TSTP Solution File: NUM852+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n018.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 02:50:55 EDT 2024

% Result   : Theorem 4.14s 1.20s
% Output   : CNFRefutation 4.14s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named f164)

% Comments : 
%------------------------------------------------------------------------------
fof(f159,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X0,X3) = X1
     => vplus(X0,sK1(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ? [X2] : vplus(X0,X2) = X1
     => vplus(X0,sK2(X0,X1)) = X1 ),
    introduced(choice_axiom,[]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( ? [X3] : vplus(X1,X3) = X0
     => vplus(X1,sK3(X0,X1)) = X0 ),
    introduced(choice_axiom,[]) ).

cnf(c_49,negated_conjecture,
    ~ greater(vmul(vd481,vd469),vmul(vd480,vd469)),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_50,plain,
    greater(vd481,vd480),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_54,plain,
    ( ~ greater(X0,X1)
    | vmul(vplus(X1,vskolem9(X0,X1)),vd469) = vmul(X0,vd469) ),
    inference(cnf_transformation,[],[f170]) ).

cnf(c_56,plain,
    vmul(vmul(X0,X1),X2) = vmul(X0,vmul(X1,X2)),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_57,plain,
    vplus(vmul(X0,X1),vmul(X0,X2)) = vmul(X0,vplus(X1,X2)),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_58,plain,
    vmul(X0,X1) = vmul(X1,X0),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_96,plain,
    greater(vplus(X0,X1),X0),
    inference(cnf_transformation,[],[f249]) ).

cnf(c_104,plain,
    vplus(X0,X1) = vplus(X1,X0),
    inference(cnf_transformation,[],[f221]) ).

cnf(c_1438,plain,
    greater(vmul(X0,vplus(X1,X2)),vmul(X0,X1)),
    inference(superposition,[status(thm)],[c_57,c_96]) ).

fof(f43,axiom,
    ! [X68,X69] :
      ( greater(X69,X68)
    <=> ? [X70] : vplus(X68,X70) = X69 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof(f249,plain,
    ! [X2,X0] : greater(vplus(X0,X2),X0),
    inference(equality_resolution,[],[f214]) ).

fof(f52,axiom,
    ! [X84] : vplus(v1,X84) = vsucc(X84),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).

fof(f231,plain,
    ! [X0] : v1 != vsucc(X0),
    inference(cnf_transformation,[],[f114]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( greater(X1,X0)
    <=> ? [X2] : vplus(X0,X2) = X1 ),
    inference(rectify,[],[f43]) ).

fof(f107,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(rectify,[],[f52]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( vsucc(X0) = vplus(X0,v1)
      & vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)) ),
    inference(rectify,[],[f54]) ).

fof(f110,plain,
    ! [X0] :
      ( v1 != X0
     => vsucc(vskolem2(X0)) = X0 ),
    inference(rectify,[],[f55]) ).

fof(f111,plain,
    ! [X0] : vsucc(X0) != X0,
    inference(rectify,[],[f56]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( X0 != X1
     => vsucc(X0) != vsucc(X1) ),
    inference(rectify,[],[f57]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( vsucc(X0) = vsucc(X1)
     => X0 = X1 ),
    inference(rectify,[],[f58]) ).

fof(f114,plain,
    ! [X0] : v1 != vsucc(X0),
    inference(rectify,[],[f59]) ).

fof(f146,plain,
    ! [X0] :
      ( vsucc(vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(ennf_transformation,[],[f110]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( vsucc(X0) != vsucc(X1)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f112]) ).

fof(f148,plain,
    ! [X0,X1] :
      ( X0 = X1
      | vsucc(X0) != vsucc(X1) ),
    inference(ennf_transformation,[],[f113]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X2] : vplus(X0,X2) = X1
        | ~ greater(X1,X0) ) ),
    inference(nnf_transformation,[],[f98]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( ? [X3] : vplus(X0,X3) = X1
        | ~ greater(X1,X0) ) ),
    inference(rectify,[],[f157]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ( greater(X1,X0)
        | ! [X2] : vplus(X0,X2) != X1 )
      & ( vplus(X0,sK1(X0,X1)) = X1
        | ~ greater(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f158,f159]) ).

