TSTP Solution File: GRP194+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n005.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 : Thu Aug 31 01:22:38 EDT 2023
% Result : Theorem 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 63 ( 19 unt; 0 def)
% Number of atoms : 155 ( 43 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 154 ( 62 ~; 53 |; 26 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 72 (; 64 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f340,plain,
$false,
inference(trivial_inequality_removal,[],[f335]) ).
fof(f335,plain,
sF3 != sF3,
inference(backward_demodulation,[],[f91,f333]) ).
fof(f333,plain,
sF3 = multiply(h,sF3,sK2(sF3,h)),
inference(resolution,[],[f332,f70]) ).
fof(f70,plain,
group_member(sF3,h),
inference(forward_demodulation,[],[f59,f47]) ).
fof(f47,plain,
phi(f_left_zero) = sF3,
introduced(function_definition,[]) ).
fof(f59,plain,
group_member(phi(f_left_zero),h),
inference(resolution,[],[f55,f37]) ).
fof(f37,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0] :
( group_member(phi(X0),h)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,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/sandbox/tmp/tmp.xmusZkskBH/Vampire---4.8_10971',homomorphism1) ).
fof(f55,plain,
group_member(f_left_zero,f),
inference(resolution,[],[f53,f39]) ).
fof(f39,plain,
! [X0,X1] :
( group_member(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( multiply(X1,X0,sK2(X0,X1)) != X0
& group_member(sK2(X0,X1),X1) )
| ~ group_member(X0,X1) )
& ( ( ! [X3] :
( multiply(X1,X0,X3) = X0
| ~ group_member(X3,X1) )
& group_member(X0,X1) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f29,f30]) ).
fof(f30,plain,
! [X0,X1] :
( ? [X2] :
( multiply(X1,X0,X2) != X0
& group_member(X2,X1) )
=> ( multiply(X1,X0,sK2(X0,X1)) != X0
& group_member(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1] :
( ( sP0(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) )
& group_member(X0,X1) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) )
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ? [X2] :
( multiply(X0,X1,X2) != X1
& group_member(X2,X0) )
| ~ group_member(X1,X0) )
& ( ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) )
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f53,plain,
sP0(f_left_zero,f),
inference(resolution,[],[f34,f43]) ).
fof(f43,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ left_zero(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( left_zero(X0,X1)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ left_zero(X0,X1) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( left_zero(X0,X1)
<=> sP0(X1,X0) ),
inference(definition_folding,[],[f18,f23]) ).
fof(f18,plain,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( ! [X2] :
( multiply(X0,X1,X2) = X1
| ~ group_member(X2,X0) )
& group_member(X1,X0) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( left_zero(X0,X1)
<=> ( ! [X2] :
( group_member(X2,X0)
=> multiply(X0,X1,X2) = X1 )
& group_member(X1,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.xmusZkskBH/Vampire---4.8_10971',left_zero) ).
fof(f34,plain,
left_zero(f,f_left_zero),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
left_zero(f,f_left_zero),
file('/export/starexec/sandbox/tmp/tmp.xmusZkskBH/Vampire---4.8_10971',left_zero_for_f) ).
fof(f332,plain,
( ~ group_member(sF3,h)
| sF3 = multiply(h,sF3,sK2(sF3,h)) ),
inference(forward_demodulation,[],[f331,f47]) ).
fof(f331,plain,
( phi(f_left_zero) = multiply(h,sF3,sK2(sF3,h))
| ~ group_member(sF3,h) ),
inference(backward_demodulation,[],[f204,f328]) ).
fof(f328,plain,
f_left_zero = multiply(f,f_left_zero,sK1(sK2(sF3,h))),
inference(resolution,[],[f98,f70]) ).
fof(f98,plain,
( ~ group_member(sF3,h)
| f_left_zero = multiply(f,f_left_zero,sK1(sK2(sF3,h))) ),
inference(resolution,[],[f71,f56]) ).
fof(f56,plain,
! [X0] :
( ~ group_member(X0,f)
| f_left_zero = multiply(f,f_left_zero,X0) ),
inference(resolution,[],[f53,f40]) ).
fof(f40,plain,
! [X3,X0,X1] :
( multiply(X1,X0,X3) = X0
| ~ group_member(X3,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f71,plain,
( group_member(sK1(sK2(sF3,h)),f)
| ~ group_member(sF3,h) ),
inference(resolution,[],[f51,f35]) ).
fof(f35,plain,
! [X0] :
( group_member(sK1(X0),f)
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( phi(sK1(X0)) = X0
& group_member(sK1(X0),f) )
| ~ group_member(X0,h) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f14,f25]) ).
fof(f25,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
=> ( phi(sK1(X0)) = X0
& group_member(sK1(X0),f) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X0] :
( ? [X1] :
( phi(X1) = X0
& group_member(X1,f) )
| ~ group_member(X0,h) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,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] :
( phi(X2) = X1
& group_member(X2,f) ) ),
file('/export/starexec/sandbox/tmp/tmp.xmusZkskBH/Vampire---4.8_10971',surjective) ).
fof(f51,plain,
( group_member(sK2(sF3,h),h)
| ~ group_member(sF3,h) ),
inference(resolution,[],[f49,f41]) ).
fof(f41,plain,
! [X0,X1] :
( sP0(X0,X1)
| group_member(sK2(X0,X1),X1)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f49,plain,
~ sP0(sF3,h),
inference(resolution,[],[f48,f44]) ).
