%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG215+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 11:48:58 AM UTC 2026
% Result : Theorem 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 176 ( 50 unt; 28 def)
% Number of atoms : 876 ( 34 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 1184 ( 484 ~; 531 |; 120 &)
% ( 32 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 48 ( 46 usr; 29 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 99 ( 95 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(B)),A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> v1_rmod_5(k1_subset_1(u1_struct_0(B)),A,B) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f5,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( v1_rmod_5(C,A,B)
<=> ! [D] :
( m2_rmod_4(D,A,B,C)
=> ( k5_rmod_4(A,B,D) = k1_rlvect_1(B)
=> k2_rmod_4(A,B,D) = k1_xboole_0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( ( l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [B] :
( ( l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_rmod_4(D,A,B)
=> ( m2_rmod_4(D,A,B,C)
<=> r1_tarski(k2_rmod_4(A,B,D),C) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A))
& v1_xboole_0(k1_subset_1(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A,B,C] :
( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B)
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) )
=> ! [D] :
( m2_rmod_4(D,A,B,C)
=> m1_rmod_4(D,A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
? [A] : v1_xboole_0(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [A] :
( r1_tarski(A,k1_xboole_0)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,plain,
? [A] :
( ? [B] :
( ~ v1_rmod_5(k1_subset_1(u1_struct_0(B)),A,B)
& l1_vectsp_2(B,A)
& v5_vectsp_2(B,A)
& v6_rlvect_1(B)
& v5_rlvect_1(B)
& v4_rlvect_1(B)
& v3_rlvect_1(B)
& ~ v3_struct_0(B) )
& l3_vectsp_1(A)
& v8_vectsp_1(A)
& v7_vectsp_1(A)
& v6_vectsp_1(A)
& v4_group_1(A)
& v6_rlvect_1(A)
& v5_rlvect_1(A)
& v4_rlvect_1(A)
& v3_rlvect_1(A)
& ~ v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f80,plain,
( ~ v1_rmod_5(k1_subset_1(u1_struct_0(sK1_skl)),sK0_skl,sK1_skl)
& l1_vectsp_2(sK1_skl,sK0_skl)
& v5_vectsp_2(sK1_skl,sK0_skl)
& v6_rlvect_1(sK1_skl)
& v5_rlvect_1(sK1_skl)
& v4_rlvect_1(sK1_skl)
& v3_rlvect_1(sK1_skl)
& ~ v3_struct_0(sK1_skl)
& l3_vectsp_1(sK0_skl)
& v8_vectsp_1(sK0_skl)
& v7_vectsp_1(sK0_skl)
& v6_vectsp_1(sK0_skl)
& v4_group_1(sK0_skl)
& v6_rlvect_1(sK0_skl)
& v5_rlvect_1(sK0_skl)
& v4_rlvect_1(sK0_skl)
& v3_rlvect_1(sK0_skl)
& ~ v3_struct_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f79]) ).
fof(f81,plain,
~ v3_struct_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
v3_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f83,plain,
v4_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,plain,
v5_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f85,plain,
v6_rlvect_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f86,plain,
v4_group_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f87,plain,
v6_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f88,plain,
v7_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f89,plain,
v8_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f90,plain,
l3_vectsp_1(sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f91,plain,
~ v3_struct_0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f92,plain,
v3_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f93,plain,
v4_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f94,plain,
v5_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f95,plain,
v6_rlvect_1(sK1_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f96,plain,
v5_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f97,plain,
l1_vectsp_2(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f98,plain,
~ v1_rmod_5(k1_subset_1(u1_struct_0(sK1_skl)),sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f104,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( v1_rmod_5(C,A,B)
<=> ! [D] :
( k2_rmod_4(A,B,D) = k1_xboole_0
| k5_rmod_4(A,B,D) != k1_rlvect_1(B)
| ~ m2_rmod_4(D,A,B,C) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f105,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ? [D] :
( k2_rmod_4(A,B,D) != k1_xboole_0
& k5_rmod_4(A,B,D) = k1_rlvect_1(B)
& m2_rmod_4(D,A,B,C) )
| v1_rmod_5(C,A,B) )
& ( ! [D] :
( k2_rmod_4(A,B,D) = k1_xboole_0
| k5_rmod_4(A,B,D) != k1_rlvect_1(B)
| ~ m2_rmod_4(D,A,B,C) )
| ~ v1_rmod_5(C,A,B) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( ( k2_rmod_4(A,B,sK2_skl(C,B,A)) != k1_xboole_0
& k5_rmod_4(A,B,sK2_skl(C,B,A)) = k1_rlvect_1(B)
& m2_rmod_4(sK2_skl(C,B,A),A,B,C) )
| v1_rmod_5(C,A,B) )
& ( ! [D] :
( k2_rmod_4(A,B,D) = k1_xboole_0
| k5_rmod_4(A,B,D) != k1_rlvect_1(B)
| ~ m2_rmod_4(D,A,B,C) )
| ~ v1_rmod_5(C,A,B) ) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B,A))],[f105]) ).
