TSTP Solution File: NUM453+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:29:12 EDT 2023
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 16 unt; 0 def)
% Number of atoms : 186 ( 59 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 180 ( 79 ~; 77 |; 12 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 44 (; 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,conjecture,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
inference(negated_conjecture,[status(cth)],[f48]) ).
fof(f53,plain,
aInteger0(sz00),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f54,plain,
aInteger0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f55,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f56,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f55]) ).
fof(f57,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| aInteger0(sdtpldt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f58,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f61,plain,
! [W0,W1,W2] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| ~ aInteger0(W2)
| sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtpldt0(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [W0,W1] :
( ~ aInteger0(W0)
| ~ aInteger0(W1)
| sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f65,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,sz00) = W0
& W0 = sdtpldt0(sz00,W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f66,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ aInteger0(X0)
| X0 = sdtpldt0(sz00,X0) ),
inference(cnf_transformation,[status(esa)],[f65]) ).
fof(f68,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f69,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(X0)) = sz00 ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f68]) ).
fof(f229,plain,
aInteger0(xp),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f230,plain,
xp != sz00,
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f234,plain,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(pre_NNF_transformation,[status(esa)],[f49]) ).
fof(f235,plain,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(cnf_transformation,[status(esa)],[f234]) ).
fof(f245,plain,
( spl0_0
<=> sdtpldt0(sz10,xp) = sz10 ),
introduced(split_symbol_definition) ).
fof(f246,plain,
( sdtpldt0(sz10,xp) = sz10
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( spl0_1
<=> sdtpldt0(sz10,smndt0(xp)) = sz10 ),
introduced(split_symbol_definition) ).
fof(f249,plain,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f235,f245,f248]) ).
fof(f289,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,xp) = sdtpldt0(xp,X0) ),
inference(resolution,[status(thm)],[f64,f229]) ).
fof(f290,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sz10,X0) ),
inference(resolution,[status(thm)],[f64,f54]) ).
fof(f292,plain,
sdtpldt0(xp,sz10) = sdtpldt0(sz10,xp),
inference(resolution,[status(thm)],[f290,f229]) ).
fof(f306,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(X1,xp)) = sdtpldt0(sdtpldt0(X0,X1),xp) ),
inference(resolution,[status(thm)],[f62,f229]) ).
fof(f307,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| sdtpldt0(X0,sdtpldt0(X1,sz10)) = sdtpldt0(sdtpldt0(X0,X1),sz10) ),
inference(resolution,[status(thm)],[f62,f54]) ).
fof(f314,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(sz10,xp)) = sdtpldt0(sdtpldt0(X0,sz10),xp) ),
inference(resolution,[status(thm)],[f306,f54]) ).
fof(f315,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,sz10),xp)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f246,f314]) ).
fof(f316,plain,
! [X0] :
( sdtpldt0(smndt0(X0),sz10) = sdtpldt0(sdtpldt0(smndt0(X0),sz10),xp)
| ~ aInteger0(X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f315,f56]) ).
fof(f323,plain,
( sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f316,f54]) ).
fof(f345,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[f66,f229]) ).
fof(f347,plain,
( spl0_6
<=> aInteger0(sz00) ),
introduced(split_symbol_definition) ).
fof(f349,plain,
( ~ aInteger0(sz00)
| spl0_6 ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,plain,
( spl0_7
<=> sdtpldt0(sz00,xp) = xp ),
introduced(split_symbol_definition) ).
fof(f351,plain,
( sdtpldt0(sz00,xp) = xp
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( ~ aInteger0(sz00)
| sdtpldt0(sz00,xp) = xp ),
inference(paramodulation,[status(thm)],[f345,f289]) ).
fof(f354,plain,
( ~ spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f353,f347,f350]) ).
fof(f355,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f53]) ).
fof(f356,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f358,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(sdtpldt0(X0,xp)) ),
inference(resolution,[status(thm)],[f58,f229]) ).
