%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW393+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 03:07:47 PM UTC 2026
% Result : Theorem 108.41s 14.63s
% Output : CNFRefutation 85.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 26
% Syntax : Number of formulae : 124 ( 49 unt; 0 def)
% Number of atoms : 238 ( 148 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 197 ( 83 ~; 86 |; 14 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 6 con; 0-3 aty)
% Number of variables : 213 ( 208 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,axiom,
! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [V_A_2,V_x_2,T_b] :
( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
<=> hBOOL(hAPP(V_A_2,V_x_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [V_Pa_2,T_b] :
( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
<=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,axiom,
! [V_Pa_2,T_b] :
( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
<=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Otop(T_b)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,axiom,
! [V_x_2,T_c,T_b] :
( class_Orderings_Obot(T_b)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f146,axiom,
! [V_A_2,T_b] :
( ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
=> c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = V_A_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f419,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Orderings_Oorder(T_b)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
=> c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f629,axiom,
! [V_A_2,T_b] :
( class_Finite__Set_Ofinite(T_b)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1078,axiom,
! [V_a_2,V_b_2,T_b] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
=> ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2030,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2053,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2088,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2138,axiom,
! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2157,axiom,
! [V_l_2] :
( c_Int_OMin = c_Int_OBit1(V_l_2)
<=> c_Int_OMin = V_l_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2226,axiom,
! [V_k_2] :
( c_Int_OBit0(V_k_2) = c_Int_OPls
<=> V_k_2 = c_Int_OPls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2236,axiom,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2260,axiom,
! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2266,axiom,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5007,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5062,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5141,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5143,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5170,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5224,axiom,
! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5230,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5320,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f5324,plain,
! [V_A_2,V_x_2,T_b] :
( ( ~ hBOOL(hAPP(V_A_2,V_x_2))
| hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ( hBOOL(hAPP(V_A_2,V_x_2))
| ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f5325,plain,
( ! [V_A_2,V_x_2] :
( ~ hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
& ! [V_A_2,V_x_2] :
( hBOOL(hAPP(V_A_2,V_x_2))
| ! [T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
inference(miniscoping,[status(thm)],[f5324]) ).
fof(f5327,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ),
inference(cnf_transformation,[status(thm)],[f5325]) ).
fof(f5523,plain,
! [V_Pa_2,T_b] :
( ( ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_Pa_2) ) ),
inference(NNF_transformation,[status(thm)],[f88]) ).
fof(f5524,plain,
( ! [V_Pa_2] :
( ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x))
| ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) )
& ! [V_Pa_2] :
( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_Pa_2) ) ),
inference(miniscoping,[status(thm)],[f5523]) ).
fof(f5525,plain,
( ! [V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,sK16_skl(V_Pa_2)))
| ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2) )
& ! [V_Pa_2] :
( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_Pa_2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(B_x,sK16_skl(V_Pa_2))],[f5524]) ).
fof(f5526,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f5525]) ).
fof(f5527,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,sK16_skl(X1)))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f5525]) ).
fof(f5528,plain,
! [V_Pa_2,T_b] :
( ( ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x))
| hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| hAPP(c_Set_OCollect(T_b),V_Pa_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f5529,plain,
( ! [V_Pa_2] :
( ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x))
| ! [T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ! [V_Pa_2] :
( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| ! [T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(miniscoping,[status(thm)],[f5528]) ).
fof(f5530,plain,
( ! [V_Pa_2] :
( hBOOL(hAPP(V_Pa_2,sK17_skl(V_Pa_2)))
| ! [T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
& ! [V_Pa_2] :
( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
| ! [T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl]),skolemize(B_x,sK17_skl(V_Pa_2))],[f5529]) ).
fof(f5532,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,sK17_skl(X1)))
| hAPP(c_Set_OCollect(X0),X1) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) ),
inference(cnf_transformation,[status(thm)],[f5530]) ).
