TSTP Solution File: KLE048+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE048+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 12:15:39 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 34 unt; 0 def)
% Number of atoms : 131 ( 58 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 104 ( 42 ~; 38 |; 14 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 84 (; 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,conjecture,
! [X0] :
( test(X0)
=> star(X0) = one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
~ ! [X0] :
( test(X0)
=> star(X0) = one ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f25,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f26,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f29,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f34,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f35,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f39,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f42,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,B),C),A)
| leq(multiplication(C,star(B)),A) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f49,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(NNF_transformation,[status(esa)],[f18]) ).
fof(f50,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ! [X0,X1] :
( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(miniscoping,[status(esa)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f55,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f56,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f62,plain,
? [X0] :
( test(X0)
& star(X0) != one ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f63,plain,
( test(sk0_1)
& star(sk0_1) != one ),
inference(skolemization,[status(esa)],[f62]) ).
fof(f64,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f65,plain,
star(sk0_1) != one,
inference(cnf_transformation,[status(esa)],[f63]) ).
fof(f70,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),one)
| leq(multiplication(X1,star(X0)),one) ),
inference(paramodulation,[status(thm)],[f29,f43]) ).
fof(f120,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f169,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f36,f39]) ).
fof(f170,plain,
! [X0] : addition(addition(multiplication(star(X0),X0),one),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f23,f169]) ).
fof(f175,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f37,f26]) ).
fof(f191,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f26,f24]) ).
fof(f363,plain,
( spl0_23
<=> leq(one,one) ),
introduced(split_symbol_definition) ).
fof(f365,plain,
( ~ leq(one,one)
| spl0_23 ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f389,plain,
( $false
| spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f365,f175]) ).
fof(f390,plain,
spl0_23,
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f915,plain,
! [X0] :
( c(sk0_1) != X0
| complement(sk0_1,X0) ),
inference(resolution,[status(thm)],[f58,f64]) ).
fof(f1180,plain,
complement(sk0_1,addition(zero,c(sk0_1))),
inference(resolution,[status(thm)],[f915,f120]) ).
fof(f1181,plain,
complement(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f120,f1180]) ).
fof(f1201,plain,
addition(c(sk0_1),sk0_1) = one,
inference(resolution,[status(thm)],[f1181,f53]) ).
fof(f1289,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(paramodulation,[status(thm)],[f23,f1201]) ).
fof(f1557,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f191,f37]) ).
fof(f1561,plain,
addition(sk0_1,one) = addition(sk0_1,c(sk0_1)),
inference(paramodulation,[status(thm)],[f1289,f191]) ).
fof(f1562,plain,
addition(sk0_1,one) = one,
inference(forward_demodulation,[status(thm)],[f1289,f1561]) ).
fof(f1597,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f1557]) ).
fof(f1608,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f24,f1597]) ).
fof(f1656,plain,
( spl0_112
<=> leq(multiplication(one,star(sk0_1)),one) ),
introduced(split_symbol_definition) ).
fof(f1657,plain,
( leq(multiplication(one,star(sk0_1)),one)
| ~ spl0_112 ),
inference(component_clause,[status(thm)],[f1656]) ).
fof(f1659,plain,
( ~ leq(one,one)
| leq(multiplication(one,star(sk0_1)),one) ),
inference(paramodulation,[status(thm)],[f1562,f70]) ).
fof(f1660,plain,
( ~ spl0_23
| spl0_112 ),
inference(split_clause,[status(thm)],[f1659,f363,f1656]) ).
fof(f1666,plain,
( leq(star(sk0_1),one)
| ~ spl0_112 ),
inference(forward_demodulation,[status(thm)],[f29,f1657]) ).
fof(f1833,plain,
( addition(star(sk0_1),one) = one
| ~ spl0_112 ),
inference(resolution,[status(thm)],[f1666,f36]) ).
fof(f1874,plain,
( addition(one,star(sk0_1)) = one
| ~ spl0_112 ),
inference(paramodulation,[status(thm)],[f23,f1833]) ).
fof(f2328,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f23,f1608]) ).
fof(f2965,plain,
! [X0] : leq(one,star(X0)),
inference(paramodulation,[status(thm)],[f170,f2328]) ).
fof(f2986,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(resolution,[status(thm)],[f2965,f36]) ).
fof(f3030,plain,
( one = star(sk0_1)
| ~ spl0_112 ),
inference(paramodulation,[status(thm)],[f1874,f2986]) ).
fof(f3031,plain,
( $false
| ~ spl0_112 ),
inference(forward_subsumption_resolution,[status(thm)],[f3030,f65]) ).
fof(f3032,plain,
~ spl0_112,
inference(contradiction_clause,[status(thm)],[f3031]) ).
fof(f3033,plain,
$false,
inference(sat_refutation,[status(thm)],[f390,f1660,f3032]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE048+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n014.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 : Tue May 30 11:44:33 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.35 % Drodi V3.5.1
% 0.19/0.40 % Refutation found
% 0.19/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42 % Elapsed time: 0.073813 seconds
% 0.19/0.42 % CPU time: 0.432397 seconds
% 0.19/0.42 % Memory used: 36.097 MB
%------------------------------------------------------------------------------