TSTP Solution File: SEU055+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU055+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 20:40:57 EDT 2024
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 86 ( 17 unt; 0 def)
% Number of atoms : 249 ( 72 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 274 ( 111 ~; 117 |; 24 &)
% ( 14 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 71 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( in(B,relation_dom(A))
& in(C,relation_dom(A))
& apply(A,B) = apply(A,C) )
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( in(A,relation_dom(B))
=> relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A] :
( ( relation(A)
& function(A) )
=> ( ! [B,C] : relation_image(A,set_difference(B,C)) = set_difference(relation_image(A,B),relation_image(A,C))
=> one_to_one(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( ! [B,C] : relation_image(A,set_difference(B,C)) = set_difference(relation_image(A,B),relation_image(A,C))
=> one_to_one(A) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,axiom,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( one_to_one(A)
<=> ! [B,C] :
( ~ in(B,relation_dom(A))
| ~ in(C,relation_dom(A))
| apply(A,B) != apply(A,C)
| B = C ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f60,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ( ~ one_to_one(A)
| ! [B,C] :
( ~ in(B,relation_dom(A))
| ~ in(C,relation_dom(A))
| apply(A,B) != apply(A,C)
| B = C ) )
& ( one_to_one(A)
| ? [B,C] :
( in(B,relation_dom(A))
& in(C,relation_dom(A))
& apply(A,B) = apply(A,C)
& B != C ) ) ) ),
inference(NNF_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ( ~ one_to_one(A)
| ! [B,C] :
( ~ in(B,relation_dom(A))
| ~ in(C,relation_dom(A))
| apply(A,B) != apply(A,C)
| B = C ) )
& ( one_to_one(A)
| ( in(sk0_1(A),relation_dom(A))
& in(sk0_2(A),relation_dom(A))
& apply(A,sk0_1(A)) = apply(A,sk0_2(A))
& sk0_1(A) != sk0_2(A) ) ) ) ),
inference(skolemization,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_1(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_2(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| apply(X0,sk0_1(X0)) = apply(X0,sk0_2(X0)) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f66,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| sk0_1(X0) != sk0_2(X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f115,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f116,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ~ in(A,relation_dom(B))
| relation_image(B,singleton(A)) = singleton(apply(B,A)) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f118,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [A] :
( ~ in(A,relation_dom(B))
| relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
inference(miniscoping,[status(esa)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| relation_image(X0,singleton(X1)) = singleton(apply(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f118]) ).
fof(f120,plain,
? [A] :
( relation(A)
& function(A)
& ! [B,C] : relation_image(A,set_difference(B,C)) = set_difference(relation_image(A,B),relation_image(A,C))
& ~ one_to_one(A) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f121,plain,
( relation(sk0_14)
& function(sk0_14)
& ! [B,C] : relation_image(sk0_14,set_difference(B,C)) = set_difference(relation_image(sk0_14,B),relation_image(sk0_14,C))
& ~ one_to_one(sk0_14) ),
inference(skolemization,[status(esa)],[f120]) ).
fof(f122,plain,
relation(sk0_14),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f123,plain,
function(sk0_14),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f124,plain,
! [X0,X1] : relation_image(sk0_14,set_difference(X0,X1)) = set_difference(relation_image(sk0_14,X0),relation_image(sk0_14,X1)),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f125,plain,
~ one_to_one(sk0_14),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f128,plain,
! [A,B] :
( ( set_difference(singleton(A),singleton(B)) != singleton(A)
| A != B )
& ( set_difference(singleton(A),singleton(B)) = singleton(A)
| A = B ) ),
inference(NNF_transformation,[status(esa)],[f31]) ).
fof(f129,plain,
( ! [A,B] :
( set_difference(singleton(A),singleton(B)) != singleton(A)
| A != B )
& ! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
| A = B ) ),
inference(miniscoping,[status(esa)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) != singleton(X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f134,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f33]) ).
fof(f135,plain,
( ! [A,B] :
( set_difference(A,B) != empty_set
| subset(A,B) )
& ! [A,B] :
( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f134]) ).
fof(f137,plain,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f135]) ).
fof(f160,plain,
! [X0] : set_difference(singleton(X0),singleton(X0)) != singleton(X0),
inference(destructive_equality_resolution,[status(esa)],[f130]) ).
fof(f165,plain,
( spl0_1
<=> one_to_one(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f166,plain,
( one_to_one(sk0_14)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f2127,plain,
( spl0_110
<=> function(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f2129,plain,
( ~ function(sk0_14)
| spl0_110 ),
inference(component_clause,[status(thm)],[f2127]) ).
fof(f2130,plain,
( spl0_111
<=> in(sk0_1(sk0_14),relation_dom(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f2131,plain,
( in(sk0_1(sk0_14),relation_dom(sk0_14))
| ~ spl0_111 ),
inference(component_clause,[status(thm)],[f2130]) ).
