%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWX034+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:13:12 PM UTC 2026
% Result : Theorem 26.06s 4.01s
% Output : CNFRefutation 26.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 65 ( 7 unt; 7 def)
% Number of atoms : 256 ( 44 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 290 ( 99 ~; 119 |; 54 &)
% ( 8 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 145 ( 122 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Xx3] : '0' != s(Xx3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Xx4,Xx5] :
( s(Xx4) = s(Xx5)
=> Xx4 = Xx5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Xx1,Xx2,Xx3] :
( times_terminates(Xx1,Xx2,Xx3)
<=> ( ( $true
| Xx1 != '0' )
& $true
& ! [Xx4,Xx5] :
( ( ( ( plus_terminates(Xx2,Xx5,Xx3)
| times_fails(Xx4,Xx2,Xx5) )
& times_terminates(Xx4,Xx2,Xx5) )
| Xx1 != s(Xx4) )
& $true ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [Xx,Xy,Xz] :
( nat_succeeds(Xx)
=> plus_terminates(Xx,Xy,Xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
( ! [Xx] :
( ( Xx = '0'
| ? [Xx2] :
( ! [Xy,Xz] :
( nat_succeeds(Xy)
=> times_terminates(Xx2,Xy,Xz) )
& nat_succeeds(Xx2)
& Xx = s(Xx2) ) )
=> ! [Xy,Xz] :
( nat_succeeds(Xy)
=> times_terminates(Xx,Xy,Xz) ) )
=> ! [Xx] :
( nat_succeeds(Xx)
=> ! [Xy,Xz] :
( nat_succeeds(Xy)
=> times_terminates(Xx,Xy,Xz) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,conjecture,
! [Xx,Xy,Xz] :
( ( nat_succeeds(Xy)
& nat_succeeds(Xx) )
=> times_terminates(Xx,Xy,Xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
~ ! [Xx,Xy,Xz] :
( ( nat_succeeds(Xy)
& nat_succeeds(Xx) )
=> times_terminates(Xx,Xy,Xz) ),
inference(negated_conjecture,[status(cth)],[f58]) ).
fof(f60,plain,
! [X0] : '0' != s(X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f61,plain,
! [Xx4,Xx5] :
( Xx4 = Xx5
| s(Xx4) != s(Xx5) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f62,plain,
! [X0,X1] :
( X0 = X1
| s(X0) != s(X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f106,plain,
! [Xx1,Xx2,Xx3] :
( ( ( $false
& Xx1 = '0' )
| $false
| ? [Xx4,Xx5] :
( ( ( ( ~ plus_terminates(Xx2,Xx5,Xx3)
& ~ times_fails(Xx4,Xx2,Xx5) )
| ~ times_terminates(Xx4,Xx2,Xx5) )
& Xx1 = s(Xx4) )
| $false )
| times_terminates(Xx1,Xx2,Xx3) )
& ( ( ( $true
| Xx1 != '0' )
& $true
& ! [Xx4,Xx5] :
( ( ( ( plus_terminates(Xx2,Xx5,Xx3)
| times_fails(Xx4,Xx2,Xx5) )
& times_terminates(Xx4,Xx2,Xx5) )
| Xx1 != s(Xx4) )
& $true ) )
| ~ times_terminates(Xx1,Xx2,Xx3) ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f107,plain,
( ! [Xx1,Xx2,Xx3] :
( ( $false
& Xx1 = '0' )
| $false
| ? [Xx4] :
( ( ? [Xx5] :
( ~ plus_terminates(Xx2,Xx5,Xx3)
& ~ times_fails(Xx4,Xx2,Xx5) )
| ? [Xx5] : ~ times_terminates(Xx4,Xx2,Xx5) )
& Xx1 = s(Xx4) )
| $false
| times_terminates(Xx1,Xx2,Xx3) )
& ! [Xx1,Xx2,Xx3] :
( ( ( $true
| Xx1 != '0' )
& $true
& ! [Xx4] :
( ( ! [Xx5] :
( plus_terminates(Xx2,Xx5,Xx3)
| times_fails(Xx4,Xx2,Xx5) )
& ! [Xx5] : times_terminates(Xx4,Xx2,Xx5) )
| Xx1 != s(Xx4) )
& $true )
| ~ times_terminates(Xx1,Xx2,Xx3) ) ),
inference(miniscoping,[status(thm)],[f106]) ).