fof(f5536,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b)
| ~ class_Orderings_Otop(T_b) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f5537,plain,
! [T_b] :
( ! [V_x_2,T_c] : hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b)
| ~ class_Orderings_Otop(T_b) ),
inference(miniscoping,[status(thm)],[f5536]) ).
fof(f5538,plain,
! [X0,X1,X2] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X0)),X2) = c_Orderings_Otop__class_Otop(X0)
| ~ class_Orderings_Otop(X0) ),
inference(cnf_transformation,[status(thm)],[f5537]) ).
fof(f5540,plain,
! [V_x_2,T_c,T_b] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Orderings_Obot(T_b) ),
inference(pre_NNF_transformation,[status(thm)],[f93]) ).
fof(f5541,plain,
! [T_b] :
( ! [V_x_2,T_c] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b)
| ~ class_Orderings_Obot(T_b) ),
inference(miniscoping,[status(thm)],[f5540]) ).
fof(f5542,plain,
! [X0,X1,X2] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2) = c_Orderings_Obot__class_Obot(X0)
| ~ class_Orderings_Obot(X0) ),
inference(cnf_transformation,[status(thm)],[f5541]) ).
fof(f5720,plain,
! [V_A_2,T_b] :
( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = V_A_2
| ? [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ),
inference(pre_NNF_transformation,[status(thm)],[f146]) ).
fof(f5721,plain,
! [V_A_2,T_b] :
( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = V_A_2
| ~ hBOOL(hAPP(hAPP(c_member(T_b),sK28_skl(T_b,V_A_2)),V_A_2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl]),skolemize(B_x,sK28_skl(T_b,V_A_2))],[f5720]) ).
fof(f5722,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = X1
| ~ hBOOL(hAPP(hAPP(c_member(X0),sK28_skl(X0,X1)),X1)) ),
inference(cnf_transformation,[status(thm)],[f5721]) ).
fof(f6502,plain,
! [V_a_2,V_b_2,T_b] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
| ~ class_Orderings_Oorder(T_b) ),
inference(pre_NNF_transformation,[status(thm)],[f419]) ).
fof(f6503,plain,
! [T_b] :
( ! [V_a_2,V_b_2] :
( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) )
| ~ class_Orderings_Oorder(T_b) ),
inference(miniscoping,[status(thm)],[f6502]) ).
fof(f6504,plain,
! [X0,X1,X2] :
( c_SetInterval_Oord__class_OatLeastAtMost(X0,X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),X1),X2))
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f6503]) ).
fof(f7194,plain,
! [V_A_2,T_b] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(pre_NNF_transformation,[status(thm)],[f629]) ).
fof(f7195,plain,
! [T_b] :
( ! [V_A_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
| ~ class_Finite__Set_Ofinite(T_b) ),
inference(miniscoping,[status(thm)],[f7194]) ).
fof(f7196,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[status(thm)],[f7195]) ).
fof(f8569,plain,
! [V_a_2,V_b_2,T_b] :
( ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(pre_NNF_transformation,[status(thm)],[f1078]) ).
fof(f8570,plain,
! [V_a_2,V_b_2,T_b] :
( ( ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
| V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(NNF_transformation,[status(thm)],[f8569]) ).
fof(f8571,plain,
! [T_b] :
( ( ! [V_a_2] :
( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
| ! [V_b_2] : V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) )
& ! [V_a_2] :
( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
| ! [V_b_2] : V_b_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b) ),
inference(miniscoping,[status(thm)],[f8570]) ).
fof(f8572,plain,
! [X0,X1,X2] :
( X2 = c_Groups_Ozero__class_Ozero(X0)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X0),X1),X2)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X0) ),
inference(cnf_transformation,[status(thm)],[f8571]) ).
fof(f11769,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f2030]) ).
fof(f11820,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[status(thm)],[f2053]) ).
fof(f11913,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[status(thm)],[f2088]) ).
fof(f12073,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) = c_Int_Opred(X0),
inference(cnf_transformation,[status(thm)],[f2138]) ).
