TSTP Solution File: SEU362+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU362+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:36:49 EDT 2023
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 92 ( 22 unt; 0 def)
% Number of atoms : 274 ( 10 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 293 ( 111 ~; 113 |; 32 &)
% ( 14 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 10 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 102 (; 96 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( rel_str(B)
=> ( subrelstr(B,A)
<=> ( subset(the_carrier(B),the_carrier(A))
& subset(the_InternalRel(B),the_InternalRel(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> rel_str(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [A,B,C] :
( ( in(A,B)
& element(B,powerset(C)) )
=> element(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B,C] :
~ ( in(A,B)
& element(B,powerset(C))
& empty(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,conjecture,
! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( E = C
& F = D
& related(B,E,F) )
=> related(A,C,D) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
~ ! [A] :
( rel_str(A)
=> ! [B] :
( subrelstr(B,A)
=> ! [C] :
( element(C,the_carrier(A))
=> ! [D] :
( element(D,the_carrier(A))
=> ! [E] :
( element(E,the_carrier(B))
=> ! [F] :
( element(F,the_carrier(B))
=> ( ( E = C
& F = D
& related(B,E,F) )
=> related(A,C,D) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
fof(f53,plain,
! [A] :
( ~ rel_str(A)
| ! [B] :
( ~ rel_str(B)
| ( subrelstr(B,A)
<=> ( subset(the_carrier(B),the_carrier(A))
& subset(the_InternalRel(B),the_InternalRel(A)) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f54,plain,
! [A] :
( ~ rel_str(A)
| ! [B] :
( ~ rel_str(B)
| ( ( ~ subrelstr(B,A)
| ( subset(the_carrier(B),the_carrier(A))
& subset(the_InternalRel(B),the_InternalRel(A)) ) )
& ( subrelstr(B,A)
| ~ subset(the_carrier(B),the_carrier(A))
| ~ subset(the_InternalRel(B),the_InternalRel(A)) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f53]) ).
fof(f56,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ rel_str(X1)
| ~ subrelstr(X1,X0)
| subset(the_InternalRel(X1),the_InternalRel(X0)) ),
inference(cnf_transformation,[status(esa)],[f54]) ).
fof(f58,plain,
! [A] :
( ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ! [C] :
( ~ element(C,the_carrier(A))
| ( related(A,B,C)
<=> in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f59,plain,
! [A] :
( ~ rel_str(A)
| ! [B] :
( ~ element(B,the_carrier(A))
| ! [C] :
( ~ element(C,the_carrier(A))
| ( ( ~ related(A,B,C)
| in(ordered_pair(B,C),the_InternalRel(A)) )
& ( related(A,B,C)
| ~ in(ordered_pair(B,C),the_InternalRel(A)) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ related(X0,X1,X2)
| in(ordered_pair(X1,X2),the_InternalRel(X0)) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f64,plain,
! [A] :
( ~ rel_str(A)
| ! [B] :
( ~ subrelstr(B,A)
| rel_str(B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f65,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(X1,X0)
| rel_str(X1) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f111,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f112,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f113,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f36]) ).
fof(f114,plain,
( ! [A,B] :
( ~ element(A,powerset(B))
| subset(A,B) )
& ! [A,B] :
( element(A,powerset(B))
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f113]) ).
fof(f116,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f114]) ).
fof(f117,plain,
! [A,B,C] :
( ~ in(A,B)
| ~ element(B,powerset(C))
| element(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f118,plain,
! [A,C] :
( ! [B] :
( ~ in(A,B)
| ~ element(B,powerset(C)) )
| element(A,C) ),
inference(miniscoping,[status(esa)],[f117]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| element(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f118]) ).
fof(f120,plain,
! [A,B,C] :
( ~ in(A,B)
| ~ element(B,powerset(C))
| ~ empty(C) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f121,plain,
! [C] :
( ! [B] :
( ! [A] : ~ in(A,B)
| ~ element(B,powerset(C)) )
| ~ empty(C) ),
inference(miniscoping,[status(esa)],[f120]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f123,plain,
? [A] :
( rel_str(A)
& ? [B] :
( subrelstr(B,A)
& ? [C] :
( element(C,the_carrier(A))
& ? [D] :
( element(D,the_carrier(A))
& ? [E] :
( element(E,the_carrier(B))
& ? [F] :
( element(F,the_carrier(B))
& E = C
& F = D
& related(B,E,F)
& ~ related(A,C,D) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f40]) ).
