%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG227+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 : n007.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 11:49:02 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 11 unt; 5 def)
% Number of atoms : 185 ( 54 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 204 ( 74 ~; 75 |; 34 &)
% ( 9 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 68 ( 60 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ( ~ r2_hidden(C,k1_closure3(A,B))
=> k1_funct_1(B,C) = k1_xboole_0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_pboole(B,A)
=> ! [C] :
( C = k1_closure3(A,B)
<=> C = a_2_0_closure3(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A,B,C] :
( ( m1_pboole(C,B)
& ~ v1_xboole_0(B) )
=> ( r2_hidden(A,a_2_0_closure3(B,C))
<=> ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
? [A] :
( v1_fraenkel(A)
& v1_finset_1(A)
& v2_funct_1(A)
& v1_funct_1(A)
& v1_relat_1(A)
& v1_xboole_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,plain,
? [A] :
( ? [B] :
( ? [C] :
( k1_funct_1(B,C) != k1_xboole_0
& ~ r2_hidden(C,k1_closure3(A,B))
& m1_subset_1(C,A) )
& m1_pboole(B,A) )
& ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f32,plain,
( k1_funct_1(sK1_skl,sK2_skl) != k1_xboole_0
& ~ r2_hidden(sK2_skl,k1_closure3(sK0_skl,sK1_skl))
& m1_subset_1(sK2_skl,sK0_skl)
& m1_pboole(sK1_skl,sK0_skl)
& ~ v1_xboole_0(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f31]) ).
fof(f33,plain,
~ v1_xboole_0(sK0_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
m1_pboole(sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
m1_subset_1(sK2_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,plain,
~ r2_hidden(sK2_skl,k1_closure3(sK0_skl,sK1_skl)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f37,plain,
k1_funct_1(sK1_skl,sK2_skl) != k1_xboole_0,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f50,plain,
! [A] :
( ! [B] :
( ! [C] :
( C = k1_closure3(A,B)
<=> C = a_2_0_closure3(A,B) )
| ~ m1_pboole(B,A) )
| v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f51,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( C != a_2_0_closure3(A,B)
| C = k1_closure3(A,B) )
& ( C = a_2_0_closure3(A,B)
| C != k1_closure3(A,B) ) )
| ~ m1_pboole(B,A) )
| v1_xboole_0(A) ),
inference(NNF_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( C != a_2_0_closure3(A,B)
| C = k1_closure3(A,B) )
& ! [C] :
( C = a_2_0_closure3(A,B)
| C != k1_closure3(A,B) ) )
| ~ m1_pboole(B,A) )
| v1_xboole_0(A) ),
inference(miniscoping,[status(thm)],[f51]) ).
fof(f53,plain,
! [X0,X1,X2] :
( X2 = a_2_0_closure3(X0,X1)
| X2 != k1_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f64,plain,
! [A,B,C] :
( ( r2_hidden(A,a_2_0_closure3(B,C))
<=> ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) ) )
| ~ m1_pboole(C,B)
| v1_xboole_0(B) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f65,plain,
! [A,B,C] :
( ( ( ! [D] :
( k1_funct_1(C,D) = k1_xboole_0
| A != D
| ~ m1_subset_1(D,B) )
| r2_hidden(A,a_2_0_closure3(B,C)) )
& ( ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) )
| ~ r2_hidden(A,a_2_0_closure3(B,C)) ) )
| ~ m1_pboole(C,B)
| v1_xboole_0(B) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [B,C] :
( ( ! [A] :
( ! [D] :
( k1_funct_1(C,D) = k1_xboole_0
| A != D
| ~ m1_subset_1(D,B) )
| r2_hidden(A,a_2_0_closure3(B,C)) )
& ! [A] :
( ? [D] :
( k1_funct_1(C,D) != k1_xboole_0
& A = D
& m1_subset_1(D,B) )
| ~ r2_hidden(A,a_2_0_closure3(B,C)) ) )
| ~ m1_pboole(C,B)
| v1_xboole_0(B) ),
inference(miniscoping,[status(thm)],[f65]) ).
fof(f67,plain,
! [B,C] :
( ( ! [A] :
( ! [D] :
( k1_funct_1(C,D) = k1_xboole_0
| A != D
| ~ m1_subset_1(D,B) )
| r2_hidden(A,a_2_0_closure3(B,C)) )
& ! [A] :
( ( k1_funct_1(C,sK5_skl(A,C,B)) != k1_xboole_0
& A = sK5_skl(A,C,B)
& m1_subset_1(sK5_skl(A,C,B),B) )
| ~ r2_hidden(A,a_2_0_closure3(B,C)) ) )
| ~ m1_pboole(C,B)
| v1_xboole_0(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(D,sK5_skl(A,C,B))],[f66]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( k1_funct_1(X1,X3) = k1_xboole_0
| X2 != X3
| ~ m1_subset_1(X3,X0)
| r2_hidden(X2,a_2_0_closure3(X0,X1))
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,plain,
( v1_fraenkel(sK6_skl)
& v1_finset_1(sK6_skl)
& v2_funct_1(sK6_skl)
& v1_funct_1(sK6_skl)
& v1_relat_1(sK6_skl)
& v1_xboole_0(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f18]) ).