fof(f12125,plain,
! [V_l_2] :
( ( c_Int_OMin != V_l_2
| c_Int_OMin = c_Int_OBit1(V_l_2) )
& ( c_Int_OMin = V_l_2
| c_Int_OMin != c_Int_OBit1(V_l_2) ) ),
inference(NNF_transformation,[status(thm)],[f2157]) ).
fof(f12126,plain,
( ! [V_l_2] :
( c_Int_OMin != V_l_2
| c_Int_OMin = c_Int_OBit1(V_l_2) )
& ! [V_l_2] :
( c_Int_OMin = V_l_2
| c_Int_OMin != c_Int_OBit1(V_l_2) ) ),
inference(miniscoping,[status(thm)],[f12125]) ).
fof(f12127,plain,
! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ),
inference(cnf_transformation,[status(thm)],[f12126]) ).
fof(f12303,plain,
! [V_k_2] :
( ( V_k_2 != c_Int_OPls
| c_Int_OBit0(V_k_2) = c_Int_OPls )
& ( V_k_2 = c_Int_OPls
| c_Int_OBit0(V_k_2) != c_Int_OPls ) ),
inference(NNF_transformation,[status(thm)],[f2226]) ).
fof(f12304,plain,
( ! [V_k_2] :
( V_k_2 != c_Int_OPls
| c_Int_OBit0(V_k_2) = c_Int_OPls )
& ! [V_k_2] :
( V_k_2 = c_Int_OPls
| c_Int_OBit0(V_k_2) != c_Int_OPls ) ),
inference(miniscoping,[status(thm)],[f12303]) ).
fof(f12305,plain,
! [X0] :
( X0 = c_Int_OPls
| c_Int_OBit0(X0) != c_Int_OPls ),
inference(cnf_transformation,[status(thm)],[f12304]) ).
fof(f12334,plain,
! [X0] : c_Int_OBit0(X0) != c_Int_OMin,
inference(cnf_transformation,[status(thm)],[f2236]) ).
fof(f12397,plain,
! [X0] : c_Int_Opred(c_Int_OBit0(X0)) = c_Int_OBit1(c_Int_Opred(X0)),
inference(cnf_transformation,[status(thm)],[f2260]) ).
fof(f12409,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(cnf_transformation,[status(thm)],[f2266]) ).
fof(f19909,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f5007]) ).
fof(f19964,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[status(thm)],[f5062]) ).
fof(f20043,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[status(thm)],[f5141]) ).
fof(f20045,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[status(thm)],[f5143]) ).
fof(f20080,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f5170]) ).
fof(f20134,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X0,X1),X2),X3) = X2,
inference(cnf_transformation,[status(thm)],[f5224]) ).
fof(f20140,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[status(thm)],[f5230]) ).
fof(f21282,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X2))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X1 ),
inference(forward_demodulation,[status(thm)],[f5320,f5526]) ).
fof(f21283,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)),
inference(destructive_equality_resolution,[status(thm)],[f21282]) ).
fof(f21286,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,sK16_skl(X1)))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 ),
inference(forward_demodulation,[status(thm)],[f5320,f5527]) ).
fof(f21287,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(resolution,[status(thm)],[f21286,f21283]) ).
fof(f21304,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,sK17_skl(X0)))
| X0 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(forward_demodulation,[status(thm)],[f5320,f5532]) ).
fof(f21328,plain,
! [X0,X1] : hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1) = c_Orderings_Otop__class_Otop(tc_HOL_Obool),
inference(resolution,[status(thm)],[f5538,f20043]) ).
fof(f21329,plain,
! [X0,X1] : hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(resolution,[status(thm)],[f5542,f20045]) ).
fof(f21508,plain,
( c_Int_OMin = c_Int_OPls
| c_Int_Opred(c_Int_OMin) != c_Int_OPls ),
inference(paramodulation,[status(thm)],[f12409,f12305]) ).
fof(f21510,plain,
c_Int_Opred(c_Int_OMin) != c_Int_OMin,
inference(paramodulation,[status(thm)],[f12409,f12334]) ).