fof(f44,axiom,
    ! [X71,X72] :
      ( ? [X74] : vplus(X71,X74) = X72
      | ? [X73] : vplus(X72,X73) = X71
      | X71 = X72 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).

fof(f213,plain,
    ! [X0,X1] :
      ( vplus(X0,sK1(X0,X1)) = X1
      | ~ greater(X1,X0) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X2] : vplus(X0,X2) = X1
      | ? [X3] : vplus(X1,X3) = X0
      | X0 = X1 ),
    inference(rectify,[],[f44]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( vplus(X0,sK2(X0,X1)) = X1
      | vplus(X1,sK3(X0,X1)) = X0
      | X0 = X1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f99,f162,f161]) ).

fof(f45,axiom,
    ! [X71,X72] :
      ( ~ ? [X74] : vplus(X71,X74) = X72
      | X71 != X72 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).

fof(f215,plain,
    ! [X0,X1] :
      ( vplus(X0,sK2(X0,X1)) = X1
      | vplus(X1,sK3(X0,X1)) = X0
      | X0 = X1 ),
    inference(cnf_transformation,[],[f163]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X0,X2) = X1
      | X0 != X1 ),
    inference(rectify,[],[f45]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X0,X2) != X1
      | X0 != X1 ),
    inference(ennf_transformation,[],[f100]) ).

fof(f214,plain,
    ! [X2,X0,X1] :
      ( greater(X1,X0)
      | vplus(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f160]) ).

fof(f216,plain,
    ! [X2,X0,X1] :
      ( vplus(X0,X2) != X1
      | X0 != X1 ),
    inference(cnf_transformation,[],[f142]) ).

fof(f46,axiom,
    ! [X71,X72] :
      ( ~ ? [X74] : vplus(X71,X74) = X72
      | ~ ? [X73] : vplus(X72,X73) = X71 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).

fof(f250,plain,
    ! [X2,X0] : vplus(X0,X2) != X0,
    inference(equality_resolution,[],[f216]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X0,X2) = X1
      | ~ ? [X3] : vplus(X1,X3) = X0 ),
    inference(rectify,[],[f46]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X0,X2) != X1
      | ! [X3] : vplus(X1,X3) != X0 ),
    inference(ennf_transformation,[],[f101]) ).

fof(f217,plain,
    ! [X2,X3,X0,X1] :
      ( vplus(X0,X2) != X1
      | vplus(X1,X3) != X0 ),
    inference(cnf_transformation,[],[f143]) ).

fof(f47,axiom,
    ! [X71,X72] :
      ( ~ ? [X73] : vplus(X72,X73) = X71
      | X71 != X72 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).

fof(f251,plain,
    ! [X2,X3,X0] : vplus(vplus(X0,X2),X3) != X0,
    inference(equality_resolution,[],[f217]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ~ ? [X2] : vplus(X1,X2) = X0
      | X0 != X1 ),
    inference(rectify,[],[f47]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(ennf_transformation,[],[f102]) ).

fof(f218,plain,
    ! [X2,X0,X1] :
      ( vplus(X1,X2) != X0
      | X0 != X1 ),
    inference(cnf_transformation,[],[f144]) ).

fof(f48,axiom,
    ! [X75,X76] :
      ( X75 != X76
     => ! [X77] : vplus(X77,X75) != vplus(X77,X76) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).

fof(f252,plain,
    ! [X2,X1] : vplus(X1,X2) != X1,
    inference(equality_resolution,[],[f218]) ).

fof(f103,plain,
    ! [X0,X1] :
      ( X0 != X1
     => ! [X2] : vplus(X2,X0) != vplus(X2,X1) ),
    inference(rectify,[],[f48]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( ! [X2] : vplus(X2,X0) != vplus(X2,X1)
      | X0 = X1 ),
    inference(ennf_transformation,[],[f103]) ).