fof(f44,plain,
! [X0,X1] :
( left_zero(X0,X1)
| ~ sP0(X1,X0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f48,plain,
~ left_zero(h,sF3),
inference(definition_folding,[],[f33,f47]) ).
fof(f33,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/sandbox/tmp/tmp.xmusZkskBH/Vampire---4.8_10971',prove_left_zero_h) ).
fof(f204,plain,
( multiply(h,sF3,sK2(sF3,h)) = phi(multiply(f,f_left_zero,sK1(sK2(sF3,h))))
| ~ group_member(sF3,h) ),
inference(forward_demodulation,[],[f198,f129]) ).
fof(f129,plain,
sK2(sF3,h) = phi(sK1(sK2(sF3,h))),
inference(resolution,[],[f72,f70]) ).
fof(f72,plain,
( ~ group_member(sF3,h)
| sK2(sF3,h) = phi(sK1(sK2(sF3,h))) ),
inference(resolution,[],[f51,f36]) ).
fof(f36,plain,
! [X0] :
( phi(sK1(X0)) = X0
| ~ group_member(X0,h) ),
inference(cnf_transformation,[],[f26]) ).
fof(f198,plain,
( phi(multiply(f,f_left_zero,sK1(sK2(sF3,h)))) = multiply(h,sF3,phi(sK1(sK2(sF3,h))))
| ~ group_member(sF3,h) ),
inference(resolution,[],[f68,f71]) ).
fof(f68,plain,
! [X0] :
( ~ group_member(X0,f)
| phi(multiply(f,f_left_zero,X0)) = multiply(h,sF3,phi(X0)) ),
inference(forward_demodulation,[],[f57,f47]) ).
fof(f57,plain,
! [X0] :
( multiply(h,phi(f_left_zero),phi(X0)) = phi(multiply(f,f_left_zero,X0))
| ~ group_member(X0,f) ),
inference(resolution,[],[f55,f38]) ).
fof(f38,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(flattening,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1))
| ~ group_member(X1,f)
| ~ group_member(X0,f) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
! [X0,X1] :
( ( group_member(X1,f)
& group_member(X0,f) )
=> multiply(h,phi(X0),phi(X1)) = phi(multiply(f,X0,X1)) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2] :
( ( group_member(X2,f)
& group_member(X1,f) )
=> multiply(h,phi(X1),phi(X2)) = phi(multiply(f,X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.xmusZkskBH/Vampire---4.8_10971',homomorphism2) ).
fof(f91,plain,
sF3 != multiply(h,sF3,sK2(sF3,h)),
inference(resolution,[],[f52,f70]) ).
fof(f52,plain,
( ~ group_member(sF3,h)
| sF3 != multiply(h,sF3,sK2(sF3,h)) ),
inference(resolution,[],[f49,f42]) ).
fof(f42,plain,
! [X0,X1] :
( sP0(X0,X1)
| multiply(X1,X0,sK2(X0,X1)) != X0
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP194+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 21:12:53 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.xmusZkskBH/Vampire---4.8_10971
% 0.14/0.36 % (11078)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (11085)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_501 on Vampire---4 for (501ds/0Mi)
% 0.20/0.41 % (11082)lrs+3_20_av=off:bd=preordered:drc=off:fsd=off:fsr=off:fde=unused:irw=on:lcm=reverse:sos=theory:stl=315_961 on Vampire---4 for (961ds/0Mi)
% 0.20/0.41 % (11080)lrs-11_28_aac=none:afr=on:anc=none:bs=on:drc=off:fde=unused:gs=on:nm=2:nwc=1.3:sp=frequency:stl=188_1092 on Vampire---4 for (1092ds/0Mi)
% 0.20/0.41 % (11081)ott-4_11_av=off:bd=preordered:bce=on:drc=off:flr=on:fsr=off:lma=on:nwc=2.0:sp=occurrence:tgt=ground:urr=ec_only_1010 on Vampire---4 for (1010ds/0Mi)
% 0.20/0.41 % (11083)ott+1003_4:1_av=off:cond=on:drc=off:fsd=off:fsr=off:fde=none:gsp=on:nm=2:nwc=1.5:sos=all:sp=reverse_arity:tgt=full_871 on Vampire---4 for (871ds/0Mi)
% 0.20/0.41 % (11084)lrs-11_32_av=off:bd=off:bs=on:bsr=on:drc=off:flr=on:fsd=off:fsr=off:fde=none:gsp=on:irw=on:lcm=predicate:nm=4:sp=scramble:stl=125_825 on Vampire---4 for (825ds/0Mi)
% 0.20/0.41 % (11079)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_1169 on Vampire---4 for (1169ds/0Mi)
% 0.20/0.43 % (11083)First to succeed.
% 0.20/0.43 % (11083)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for Vampire---4
% 0.20/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.20/0.43 % (11083)------------------------------
% 0.20/0.43 % (11083)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.20/0.43 % (11083)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.20/0.43 % (11083)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (11083)Memory used [KB]: 1407
% 0.20/0.43 % (11083)Time elapsed: 0.017 s
% 0.20/0.43 % (11083)------------------------------
% 0.20/0.43 % (11083)------------------------------
% 0.20/0.43 % (11078)Success in time 0.074 s
% 0.20/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------