TSTP Solution File: GRP748+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP748+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 12:12:38 EDT 2023
% Result : Theorem 96.17s 13.23s
% Output : CNFRefutation 97.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 82 ( 52 unt; 0 def)
% Number of atoms : 122 ( 121 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 13 ~; 34 |; 6 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 13 con; 0-2 aty)
% Number of variables : 169 (; 157 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [C,B,A] : mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,A] : mult(mult(A,B),i(B)) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [B,A] :
( mult(A,B) = mult(B,A)
| mult(i(A),mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
( ! [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)
| ! [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)
| ! [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)
| ! [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ( ! [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)
| ! [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)
| ! [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)
| ! [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f16,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f17,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f18,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f19,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f20,plain,
! [X0,X1,X2] : mult(mult(mult(X0,X1),X2),X1) = mult(X0,mult(mult(X1,X2),X1)),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f21,plain,
! [X0,X1] : mult(mult(X0,X1),i(X1)) = X0,
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f22,plain,
! [X0] : mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f23,plain,
! [X0] : mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f24,plain,
! [X0,X1] :
( mult(X0,X1) = mult(X1,X0)
| mult(i(X0),mult(X0,X1)) = X1 ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f25,plain,
( ? [X0,X1,X2] : mult(X2,mult(X0,mult(X2,X1))) != mult(mult(mult(X2,X0),X2),X1)
& ? [X3,X4,X5] : mult(X3,mult(X5,mult(X4,X5))) != mult(mult(mult(X3,X5),X4),X5)
& ? [X6,X7,X8] : mult(mult(X8,X6),mult(X7,X8)) != mult(mult(X8,mult(X6,X7)),X8)
& ? [X9,X10,X11] : mult(mult(X11,X9),mult(X10,X11)) != mult(X11,mult(mult(X9,X10),X11)) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f26,plain,
( mult(sk0_2,mult(sk0_0,mult(sk0_2,sk0_1))) != mult(mult(mult(sk0_2,sk0_0),sk0_2),sk0_1)
& mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(mult(mult(sk0_3,sk0_5),sk0_4),sk0_5)
& mult(mult(sk0_8,sk0_6),mult(sk0_7,sk0_8)) != mult(mult(sk0_8,mult(sk0_6,sk0_7)),sk0_8)
& mult(mult(sk0_11,sk0_9),mult(sk0_10,sk0_11)) != mult(sk0_11,mult(mult(sk0_9,sk0_10),sk0_11)) ),
inference(skolemization,[status(esa)],[f25]) ).
fof(f28,plain,
mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(mult(mult(sk0_3,sk0_5),sk0_4),sk0_5),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f31,plain,
mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(sk0_3,mult(mult(sk0_5,sk0_4),sk0_5)),
inference(backward_demodulation,[status(thm)],[f20,f28]) ).
fof(f759,plain,
! [X0,X1] : mult(mult(X0,X1),X1) = mult(X0,mult(mult(X1,unit),X1)),
inference(paramodulation,[status(thm)],[f18,f20]) ).
fof(f760,plain,
! [X0,X1] : mult(mult(X0,X1),X1) = mult(X0,mult(X1,X1)),
inference(forward_demodulation,[status(thm)],[f18,f759]) ).
fof(f979,plain,
! [X0,X1] : mult(unit,X0) = mult(X1,mult(mult(X0,i(mult(X1,X0))),X0)),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f980,plain,
! [X0,X1] : X0 = mult(X1,mult(mult(X0,i(mult(X1,X0))),X0)),
inference(forward_demodulation,[status(thm)],[f19,f979]) ).
fof(f1199,plain,
! [X0,X1] : mult(mult(unit,X0),X1) = mult(i(X1),mult(mult(X1,X0),X1)),
inference(paramodulation,[status(thm)],[f23,f20]) ).
fof(f1200,plain,
! [X0,X1] : mult(X0,X1) = mult(i(X1),mult(mult(X1,X0),X1)),
inference(forward_demodulation,[status(thm)],[f19,f1199]) ).
fof(f1243,plain,
! [X0,X1] :
( mult(X0,i(mult(X1,X0))) = i(X1)
| mult(X1,X0) = mult(X0,X1) ),
inference(paramodulation,[status(thm)],[f24,f21]) ).
fof(f1245,plain,
! [X0,X1] :
( ld(i(X0),X1) = mult(X0,X1)
| mult(X0,X1) = mult(X1,X0) ),
inference(paramodulation,[status(thm)],[f24,f15]) ).
fof(f1270,plain,
! [X0] : mult(unit,X0) = mult(i(X0),mult(X0,X0)),
inference(paramodulation,[status(thm)],[f23,f760]) ).