fof(f362,plain,
sz10 = sdtpldt0(sz00,sz10),
inference(resolution,[status(thm)],[f67,f54]) ).
fof(f364,plain,
sdtpldt0(xp,smndt0(xp)) = sz00,
inference(resolution,[status(thm)],[f69,f229]) ).
fof(f368,plain,
aInteger0(sdtpldt0(sz10,xp)),
inference(resolution,[status(thm)],[f358,f54]) ).
fof(f437,plain,
sz00 = sdtpldt0(smndt0(sz10),sz10),
inference(resolution,[status(thm)],[f70,f54]) ).
fof(f477,plain,
( spl0_8
<=> aInteger0(smndt0(xp)) ),
introduced(split_symbol_definition) ).
fof(f478,plain,
( aInteger0(smndt0(xp))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f479,plain,
( ~ aInteger0(smndt0(xp))
| spl0_8 ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f485,plain,
( ~ aInteger0(xp)
| spl0_8 ),
inference(resolution,[status(thm)],[f479,f56]) ).
fof(f486,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f229]) ).
fof(f487,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f509,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sdtpldt0(smndt0(xp),sz10)) = sdtpldt0(sdtpldt0(X0,smndt0(xp)),sz10)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f478,f307]) ).
fof(f517,plain,
( sdtpldt0(smndt0(xp),sz10) = sdtpldt0(sz10,smndt0(xp))
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f478,f290]) ).
fof(f518,plain,
( sdtpldt0(smndt0(xp),sz10) = sz10
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f249,f517]) ).
fof(f522,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz10) = sdtpldt0(sdtpldt0(X0,smndt0(xp)),sz10)
| ~ spl0_1
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f518,f509]) ).
fof(f538,plain,
( sdtpldt0(xp,sz10) = sdtpldt0(sdtpldt0(xp,smndt0(xp)),sz10)
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f522,f229]) ).
fof(f539,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sdtpldt0(xp,smndt0(xp)),sz10)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f292,f538]) ).
fof(f540,plain,
( sdtpldt0(sz10,xp) = sdtpldt0(sz00,sz10)
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f364,f539]) ).
fof(f541,plain,
( sdtpldt0(sz10,xp) = sz10
| ~ spl0_1
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f362,f540]) ).
fof(f617,plain,
( spl0_12
<=> aInteger0(sdtpldt0(xp,sz10)) ),
introduced(split_symbol_definition) ).
fof(f619,plain,
( ~ aInteger0(sdtpldt0(xp,sz10))
| spl0_12 ),
inference(component_clause,[status(thm)],[f617]) ).
fof(f625,plain,
( sz00 = sdtpldt0(sdtpldt0(smndt0(sz10),sz10),xp)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f437,f323]) ).
fof(f626,plain,
( sz00 = sdtpldt0(sz00,xp)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f437,f625]) ).
fof(f627,plain,
( sz00 = xp
| ~ spl0_7
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f351,f626]) ).
fof(f628,plain,
( $false
| ~ spl0_7
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f627,f230]) ).
fof(f629,plain,
( ~ spl0_7
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f630,plain,
( ~ aInteger0(sdtpldt0(sz10,xp))
| spl0_12 ),
inference(forward_demodulation,[status(thm)],[f292,f619]) ).
fof(f631,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f630,f368]) ).
fof(f632,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f634,plain,
( spl0_0
| ~ spl0_1
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f541,f245,f248,f477]) ).
fof(f651,plain,
$false,
inference(sat_refutation,[status(thm)],[f251,f354,f356,f487,f629,f632,f634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM453+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:57:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.52 % Refutation found
% 0.20/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.53 % Elapsed time: 0.180789 seconds
% 0.20/0.53 % CPU time: 1.310189 seconds
% 0.20/0.53 % Memory used: 73.468 MB
%------------------------------------------------------------------------------