(ennf_transformation,[],[f97]) ).

fof(f214,plain,
    ! [X2,X3,X0,X1] :
      ( vplus(X0,X2) != X1
      | vplus(X1,X3) != X0 ),
    inference(cnf_transformation,[],[f139]) ).

fof(f45,axiom,
    ! [X66,X67] :
      ( ~ ? [X68] : vplus(X67,X68) = X66
      | X66 != X67 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).

fof(f250,plain,
    ! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
    inference(equality_resolution,[],[f214]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X1,X2) = X0
      | X0 != X1 ),
    inference(rectify,[],[f45]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(ennf_transformation,[],[f98]) ).

fof(f215,plain,
    ! [X2,X0,X1] :
      ( vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f46,axiom,
    ! [X70,X71] :
      ( X70 != X71
     => ! [X72] : vplus(X72,X70) != vplus(X72,X71) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).

fof(f251,plain,
    ! [X2,X1] : vplus(X1,X2) != X1,
    inference(equality_resolution,[],[f215]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( X0 != X1
     => ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
    inference(rectify,[],[f46]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f99]) ).

fof(f47,axiom,
    ! [X73,X74] : vplus(X73,X74) != X74,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).

fof(f216,plain,
    ! [X2,X0,X1] :
      ( vplus(X2,X0) != vplus(X2,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f141]) ).

fof(f100,plain,
    ! [X0,X1] : vplus(X0,X1) != X1,
    inference(rectify,[],[f47]) ).

fof(f48,axiom,
    ! [X75,X76] : vplus(X76,X75) = vplus(X75,X76),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof(f217,plain,
    ! [X0,X1] : vplus(X0,X1) != X1,
    inference(cnf_transformation,[],[f100]) ).

fof(f101,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(rectify,[],[f48]) ).

fof(f49,axiom,
    ! [X77,X78] : vplus(vsucc(X77),X78) = vsucc(vplus(X77,X78)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).

fof(f218,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(cnf_transformation,[],[f101]) ).

fof(f102,plain,
    ! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
    inference(rectify,[],[f49]) ).

fof(f219,plain,
    ! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
    inference(cnf_transformation,[],[f102]) ).

fof(f220,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(cnf_transformation,[],[f103]) ).

fof(f51,axiom,
    ! [X80,X81,X82] : vplus(vplus(X80,X81),X82) = vplus(X80,vplus(X81,X82)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

fof(f234,plain,
    ! [X0,X1] : vplus(vplus(v1,X0),X1) = vplus(v1,vplus(X0,X1)),
    inference(definition_unfolding,[],[f219,f220,f220]) ).

fof(f104,plain,
    ! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(rectify,[],[f51]) ).

fof(f221,plain,
    ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(cnf_transformation,[],[f104]) ).

fof(f222,plain,
    ! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
    inference(cnf_transformation,[],[f105]) ).

fof(f53,axiom,
    ! [X85] :
      ( v1 != X85
     => vsucc(vskolem2(X85)) = X85 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(20, 0), 0)') ).

fof(f236,plain,
    ! [X0,X1] : vplus(v1,vplus(X0,X1)) = vplus(X0,vplus(v1,X1)),
    inference(definition_unfolding,[],[f222,f220,f220]) ).

fof(f223,plain,
    ! [X0] : vsucc(X0) = vplus(X0,v1),
    inference(cnf_transformation,[],[f105]) ).

fof(f52,axiom,
    ! [X83,X84] :
      ( vplus(X83,v1) = vsucc(X83)
      & vplus(X83,vsucc(X84)) = vsucc(vplus(X83,X84)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).

fof(f235,plain,
    ! [X0] : vplus(v1,X0) = vplus(X0,v1),
    inference(definition_unfolding,[],[f223,f220]) ).

fof(f224,plain,
    ! [X0] :
      ( vsucc(vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(cnf_transformation,[],[f142]) ).

fof(f54,axiom,
    ! [X86] : vsucc(X86) != X86,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).

fof(f237,plain,
    ! [X0] :
      ( vplus(v1,vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(definition_unfolding,[],[f224,f220]) ).

fof(f225,plain,
    ! [X0] : vsucc(X0) != X0,
    inference(cnf_transformation,[],[f107]) ).

fof(f55,axiom,
    ! [X87,X88] :
      ( X87 != X88
     => vsucc(X87) != vsucc(X88) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).

fof(f238,plain,
    ! [X0] : vplus(v1,X0) != X0,
    inference(definition_unfolding,[],[f225,f220]) ).

fof(f226,plain,
    ! [X0,X1] :
      ( vsucc(X0) != vsucc(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f143]) ).

fof(f56,axiom,
    ! [X89,X90] :
      ( vsucc(X89) = vsucc(X90)
     => X89 = X90 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(antec(axiom(3)), imp(antec(axiom(3))))') ).

