TSTP Solution File: SET906+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 12:35:30 EDT 2023
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 149 ( 45 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 183 ( 66 ~; 69 |; 39 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 107 (; 95 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
=> in(A,C) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f18,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f19,plain,
! [A,B,C] :
( ( C != unordered_pair(A,B)
| ! [D] :
( ( ~ in(D,C)
| D = A
| D = B )
& ( in(D,C)
| ( D != A
& D != B ) ) ) )
& ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f20,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(miniscoping,[status(esa)],[f19]) ).
fof(f21,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ( ( ~ in(sk0_0(C,B,A),C)
| ( sk0_0(C,B,A) != A
& sk0_0(C,B,A) != B ) )
& ( in(sk0_0(C,B,A),C)
| sk0_0(C,B,A) = A
| sk0_0(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X1 ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f28,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)],[f5]) ).
fof(f29,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)],[f28]) ).
fof(f30,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)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| in(X3,X0)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f37,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f38,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f37]) ).
fof(f39,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_2(B,A),A)
& ~ in(sk0_2(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f58,plain,
? [A,B,C] :
( subset(set_union2(unordered_pair(A,B),C),C)
& ~ in(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f59,plain,
? [A,C] :
( ? [B] : subset(set_union2(unordered_pair(A,B),C),C)
& ~ in(A,C) ),
inference(miniscoping,[status(esa)],[f58]) ).
fof(f60,plain,
( subset(set_union2(unordered_pair(sk0_5,sk0_7),sk0_6),sk0_6)
& ~ in(sk0_5,sk0_6) ),
inference(skolemization,[status(esa)],[f59]) ).
fof(f61,plain,
subset(set_union2(unordered_pair(sk0_5,sk0_7),sk0_6),sk0_6),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
~ in(sk0_5,sk0_6),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f64,plain,
! [X0,X1] : in(X0,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f23]) ).
fof(f68,plain,
! [X0,X1,X2] :
( in(X0,set_union2(X1,X2))
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f33]) ).
fof(f79,plain,
subset(set_union2(sk0_6,unordered_pair(sk0_5,sk0_7)),sk0_6),
inference(paramodulation,[status(thm)],[f18,f61]) ).
fof(f137,plain,
! [X0] :
( ~ in(X0,set_union2(sk0_6,unordered_pair(sk0_5,sk0_7)))
| in(X0,sk0_6) ),
inference(resolution,[status(thm)],[f41,f79]) ).
fof(f141,plain,
! [X0] :
( in(X0,sk0_6)
| ~ in(X0,unordered_pair(sk0_5,sk0_7)) ),
inference(resolution,[status(thm)],[f137,f68]) ).
fof(f144,plain,
in(sk0_5,sk0_6),
inference(resolution,[status(thm)],[f141,f64]) ).
fof(f145,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f144,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET906+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 10:38:03 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 0.14/0.36 % Refutation found
% 0.14/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.60 % Elapsed time: 0.039803 seconds
% 0.25/0.60 % CPU time: 0.025055 seconds
% 0.25/0.60 % Memory used: 3.675 MB
%------------------------------------------------------------------------------