TSTP Solution File: SET928+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET928+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 12:35:33 EDT 2023
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 3 unt; 0 def)
% Number of atoms : 104 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 115 ( 53 ~; 43 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 52 (; 46 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
~ ( disjoint(unordered_pair(A,B),C)
& in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] :
~ ( ~ in(A,B)
& ~ in(C,B)
& ~ disjoint(unordered_pair(A,C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(A,C)
& ~ in(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<=> ( ~ in(A,C)
& ~ in(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f20,plain,
! [A,B,C] :
( ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f21,plain,
! [A,C] :
( ! [B] : ~ disjoint(unordered_pair(A,B),C)
| ~ in(A,C) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [A,B,C] :
( in(A,B)
| in(C,B)
| disjoint(unordered_pair(A,C),B) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f24,plain,
! [X0,X1,X2] :
( in(X0,X1)
| in(X2,X1)
| disjoint(unordered_pair(X0,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
? [A,B,C] :
( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
<~> ( ~ in(A,C)
& ~ in(B,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f26,plain,
? [A,B,C] :
( ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
| ( ~ in(A,C)
& ~ in(B,C) ) )
& ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
| in(A,C)
| in(B,C) ) ),
inference(NNF_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
( ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
| ( ~ in(sk0_2,sk0_4)
& ~ in(sk0_3,sk0_4) ) )
& ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3)
| in(sk0_2,sk0_4)
| in(sk0_3,sk0_4) ) ),
inference(skolemization,[status(esa)],[f26]) ).
fof(f28,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
| ~ in(sk0_2,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
| ~ in(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f30,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3)
| in(sk0_2,sk0_4)
| in(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f31,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| set_difference(A,B) = A )
& ( disjoint(A,B)
| set_difference(A,B) != A ) ),
inference(NNF_transformation,[status(esa)],[f10]) ).
fof(f32,plain,
( ! [A,B] :
( ~ disjoint(A,B)
| set_difference(A,B) = A )
& ! [A,B] :
( disjoint(A,B)
| set_difference(A,B) != A ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_difference(X0,X1) = X0 ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
( spl0_0
<=> set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f36,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) = unordered_pair(sk0_2,sk0_3)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3)
| spl0_0 ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,plain,
( spl0_1
<=> in(sk0_2,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f39,plain,
( in(sk0_2,sk0_4)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f28,f35,f38]) ).
fof(f42,plain,
( spl0_2
<=> in(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f45,plain,
( spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f29,f35,f42]) ).
fof(f46,plain,
( ~ spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f30,f35,f38,f42]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ disjoint(unordered_pair(X0,X1),X2)
| ~ in(X1,X2) ),
inference(paramodulation,[status(thm)],[f13,f22]) ).
fof(f64,plain,
( disjoint(unordered_pair(sk0_2,sk0_3),sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f36,f34]) ).
fof(f75,plain,
( ~ in(sk0_3,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f64,f47]) ).
fof(f76,plain,
( ~ in(sk0_2,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f64,f22]) ).
fof(f77,plain,
( $false
| ~ spl0_1
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f39]) ).
fof(f78,plain,
( ~ spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( ~ disjoint(unordered_pair(sk0_2,sk0_3),sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f37,f33]) ).
fof(f80,plain,
( in(sk0_2,sk0_4)
| in(sk0_3,sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f79,f24]) ).
fof(f81,plain,
( spl0_1
| spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f80,f38,f42,f35]) ).
fof(f83,plain,
( ~ spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f75,f42,f35]) ).
fof(f84,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f45,f46,f78,f81,f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET928+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n022.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 : Tue May 30 10:16:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 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
% 0.22/0.62 % Elapsed time: 0.044000 seconds
% 0.22/0.62 % CPU time: 0.023339 seconds
% 0.22/0.62 % Memory used: 3.604 MB
%------------------------------------------------------------------------------