fof(f1271,plain,
! [X0] : X0 = mult(i(X0),mult(X0,X0)),
inference(forward_demodulation,[status(thm)],[f19,f1270]) ).
fof(f1284,plain,
! [X0] : mult(unit,i(X0)) = mult(X0,mult(i(X0),i(X0))),
inference(paramodulation,[status(thm)],[f22,f760]) ).
fof(f1285,plain,
! [X0] : i(X0) = mult(X0,mult(i(X0),i(X0))),
inference(forward_demodulation,[status(thm)],[f19,f1284]) ).
fof(f1379,plain,
! [X0] : mult(X0,i(mult(X0,X0))) = i(X0),
inference(paramodulation,[status(thm)],[f1271,f21]) ).
fof(f1552,plain,
! [X0] : ld(X0,i(X0)) = i(mult(X0,X0)),
inference(paramodulation,[status(thm)],[f1379,f15]) ).
fof(f1709,plain,
! [X0] : mult(i(X0),i(mult(i(X0),i(X0)))) = X0,
inference(paramodulation,[status(thm)],[f1285,f21]) ).
fof(f1710,plain,
! [X0] : mult(i(X0),ld(i(X0),i(i(X0)))) = X0,
inference(forward_demodulation,[status(thm)],[f1552,f1709]) ).
fof(f1711,plain,
! [X0] : i(i(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f14,f1710]) ).
fof(f2019,plain,
! [X0,X1] : mult(mult(X0,i(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f1711,f21]) ).
fof(f2028,plain,
! [X0,X1] : mult(X0,X1) = rd(X0,i(X1)),
inference(paramodulation,[status(thm)],[f16,f2019]) ).
fof(f2113,plain,
! [X0,X1] : rd(X0,X1) = mult(X0,i(X1)),
inference(paramodulation,[status(thm)],[f2019,f17]) ).
fof(f2114,plain,
! [X0,X1] : ld(mult(X0,i(X1)),X0) = X1,
inference(paramodulation,[status(thm)],[f2019,f15]) ).
fof(f2358,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f2113,f2114]) ).
fof(f2717,plain,
! [X0,X1] : X0 = mult(X1,mult(rd(X0,mult(X1,X0)),X0)),
inference(forward_demodulation,[status(thm)],[f2113,f980]) ).
fof(f2782,plain,
! [X0,X1] : ld(X0,X1) = mult(rd(X1,mult(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f2717,f15]) ).
fof(f3832,plain,
! [X0,X1] : ld(i(X0),mult(X1,X0)) = mult(mult(X0,X1),X0),
inference(paramodulation,[status(thm)],[f1200,f15]) ).
fof(f6803,plain,
! [X0,X1] : rd(ld(X0,X1),X1) = rd(X1,mult(X0,X1)),
inference(paramodulation,[status(thm)],[f2782,f17]) ).
fof(f6804,plain,
! [X0,X1] : ld(rd(X0,mult(X1,X0)),ld(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f2782,f15]) ).
fof(f13517,plain,
! [X0,X1] :
( rd(X0,mult(X1,X0)) = i(X1)
| mult(X1,X0) = mult(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f2113,f1243]) ).
fof(f13615,plain,
! [X0,X1] :
( ld(i(X0),ld(X0,X1)) = X1
| mult(X0,X1) = mult(X1,X0) ),
inference(paramodulation,[status(thm)],[f13517,f6804]) ).
fof(f26707,plain,
! [X0,X1] :
( ld(X0,X1) = mult(i(X0),X1)
| mult(i(X0),X1) = mult(X1,i(X0)) ),
inference(paramodulation,[status(thm)],[f1711,f1245]) ).
fof(f26708,plain,
! [X0,X1] :
( ld(X0,X1) = mult(i(X0),X1)
| mult(i(X0),X1) = rd(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f2113,f26707]) ).
fof(f44338,plain,
! [X0,X1] :
( ld(X0,ld(i(X0),X1)) = X1
| mult(i(X0),X1) = mult(X1,i(X0)) ),
inference(paramodulation,[status(thm)],[f1711,f13615]) ).
fof(f44339,plain,
! [X0,X1] :
( ld(X0,ld(i(X0),X1)) = X1
| mult(i(X0),X1) = rd(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f2113,f44338]) ).
fof(f184409,plain,
! [X0,X1] :
( ld(i(X0),rd(X1,X0)) = X1
| ld(X0,X1) = mult(i(X0),X1) ),
inference(paramodulation,[status(thm)],[f26708,f15]) ).
