TSTP Solution File: GRP665+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP665+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 12:12:30 EDT 2023
% Result : Theorem 0.16s 0.34s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 54 ( 33 unt; 0 def)
% Number of atoms : 82 ( 58 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 24 ~; 21 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 69 (; 61 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C,B,A] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [C,B,A] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : mult(op_c,A) = mult(A,op_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [X0,X1] :
( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [X0,X1] :
( mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1)
& mult(mult(X0,op_c),X1) = mult(X0,mult(op_c,X1))
& mult(mult(X0,X1),op_c) = mult(X0,mult(X1,op_c)) ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f13,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f14,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f15,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] : mult(X0,mult(X1,X2)) = mult(rd(mult(X0,X1),X0),mult(X0,X2)),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),ld(X2,mult(X1,X2))),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f20,plain,
! [X0] : mult(op_c,X0) = mult(X0,op_c),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f21,plain,
? [X0,X1] :
( mult(op_c,mult(X0,X1)) != mult(mult(op_c,X0),X1)
| mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
| mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c)) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f22,plain,
( ? [X0,X1] : mult(op_c,mult(X0,X1)) != mult(mult(op_c,X0),X1)
| ? [X0,X1] : mult(mult(X0,op_c),X1) != mult(X0,mult(op_c,X1))
| ? [X0,X1] : mult(mult(X0,X1),op_c) != mult(X0,mult(X1,op_c)) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
( mult(op_c,mult(sk0_0,sk0_1)) != mult(mult(op_c,sk0_0),sk0_1)
| mult(mult(sk0_2,op_c),sk0_3) != mult(sk0_2,mult(op_c,sk0_3))
| mult(mult(sk0_4,sk0_5),op_c) != mult(sk0_4,mult(sk0_5,op_c)) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f24,plain,
( mult(op_c,mult(sk0_0,sk0_1)) != mult(mult(op_c,sk0_0),sk0_1)
| mult(mult(sk0_2,op_c),sk0_3) != mult(sk0_2,mult(op_c,sk0_3))
| mult(mult(sk0_4,sk0_5),op_c) != mult(sk0_4,mult(sk0_5,op_c)) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
( spl0_0
<=> mult(op_c,mult(sk0_0,sk0_1)) = mult(mult(op_c,sk0_0),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f27,plain,
( mult(op_c,mult(sk0_0,sk0_1)) != mult(mult(op_c,sk0_0),sk0_1)
| spl0_0 ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( spl0_1
<=> mult(mult(sk0_2,op_c),sk0_3) = mult(sk0_2,mult(op_c,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f30,plain,
( mult(mult(sk0_2,op_c),sk0_3) != mult(sk0_2,mult(op_c,sk0_3))
| spl0_1 ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,plain,
( spl0_2
<=> mult(mult(sk0_4,sk0_5),op_c) = mult(sk0_4,mult(sk0_5,op_c)) ),
introduced(split_symbol_definition) ).
fof(f33,plain,
( mult(mult(sk0_4,sk0_5),op_c) != mult(sk0_4,mult(sk0_5,op_c))
| spl0_2 ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f24,f25,f28,f31]) ).
fof(f35,plain,
( mult(op_c,mult(sk0_4,sk0_5)) != mult(sk0_4,mult(sk0_5,op_c))
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f20,f33]) ).
fof(f36,plain,
( mult(op_c,mult(sk0_4,sk0_5)) != mult(sk0_4,mult(op_c,sk0_5))
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f20,f35]) ).
fof(f44,plain,
! [X0] : ld(op_c,mult(X0,op_c)) = X0,
inference(paramodulation,[status(thm)],[f20,f13]) ).
fof(f69,plain,
! [X0] : ld(op_c,X0) = rd(X0,op_c),
inference(paramodulation,[status(thm)],[f14,f44]) ).
fof(f79,plain,
! [X0] : rd(mult(X0,op_c),X0) = op_c,
inference(paramodulation,[status(thm)],[f20,f15]) ).
fof(f98,plain,
! [X0,X1] : mult(X0,mult(op_c,X1)) = mult(op_c,mult(X0,X1)),
inference(paramodulation,[status(thm)],[f79,f18]) ).
fof(f123,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(rd(mult(op_c,X0),op_c),mult(X1,op_c)),
inference(paramodulation,[status(thm)],[f20,f18]) ).
fof(f124,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(ld(op_c,mult(op_c,X0)),mult(X1,op_c)),
inference(forward_demodulation,[status(thm)],[f69,f123]) ).
fof(f125,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(X0,mult(X1,op_c)),
inference(forward_demodulation,[status(thm)],[f13,f124]) ).
fof(f133,plain,
( $false
| spl0_2 ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f98]) ).
fof(f134,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f159,plain,
! [X0,X1] : mult(op_c,mult(X0,rd(X1,op_c))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f14,f125]) ).
fof(f160,plain,
! [X0,X1] : mult(op_c,mult(X0,ld(op_c,X1))) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f69,f159]) ).
fof(f166,plain,
! [X0,X1] : ld(op_c,mult(X0,mult(X1,op_c))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f125,f13]) ).
fof(f293,plain,
! [X0,X1] : ld(op_c,mult(X0,X1)) = mult(X0,ld(op_c,X1)),
inference(paramodulation,[status(thm)],[f160,f13]) ).
fof(f680,plain,
! [X0,X1] : mult(mult(X0,X1),op_c) = mult(mult(op_c,X0),ld(op_c,mult(X1,op_c))),
inference(paramodulation,[status(thm)],[f20,f19]) ).
fof(f681,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),ld(op_c,mult(X1,op_c))),
inference(forward_demodulation,[status(thm)],[f20,f680]) ).
fof(f682,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = ld(op_c,mult(mult(op_c,X0),mult(X1,op_c))),
inference(forward_demodulation,[status(thm)],[f293,f681]) ).
fof(f683,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(op_c,X0),X1),
inference(forward_demodulation,[status(thm)],[f166,f682]) ).
fof(f691,plain,
! [X0,X1] : mult(mult(X0,X1),op_c) = mult(mult(X0,op_c),X1),
inference(paramodulation,[status(thm)],[f44,f19]) ).
fof(f692,plain,
! [X0,X1] : mult(op_c,mult(X0,X1)) = mult(mult(X0,op_c),X1),
inference(forward_demodulation,[status(thm)],[f20,f691]) ).
fof(f747,plain,
( mult(op_c,mult(sk0_0,sk0_1)) != mult(op_c,mult(sk0_0,sk0_1))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f683,f27]) ).
fof(f748,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f747]) ).
fof(f749,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f748]) ).
fof(f755,plain,
( mult(op_c,mult(sk0_2,sk0_3)) != mult(sk0_2,mult(op_c,sk0_3))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f692,f30]) ).
fof(f756,plain,
( mult(op_c,mult(sk0_2,sk0_3)) != mult(op_c,mult(sk0_2,sk0_3))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f98,f755]) ).
fof(f757,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f756]) ).
fof(f758,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f757]) ).
fof(f759,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f134,f749,f758]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP665+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31 % Computer : n019.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue May 30 11:32:40 EDT 2023
% 0.16/0.32 % CPUTime :
% 0.16/0.32 % Drodi V3.5.1
% 0.16/0.34 % Refutation found
% 0.16/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.58 % Elapsed time: 0.037975 seconds
% 0.19/0.58 % CPU time: 0.049183 seconds
% 0.19/0.58 % Memory used: 6.432 MB
%------------------------------------------------------------------------------