fof(f108,plain,
! [X0,X1,X2] :
( m2_rmod_4(sK2_skl(X2,X1,X0),X0,X1,X2)
| v1_rmod_5(X2,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f110,plain,
! [X0,X1,X2] :
( k2_rmod_4(X0,X1,sK2_skl(X2,X1,X0)) != k1_xboole_0
| v1_rmod_5(X2,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f113,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( m2_rmod_4(D,A,B,C)
<=> r1_tarski(k2_rmod_4(A,B,D),C) )
| ~ m1_rmod_4(D,A,B) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f114,plain,
! [A] :
( ! [B] :
( ! [C] :
( ! [D] :
( ( ( ~ r1_tarski(k2_rmod_4(A,B,D),C)
| m2_rmod_4(D,A,B,C) )
& ( r1_tarski(k2_rmod_4(A,B,D),C)
| ~ m2_rmod_4(D,A,B,C) ) )
| ~ m1_rmod_4(D,A,B) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B) )
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( r1_tarski(k2_rmod_4(X0,X1,X3),X2)
| ~ m2_rmod_4(X3,X0,X1,X2)
| ~ m1_rmod_4(X3,X0,X1)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f122,plain,
( ! [A] : m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A))
& ! [A] : v1_xboole_0(k1_subset_1(A)) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f123,plain,
! [X0] : v1_xboole_0(k1_subset_1(X0)),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f124,plain,
! [X0] : m1_subset_1(k1_subset_1(X0),k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f160,plain,
! [A,B,C] :
( ! [D] :
( m1_rmod_4(D,A,B)
| ~ m2_rmod_4(D,A,B,C) )
| ~ m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
| ~ l1_vectsp_2(B,A)
| ~ v5_vectsp_2(B,A)
| ~ v6_rlvect_1(B)
| ~ v5_rlvect_1(B)
| ~ v4_rlvect_1(B)
| ~ v3_rlvect_1(B)
| v3_struct_0(B)
| ~ l3_vectsp_1(A)
| ~ v8_vectsp_1(A)
| ~ v7_vectsp_1(A)
| ~ v6_vectsp_1(A)
| ~ v4_group_1(A)
| ~ v6_rlvect_1(A)
| ~ v5_rlvect_1(A)
| ~ v4_rlvect_1(A)
| ~ v3_rlvect_1(A)
| v3_struct_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f33]) ).
fof(f161,plain,
! [X0,X1,X2,X3] :
( m1_rmod_4(X3,X0,X1)
| ~ m2_rmod_4(X3,X0,X1,X2)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f214,plain,
v1_xboole_0(sK20_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(A,sK20_skl)],[f56]) ).
fof(f215,plain,
v1_xboole_0(sK20_skl),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f269,plain,
! [A] :
( A = k1_xboole_0
| ~ r1_tarski(A,k1_xboole_0) ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f270,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r1_tarski(X0,k1_xboole_0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f277,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f278,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f277]) ).
fof(f289,definition,
( sQ0_spl
<=> v3_struct_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ0_spl
| v3_struct_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,definition,
( sQ1_spl
<=> v3_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ1_spl
| ~ v3_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ2_spl
<=> v4_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( sQ2_spl
| ~ v4_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,definition,
( sQ3_spl
<=> v5_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ3_spl
| ~ v5_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,definition,
( sQ4_spl
<=> v6_rlvect_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ4_spl
| ~ v6_rlvect_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,definition,
( sQ5_spl
<=> v4_group_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( sQ5_spl
| ~ v4_group_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ6_spl
<=> v7_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( sQ6_spl
| ~ v7_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,definition,
( sQ7_spl
<=> v8_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( sQ7_spl
| ~ v8_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,definition,
( sQ8_spl
<=> l3_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ8_spl
| ~ l3_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f320,definition,
( sQ10_spl
<=> v6_vectsp_1(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ10_spl
| ~ v6_vectsp_1(sK0_skl) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f326,definition,
( sQ11_spl
<=> v3_struct_0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( ~ sQ11_spl
| v3_struct_0(sK1_skl) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,definition,
( sQ12_spl
<=> v3_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ12_spl
| ~ v3_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ13_spl
<=> v4_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ13_spl
| ~ v4_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ14_spl
<=> v5_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ14_spl
| ~ v5_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,definition,
( sQ15_spl
<=> v6_rlvect_1(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ15_spl
| ~ v6_rlvect_1(sK1_skl) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,definition,
( sQ16_spl
<=> l1_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ16_spl
| ~ l1_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f348,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f90]) ).