fof(f184488,plain,
! [X0,X1] :
( rd(X0,X1) != ld(X1,X0)
| mult(i(X1),X0) = ld(X1,X0) ),
inference(equality_factoring,[status(esa)],[f26708]) ).
fof(f219912,plain,
! [X0,X1] :
( ld(i(X0),rd(X1,X0)) = X1
| ld(X0,ld(i(X0),X1)) = X1 ),
inference(paramodulation,[status(thm)],[f44339,f15]) ).
fof(f342332,plain,
! [X0,X1] :
( ld(i(i(X0)),rd(X1,i(X0))) = X1
| ld(i(X0),X1) = mult(X0,X1) ),
inference(paramodulation,[status(thm)],[f1711,f184409]) ).
fof(f342333,plain,
! [X0,X1] :
( ld(X0,rd(X1,i(X0))) = X1
| ld(i(X0),X1) = mult(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f1711,f342332]) ).
fof(f342334,plain,
! [X0,X1] :
( ld(X0,mult(X1,X0)) = X1
| ld(i(X0),X1) = mult(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f2028,f342333]) ).
fof(f344884,plain,
! [X0,X1] :
( rd(mult(X0,X1),X1) = rd(X1,mult(i(X0),X1))
| ld(X0,mult(X1,X0)) = X1 ),
inference(paramodulation,[status(thm)],[f342334,f6803]) ).
fof(f344885,plain,
! [X0,X1] :
( X0 = rd(X1,mult(i(X0),X1))
| ld(X0,mult(X1,X0)) = X1 ),
inference(forward_demodulation,[status(thm)],[f17,f344884]) ).
fof(f345106,plain,
! [X0,X1] :
( ld(X0,ld(i(X0),X1)) = X1
| ld(X0,mult(X1,X0)) = X1 ),
inference(paramodulation,[status(thm)],[f344885,f6804]) ).
fof(f375095,plain,
! [X0,X1] :
( ld(X0,X1) = rd(X1,X0)
| ld(X0,mult(rd(X1,X0),X0)) = rd(X1,X0)
| ld(X0,ld(i(X0),X1)) = X1 ),
inference(paramodulation,[status(thm)],[f219912,f345106]) ).
fof(f375096,plain,
! [X0,X1] :
( ld(X0,X1) = rd(X1,X0)
| ld(X0,X1) = rd(X1,X0)
| ld(X0,ld(i(X0),X1)) = X1 ),
inference(forward_demodulation,[status(thm)],[f16,f375095]) ).
fof(f375097,plain,
! [X0,X1] :
( ld(X0,X1) = rd(X1,X0)
| ld(X0,ld(i(X0),X1)) = X1 ),
inference(duplicate_literals_removal,[status(esa)],[f375096]) ).
fof(f375496,plain,
! [X0,X1] :
( mult(X0,X1) = ld(i(X0),X1)
| ld(X0,X1) = rd(X1,X0) ),
inference(paramodulation,[status(thm)],[f375097,f14]) ).
fof(f376045,plain,
! [X0,X1] :
( rd(mult(X0,X1),X1) = rd(X1,mult(i(X0),X1))
| ld(X0,X1) = rd(X1,X0) ),
inference(paramodulation,[status(thm)],[f375496,f6803]) ).
fof(f376046,plain,
! [X0,X1] :
( X0 = rd(X1,mult(i(X0),X1))
| ld(X0,X1) = rd(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f17,f376045]) ).
fof(f376424,plain,
! [X0,X1] :
( ld(X0,X1) = mult(i(X0),X1)
| ld(X0,X1) = rd(X1,X0) ),
inference(paramodulation,[status(thm)],[f376046,f2358]) ).
fof(f376425,plain,
! [X0,X1] : ld(X0,X1) = mult(i(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f376424,f184488]) ).
fof(f376522,plain,
! [X0,X1] : ld(i(X0),X1) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f1711,f376425]) ).
fof(f378735,plain,
! [X0,X1] : mult(X0,mult(X1,X0)) = mult(mult(X0,X1),X0),
inference(backward_demodulation,[status(thm)],[f376522,f3832]) ).
fof(f399051,plain,
mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))) != mult(sk0_3,mult(sk0_5,mult(sk0_4,sk0_5))),
inference(backward_demodulation,[status(thm)],[f378735,f31]) ).
fof(f399052,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f399051]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP748+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n023.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 11:47:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 96.17/13.23 % Refutation found
% 96.17/13.23 % SZS status Theorem for theBenchmark: Theorem is valid
% 96.17/13.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 97.83/13.47 % Elapsed time: 13.116501 seconds
% 97.83/13.47 % CPU time: 97.501663 seconds
% 97.83/13.47 % Memory used: 1.078 GB
%------------------------------------------------------------------------------