fof(f124,plain,
( rel_str(sk0_11)
& subrelstr(sk0_12,sk0_11)
& element(sk0_13,the_carrier(sk0_11))
& element(sk0_14,the_carrier(sk0_11))
& element(sk0_15,the_carrier(sk0_12))
& element(sk0_16,the_carrier(sk0_12))
& sk0_15 = sk0_13
& sk0_16 = sk0_14
& related(sk0_12,sk0_15,sk0_16)
& ~ related(sk0_11,sk0_13,sk0_14) ),
inference(skolemization,[status(esa)],[f123]) ).
fof(f125,plain,
rel_str(sk0_11),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f126,plain,
subrelstr(sk0_12,sk0_11),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f127,plain,
element(sk0_13,the_carrier(sk0_11)),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f128,plain,
element(sk0_14,the_carrier(sk0_11)),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f129,plain,
element(sk0_15,the_carrier(sk0_12)),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f130,plain,
element(sk0_16,the_carrier(sk0_12)),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f131,plain,
sk0_15 = sk0_13,
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f132,plain,
sk0_16 = sk0_14,
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f133,plain,
related(sk0_12,sk0_15,sk0_16),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f134,plain,
~ related(sk0_11,sk0_13,sk0_14),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f143,plain,
element(sk0_13,the_carrier(sk0_12)),
inference(forward_demodulation,[status(thm)],[f131,f129]) ).
fof(f144,plain,
element(sk0_14,the_carrier(sk0_12)),
inference(forward_demodulation,[status(thm)],[f132,f130]) ).
fof(f145,plain,
related(sk0_12,sk0_13,sk0_16),
inference(forward_demodulation,[status(thm)],[f131,f133]) ).
fof(f146,plain,
related(sk0_12,sk0_13,sk0_14),
inference(forward_demodulation,[status(thm)],[f132,f145]) ).
fof(f148,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ subrelstr(X1,X0)
| subset(the_InternalRel(X1),the_InternalRel(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f65]) ).
fof(f151,plain,
( spl0_0
<=> rel_str(sk0_12) ),
introduced(split_symbol_definition) ).
fof(f153,plain,
( ~ rel_str(sk0_12)
| spl0_0 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( spl0_1
<=> element(sk0_13,the_carrier(sk0_12)) ),
introduced(split_symbol_definition) ).
fof(f156,plain,
( ~ element(sk0_13,the_carrier(sk0_12))
| spl0_1 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( spl0_2
<=> element(sk0_14,the_carrier(sk0_12)) ),
introduced(split_symbol_definition) ).
fof(f159,plain,
( ~ element(sk0_14,the_carrier(sk0_12))
| spl0_2 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( spl0_3
<=> in(ordered_pair(sk0_13,sk0_14),the_InternalRel(sk0_12)) ),
introduced(split_symbol_definition) ).
fof(f161,plain,
( in(ordered_pair(sk0_13,sk0_14),the_InternalRel(sk0_12))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( ~ rel_str(sk0_12)
| ~ element(sk0_13,the_carrier(sk0_12))
| ~ element(sk0_14,the_carrier(sk0_12))
| in(ordered_pair(sk0_13,sk0_14),the_InternalRel(sk0_12)) ),
inference(resolution,[status(thm)],[f60,f146]) ).
fof(f164,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f163,f151,f154,f157,f160]) ).
fof(f165,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f144]) ).
fof(f166,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f167,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f143]) ).
fof(f168,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ rel_str(X0)
| ~ subrelstr(sk0_12,X0)
| spl0_0 ),
inference(resolution,[status(thm)],[f153,f65]) ).
fof(f170,plain,
( ~ rel_str(sk0_11)
| spl0_0 ),
inference(resolution,[status(thm)],[f169,f126]) ).
fof(f171,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f125]) ).
