TSTP Solution File: RNG120+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : RNG120+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n024.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 : Tue Apr 30 20:38:04 EDT 2024
% Result : Theorem 211.69s 26.98s
% Output : CNFRefutation 212.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 18
% Syntax : Number of formulae : 73 ( 18 unt; 1 def)
% Number of atoms : 205 ( 18 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 213 ( 81 ~; 78 |; 35 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 8 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 62 ( 56 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [W0] :
( aElement0(W0)
=> ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,definition,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
( aIdeal0(xI)
& xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
( aElementOf0(xu,xI)
& xu != sz00
& ! [W0] :
( ( aElementOf0(W0,xI)
& W0 != sz00 )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
( aElement0(xq)
& aElement0(xr)
& xb = sdtpldt0(sdtasdt0(xq,xu),xr)
& ( xr = sz00
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,conjecture,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f58,plain,
aElement0(sz10),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f59,plain,
! [W0] :
( ~ aElement0(W0)
| aElement0(smndt0(W0)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f60,plain,
! [X0] :
( ~ aElement0(X0)
| aElement0(smndt0(X0)) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f63,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| aElement0(sdtasdt0(W0,W1)) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f64,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| aElement0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f75,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f76,plain,
! [X0,X1] :
( ~ aElement0(X0)
| ~ aElement0(X1)
| sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f75]) ).
fof(f85,plain,
! [W0] :
( ~ aElement0(W0)
| ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0)
& smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f86,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f97,plain,
! [W0] :
( ~ aSet0(W0)
| ! [W1] :
( ~ aElementOf0(W1,W0)
| aElement0(W1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f127,plain,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f128,plain,
! [W0] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ( ? [W2] :
( aElementOf0(W2,W0)
& ~ aElementOf0(sdtpldt0(W1,W2),W0) )
| ? [W2] :
( aElement0(W2)
& ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f127]) ).
fof(f129,plain,
( ! [W0] :
( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ! [W0] :
( aIdeal0(W0)
| ~ aSet0(W0)
| ? [W1] :
( aElementOf0(W1,W0)
& ( ? [W2] :
( aElementOf0(W2,W0)
& ~ aElementOf0(sdtpldt0(W1,W2),W0) )
| ? [W2] :
( aElement0(W2)
& ~ aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f128]) ).
fof(f130,plain,
( ! [W0] :
( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1] :
( ~ aElementOf0(W1,W0)
| ( ! [W2] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ! [W0] :
( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(sk0_8(W0),W0)
& ( ( aElementOf0(sk0_9(W0),W0)
& ~ aElementOf0(sdtpldt0(sk0_8(W0),sk0_9(W0)),W0) )
| ( aElement0(sk0_10(W0))
& ~ aElementOf0(sdtasdt0(sk0_10(W0),sk0_8(W0)),W0) ) ) ) ) ),
inference(skolemization,[status(esa)],[f129]) ).
fof(f131,plain,
! [X0] :
( ~ aIdeal0(X0)
| aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f130]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ~ aIdeal0(X0)
| ~ aElementOf0(X1,X0)
| ~ aElement0(X2)
| aElementOf0(sdtasdt0(X2,X1),X0) ),
inference(cnf_transformation,[status(esa)],[f130]) ).
fof(f210,plain,
aIdeal0(xI),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f219,plain,
( aElementOf0(xu,xI)
& xu != sz00
& ! [W0] :
( ~ aElementOf0(W0,xI)
| W0 = sz00
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f45]) ).
fof(f220,plain,
aElementOf0(xu,xI),
inference(cnf_transformation,[status(esa)],[f219]) ).
fof(f231,plain,
aElement0(xq),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f236,plain,
~ aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f296,plain,
! [X0] :
( ~ aElement0(X0)
| sdtasdt0(X0,xq) = sdtasdt0(xq,X0) ),
inference(resolution,[status(thm)],[f76,f231]) ).
fof(f429,plain,
aSet0(xI),
inference(resolution,[status(thm)],[f131,f210]) ).
fof(f493,plain,
( spl0_7
<=> aElement0(xq) ),
introduced(split_symbol_definition) ).
fof(f495,plain,
( ~ aElement0(xq)
| spl0_7 ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f501,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f231]) ).
fof(f502,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f961,plain,
( spl0_37
<=> aElement0(smndt0(sz10)) ),
introduced(split_symbol_definition) ).
fof(f963,plain,
( ~ aElement0(smndt0(sz10))
| spl0_37 ),
inference(component_clause,[status(thm)],[f961]) ).
fof(f1118,plain,
! [X0] :
( ~ aElementOf0(X0,xI)
| aElement0(X0) ),
inference(resolution,[status(thm)],[f98,f429]) ).
fof(f1120,plain,
aElement0(xu),
inference(resolution,[status(thm)],[f1118,f220]) ).
fof(f1200,plain,
sdtasdt0(xu,xq) = sdtasdt0(xq,xu),
inference(resolution,[status(thm)],[f1120,f296]) ).
fof(f1205,plain,
~ aElementOf0(smndt0(sdtasdt0(xu,xq)),xI),
inference(backward_demodulation,[status(thm)],[f1200,f236]) ).
