TSTP Solution File: NUM385+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 20:34:34 EDT 2024
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 10 unt; 0 def)
% Number of atoms : 160 ( 45 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 179 ( 69 ~; 73 |; 26 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 77 ( 71 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [A] : in(A,succ(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B] :
( succ(A) = succ(B)
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B] :
( succ(A) = succ(B)
=> A = B ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f37,plain,
! [A,B] :
( ~ in(A,B)
| ~ in(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f37]) ).
fof(f48,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f49,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f50,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f49]) ).
fof(f51,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f56,plain,
! [A,B,C] :
( ( C != set_union2(A,B)
| ! [D] :
( ( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f57,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(miniscoping,[status(esa)],[f56]) ).
fof(f58,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( ~ in(sk0_1(C,B,A),A)
& ~ in(sk0_1(C,B,A),B) ) )
& ( in(sk0_1(C,B,A),C)
| in(sk0_1(C,B,A),A)
| in(sk0_1(C,B,A),B) ) ) ) ),
inference(skolemization,[status(esa)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f58]) ).
fof(f116,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f117,plain,
? [A,B] :
( succ(A) = succ(B)
& A != B ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f118,plain,
( succ(sk0_13) = succ(sk0_14)
& sk0_13 != sk0_14 ),
inference(skolemization,[status(esa)],[f117]) ).
fof(f119,plain,
succ(sk0_13) = succ(sk0_14),
inference(cnf_transformation,[status(esa)],[f118]) ).
fof(f120,plain,
sk0_13 != sk0_14,
inference(cnf_transformation,[status(esa)],[f118]) ).
fof(f134,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f52]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f59]) ).
fof(f140,plain,
in(sk0_14,succ(sk0_13)),
inference(paramodulation,[status(thm)],[f119,f116]) ).
fof(f333,plain,
! [X0,X1] :
( ~ in(X0,succ(X1))
| in(X0,X1)
| in(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f48,f136]) ).
fof(f337,plain,
( spl0_26
<=> in(sk0_14,sk0_13) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( in(sk0_14,sk0_13)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,plain,
( spl0_27
<=> in(sk0_14,singleton(sk0_13)) ),
introduced(split_symbol_definition) ).
fof(f341,plain,
( in(sk0_14,singleton(sk0_13))
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( in(sk0_14,sk0_13)
| in(sk0_14,singleton(sk0_13)) ),
inference(resolution,[status(thm)],[f333,f140]) ).
fof(f344,plain,
( spl0_26
| spl0_27 ),
inference(split_clause,[status(thm)],[f343,f337,f340]) ).
fof(f346,plain,
! [X0] :
( ~ in(X0,succ(sk0_13))
| in(X0,sk0_14)
| in(X0,singleton(sk0_14)) ),
inference(paramodulation,[status(thm)],[f119,f333]) ).
fof(f356,plain,
( spl0_30
<=> in(sk0_13,sk0_14) ),
introduced(split_symbol_definition) ).
fof(f357,plain,
( in(sk0_13,sk0_14)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( spl0_31
<=> in(sk0_13,singleton(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f360,plain,
( in(sk0_13,singleton(sk0_14))
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f359]) ).
fof(f362,plain,
( in(sk0_13,sk0_14)
| in(sk0_13,singleton(sk0_14)) ),
inference(resolution,[status(thm)],[f346,f116]) ).
fof(f363,plain,
( spl0_30
| spl0_31 ),
inference(split_clause,[status(thm)],[f362,f356,f359]) ).
fof(f541,plain,
( ~ in(sk0_14,sk0_13)
| ~ spl0_30 ),
inference(resolution,[status(thm)],[f357,f38]) ).
fof(f542,plain,
( $false
| ~ spl0_26
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f338]) ).
fof(f543,plain,
( ~ spl0_26
| ~ spl0_30 ),
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f550,plain,
( sk0_14 = sk0_13
| ~ spl0_27 ),
inference(resolution,[status(thm)],[f341,f134]) ).
fof(f551,plain,
( $false
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f120]) ).
fof(f552,plain,
~ spl0_27,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f558,plain,
( sk0_13 = sk0_14
| ~ spl0_31 ),
inference(resolution,[status(thm)],[f360,f134]) ).
fof(f559,plain,
( $false
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f120]) ).
fof(f560,plain,
~ spl0_31,
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f561,plain,
$false,
inference(sat_refutation,[status(thm)],[f344,f363,f543,f552,f560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM385+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 20:30:49 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.027232 seconds
% 0.13/0.38 % CPU time: 0.074184 seconds
% 0.13/0.38 % Total memory used: 15.706 MB
% 0.13/0.38 % Net memory used: 15.667 MB
%------------------------------------------------------------------------------