fof(f73,plain,
v1_xboole_0(sK6_skl),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f106,plain,
! [A] :
( A = k1_xboole_0
| ~ v1_xboole_0(A) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f107,plain,
! [X0] :
( X0 = k1_xboole_0
| ~ v1_xboole_0(X0) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f114,plain,
! [X0,X1] :
( k1_closure3(X0,X1) = a_2_0_closure3(X0,X1)
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f53]) ).
fof(f116,plain,
! [X0,X1,X2] :
( k1_funct_1(X1,X2) = k1_xboole_0
| ~ m1_subset_1(X2,X0)
| r2_hidden(X2,a_2_0_closure3(X0,X1))
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f71]) ).
fof(f118,plain,
( k1_closure3(sK0_skl,sK1_skl) = a_2_0_closure3(sK0_skl,sK1_skl)
| v1_xboole_0(sK0_skl) ),
inference(resolution,[status(thm)],[f114,f34]) ).
fof(f119,definition,
( sQ0_spl
<=> v1_xboole_0(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ0_spl
| v1_xboole_0(sK0_skl) ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,definition,
( sQ1_spl
<=> k1_closure3(sK0_skl,sK1_skl) = a_2_0_closure3(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ1_spl
| k1_closure3(sK0_skl,sK1_skl) = a_2_0_closure3(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f118,f119,f122]) ).
fof(f126,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f33]) ).
fof(f127,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f128,plain,
sK6_skl = k1_xboole_0,
inference(resolution,[status(thm)],[f73,f107]) ).
fof(f129,plain,
( ~ sQ1_spl
| ~ r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl)) ),
inference(backward_demodulation,[status(thm)],[f123,f36]) ).
fof(f130,plain,
k1_funct_1(sK1_skl,sK2_skl) != sK6_skl,
inference(backward_demodulation,[status(thm)],[f128,f37]) ).
fof(f144,plain,
! [X0,X1,X2] :
( k1_funct_1(X1,X2) = sK6_skl
| ~ m1_subset_1(X2,X0)
| r2_hidden(X2,a_2_0_closure3(X0,X1))
| ~ m1_pboole(X1,X0)
| v1_xboole_0(X0) ),
inference(forward_demodulation,[status(thm)],[f128,f116]) ).
fof(f145,plain,
! [X0] :
( k1_funct_1(sK1_skl,X0) = sK6_skl
| ~ m1_subset_1(X0,sK0_skl)
| r2_hidden(X0,a_2_0_closure3(sK0_skl,sK1_skl))
| v1_xboole_0(sK0_skl) ),
inference(resolution,[status(thm)],[f144,f34]) ).
fof(f146,definition,
! [X0] :
( sQ3_spl
<=> ( k1_funct_1(sK1_skl,X0) = sK6_skl
| ~ m1_subset_1(X0,sK0_skl)
| r2_hidden(X0,a_2_0_closure3(sK0_skl,sK1_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f147,plain,
! [X0] :
( ~ sQ3_spl
| k1_funct_1(sK1_skl,X0) = sK6_skl
| ~ m1_subset_1(X0,sK0_skl)
| r2_hidden(X0,a_2_0_closure3(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f145,f119,f146]) ).
fof(f157,plain,
( ~ sQ3_spl
| k1_funct_1(sK1_skl,sK2_skl) = sK6_skl
| r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f147,f35]) ).
fof(f159,definition,
( sQ4_spl
<=> r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ4_spl
| r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,definition,
( sQ5_spl
<=> k1_funct_1(sK1_skl,sK2_skl) = sK6_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ5_spl
| k1_funct_1(sK1_skl,sK2_skl) = sK6_skl ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,plain,
( ~ sQ3_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f157,f159,f162,f146]) ).
fof(f166,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f160,f129]) ).
fof(f167,plain,
( ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f130]) ).
fof(f169,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f170,plain,
$false,
inference(sat_refutation,[status(thm)],[f125,f127,f149,f165,f167,f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 13:04:51 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.42 % Elapsed time: 0.058631 seconds
% 0.09/0.42 % CPU time: 0.151490 seconds
% 0.09/0.42 % Total memory used: 81.377 MB
% 0.09/0.42 % Net memory used: 81.335 MB
%------------------------------------------------------------------------------