TSTP Solution File: GRP194+1 by SnakeForV---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n029.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 Aug 31 16:14:50 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 54 ( 13 unt; 0 def)
% Number of atoms : 149 ( 37 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 159 ( 64 ~; 57 |; 25 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 69 ( 61 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f809,plain,
$false,
inference(subsumption_resolution,[],[f808,f51]) ).
fof(f51,plain,
group_member(sF2,h),
inference(subsumption_resolution,[],[f50,f49]) ).
fof(f49,plain,
group_member(f_left_zero,f),
inference(resolution,[],[f43,f40]) ).
fof(f40,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero_for_f) ).
fof(f43,plain,
! [X0,X1] :
( ~ left_zero(X1,X0)
| group_member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( left_zero(X1,X0)
| ~ group_member(X0,X1)
| ( multiply(X1,X0,sK1(X0,X1)) != X0
& group_member(sK1(X0,X1),X1) ) )
& ( ( group_member(X0,X1)
& ! [X3] :
( multiply(X1,X0,X3) = X0
| ~ group_member(X3,X1) ) )
| ~ left_zero(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f32,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ? [X2] :
( multiply(X1,X0,X2) != X0
& group_member(X2,X1) )
=> ( multiply(X1,X0,sK1(X0,X1)) != X0
& group_member(sK1(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1] :
( ( left_zero(X1,X0)
| ~ group_member(X0,X1)
| ? [X2] :
( multiply(X1,X0,X2) != X0
& group_member(X2,X1) ) )
& ( ( group_member(X0,X1)
& ! [X3] :
( multiply(X1,X0,X3) = X0
| ~ group_member(X3,X1) ) )
| ~ left_zero(X1,X0) ) ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( left_zero(X1,X0)
| ~ group_member(X0,X1)
| ? [X2] :
( multiply(X1,X0,X2) != X0
& group_member(X2,X1) ) )
& ( ( group_member(X0,X1)
& ! [X2] :
( multiply(X1,X0,X2) = X0
| ~ group_member(X2,X1) ) )
| ~ left_zero(X1,X0) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( left_zero(X1,X0)
| ~ group_member(X0,X1)
| ? [X2] :
( multiply(X1,X0,X2) != X0
& group_member(X2,X1) ) )
& ( ( group_member(X0,X1)
& ! [X2] :
( multiply(X1,X0,X2) = X0
| ~ group_member(X2,X1) ) )
| ~ left_zero(X1,X0) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( left_zero(X1,X0)
<=> ( group_member(X0,X1)
& ! [X2] :
( multiply(X1,X0,X2) = X0
| ~ group_member(X2,X1) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] :
( left_zero(X1,X0)
<=> ( group_member(X0,X1)
& ! [X2] :
( group_member(X2,X1)
=> multiply(X1,X0,X2) = X0 ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X0] :
( ( ! [X2] :
( group_member(X2,X0)
=> multiply(X0,X1,X2) = X1 )
& group_member(X1,X0) )
<=> left_zero(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_zero) ).
fof(f50,plain,
( group_member(sF2,h)
| ~ group_member(f_left_zero,f) ),
inference(superposition,[],[f35,f47]) ).
fof(f47,plain,
phi(f_left_zero) = sF2,
introduced(function_definition,[]) ).
fof(f35,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( group_member(X0,f)
=> group_member(phi(X0),h) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1] :
( group_member(X1,f)
=> group_member(phi(X1),h) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f808,plain,
~ group_member(sF2,h),
inference(subsumption_resolution,[],[f807,f48]) ).
fof(f48,plain,
~ left_zero(h,sF2),
inference(definition_folding,[],[f46,f47]) ).
fof(f46,plain,
~ left_zero(h,phi(f_left_zero)),
inference(cnf_transformation,[],[f10]) ).
fof(f10,plain,
~ left_zero(h,phi(f_left_zero)),
inference(flattening,[],[f9]) ).
fof(f9,negated_conjecture,
~ left_zero(h,phi(f_left_zero)),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
left_zero(h,phi(f_left_zero)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_left_zero_h) ).
fof(f807,plain,
( left_zero(h,sF2)
| ~ group_member(sF2,h) ),
inference(resolution,[],[f804,f44]) ).
fof(f44,plain,
! [X0,X1] :
( group_member(sK1(X0,X1),X1)
| left_zero(X1,X0)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f804,plain,
~ group_member(sK1(sF2,h),h),
inference(subsumption_resolution,[],[f803,f48]) ).
fof(f803,plain,
( left_zero(h,sF2)
| ~ group_member(sK1(sF2,h),h) ),
inference(subsumption_resolution,[],[f797,f51]) ).
fof(f797,plain,
( ~ group_member(sF2,h)
| left_zero(h,sF2)
| ~ group_member(sK1(sF2,h),h) ),
inference(trivial_inequality_removal,[],[f790]) ).