fof(f239,plain,
    ! [X0,X1] :
      ( vplus(v1,X0) != vplus(v1,X1)
      | X0 = X1 ),
    inference(definition_unfolding,[],[f226,f220,f220]) ).

fof(f227,plain,
    ! [X0,X1] :
      ( X0 = X1
      | vsucc(X0) != vsucc(X1) ),
    inference(cnf_transformation,[],[f144]) ).

fof(f57,axiom,
    ! [X91] : v1 != vsucc(X91),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(restrictor(axiom(1)), holds(scope(axiom(1)), 2, 0))') ).

fof(f240,plain,
    ! [X0,X1] :
      ( X0 = X1
      | vplus(v1,X0) != vplus(v1,X1) ),
    inference(definition_unfolding,[],[f227,f220,f220]) ).

cnf(c_106,plain,
    vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(cnf_transformation,[],[f221]) ).

cnf(c_154,plain,
    vplus(X0,vmul(X1,X0)) = vmul(vplus(v1,X1),X0),
    inference(theory_normalisation,[status(thm)],[c_59,c_106,c_104]) ).

cnf(c_155,plain,
    vplus(X0,vmul(X0,X1)) = vmul(X0,vplus(v1,X1)),
    inference(theory_normalisation,[status(thm)],[c_62,c_106,c_104]) ).

cnf(c_493,plain,
    vmul(vplus(v1,sK0),vmul(vd449,vd448)) != vmul(vd448,vplus(vd449,vmul(vd449,sK0))),
    inference(demodulation,[status(thm)],[c_49,c_58,c_155]) ).

cnf(c_1332,plain,
    vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,sK0))) = vmul(vplus(v1,sK0),vmul(vd449,vd448)),
    inference(superposition,[status(thm)],[c_460,c_154]) ).

cnf(c_5489,plain,
    vmul(vplus(v1,sK0),vmul(vd449,vd448)) = vmul(vd448,vplus(vd449,vmul(vd449,sK0))),
    inference(demodulation,[status(thm)],[c_1332,c_5352]) ).

cnf(c_5490,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_5489,c_493]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : NUM849+1 : TPTP v8.1.2. Released v4.1.0.
% 0.09/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.31  % Computer : n031.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Thu May  2 20:12:01 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.16/0.42  Running first-order theorem proving
% 0.16/0.42  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.92/1.12  % SZS status Started for theBenchmark.p
% 3.92/1.12  % SZS status Theorem for theBenchmark.p
% 3.92/1.12  
% 3.92/1.12  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.92/1.12  
% 3.92/1.12  ------  iProver source info
% 3.92/1.12  
% 3.92/1.12  git: date: 2024-05-02 19:28:25 +0000
% 3.92/1.12  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.92/1.12  git: non_committed_changes: false
% 3.92/1.12  
% 3.92/1.12  ------ Parsing...
% 3.92/1.12  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 3.92/1.12  
% 3.92/1.12  ------ Preprocessing... sup_sim: 5  sf_s  rm: 1 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe_e 
% 3.92/1.12  
% 3.92/1.12  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.92/1.12  
% 3.92/1.12  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 3.92/1.12  ------ Proving...
% 3.92/1.12  ------ Problem Properties 
% 3.92/1.12  
% 3.92/1.12  
% 3.92/1.12  clauses                                 50
% 3.92/1.12  conjectures                             0
% 3.92/1.12  EPR                                     19
% 3.92/1.12  Horn                                    45
% 3.92/1.12  unary                                   19
% 3.92/1.12  binary                                  19
% 3.92/1.12  lits                                    93
% 3.92/1.12  lits eq                                 28
% 3.92/1.12  fd_pure                                 0
% 3.92/1.12  fd_pseudo                               0
% 3.92/1.12  fd_cond                                 0
% 3.92/1.12  fd_pseudo_cond                          5
% 3.92/1.12  AC symbols                              1
% 3.92/1.12  
% 3.92/1.12  ------ Schedule dynamic 5 is on 
% 3.92/1.12  
% 3.92/1.12  ------ no conjectures: strip conj schedule 
% 3.92/1.12  
% 3.92/1.12  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.92/1.12  
% 3.92/1.12  
% 3.92/1.12  ------ 
% 3.92/1.12  Current options:
% 3.92/1.12  ------ 
% 3.92/1.12  
% 3.92/1.12  
% 3.92/1.12  
% 3.92/1.12  
% 3.92/1.12  ------ Proving...
% 3.92/1.12  
% 3.92/1.12  
% 3.92/1.12  % SZS status Theorem for theBenchmark.p
% 3.92/1.12  
% 3.92/1.12  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.92/1.12  
% 3.92/1.12  
%------------------------------------------------------------------------------