fof(f108,plain,
( ! [Xx1,Xx2,Xx3] :
( ( $false
& Xx1 = '0' )
| $false
| ( ( ( ~ plus_terminates(Xx2,sK6_skl(Xx3,Xx2,Xx1),Xx3)
& ~ times_fails(sK4_skl(Xx3,Xx2,Xx1),Xx2,sK6_skl(Xx3,Xx2,Xx1)) )
| ~ times_terminates(sK4_skl(Xx3,Xx2,Xx1),Xx2,sK5_skl(Xx3,Xx2,Xx1)) )
& Xx1 = s(sK4_skl(Xx3,Xx2,Xx1)) )
| $false
| times_terminates(Xx1,Xx2,Xx3) )
& ! [Xx1,Xx2,Xx3] :
( ( ( $true
| Xx1 != '0' )
& $true
& ! [Xx4] :
( ( ! [Xx5] :
( plus_terminates(Xx2,Xx5,Xx3)
| times_fails(Xx4,Xx2,Xx5) )
& ! [Xx5] : times_terminates(Xx4,Xx2,Xx5) )
| Xx1 != s(Xx4) )
& $true )
| ~ times_terminates(Xx1,Xx2,Xx3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(Xx4,sK4_skl(Xx3,Xx2,Xx1)),skolemize(Xx5,sK5_skl(Xx3,Xx2,Xx1)),skolemize(Xx5,sK6_skl(Xx3,Xx2,Xx1))],[f107]) ).
fof(f109,plain,
( ! [Xx1,Xx2,Xx3] :
( ? [Xx4] :
( ( ? [Xx5] :
( ~ plus_terminates(Xx2,sK6_skl(Xx3,Xx2,Xx1),Xx3)
& ~ times_fails(sK4_skl(Xx3,Xx2,Xx1),Xx2,sK6_skl(Xx3,Xx2,Xx1)) )
| ? [Xx5] : ~ times_terminates(sK4_skl(Xx3,Xx2,Xx1),Xx2,sK5_skl(Xx3,Xx2,Xx1)) )
& Xx1 = s(sK4_skl(Xx3,Xx2,Xx1)) )
| times_terminates(Xx1,Xx2,Xx3) )
& ! [Xx1,Xx2,Xx3] :
( ! [Xx4] :
( ( ! [Xx5] :
( plus_terminates(Xx2,Xx5,Xx3)
| times_fails(Xx4,Xx2,Xx5) )
& ! [Xx5] : times_terminates(Xx4,Xx2,Xx5) )
| Xx1 != s(Xx4) )
| ~ times_terminates(Xx1,Xx2,Xx3) ) ),
inference(true_and_false_simplification,[status(thm)],[f108]) ).
fof(f112,plain,
! [X0,X1,X2] :
( X0 = s(sK4_skl(X2,X1,X0))
| times_terminates(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f114,plain,
! [X0,X1,X2] :
( ~ plus_terminates(X1,sK6_skl(X2,X1,X0),X2)
| ~ times_terminates(sK4_skl(X2,X1,X0),X1,sK5_skl(X2,X1,X0))
| times_terminates(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f226,plain,
! [Xx,Xy,Xz] :
( plus_terminates(Xx,Xy,Xz)
| ~ nat_succeeds(Xx) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f227,plain,
! [Xx] :
( ! [Xy,Xz] : plus_terminates(Xx,Xy,Xz)
| ~ nat_succeeds(Xx) ),
inference(miniscoping,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2] :
( plus_terminates(X0,X1,X2)
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f288,plain,
( ! [Xx] :
( ! [Xy,Xz] :
( times_terminates(Xx,Xy,Xz)
| ~ nat_succeeds(Xy) )
| ~ nat_succeeds(Xx) )
| ? [Xx] :
( ? [Xy,Xz] :
( ~ times_terminates(Xx,Xy,Xz)
& nat_succeeds(Xy) )
& ( Xx = '0'
| ? [Xx2] :
( ! [Xy,Xz] :
( times_terminates(Xx2,Xy,Xz)
| ~ nat_succeeds(Xy) )
& nat_succeeds(Xx2)
& Xx = s(Xx2) ) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f289,plain,
( ! [Xx] :
( ! [Xy] :
( ! [Xz] : times_terminates(Xx,Xy,Xz)
| ~ nat_succeeds(Xy) )
| ~ nat_succeeds(Xx) )
| ? [Xx] :
( ? [Xy] :
( ? [Xz] : ~ times_terminates(Xx,Xy,Xz)
& nat_succeeds(Xy) )
& ( Xx = '0'
| ? [Xx2] :
( ! [Xy] :
( ! [Xz] : times_terminates(Xx2,Xy,Xz)
| ~ nat_succeeds(Xy) )
& nat_succeeds(Xx2)
& Xx = s(Xx2) ) ) ) ),
inference(miniscoping,[status(thm)],[f288]) ).