fof(f1364,plain,
( ~ aElement0(sz10)
| spl0_37 ),
inference(resolution,[status(thm)],[f963,f60]) ).
fof(f1365,plain,
( $false
| spl0_37 ),
inference(forward_subsumption_resolution,[status(thm)],[f1364,f58]) ).
fof(f1366,plain,
spl0_37,
inference(contradiction_clause,[status(thm)],[f1365]) ).
fof(f1776,plain,
( spl0_64
<=> aElement0(sdtasdt0(xu,xq)) ),
introduced(split_symbol_definition) ).
fof(f1777,plain,
( aElement0(sdtasdt0(xu,xq))
| ~ spl0_64 ),
inference(component_clause,[status(thm)],[f1776]) ).
fof(f1791,plain,
( spl0_67
<=> aElement0(xu) ),
introduced(split_symbol_definition) ).
fof(f1793,plain,
( ~ aElement0(xu)
| spl0_67 ),
inference(component_clause,[status(thm)],[f1791]) ).
fof(f1799,plain,
( $false
| spl0_67 ),
inference(forward_subsumption_resolution,[status(thm)],[f1793,f1120]) ).
fof(f1800,plain,
spl0_67,
inference(contradiction_clause,[status(thm)],[f1799]) ).
fof(f1806,plain,
( ~ aElement0(xq)
| ~ aElement0(xu)
| aElement0(sdtasdt0(xu,xq)) ),
inference(paramodulation,[status(thm)],[f1200,f64]) ).
fof(f1807,plain,
( ~ spl0_7
| ~ spl0_67
| spl0_64 ),
inference(split_clause,[status(thm)],[f1806,f493,f1791,f1776]) ).
fof(f2474,plain,
( sdtasdt0(smndt0(sz10),sdtasdt0(xu,xq)) = smndt0(sdtasdt0(xu,xq))
| ~ spl0_64 ),
inference(resolution,[status(thm)],[f1777,f86]) ).
fof(f35211,plain,
! [X0,X1] :
( ~ aElementOf0(X0,xI)
| ~ aElement0(X1)
| aElementOf0(sdtasdt0(X1,X0),xI) ),
inference(resolution,[status(thm)],[f133,f210]) ).
fof(f35230,plain,
( spl0_293
<=> aElementOf0(xu,xI) ),
introduced(split_symbol_definition) ).
fof(f35232,plain,
( ~ aElementOf0(xu,xI)
| spl0_293 ),
inference(component_clause,[status(thm)],[f35230]) ).
fof(f35257,plain,
( $false
| spl0_293 ),
inference(forward_subsumption_resolution,[status(thm)],[f35232,f220]) ).
fof(f35258,plain,
spl0_293,
inference(contradiction_clause,[status(thm)],[f35257]) ).
fof(f50627,plain,
( spl0_298
<=> aElementOf0(smndt0(sdtasdt0(xu,xq)),xI) ),
introduced(split_symbol_definition) ).
fof(f50628,plain,
( aElementOf0(smndt0(sdtasdt0(xu,xq)),xI)
| ~ spl0_298 ),
inference(component_clause,[status(thm)],[f50627]) ).
fof(f50647,plain,
( spl0_302
<=> aElementOf0(sdtasdt0(xu,xq),xI) ),
introduced(split_symbol_definition) ).
fof(f50650,plain,
( ~ aElementOf0(sdtasdt0(xu,xq),xI)
| ~ aElement0(smndt0(sz10))
| aElementOf0(smndt0(sdtasdt0(xu,xq)),xI)
| ~ spl0_64 ),
inference(paramodulation,[status(thm)],[f2474,f35211]) ).
fof(f50651,plain,
( ~ spl0_302
| ~ spl0_37
| spl0_298
| ~ spl0_64 ),
inference(split_clause,[status(thm)],[f50650,f50647,f961,f50627,f1776]) ).
fof(f50682,plain,
( ~ aElementOf0(xu,xI)
| ~ aElement0(xq)
| aElementOf0(sdtasdt0(xu,xq),xI) ),
inference(paramodulation,[status(thm)],[f1200,f35211]) ).
fof(f50683,plain,
( ~ spl0_293
| ~ spl0_7
| spl0_302 ),
inference(split_clause,[status(thm)],[f50682,f35230,f493,f50647]) ).
fof(f50693,plain,
( $false
| ~ spl0_298 ),
inference(forward_subsumption_resolution,[status(thm)],[f50628,f1205]) ).
fof(f50694,plain,
~ spl0_298,
inference(contradiction_clause,[status(thm)],[f50693]) ).
fof(f50695,plain,
$false,
inference(sat_refutation,[status(thm)],[f502,f1366,f1800,f1807,f35258,f50651,f50683,f50694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG120+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n024.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 22:17:51 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.35 % Drodi V3.6.0
% 211.69/26.98 % Refutation found
% 211.69/26.98 % SZS status Theorem for theBenchmark: Theorem is valid
% 211.69/26.98 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 212.78/27.14 % Elapsed time: 26.789165 seconds
% 212.78/27.14 % CPU time: 212.572680 seconds
% 212.78/27.14 % Total memory used: 877.300 MB
% 212.78/27.14 % Net memory used: 821.719 MB
%------------------------------------------------------------------------------