TSTP Solution File: SWW225+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:44:31 EDT 2023
% Result : Theorem 1.78s 0.66s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 76 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 65 ( 29 ~; 26 |; 4 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 36 (; 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> V_m = V_n ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,axiom,
! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [V_w,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1269,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1270,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(negated_conjecture,[status(cth)],[f1269]) ).
fof(f1275,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f1279,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Nat_OSuc(X1)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f1314,plain,
! [V_n,V_m] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| V_m = V_n ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f1315,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f1314]) ).
fof(f1322,plain,
! [V_m_2,V_n_2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(NNF_transformation,[status(esa)],[f23]) ).
fof(f1323,plain,
( ! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
& ! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(miniscoping,[status(esa)],[f1322]) ).
fof(f1324,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),c_Nat_OSuc(X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1323]) ).
fof(f1465,plain,
! [V_m_2,V_n_2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(NNF_transformation,[status(esa)],[f69]) ).
fof(f1466,plain,
( ! [V_m_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
& ! [V_m_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_n_2),hAPP(c_RealDef_Oreal(tc_Nat_Onat),V_m_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
inference(miniscoping,[status(esa)],[f1465]) ).
fof(f1467,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1466]) ).
fof(f1500,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f1501,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[status(esa)],[f81]) ).
fof(f4720,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnf_transformation,[status(esa)],[f1270]) ).
fof(f4890,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(backward_demodulation,[status(thm)],[f1279,f4720]) ).
fof(f4905,plain,
( spl0_0
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) ),
introduced(split_symbol_definition) ).
fof(f4907,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| spl0_0 ),
inference(component_clause,[status(thm)],[f4905]) ).
fof(f4908,plain,
( spl0_1
<=> hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) ),
introduced(split_symbol_definition) ).
fof(f4909,plain,
( hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f4908]) ).
fof(f4911,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))
| hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____) ),
inference(resolution,[status(thm)],[f1315,f1275]) ).
fof(f4912,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f4911,f4905,f4908]) ).
fof(f4931,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f4909,f4890]) ).
fof(f4932,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))))
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1279,f4931]) ).
fof(f4933,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f4932,f1501]) ).
fof(f4934,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f4933]) ).
fof(f5441,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| spl0_0 ),
inference(resolution,[status(thm)],[f4907,f1324]) ).
fof(f5442,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____)))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f1279,f5441]) ).
fof(f5460,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____)))),
inference(resolution,[status(thm)],[f4890,f1500]) ).
fof(f7254,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Nat_OSuc(v_N2____))),
inference(resolution,[status(thm)],[f5460,f1467]) ).
fof(f7255,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f7254,f5442]) ).
fof(f7256,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f7255]) ).
fof(f7257,plain,
$false,
inference(sat_refutation,[status(thm)],[f4912,f4934,f7256]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:57:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.43 % Drodi V3.5.1
% 1.78/0.66 % Refutation found
% 1.78/0.66 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.78/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.78/0.69 % Elapsed time: 0.343367 seconds
% 1.78/0.69 % CPU time: 1.946194 seconds
% 1.78/0.69 % Memory used: 163.322 MB
%------------------------------------------------------------------------------