fof(f290,plain,
( ! [Xx] :
( ! [Xy] :
( ! [Xz] : times_terminates(Xx,Xy,Xz)
| ~ nat_succeeds(Xy) )
| ~ nat_succeeds(Xx) )
| ( ~ times_terminates(sK31_skl,sK33_skl,sK34_skl)
& nat_succeeds(sK33_skl)
& ( sK31_skl = '0'
| ( ! [Xy] :
( ! [Xz] : times_terminates(sK32_skl,Xy,Xz)
| ~ nat_succeeds(Xy) )
& nat_succeeds(sK32_skl)
& sK31_skl = s(sK32_skl) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31_skl,sK32_skl,sK33_skl,sK34_skl]),skolemize(Xx,sK31_skl),skolemize(Xx2,sK32_skl),skolemize(Xy,sK33_skl),skolemize(Xz,sK34_skl)],[f289]) ).
fof(f291,plain,
! [X0,X1,X2] :
( times_terminates(X0,X1,X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| sK31_skl = '0'
| sK31_skl = s(sK32_skl) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f293,plain,
! [X0,X1,X2,X3,X4] :
( times_terminates(X2,X3,X4)
| ~ nat_succeeds(X3)
| ~ nat_succeeds(X2)
| sK31_skl = '0'
| times_terminates(sK32_skl,X0,X1)
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f294,plain,
! [X0,X1,X2] :
( times_terminates(X0,X1,X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| nat_succeeds(sK33_skl) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f295,plain,
! [X0,X1,X2] :
( times_terminates(X0,X1,X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| ~ times_terminates(sK31_skl,sK33_skl,sK34_skl) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f296,plain,
? [Xx,Xy,Xz] :
( ~ times_terminates(Xx,Xy,Xz)
& nat_succeeds(Xy)
& nat_succeeds(Xx) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f297,plain,
? [Xx,Xy] :
( ? [Xz] : ~ times_terminates(Xx,Xy,Xz)
& nat_succeeds(Xy)
& nat_succeeds(Xx) ),
inference(miniscoping,[status(thm)],[f296]) ).
fof(f298,plain,
( ~ times_terminates(sK35_skl,sK36_skl,sK37_skl)
& nat_succeeds(sK36_skl)
& nat_succeeds(sK35_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl,sK37_skl]),skolemize(Xx,sK35_skl),skolemize(Xy,sK36_skl),skolemize(Xz,sK37_skl)],[f297]) ).
fof(f299,plain,
nat_succeeds(sK35_skl),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f300,plain,
nat_succeeds(sK36_skl),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f301,plain,
~ times_terminates(sK35_skl,sK36_skl,sK37_skl),
inference(cnf_transformation,[status(thm)],[f298]) ).
fof(f338,definition,
( sQ0_spl
<=> sK31_skl = s(sK32_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( ~ sQ0_spl
| sK31_skl = s(sK32_skl) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,definition,
( sQ1_spl
<=> sK31_skl = '0' ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f344,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( times_terminates(X0,X1,X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f345,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| times_terminates(X0,X1,X2)
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f291,f338,f341,f344]) ).
fof(f352,definition,
! [X0,X1] :
( sQ4_spl
<=> ( times_terminates(sK32_skl,X0,X1)
| ~ nat_succeeds(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f353,plain,
! [X0,X1] :
( ~ sQ4_spl
| times_terminates(sK32_skl,X0,X1)
| ~ nat_succeeds(X0) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( sQ2_spl
| sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f293,f352,f341,f344]) ).