fof(f21511,plain,
c_Int_Opred(c_Int_OMin) != c_Int_OPls,
inference(forward_subsumption_resolution,[status(thm)],[f21508,f11820]) ).
fof(f21786,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X1,sK28_skl(X0,X1)))
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = X1 ),
inference(resolution,[status(thm)],[f5722,f5327]) ).
fof(f22083,plain,
! [X0] :
( c_Int_OMin = c_Int_Opred(X0)
| c_Int_OMin != c_Int_Opred(c_Int_OBit0(X0)) ),
inference(paramodulation,[status(thm)],[f12397,f12127]) ).
fof(f23362,plain,
! [X0,X1,X2,X3] :
( hBOOL(X2)
| hAPP(c_COMBK(X0,X1),X2) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
inference(paramodulation,[status(thm)],[f20134,f21304]) ).
fof(f26065,plain,
( c_Int_OMin = c_Int_Opred(c_Int_OMin)
| c_Int_OMin != c_Int_Opred(c_Int_Opred(c_Int_OMin)) ),
inference(paramodulation,[status(thm)],[f12409,f22083]) ).
fof(f26068,plain,
c_Int_OMin != c_Int_Opred(c_Int_Opred(c_Int_OMin)),
inference(forward_subsumption_resolution,[status(thm)],[f26065,f21510]) ).
fof(f29257,plain,
( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,c_Int_OMin) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))
| ~ class_Orderings_Oorder(tc_Int_Oint) ),
inference(resolution,[status(thm)],[f6504,f11913]) ).
fof(f29269,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,c_Int_OMin) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)),
inference(forward_subsumption_resolution,[status(thm)],[f29257,f19964]) ).
fof(f37265,plain,
! [X0] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,c_Int_OMin) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),
inference(paramodulation,[status(thm)],[f21287,f29269]) ).
fof(f37289,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,c_Int_OMin),X0) = c_Orderings_Obot__class_Obot(tc_HOL_Obool),
inference(paramodulation,[status(thm)],[f29269,f21329]) ).
fof(f39703,plain,
! [X0,X1] :
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) ),
inference(resolution,[status(thm)],[f8572,f19909]) ).
fof(f39705,plain,
! [X0,X1] :
( X1 = c_Int_OPls
| X0 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) ),
inference(forward_demodulation,[status(thm)],[f11769,f39703]) ).
fof(f39711,plain,
! [X0] :
( c_Int_OMin = c_Int_OPls
| X0 != c_Int_Opred(X0) ),
inference(paramodulation,[status(thm)],[f12073,f39705]) ).
fof(f39715,plain,
! [X0] : X0 != c_Int_Opred(X0),
inference(forward_subsumption_resolution,[status(thm)],[f39711,f11820]) ).
fof(f41356,plain,
! [X0,X1] :
( ~ class_Finite__Set_Ofinite(X1)
| c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = c_Finite__Set_Ofinite(X1) ),
inference(resolution,[status(thm)],[f21786,f7196]) ).
fof(f41458,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = c_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(resolution,[status(thm)],[f41356,f20080]) ).
fof(f41476,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,sK28_skl(X1,X0)))
| c_Finite__Set_Ofinite(tc_Product__Type_Ounit) = X0 ),
inference(backward_demodulation,[status(thm)],[f41458,f21786]) ).
fof(f41494,plain,
! [X0] : hAPP(c_Finite__Set_Ofinite(tc_Product__Type_Ounit),X0) = c_Orderings_Otop__class_Otop(tc_HOL_Obool),
inference(backward_demodulation,[status(thm)],[f41458,f21328]) ).
fof(f45617,plain,
! [X0,X1,X2] :
( hBOOL(X2)
| hAPP(c_COMBK(X0,X1),X2) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,c_Int_OMin) ),
inference(forward_demodulation,[status(thm)],[f37265,f23362]) ).