fof(f49,axiom,
    ! [X78,X79] : vplus(X78,X79) != X79,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).

fof(f219,plain,
    ! [X2,X0,X1] :
      ( vplus(X2,X0) != vplus(X2,X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f145]) ).

fof(f104,plain,
    ! [X0,X1] : vplus(X0,X1) != X1,
    inference(rectify,[],[f49]) ).

fof(f50,axiom,
    ! [X80,X81] : vplus(X81,X80) = vplus(X80,X81),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof(f220,plain,
    ! [X0,X1] : vplus(X0,X1) != X1,
    inference(cnf_transformation,[],[f104]) ).

fof(f105,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(rectify,[],[f50]) ).

fof(f51,axiom,
    ! [X82,X83] : vplus(vsucc(X82),X83) = vsucc(vplus(X82,X83)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(52, 0), 0)') ).

fof(f221,plain,
    ! [X0,X1] : vplus(X0,X1) = vplus(X1,X0),
    inference(cnf_transformation,[],[f105]) ).

fof(f106,plain,
    ! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
    inference(rectify,[],[f51]) ).

fof(f222,plain,
    ! [X0,X1] : vplus(vsucc(X0),X1) = vsucc(vplus(X0,X1)),
    inference(cnf_transformation,[],[f106]) ).

fof(f223,plain,
    ! [X0] : vsucc(X0) = vplus(v1,X0),
    inference(cnf_transformation,[],[f107]) ).

fof(f53,axiom,
    ! [X85,X86,X87] : vplus(vplus(X85,X86),X87) = vplus(X85,vplus(X86,X87)),
    file('/export/starexec/sandbox2/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,[],[f222,f223,f223]) ).

fof(f108,plain,
    ! [X0,X1,X2] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(rectify,[],[f53]) ).

fof(f224,plain,
    ! [X2,X0,X1] : vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(cnf_transformation,[],[f108]) ).

fof(f225,plain,
    ! [X0,X1] : vsucc(vplus(X0,X1)) = vplus(X0,vsucc(X1)),
    inference(cnf_transformation,[],[f109]) ).

fof(f55,axiom,
    ! [X90] :
      ( v1 != X90
     => vsucc(vskolem2(X90)) = X90 ),
    file('/export/starexec/sandbox2/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,[],[f225,f223,f223]) ).

fof(f226,plain,
    ! [X0] : vsucc(X0) = vplus(X0,v1),
    inference(cnf_transformation,[],[f109]) ).

fof(f54,axiom,
    ! [X88,X89] :
      ( vplus(X88,v1) = vsucc(X88)
      & vplus(X88,vsucc(X89)) = vsucc(vplus(X88,X89)) ),
    file('/export/starexec/sandbox2/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,[],[f226,f223]) ).

fof(f227,plain,
    ! [X0] :
      ( vsucc(vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(cnf_transformation,[],[f146]) ).

fof(f56,axiom,
    ! [X91] : vsucc(X91) != X91,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(12, 0), 0)') ).

fof(f237,plain,
    ! [X0] :
      ( vplus(v1,vskolem2(X0)) = X0
      | v1 = X0 ),
    inference(definition_unfolding,[],[f227,f223]) ).

fof(f228,plain,
    ! [X0] : vsucc(X0) != X0,
    inference(cnf_transformation,[],[f111]) ).

fof(f57,axiom,
    ! [X92,X93] :
      ( X92 != X93
     => vsucc(X92) != vsucc(X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(6, 0), 0)') ).

fof(f238,plain,
    ! [X0] : vplus(v1,X0) != X0,
    inference(definition_unfolding,[],[f228,f223]) ).

fof(f229,plain,
    ! [X0,X1] :
      ( vsucc(X0) != vsucc(X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f147]) ).

fof(f58,axiom,
    ! [X94,X95] :
      ( vsucc(X94) = vsucc(X95)
     => X94 = X95 ),
    file('/export/starexec/sandbox2/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,[],[f229,f223,f223]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( X0 = X1
      | vsucc(X0) != vsucc(X1) ),
    inference(cnf_transformation,[],[f148]) ).