fof(f172,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ~ element(ordered_pair(X0,X1),the_InternalRel(X2))
| empty(the_InternalRel(X2))
| ~ rel_str(X2)
| ~ element(X0,the_carrier(X2))
| ~ element(X1,the_carrier(X2))
| related(X2,X0,X1) ),
inference(resolution,[status(thm)],[f112,f61]) ).
fof(f298,plain,
! [X0,X1,X2,X3] :
( empty(the_InternalRel(X0))
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),X3)
| ~ element(X3,powerset(the_InternalRel(X0))) ),
inference(resolution,[status(thm)],[f181,f119]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| related(X0,X1,X2)
| ~ in(ordered_pair(X1,X2),X3)
| ~ element(X3,powerset(the_InternalRel(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f122]) ).
fof(f395,plain,
! [X0] :
( ~ rel_str(X0)
| ~ element(sk0_13,the_carrier(X0))
| ~ element(sk0_14,the_carrier(X0))
| related(X0,sk0_13,sk0_14)
| ~ element(the_InternalRel(sk0_12),powerset(the_InternalRel(X0)))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f299,f161]) ).
fof(f463,plain,
( spl0_47
<=> rel_str(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f465,plain,
( ~ rel_str(sk0_11)
| spl0_47 ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( spl0_48
<=> element(sk0_13,the_carrier(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f468,plain,
( ~ element(sk0_13,the_carrier(sk0_11))
| spl0_48 ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( spl0_49
<=> element(sk0_14,the_carrier(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f471,plain,
( ~ element(sk0_14,the_carrier(sk0_11))
| spl0_49 ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f479,plain,
( $false
| spl0_49 ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f128]) ).
fof(f480,plain,
spl0_49,
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f481,plain,
( $false
| spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f127]) ).
fof(f482,plain,
spl0_48,
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( $false
| spl0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f125]) ).
fof(f484,plain,
spl0_47,
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f809,plain,
( spl0_77
<=> element(the_InternalRel(sk0_12),powerset(the_InternalRel(sk0_11))) ),
introduced(split_symbol_definition) ).
fof(f811,plain,
( ~ element(the_InternalRel(sk0_12),powerset(the_InternalRel(sk0_11)))
| spl0_77 ),
inference(component_clause,[status(thm)],[f809]) ).
fof(f812,plain,
( ~ rel_str(sk0_11)
| ~ element(sk0_13,the_carrier(sk0_11))
| ~ element(sk0_14,the_carrier(sk0_11))
| ~ element(the_InternalRel(sk0_12),powerset(the_InternalRel(sk0_11)))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f395,f134]) ).
fof(f813,plain,
( ~ spl0_47
| ~ spl0_48
| ~ spl0_49
| ~ spl0_77
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f812,f463,f466,f469,f809,f160]) ).
fof(f829,plain,
( ~ subset(the_InternalRel(sk0_12),the_InternalRel(sk0_11))
| spl0_77 ),
inference(resolution,[status(thm)],[f811,f116]) ).
fof(f832,plain,
( spl0_79
<=> subrelstr(sk0_12,sk0_11) ),
introduced(split_symbol_definition) ).
fof(f834,plain,
( ~ subrelstr(sk0_12,sk0_11)
| spl0_79 ),
inference(component_clause,[status(thm)],[f832]) ).
fof(f835,plain,
( ~ rel_str(sk0_11)
| ~ subrelstr(sk0_12,sk0_11)
| spl0_77 ),
inference(resolution,[status(thm)],[f829,f148]) ).
fof(f836,plain,
( ~ spl0_47
| ~ spl0_79
| spl0_77 ),
inference(split_clause,[status(thm)],[f835,f463,f832,f809]) ).
fof(f838,plain,
( $false
| spl0_79 ),
inference(forward_subsumption_resolution,[status(thm)],[f834,f126]) ).
fof(f839,plain,
spl0_79,
inference(contradiction_clause,[status(thm)],[f838]) ).
fof(f840,plain,
$false,
inference(sat_refutation,[status(thm)],[f164,f166,f168,f172,f480,f482,f484,f813,f836,f839]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU362+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 09:09:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.5.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.52 % Elapsed time: 0.179853 seconds
% 0.19/0.52 % CPU time: 0.651775 seconds
% 0.19/0.52 % Memory used: 63.033 MB
%------------------------------------------------------------------------------