fof(f2133,plain,
( ~ function(sk0_14)
| one_to_one(sk0_14)
| in(sk0_1(sk0_14),relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f63,f122]) ).
fof(f2134,plain,
( ~ spl0_110
| spl0_1
| spl0_111 ),
inference(split_clause,[status(thm)],[f2133,f2127,f165,f2130]) ).
fof(f2135,plain,
( $false
| spl0_110 ),
inference(forward_subsumption_resolution,[status(thm)],[f2129,f123]) ).
fof(f2136,plain,
spl0_110,
inference(contradiction_clause,[status(thm)],[f2135]) ).
fof(f2141,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f125]) ).
fof(f2142,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f2141]) ).
fof(f2303,plain,
( spl0_144
<=> in(sk0_2(sk0_14),relation_dom(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f2304,plain,
( in(sk0_2(sk0_14),relation_dom(sk0_14))
| ~ spl0_144 ),
inference(component_clause,[status(thm)],[f2303]) ).
fof(f2306,plain,
( ~ function(sk0_14)
| one_to_one(sk0_14)
| in(sk0_2(sk0_14),relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f64,f122]) ).
fof(f2307,plain,
( ~ spl0_110
| spl0_1
| spl0_144 ),
inference(split_clause,[status(thm)],[f2306,f2127,f165,f2303]) ).
fof(f2468,plain,
( spl0_177
<=> apply(sk0_14,sk0_1(sk0_14)) = apply(sk0_14,sk0_2(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f2469,plain,
( apply(sk0_14,sk0_1(sk0_14)) = apply(sk0_14,sk0_2(sk0_14))
| ~ spl0_177 ),
inference(component_clause,[status(thm)],[f2468]) ).
fof(f2471,plain,
( ~ function(sk0_14)
| one_to_one(sk0_14)
| apply(sk0_14,sk0_1(sk0_14)) = apply(sk0_14,sk0_2(sk0_14)) ),
inference(resolution,[status(thm)],[f65,f122]) ).
fof(f2472,plain,
( ~ spl0_110
| spl0_1
| spl0_177 ),
inference(split_clause,[status(thm)],[f2471,f2127,f165,f2468]) ).
fof(f2473,plain,
( spl0_178
<=> relation(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f2475,plain,
( ~ relation(sk0_14)
| spl0_178 ),
inference(component_clause,[status(thm)],[f2473]) ).
fof(f2481,plain,
( spl0_180
<=> relation_image(sk0_14,singleton(sk0_1(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f2482,plain,
( relation_image(sk0_14,singleton(sk0_1(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14)))
| ~ spl0_180 ),
inference(component_clause,[status(thm)],[f2481]) ).
fof(f2484,plain,
( ~ relation(sk0_14)
| ~ function(sk0_14)
| relation_image(sk0_14,singleton(sk0_1(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14)))
| ~ spl0_111 ),
inference(resolution,[status(thm)],[f2131,f119]) ).
fof(f2485,plain,
( ~ spl0_178
| ~ spl0_110
| spl0_180
| ~ spl0_111 ),
inference(split_clause,[status(thm)],[f2484,f2473,f2127,f2481,f2130]) ).
fof(f2488,plain,
( $false
| spl0_178 ),
inference(forward_subsumption_resolution,[status(thm)],[f2475,f122]) ).
fof(f2489,plain,
spl0_178,
inference(contradiction_clause,[status(thm)],[f2488]) ).
fof(f2495,plain,
( spl0_182
<=> relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_2(sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f2496,plain,
( relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_2(sk0_14)))
| ~ spl0_182 ),
inference(component_clause,[status(thm)],[f2495]) ).
fof(f2498,plain,
( ~ relation(sk0_14)
| ~ function(sk0_14)
| relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_2(sk0_14)))
| ~ spl0_144 ),
inference(resolution,[status(thm)],[f2304,f119]) ).
fof(f2499,plain,
( ~ spl0_178
| ~ spl0_110
| spl0_182
| ~ spl0_144 ),
inference(split_clause,[status(thm)],[f2498,f2473,f2127,f2495,f2303]) ).
fof(f2502,plain,
! [X0] :
( relation_image(sk0_14,set_difference(singleton(sk0_1(sk0_14)),X0)) = set_difference(singleton(apply(sk0_14,sk0_1(sk0_14))),relation_image(sk0_14,X0))
| ~ spl0_180 ),
inference(paramodulation,[status(thm)],[f2482,f124]) ).
fof(f2503,plain,
( relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14)))
| ~ spl0_177
| ~ spl0_182 ),
inference(forward_demodulation,[status(thm)],[f2469,f2496]) ).