fof(f59,axiom,
    ! [X96] : v1 != vsucc(X96),
    file('/export/starexec/sandbox2/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,[],[f230,f223,f223]) ).

cnf(c_106,plain,
    vplus(vplus(X0,X1),X2) = vplus(X0,vplus(X1,X2)),
    inference(cnf_transformation,[],[f224]) ).

cnf(c_140,negated_conjecture,
    ~ greater(vmul(vd481,vd469),vmul(vd469,vd480)),
    inference(theory_normalisation,[status(thm)],[c_49,c_106,c_104,c_56,c_58]) ).

cnf(c_143,plain,
    ( ~ greater(X0,X1)
    | vmul(vd469,vplus(X1,vskolem9(X0,X1))) = vmul(X0,vd469) ),
    inference(theory_normalisation,[status(thm)],[c_54,c_106,c_104,c_56,c_58]) ).

cnf(c_1502,plain,
    vmul(vd469,vplus(vd480,vskolem9(vd481,vd480))) = vmul(vd481,vd469),
    inference(superposition,[status(thm)],[c_50,c_143]) ).

cnf(c_2737,plain,
    greater(vmul(vd481,vd469),vmul(vd469,vd480)),
    inference(superposition,[status(thm)],[c_1502,c_1438]) ).

cnf(c_2751,plain,
    $false,
    inference(backward_subsumption_resolution,[status(thm)],[c_140,c_2737]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : NUM852+1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.35  % Computer : n018.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 : Thu May  2 20:01:01 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.21/0.49  Running first-order theorem proving
% 0.21/0.49  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.14/1.20  % SZS status Started for theBenchmark.p
% 4.14/1.20  % SZS status Theorem for theBenchmark.p
% 4.14/1.20  
% 4.14/1.20  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 4.14/1.20  
% 4.14/1.20  ------  iProver source info
% 4.14/1.20  
% 4.14/1.20  git: date: 2024-05-02 19:28:25 +0000
% 4.14/1.20  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 4.14/1.20  git: non_committed_changes: false
% 4.14/1.20  
% 4.14/1.20  ------ Parsing...
% 4.14/1.20  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 4.14/1.20  
% 4.14/1.20  ------ Preprocessing... sup_sim: 1  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 
% 4.14/1.20  
% 4.14/1.20  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 4.14/1.20  
% 4.14/1.20  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 4.14/1.20  ------ Proving...
% 4.14/1.20  ------ Problem Properties 
% 4.14/1.20  
% 4.14/1.20  
% 4.14/1.20  clauses                                 53
% 4.14/1.20  conjectures                             1
% 4.14/1.20  EPR                                     21
% 4.14/1.20  Horn                                    48
% 4.14/1.20  unary                                   20
% 4.14/1.20  binary                                  21
% 4.14/1.20  lits                                    98
% 4.14/1.20  lits eq                                 27
% 4.14/1.20  fd_pure                                 0
% 4.14/1.20  fd_pseudo                               0
% 4.14/1.20  fd_cond                                 0
% 4.14/1.20  fd_pseudo_cond                          5
% 4.14/1.20  AC symbols                              2
% 4.14/1.20  
% 4.14/1.20  ------ Input Options Time Limit: Unbounded
% 4.14/1.20  
% 4.14/1.20  
% 4.14/1.20  ------ 
% 4.14/1.20  Current options:
% 4.14/1.20  ------ 
% 4.14/1.20  
% 4.14/1.20  
% 4.14/1.20  
% 4.14/1.20  
% 4.14/1.20  ------ Proving...
% 4.14/1.20  
% 4.14/1.20  
% 4.14/1.20  % SZS status Theorem for theBenchmark.p
% 4.14/1.20  
% 4.14/1.20  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.14/1.20  
% 4.14/1.21  
%------------------------------------------------------------------------------