fof(f349,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f348]) ).
fof(f350,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f86]) ).
fof(f351,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f352,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f85]) ).
fof(f353,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f84]) ).
fof(f355,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f356,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f297,f83]) ).
fof(f357,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f358,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f294,f82]) ).
fof(f359,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f360,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f81]) ).
fof(f361,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f309,f88]) ).
fof(f363,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f364,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f87]) ).
fof(f365,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f89]) ).
fof(f367,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f369,definition,
( sQ18_spl
<=> m1_subset_1(k1_subset_1(u1_struct_0(sK1_skl)),k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( sQ18_spl
| ~ m1_subset_1(k1_subset_1(u1_struct_0(sK1_skl)),k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f376,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f124]) ).
fof(f377,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f378,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f97]) ).
fof(f379,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f95]) ).
fof(f381,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f382,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f337,f94]) ).
fof(f383,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f382]) ).
fof(f384,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f334,f93]) ).
fof(f385,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f386,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f92]) ).
fof(f387,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f388,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f91]) ).
fof(f389,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f392,definition,
( sQ20_spl
<=> v5_vectsp_2(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( sQ20_spl
| ~ v5_vectsp_2(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f398,definition,
( sQ22_spl
<=> k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(k1_subset_1(u1_struct_0(sK1_skl)),sK1_skl,sK0_skl)) = k1_xboole_0 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( ~ sQ22_spl
| k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(k1_subset_1(u1_struct_0(sK1_skl)),sK1_skl,sK0_skl)) = k1_xboole_0 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f400,plain,
( sQ22_spl
| k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(k1_subset_1(u1_struct_0(sK1_skl)),sK1_skl,sK0_skl)) != k1_xboole_0 ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f408,plain,
( ~ sQ22_spl
| v1_rmod_5(k1_subset_1(u1_struct_0(sK1_skl)),sK0_skl,sK1_skl)
| ~ m1_subset_1(k1_subset_1(u1_struct_0(sK1_skl)),k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f399,f110]) ).
fof(f410,definition,
( sQ24_spl
<=> v1_rmod_5(k1_subset_1(u1_struct_0(sK1_skl)),sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( ~ sQ24_spl
| v1_rmod_5(k1_subset_1(u1_struct_0(sK1_skl)),sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( ~ sQ22_spl
| sQ24_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f408,f289,f292,f295,f298,f301,f304,f320,f307,f310,f313,f326,f329,f332,f335,f338,f392,f341,f369,f410,f398]) ).
fof(f418,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f394,f96]) ).
fof(f419,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f420,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f98]) ).
fof(f421,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f431,plain,
sK20_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f278,f215]) ).
fof(f433,plain,
! [X0] : k1_subset_1(X0) = k1_xboole_0,
inference(resolution,[status(thm)],[f278,f123]) ).
fof(f435,plain,
( sQ22_spl
| k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(k1_subset_1(u1_struct_0(sK1_skl)),sK1_skl,sK0_skl)) != sK20_skl ),
inference(backward_demodulation,[status(thm)],[f431,f400]) ).
fof(f444,plain,
~ v1_rmod_5(sK20_skl,sK0_skl,sK1_skl),
inference(backward_demodulation,[status(thm)],[f447,f98]) ).
fof(f445,plain,
! [X0] : m1_subset_1(sK20_skl,k1_zfmisc_1(X0)),
inference(backward_demodulation,[status(thm)],[f447,f124]) ).
fof(f447,plain,
! [X0] : k1_subset_1(X0) = sK20_skl,
inference(forward_demodulation,[status(thm)],[f431,f433]) ).
fof(f450,definition,
( sQ26_spl
<=> m1_subset_1(sK20_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( sQ26_spl
| ~ m1_subset_1(sK20_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f457,plain,
( sQ22_spl
| k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(sK20_skl,sK1_skl,sK0_skl)) != sK20_skl ),
inference(forward_demodulation,[status(thm)],[f447,f435]) ).