fof(f2505,plain,
! [X0] :
( relation_image(sk0_14,set_difference(singleton(sk0_2(sk0_14)),X0)) = set_difference(singleton(apply(sk0_14,sk0_1(sk0_14))),relation_image(sk0_14,X0))
| ~ spl0_177
| ~ spl0_182 ),
inference(paramodulation,[status(thm)],[f2503,f124]) ).
fof(f3524,plain,
( spl0_346
<=> sk0_1(sk0_14) = sk0_2(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f3527,plain,
( ~ function(sk0_14)
| one_to_one(sk0_14)
| sk0_1(sk0_14) != sk0_2(sk0_14) ),
inference(resolution,[status(thm)],[f66,f122]) ).
fof(f3528,plain,
( ~ spl0_110
| spl0_1
| ~ spl0_346 ),
inference(split_clause,[status(thm)],[f3527,f2127,f165,f3524]) ).
fof(f3558,plain,
! [X0] :
( relation_image(sk0_14,set_difference(singleton(sk0_2(sk0_14)),X0)) = relation_image(sk0_14,set_difference(singleton(sk0_1(sk0_14)),X0))
| ~ spl0_180
| ~ spl0_177
| ~ spl0_182 ),
inference(forward_demodulation,[status(thm)],[f2502,f2505]) ).
fof(f3569,plain,
! [X0] :
( relation_image(sk0_14,singleton(sk0_2(sk0_14))) = relation_image(sk0_14,set_difference(singleton(sk0_1(sk0_14)),singleton(X0)))
| sk0_2(sk0_14) = X0
| ~ spl0_180
| ~ spl0_177
| ~ spl0_182 ),
inference(paramodulation,[status(thm)],[f131,f3558]) ).
fof(f3570,plain,
! [X0] :
( singleton(apply(sk0_14,sk0_1(sk0_14))) = relation_image(sk0_14,set_difference(singleton(sk0_1(sk0_14)),singleton(X0)))
| sk0_2(sk0_14) = X0
| ~ spl0_180
| ~ spl0_177
| ~ spl0_182 ),
inference(forward_demodulation,[status(thm)],[f2503,f3569]) ).
fof(f4066,plain,
! [X0] : set_difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f4169,plain,
! [X0] : empty_set != singleton(X0),
inference(backward_demodulation,[status(thm)],[f4066,f160]) ).
fof(f4171,plain,
! [X0] : relation_image(sk0_14,set_difference(X0,X0)) = empty_set,
inference(paramodulation,[status(thm)],[f124,f4066]) ).
fof(f4172,plain,
relation_image(sk0_14,empty_set) = empty_set,
inference(forward_demodulation,[status(thm)],[f4066,f4171]) ).
fof(f4175,plain,
( spl0_410
<=> singleton(apply(sk0_14,sk0_1(sk0_14))) = relation_image(sk0_14,empty_set) ),
introduced(split_symbol_definition) ).
fof(f4176,plain,
( singleton(apply(sk0_14,sk0_1(sk0_14))) = relation_image(sk0_14,empty_set)
| ~ spl0_410 ),
inference(component_clause,[status(thm)],[f4175]) ).
fof(f4178,plain,
( singleton(apply(sk0_14,sk0_1(sk0_14))) = relation_image(sk0_14,empty_set)
| sk0_2(sk0_14) = sk0_1(sk0_14)
| ~ spl0_180
| ~ spl0_177
| ~ spl0_182 ),
inference(paramodulation,[status(thm)],[f4066,f3570]) ).
fof(f4179,plain,
( spl0_410
| spl0_346
| ~ spl0_180
| ~ spl0_177
| ~ spl0_182 ),
inference(split_clause,[status(thm)],[f4178,f4175,f3524,f2481,f2468,f2495]) ).
fof(f4678,plain,
( singleton(apply(sk0_14,sk0_1(sk0_14))) = empty_set
| ~ spl0_410 ),
inference(forward_demodulation,[status(thm)],[f4172,f4176]) ).
fof(f4679,plain,
( $false
| ~ spl0_410 ),
inference(forward_subsumption_resolution,[status(thm)],[f4678,f4169]) ).
fof(f4680,plain,
~ spl0_410,
inference(contradiction_clause,[status(thm)],[f4679]) ).
fof(f4681,plain,
$false,
inference(sat_refutation,[status(thm)],[f2134,f2136,f2142,f2307,f2472,f2485,f2489,f2499,f3528,f4179,f4680]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU055+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n016.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 20:26:55 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.20/0.51 % Refutation found
% 0.20/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.54 % Elapsed time: 0.179244 seconds
% 0.20/0.54 % CPU time: 1.275180 seconds
% 0.20/0.54 % Total memory used: 83.037 MB
% 0.20/0.54 % Net memory used: 82.026 MB
%------------------------------------------------------------------------------