fof(f790,plain,
( left_zero(h,sF2)
| sF2 != sF2
| ~ group_member(sF2,h)
| ~ group_member(sK1(sF2,h),h) ),
inference(superposition,[],[f45,f773]) ).
fof(f773,plain,
! [X0] :
( multiply(h,sF2,X0) = sF2
| ~ group_member(X0,h) ),
inference(forward_demodulation,[],[f772,f47]) ).
fof(f772,plain,
! [X0] :
( phi(f_left_zero) = multiply(h,sF2,X0)
| ~ group_member(X0,h) ),
inference(subsumption_resolution,[],[f771,f37]) ).
fof(f37,plain,
! [X0] :
( group_member(sK0(X0),f)
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ( phi(sK0(X0)) = X0
& group_member(sK0(X0),f) )
| ~ group_member(X0,h) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f27]) ).
fof(f27,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
=> ( phi(sK0(X0)) = X0
& group_member(sK0(X0),f) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
| ~ group_member(X0,h) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( group_member(X0,h)
=> ? [X1] :
( phi(X1) = X0
& group_member(X1,f) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1] :
( group_member(X1,h)
=> ? [X2] :
( group_member(X2,f)
& phi(X2) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective) ).
fof(f771,plain,
! [X0] :
( ~ group_member(X0,h)
| phi(f_left_zero) = multiply(h,sF2,X0)
| ~ group_member(sK0(X0),f) ),
inference(subsumption_resolution,[],[f750,f40]) ).
fof(f750,plain,
! [X0] :
( ~ group_member(X0,h)
| ~ left_zero(f,f_left_zero)
| phi(f_left_zero) = multiply(h,sF2,X0)
| ~ group_member(sK0(X0),f) ),
inference(superposition,[],[f176,f42]) ).
fof(f42,plain,
! [X3,X0,X1] :
( multiply(X1,X0,X3) = X0
| ~ left_zero(X1,X0)
| ~ group_member(X3,X1) ),
inference(cnf_transformation,[],[f34]) ).
fof(f176,plain,
! [X0] :
( multiply(h,sF2,X0) = phi(multiply(f,f_left_zero,sK0(X0)))
| ~ group_member(X0,h) ),
inference(subsumption_resolution,[],[f169,f37]) ).
fof(f169,plain,
! [X0] :
( multiply(h,sF2,X0) = phi(multiply(f,f_left_zero,sK0(X0)))
| ~ group_member(sK0(X0),f)
| ~ group_member(X0,h) ),
inference(superposition,[],[f66,f38]) ).
fof(f38,plain,
! [X0] :
( phi(sK0(X0)) = X0
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f28]) ).
fof(f66,plain,
! [X0] :
( phi(multiply(f,f_left_zero,X0)) = multiply(h,sF2,phi(X0))
| ~ group_member(X0,f) ),
inference(subsumption_resolution,[],[f56,f49]) ).
fof(f56,plain,
! [X0] :
( ~ group_member(f_left_zero,f)
| ~ group_member(X0,f)
| phi(multiply(f,f_left_zero,X0)) = multiply(h,sF2,phi(X0)) ),
inference(superposition,[],[f41,f47]) ).
fof(f41,plain,
! [X0,X1] :
( multiply(h,phi(X1),phi(X0)) = phi(multiply(f,X1,X0))
| ~ group_member(X0,f)
| ~ group_member(X1,f) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( multiply(h,phi(X1),phi(X0)) = phi(multiply(f,X1,X0))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X1,X0] :
( multiply(h,phi(X1),phi(X0)) = phi(multiply(f,X1,X0))
| ~ group_member(X0,f)
| ~ group_member(X1,f) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ( group_member(X0,f)
& group_member(X1,f) )
=> multiply(h,phi(X1),phi(X0)) = phi(multiply(f,X1,X0)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X1] :
( ( group_member(X2,f)
& group_member(X1,f) )
=> multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f45,plain,
! [X0,X1] :
( multiply(X1,X0,sK1(X0,X1)) != X0
| ~ group_member(X0,X1)
| left_zero(X1,X0) ),
inference(cnf_transformation,[],[f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n029.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 Aug 29 22:30:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.47 % (31190)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.49 % (31213)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.20/0.50 % (31190)First to succeed.
% 0.20/0.50 % (31190)Refutation found. Thanks to Tanya!
% 0.20/0.50 % SZS status Theorem for theBenchmark
% 0.20/0.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50 % (31190)------------------------------
% 0.20/0.50 % (31190)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50 % (31190)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50 % (31190)Termination reason: Refutation
% 0.20/0.50
% 0.20/0.50 % (31190)Memory used [KB]: 6268
% 0.20/0.50 % (31190)Time elapsed: 0.073 s
% 0.20/0.50 % (31190)Instructions burned: 25 (million)
% 0.20/0.50 % (31190)------------------------------
% 0.20/0.50 % (31190)------------------------------
% 0.20/0.50 % (31189)Success in time 0.153 s
%------------------------------------------------------------------------------