fof(f458,plain,
( sQ26_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f452,f445]) ).
fof(f459,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f458]) ).
fof(f463,definition,
( sQ28_spl
<=> v1_rmod_5(sK20_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( ~ sQ28_spl
| v1_rmod_5(sK20_skl,sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f469,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ r1_tarski(X0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f431,f270]) ).
fof(f470,plain,
! [X0] :
( X0 = sK20_skl
| ~ r1_tarski(X0,sK20_skl) ),
inference(forward_demodulation,[status(thm)],[f431,f469]) ).
fof(f471,plain,
! [X0,X1,X2] :
( ~ m2_rmod_4(X2,X0,X1,sK20_skl)
| ~ m1_rmod_4(X2,X0,X1)
| ~ m1_subset_1(sK20_skl,k1_zfmisc_1(u1_struct_0(X1)))
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| k2_rmod_4(X0,X1,X2) = sK20_skl ),
inference(resolution,[status(thm)],[f470,f115]) ).
fof(f473,plain,
! [X0,X1,X2] :
( ~ m2_rmod_4(X2,X0,X1,sK20_skl)
| ~ m1_rmod_4(X2,X0,X1)
| ~ l1_vectsp_2(X1,X0)
| ~ v5_vectsp_2(X1,X0)
| ~ v6_rlvect_1(X1)
| ~ v5_rlvect_1(X1)
| ~ v4_rlvect_1(X1)
| ~ v3_rlvect_1(X1)
| v3_struct_0(X1)
| ~ l3_vectsp_1(X0)
| ~ v8_vectsp_1(X0)
| ~ v7_vectsp_1(X0)
| ~ v6_vectsp_1(X0)
| ~ v4_group_1(X0)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| k2_rmod_4(X0,X1,X2) = sK20_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f445]) ).
fof(f494,plain,
! [X0,X1,X2] :
( m1_rmod_4(X2,sK0_skl,X0)
| ~ m2_rmod_4(X2,sK0_skl,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f161,f87]) ).
fof(f497,definition,
! [X0,X1,X2] :
( sQ31_spl
<=> ( m1_rmod_4(X2,sK0_skl,X0)
| ~ m2_rmod_4(X2,sK0_skl,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f498,plain,
! [X0,X1,X2] :
( ~ sQ31_spl
| m1_rmod_4(X2,sK0_skl,X0)
| ~ m2_rmod_4(X2,sK0_skl,X0,X1)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_vectsp_2(X0,sK0_skl)
| ~ v5_vectsp_2(X0,sK0_skl)
| ~ v6_rlvect_1(X0)
| ~ v5_rlvect_1(X0)
| ~ v4_rlvect_1(X0)
| ~ v3_rlvect_1(X0)
| v3_struct_0(X0) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f494,f289,f292,f295,f298,f301,f304,f307,f310,f313,f497]) ).
fof(f503,plain,
! [X0,X1] :
( ~ sQ31_spl
| m1_rmod_4(X1,sK0_skl,sK1_skl)
| ~ m2_rmod_4(X1,sK0_skl,sK1_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl) ),
inference(resolution,[status(thm)],[f498,f96]) ).
fof(f504,definition,
! [X0,X1] :
( sQ32_spl
<=> ( m1_rmod_4(X1,sK0_skl,sK1_skl)
| ~ m2_rmod_4(X1,sK0_skl,sK1_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f505,plain,
! [X0,X1] :
( ~ sQ32_spl
| m1_rmod_4(X1,sK0_skl,sK1_skl)
| ~ m2_rmod_4(X1,sK0_skl,sK1_skl,X0)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( ~ sQ31_spl
| sQ32_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f503,f326,f329,f332,f335,f338,f341,f504,f497]) ).
fof(f508,plain,
! [X0] :
( ~ sQ32_spl
| v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| m1_rmod_4(sK2_skl(X0,sK1_skl,sK0_skl),sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f505,f108]) ).
fof(f509,definition,
! [X0] :
( sQ33_spl
<=> ( v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| m1_rmod_4(sK2_skl(X0,sK1_skl,sK0_skl),sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f510,plain,
! [X0] :
( ~ sQ33_spl
| v1_rmod_5(X0,sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| m1_rmod_4(sK2_skl(X0,sK1_skl,sK0_skl),sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( ~ sQ32_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f508,f509,f289,f292,f295,f298,f301,f304,f320,f307,f310,f313,f326,f329,f332,f335,f338,f392,f341,f504]) ).
