TSTP Solution File: GRP194+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n008.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 12:10:57 EDT 2023
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 80 ( 22 unt; 0 def)
% Number of atoms : 176 ( 41 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 163 ( 67 ~; 68 |; 16 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 66 (; 62 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [G,X,Y] :
( ( group_member(X,G)
& group_member(Y,G) )
=> group_member(multiply(G,X,Y),G) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( group_member(X,f)
=> group_member(phi(X),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( ( group_member(X,f)
& group_member(Y,f) )
=> multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( group_member(X,h)
=> ? [Y] :
( group_member(Y,f)
& phi(Y) = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [G,X] :
( left_zero(G,X)
<=> ( group_member(X,G)
& ! [Y] :
( group_member(Y,G)
=> multiply(G,X,Y) = X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,hypothesis,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [G,X,Y] :
( ~ group_member(X,G)
| ~ group_member(Y,G)
| group_member(multiply(G,X,Y),G) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ group_member(X0,X1)
| ~ group_member(X2,X1)
| group_member(multiply(X1,X0,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f14,plain,
! [X] :
( ~ group_member(X,f)
| group_member(phi(X),h) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f15,plain,
! [X0] :
( ~ group_member(X0,f)
| group_member(phi(X0),h) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [X,Y] :
( ~ group_member(X,f)
| ~ group_member(Y,f)
| multiply(h,phi(X),phi(Y)) = phi(multiply(f,X,Y)) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f17,plain,
! [X0,X1] :
( ~ group_member(X0,f)
| ~ group_member(X1,f)
| multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X] :
( ~ group_member(X,h)
| ? [Y] :
( group_member(Y,f)
& phi(Y) = X ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f19,plain,
! [X] :
( ~ group_member(X,h)
| ( group_member(sk0_0(X),f)
& phi(sk0_0(X)) = X ) ),
inference(skolemization,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0] :
( ~ group_member(X0,h)
| group_member(sk0_0(X0),f) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [X0] :
( ~ group_member(X0,h)
| phi(sk0_0(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f22,plain,
! [G,X] :
( left_zero(G,X)
<=> ( group_member(X,G)
& ! [Y] :
( ~ group_member(Y,G)
| multiply(G,X,Y) = X ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f23,plain,
! [G,X] :
( ( ~ left_zero(G,X)
| ( group_member(X,G)
& ! [Y] :
( ~ group_member(Y,G)
| multiply(G,X,Y) = X ) ) )
& ( left_zero(G,X)
| ~ group_member(X,G)
| ? [Y] :
( group_member(Y,G)
& multiply(G,X,Y) != X ) ) ),
inference(NNF_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
( ! [G,X] :
( ~ left_zero(G,X)
| ( group_member(X,G)
& ! [Y] :
( ~ group_member(Y,G)
| multiply(G,X,Y) = X ) ) )
& ! [G,X] :
( left_zero(G,X)
| ~ group_member(X,G)
| ? [Y] :
( group_member(Y,G)
& multiply(G,X,Y) != X ) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f25,plain,
( ! [G,X] :
( ~ left_zero(G,X)
| ( group_member(X,G)
& ! [Y] :
( ~ group_member(Y,G)
| multiply(G,X,Y) = X ) ) )
& ! [G,X] :
( left_zero(G,X)
| ~ group_member(X,G)
| ( group_member(sk0_1(X,G),G)
& multiply(G,X,sk0_1(X,G)) != X ) ) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ~ left_zero(X0,X1)
| group_member(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ~ left_zero(X0,X1)
| ~ group_member(X2,X0)
| multiply(X0,X1,X2) = X1 ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( left_zero(X0,X1)
| ~ group_member(X1,X0)
| group_member(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( left_zero(X0,X1)
| ~ group_member(X1,X0)
| multiply(X0,X1,sk0_1(X1,X0)) != X1 ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f30,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f31,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f32,plain,
group_member(f_left_zero,f),
inference(resolution,[status(thm)],[f26,f30]) ).
fof(f33,plain,
! [X0] :
( ~ group_member(X0,f)
| multiply(h,phi(X0),phi(f_left_zero)) = phi(multiply(f,X0,f_left_zero)) ),
inference(resolution,[status(thm)],[f17,f32]) ).
fof(f34,plain,
! [X0] :
( ~ group_member(X0,f)
| multiply(f,f_left_zero,X0) = f_left_zero ),
inference(resolution,[status(thm)],[f27,f30]) ).
fof(f35,plain,
multiply(f,f_left_zero,f_left_zero) = f_left_zero,
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f36,plain,
multiply(h,phi(f_left_zero),phi(f_left_zero)) = phi(multiply(f,f_left_zero,f_left_zero)),
inference(resolution,[status(thm)],[f33,f32]) ).