fof(f356,definition,
( sQ5_spl
<=> nat_succeeds(sK33_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( ~ sQ5_spl
| nat_succeeds(sK33_skl) ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f294,f356,f344]) ).
fof(f360,definition,
( sQ6_spl
<=> times_terminates(sK31_skl,sK33_skl,sK34_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( sQ6_spl
| ~ times_terminates(sK31_skl,sK33_skl,sK34_skl) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,plain,
( sQ2_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f295,f360,f344]) ).
fof(f935,plain,
! [X0,X1,X2] :
( ~ times_terminates(sK4_skl(X2,X0,X1),X0,sK5_skl(X2,X0,X1))
| times_terminates(X1,X0,X2)
| ~ nat_succeeds(X0) ),
inference(resolution,[status(thm)],[f228,f114]) ).
fof(f2505,plain,
! [X0] :
( ~ sQ0_spl
| X0 = sK32_skl
| s(X0) != sK31_skl ),
inference(paramodulation,[status(thm)],[f339,f62]) ).
fof(f2729,plain,
( sQ6_spl
| sK31_skl = s(sK4_skl(sK34_skl,sK33_skl,sK31_skl)) ),
inference(resolution,[status(thm)],[f362,f112]) ).
fof(f14739,plain,
( ~ sQ0_spl
| sQ6_spl
| sK4_skl(sK34_skl,sK33_skl,sK31_skl) = sK32_skl ),
inference(resolution,[status(thm)],[f2729,f2505]) ).
fof(f14753,plain,
( sQ6_spl
| '0' != sK31_skl ),
inference(paramodulation,[status(thm)],[f2729,f60]) ).
fof(f14898,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ times_terminates(sK32_skl,sK33_skl,sK5_skl(sK34_skl,sK33_skl,sK31_skl))
| times_terminates(sK31_skl,sK33_skl,sK34_skl)
| ~ nat_succeeds(sK33_skl) ),
inference(paramodulation,[status(thm)],[f14739,f935]) ).
fof(f14903,definition,
( sQ718_spl
<=> times_terminates(sK32_skl,sK33_skl,sK5_skl(sK34_skl,sK33_skl,sK31_skl)) ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f14905,plain,
( sQ718_spl
| ~ times_terminates(sK32_skl,sK33_skl,sK5_skl(sK34_skl,sK33_skl,sK31_skl)) ),
inference(component_clause,[status(thm)],[f14903]) ).
fof(f14907,plain,
( ~ sQ0_spl
| ~ sQ718_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f14898,f356,f360,f14903,f338]) ).
fof(f14915,plain,
( ~ sQ4_spl
| sQ718_spl
| ~ nat_succeeds(sK33_skl) ),
inference(resolution,[status(thm)],[f14905,f353]) ).
fof(f14920,plain,
( ~ sQ4_spl
| sQ718_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14915,f357]) ).
fof(f14921,plain,
( ~ sQ4_spl
| sQ718_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f14920]) ).
fof(f14925,plain,
( sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f14753,f341,f360]) ).
fof(f15955,plain,
! [X0,X1] :
( ~ sQ2_spl
| times_terminates(X0,sK36_skl,X1)
| ~ nat_succeeds(X0) ),
inference(resolution,[status(thm)],[f345,f300]) ).
fof(f16021,plain,
( ~ sQ2_spl
| ~ nat_succeeds(sK35_skl) ),
inference(resolution,[status(thm)],[f15955,f301]) ).
fof(f16029,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16021,f299]) ).
fof(f16030,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f16029]) ).
fof(f16031,plain,
$false,
inference(sat_refutation,[status(thm)],[f347,f355,f359,f363,f14907,f14921,f14925,f16030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX034+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n009.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Mon Sep 21 10:22:28 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.58 % Drodi V4.1.1
% 26.06/4.01 % Refutation found
% 26.06/4.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 26.06/4.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.88/4.10 % Elapsed time: 3.518546 seconds
% 26.88/4.10 % CPU time: 27.388422 seconds
% 26.88/4.10 % Total memory used: 305.178 MB
% 26.88/4.10 % Net memory used: 285.855 MB
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