fof(f513,plain,
! [X0] :
( ~ sQ33_spl
| v1_rmod_5(X0,sK0_skl,sK1_skl)
| m1_rmod_4(sK2_skl(X0,sK1_skl,sK0_skl),sK0_skl,sK1_skl)
| ~ m1_subset_1(X0,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(duplicate_literals_removal,[status(thm)],[f510]) ).
fof(f514,plain,
( ~ sQ33_spl
| m1_rmod_4(sK2_skl(sK20_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl)
| ~ m1_subset_1(sK20_skl,k1_zfmisc_1(u1_struct_0(sK1_skl))) ),
inference(resolution,[status(thm)],[f513,f444]) ).
fof(f516,definition,
( sQ34_spl
<=> m1_rmod_4(sK2_skl(sK20_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( ~ sQ34_spl
| m1_rmod_4(sK2_skl(sK20_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,plain,
( ~ sQ33_spl
| sQ34_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f514,f450,f516,f509]) ).
fof(f521,plain,
( ~ sQ34_spl
| ~ m2_rmod_4(sK2_skl(sK20_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,sK20_skl)
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl)
| k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(sK20_skl,sK1_skl,sK0_skl)) = sK20_skl ),
inference(resolution,[status(thm)],[f517,f473]) ).
fof(f525,definition,
( sQ35_spl
<=> k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(sK20_skl,sK1_skl,sK0_skl)) = sK20_skl ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( ~ sQ35_spl
| k2_rmod_4(sK0_skl,sK1_skl,sK2_skl(sK20_skl,sK1_skl,sK0_skl)) = sK20_skl ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,definition,
( sQ36_spl
<=> m2_rmod_4(sK2_skl(sK20_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f530,plain,
( sQ36_spl
| ~ m2_rmod_4(sK2_skl(sK20_skl,sK1_skl,sK0_skl),sK0_skl,sK1_skl,sK20_skl) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f531,plain,
( ~ sQ34_spl
| ~ sQ36_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f521,f525,f289,f292,f295,f298,f301,f304,f320,f307,f310,f313,f326,f329,f332,f335,f338,f392,f341,f528,f516]) ).
fof(f545,plain,
( ~ sQ35_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f457]) ).
fof(f546,plain,
( ~ sQ35_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f547,plain,
( sQ36_spl
| v1_rmod_5(sK20_skl,sK0_skl,sK1_skl)
| ~ m1_subset_1(sK20_skl,k1_zfmisc_1(u1_struct_0(sK1_skl)))
| ~ l1_vectsp_2(sK1_skl,sK0_skl)
| ~ v5_vectsp_2(sK1_skl,sK0_skl)
| ~ v6_rlvect_1(sK1_skl)
| ~ v5_rlvect_1(sK1_skl)
| ~ v4_rlvect_1(sK1_skl)
| ~ v3_rlvect_1(sK1_skl)
| v3_struct_0(sK1_skl)
| ~ l3_vectsp_1(sK0_skl)
| ~ v8_vectsp_1(sK0_skl)
| ~ v7_vectsp_1(sK0_skl)
| ~ v6_vectsp_1(sK0_skl)
| ~ v4_group_1(sK0_skl)
| ~ v6_rlvect_1(sK0_skl)
| ~ v5_rlvect_1(sK0_skl)
| ~ v4_rlvect_1(sK0_skl)
| ~ v3_rlvect_1(sK0_skl)
| v3_struct_0(sK0_skl) ),
inference(resolution,[status(thm)],[f530,f108]) ).
fof(f548,plain,
( sQ36_spl
| sQ28_spl
| ~ sQ26_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f547,f289,f292,f295,f298,f301,f304,f320,f307,f310,f313,f326,f329,f332,f335,f338,f392,f341,f450,f463,f528]) ).
fof(f549,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f444]) ).
fof(f550,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
$false,
inference(sat_refutation,[status(thm)],[f349,f351,f353,f355,f357,f359,f361,f363,f365,f367,f377,f379,f381,f383,f385,f387,f389,f413,f419,f421,f459,f500,f507,f512,f519,f531,f546,f548,f550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG215+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 13:02:49 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.061259 seconds
% 0.10/0.43 % CPU time: 0.193874 seconds
% 0.10/0.43 % Total memory used: 88.296 MB
% 0.10/0.43 % Net memory used: 88.178 MB
%------------------------------------------------------------------------------