fof(f37,plain,
multiply(h,phi(f_left_zero),phi(f_left_zero)) = phi(f_left_zero),
inference(forward_demodulation,[status(thm)],[f35,f36]) ).
fof(f38,plain,
! [X0] :
( phi(sk0_0(phi(X0))) = phi(X0)
| ~ group_member(X0,f) ),
inference(resolution,[status(thm)],[f21,f15]) ).
fof(f39,plain,
phi(sk0_0(phi(f_left_zero))) = phi(f_left_zero),
inference(resolution,[status(thm)],[f38,f32]) ).
fof(f43,plain,
( spl0_1
<=> group_member(phi(f_left_zero),h) ),
introduced(split_symbol_definition) ).
fof(f48,plain,
! [X0] :
( group_member(sk0_0(phi(X0)),f)
| ~ group_member(X0,f) ),
inference(resolution,[status(thm)],[f20,f15]) ).
fof(f49,plain,
group_member(sk0_0(phi(f_left_zero)),f),
inference(resolution,[status(thm)],[f48,f32]) ).
fof(f53,plain,
multiply(h,phi(sk0_0(phi(f_left_zero))),phi(f_left_zero)) = phi(multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),
inference(resolution,[status(thm)],[f49,f33]) ).
fof(f54,plain,
multiply(h,phi(f_left_zero),phi(f_left_zero)) = phi(multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),
inference(forward_demodulation,[status(thm)],[f39,f53]) ).
fof(f55,plain,
phi(f_left_zero) = phi(multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),
inference(forward_demodulation,[status(thm)],[f37,f54]) ).
fof(f72,plain,
! [X0] :
( left_zero(h,phi(X0))
| group_member(sk0_1(phi(X0),h),h)
| ~ group_member(X0,f) ),
inference(resolution,[status(thm)],[f28,f15]) ).
fof(f83,plain,
! [X0] :
( ~ group_member(X0,f)
| group_member(multiply(f,X0,f_left_zero),f) ),
inference(resolution,[status(thm)],[f11,f32]) ).
fof(f84,plain,
group_member(multiply(f,sk0_0(phi(f_left_zero)),f_left_zero),f),
inference(resolution,[status(thm)],[f83,f49]) ).
fof(f97,plain,
! [X0] :
( ~ group_member(X0,f)
| multiply(h,phi(X0),phi(multiply(f,sk0_0(phi(f_left_zero)),f_left_zero))) = phi(multiply(f,X0,multiply(f,sk0_0(phi(f_left_zero)),f_left_zero))) ),
inference(resolution,[status(thm)],[f84,f17]) ).
fof(f98,plain,
! [X0] :
( ~ group_member(X0,f)
| multiply(h,phi(X0),phi(f_left_zero)) = phi(multiply(f,X0,multiply(f,sk0_0(phi(f_left_zero)),f_left_zero))) ),
inference(forward_demodulation,[status(thm)],[f55,f97]) ).
fof(f99,plain,
! [X0] :
( ~ group_member(X0,f)
| group_member(multiply(f,X0,multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),f) ),
inference(resolution,[status(thm)],[f84,f11]) ).
fof(f108,plain,
( spl0_9
<=> multiply(h,phi(f_left_zero),sk0_1(phi(f_left_zero),h)) = phi(f_left_zero) ),
introduced(split_symbol_definition) ).
fof(f110,plain,
( multiply(h,phi(f_left_zero),sk0_1(phi(f_left_zero),h)) != phi(f_left_zero)
| spl0_9 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( ~ group_member(phi(f_left_zero),h)
| multiply(h,phi(f_left_zero),sk0_1(phi(f_left_zero),h)) != phi(f_left_zero) ),
inference(resolution,[status(thm)],[f29,f31]) ).
fof(f112,plain,
( ~ spl0_1
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f111,f43,f108]) ).
fof(f183,plain,
( spl0_22
<=> left_zero(h,phi(f_left_zero)) ),
introduced(split_symbol_definition) ).
fof(f184,plain,
( left_zero(h,phi(f_left_zero))
| ~ spl0_22 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( spl0_23
<=> group_member(sk0_1(phi(f_left_zero),h),h) ),
introduced(split_symbol_definition) ).
fof(f187,plain,
( group_member(sk0_1(phi(f_left_zero),h),h)
| ~ spl0_23 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( left_zero(h,phi(f_left_zero))
| group_member(sk0_1(phi(f_left_zero),h),h) ),
inference(resolution,[status(thm)],[f72,f32]) ).
