TSTP Solution File: SEU125+2 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU125+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 20:41:05 EDT 2024
% Result : Theorem 7.67s 1.39s
% Output : CNFRefutation 7.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 6 unt; 0 def)
% Number of atoms : 133 ( 8 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 147 ( 53 ~; 58 |; 27 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 76 ( 69 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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(f7,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B,C] :
( ( subset(A,B)
& subset(C,B) )
=> subset(set_union2(A,C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B,C] :
( ( subset(A,B)
& subset(C,B) )
=> subset(set_union2(A,C),B) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f48,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)],[f6]) ).
fof(f49,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)],[f48]) ).
fof(f50,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)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f57,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f58,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)],[f57]) ).
fof(f59,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)],[f58]) ).
fof(f60,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)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ in(X2,X0)
| in(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_2(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_2(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f123,plain,
? [A,B,C] :
( subset(A,B)
& subset(C,B)
& ~ subset(set_union2(A,C),B) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f124,plain,
( subset(sk0_8,sk0_9)
& subset(sk0_10,sk0_9)
& ~ subset(set_union2(sk0_8,sk0_10),sk0_9) ),
inference(skolemization,[status(esa)],[f123]) ).
fof(f125,plain,
subset(sk0_8,sk0_9),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f126,plain,
subset(sk0_10,sk0_9),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f127,plain,
~ subset(set_union2(sk0_8,sk0_10),sk0_9),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f51]) ).
fof(f165,plain,
! [X0] :
( ~ in(X0,sk0_10)
| in(X0,sk0_9) ),
inference(resolution,[status(thm)],[f61,f126]) ).
fof(f166,plain,
! [X0] :
( ~ in(X0,sk0_8)
| in(X0,sk0_9) ),
inference(resolution,[status(thm)],[f61,f125]) ).
fof(f621,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X1),X2)
| in(sk0_2(X2,set_union2(X0,X1)),X0)
| in(sk0_2(X2,set_union2(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f62,f131]) ).
fof(f625,plain,
! [X0] :
( subset(X0,sk0_9)
| ~ in(sk0_2(sk0_9,X0),sk0_8) ),
inference(resolution,[status(thm)],[f63,f166]) ).
fof(f2509,plain,
( spl0_80
<=> in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_8) ),
introduced(split_symbol_definition) ).
fof(f2510,plain,
( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_8)
| ~ spl0_80 ),
inference(component_clause,[status(thm)],[f2509]) ).
fof(f2512,plain,
( spl0_81
<=> in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_10) ),
introduced(split_symbol_definition) ).
fof(f2513,plain,
( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_10)
| ~ spl0_81 ),
inference(component_clause,[status(thm)],[f2512]) ).
fof(f2515,plain,
( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_8)
| in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_10) ),
inference(resolution,[status(thm)],[f621,f127]) ).
fof(f2516,plain,
( spl0_80
| spl0_81 ),
inference(split_clause,[status(thm)],[f2515,f2509,f2512]) ).
fof(f3170,plain,
( subset(set_union2(sk0_8,sk0_10),sk0_9)
| ~ spl0_80 ),
inference(resolution,[status(thm)],[f625,f2510]) ).
fof(f3171,plain,
( $false
| ~ spl0_80 ),
inference(forward_subsumption_resolution,[status(thm)],[f3170,f127]) ).
fof(f3172,plain,
~ spl0_80,
inference(contradiction_clause,[status(thm)],[f3171]) ).
fof(f3479,plain,
( in(sk0_2(sk0_9,set_union2(sk0_8,sk0_10)),sk0_9)
| ~ spl0_81 ),
inference(resolution,[status(thm)],[f2513,f165]) ).
fof(f4333,plain,
( subset(set_union2(sk0_8,sk0_10),sk0_9)
| ~ spl0_81 ),
inference(resolution,[status(thm)],[f3479,f63]) ).
fof(f4334,plain,
( $false
| ~ spl0_81 ),
inference(forward_subsumption_resolution,[status(thm)],[f4333,f127]) ).
fof(f4335,plain,
~ spl0_81,
inference(contradiction_clause,[status(thm)],[f4334]) ).
fof(f4336,plain,
$false,
inference(sat_refutation,[status(thm)],[f2516,f3172,f4335]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU125+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 20:16:28 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 7.67/1.39 % Refutation found
% 7.67/1.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.67/1.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.32/1.42 % Elapsed time: 1.059961 seconds
% 8.32/1.42 % CPU time: 8.315668 seconds
% 8.32/1.42 % Total memory used: 128.942 MB
% 8.32/1.42 % Net memory used: 124.494 MB
%------------------------------------------------------------------------------