fof(f45625,plain,
! [X0,X1] :
( hBOOL(X1)
| hAPP(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,c_Int_OMin),X0) = X1 ),
inference(paramodulation,[status(thm)],[f45617,f20134]) ).
fof(f45652,plain,
! [X0] :
( hBOOL(X0)
| c_Orderings_Obot__class_Obot(tc_HOL_Obool) = X0 ),
inference(forward_demodulation,[status(thm)],[f37289,f45625]) ).
fof(f45670,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(resolution,[status(thm)],[f45652,f20140]) ).
fof(f45885,plain,
! [X0] :
( hBOOL(X0)
| c_fFalse = X0 ),
inference(backward_demodulation,[status(thm)],[f45670,f45652]) ).
fof(f46125,plain,
! [X0,X1] :
( c_Finite__Set_Ofinite(tc_Product__Type_Ounit) = X0
| c_fFalse = hAPP(X0,sK28_skl(X1,X0)) ),
inference(resolution,[status(thm)],[f45885,f41476]) ).
fof(f48028,plain,
! [X0,X1,X2] :
( c_Finite__Set_Ofinite(tc_Product__Type_Ounit) = hAPP(c_COMBK(X1,X2),X0)
| c_fFalse = X0 ),
inference(paramodulation,[status(thm)],[f20134,f46125]) ).
fof(f49421,plain,
! [X0,X1] :
( c_fFalse = X1
| hAPP(c_Finite__Set_Ofinite(tc_Product__Type_Ounit),X0) = X1 ),
inference(paramodulation,[status(thm)],[f48028,f20134]) ).
fof(f49449,plain,
! [X0] :
( c_fFalse = X0
| c_Orderings_Otop__class_Otop(tc_HOL_Obool) = X0 ),
inference(forward_demodulation,[status(thm)],[f41494,f49421]) ).
fof(f49452,plain,
c_fFalse = c_Int_Opred(c_Orderings_Otop__class_Otop(tc_HOL_Obool)),
inference(resolution,[status(thm)],[f49449,f39715]) ).
fof(f49464,plain,
! [X0,X1] :
( c_fFalse = X0
| c_fFalse = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f49449,f49449]) ).
fof(f49479,plain,
! [X0] :
( c_fFalse = X0
| c_fFalse = c_Int_Opred(X0) ),
inference(paramodulation,[status(thm)],[f49449,f49452]) ).
fof(f49559,plain,
( c_fFalse = c_Int_Opred(c_Int_OMin)
| c_Int_OMin != c_fFalse ),
inference(paramodulation,[status(thm)],[f49479,f26068]) ).
fof(f49624,plain,
c_fFalse = c_Int_Opred(c_Int_OMin),
inference(forward_subsumption_resolution,[status(thm)],[f49559,f49479]) ).
fof(f49648,plain,
c_fFalse != c_Int_OPls,
inference(backward_demodulation,[status(thm)],[f49624,f21511]) ).
fof(f49652,plain,
! [X0] :
( c_fFalse = X0
| X0 = c_Int_OMin
| c_fFalse = c_Int_Opred(c_fFalse) ),
inference(paramodulation,[status(thm)],[f49464,f49624]) ).
fof(f49661,plain,
! [X0] :
( c_fFalse = X0
| X0 = c_Int_OMin ),
inference(forward_subsumption_resolution,[status(thm)],[f49652,f39715]) ).
fof(f49870,plain,
c_Int_OPls = c_Int_OMin,
inference(resolution,[status(thm)],[f49661,f49648]) ).
fof(f49911,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f49870,f11820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW393+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 09:50:12 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.67/1.01 % Drodi V4.1.1
% 108.41/14.63 % Refutation found
% 108.41/14.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 108.41/14.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.11/14.80 % Elapsed time: 14.437451 seconds
% 4.11/14.80 % CPU time: 109.345733 seconds
% 4.11/14.80 % Total memory used: 1.370 GB
% 4.11/14.80 % Net memory used: 1.333 GB
%------------------------------------------------------------------------------