fof(f190,plain,
( spl0_22
| spl0_23 ),
inference(split_clause,[status(thm)],[f189,f183,f186]) ).
fof(f191,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f31]) ).
fof(f192,plain,
~ spl0_22,
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f286,plain,
( group_member(sk0_0(sk0_1(phi(f_left_zero),h)),f)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f187,f20]) ).
fof(f287,plain,
( phi(sk0_0(sk0_1(phi(f_left_zero),h))) = sk0_1(phi(f_left_zero),h)
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f187,f21]) ).
fof(f319,plain,
( multiply(f,f_left_zero,sk0_0(sk0_1(phi(f_left_zero),h))) = f_left_zero
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f286,f34]) ).
fof(f320,plain,
! [X0] :
( ~ group_member(X0,f)
| multiply(h,phi(X0),phi(sk0_0(sk0_1(phi(f_left_zero),h)))) = phi(multiply(f,X0,sk0_0(sk0_1(phi(f_left_zero),h))))
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f286,f17]) ).
fof(f614,plain,
group_member(multiply(f,sk0_0(phi(f_left_zero)),multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),f),
inference(resolution,[status(thm)],[f99,f49]) ).
fof(f3476,plain,
multiply(h,phi(sk0_0(phi(f_left_zero))),phi(f_left_zero)) = phi(multiply(f,sk0_0(phi(f_left_zero)),multiply(f,sk0_0(phi(f_left_zero)),f_left_zero))),
inference(resolution,[status(thm)],[f98,f49]) ).
fof(f3477,plain,
multiply(h,phi(f_left_zero),phi(f_left_zero)) = phi(multiply(f,sk0_0(phi(f_left_zero)),multiply(f,sk0_0(phi(f_left_zero)),f_left_zero))),
inference(forward_demodulation,[status(thm)],[f39,f3476]) ).
fof(f3478,plain,
phi(f_left_zero) = phi(multiply(f,sk0_0(phi(f_left_zero)),multiply(f,sk0_0(phi(f_left_zero)),f_left_zero))),
inference(forward_demodulation,[status(thm)],[f37,f3477]) ).
fof(f3482,plain,
( spl0_249
<=> group_member(multiply(f,sk0_0(phi(f_left_zero)),multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),f) ),
introduced(split_symbol_definition) ).
fof(f3484,plain,
( ~ group_member(multiply(f,sk0_0(phi(f_left_zero)),multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),f)
| spl0_249 ),
inference(component_clause,[status(thm)],[f3482]) ).
fof(f3485,plain,
( ~ group_member(multiply(f,sk0_0(phi(f_left_zero)),multiply(f,sk0_0(phi(f_left_zero)),f_left_zero)),f)
| group_member(phi(f_left_zero),h) ),
inference(paramodulation,[status(thm)],[f3478,f15]) ).
fof(f3486,plain,
( ~ spl0_249
| spl0_1 ),
inference(split_clause,[status(thm)],[f3485,f3482,f43]) ).
fof(f3487,plain,
( $false
| spl0_249 ),
inference(forward_subsumption_resolution,[status(thm)],[f3484,f614]) ).
fof(f3488,plain,
spl0_249,
inference(contradiction_clause,[status(thm)],[f3487]) ).
fof(f4175,plain,
! [X0] :
( ~ group_member(X0,f)
| multiply(h,phi(X0),sk0_1(phi(f_left_zero),h)) = phi(multiply(f,X0,sk0_0(sk0_1(phi(f_left_zero),h))))
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f287,f320]) ).
fof(f4205,plain,
( multiply(h,phi(f_left_zero),sk0_1(phi(f_left_zero),h)) = phi(multiply(f,f_left_zero,sk0_0(sk0_1(phi(f_left_zero),h))))
| ~ spl0_23 ),
inference(resolution,[status(thm)],[f4175,f32]) ).
fof(f4206,plain,
( multiply(h,phi(f_left_zero),sk0_1(phi(f_left_zero),h)) = phi(f_left_zero)
| ~ spl0_23 ),
inference(forward_demodulation,[status(thm)],[f319,f4205]) ).
fof(f4207,plain,
( $false
| spl0_9
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[status(thm)],[f4206,f110]) ).
fof(f4208,plain,
( spl0_9
| ~ spl0_23 ),
inference(contradiction_clause,[status(thm)],[f4207]) ).
fof(f4209,plain,
$false,
inference(sat_refutation,[status(thm)],[f112,f190,f192,f3486,f3488,f4208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n008.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:30:08 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.39 % Elapsed time: 0.092987 seconds
% 0.14/0.39 % CPU time: 0.303436 seconds
% 0.48/0.61 % Memory used: 33.582 MB
%------------------------------------------------------------------------------