TSTP Solution File: SWW198+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n004.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 : Sat Sep 2 14:04:43 EDT 2023
% Result : Theorem 6.29s 1.50s
% Output : Refutation 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 38 ( 30 unt; 0 def)
% Number of atoms : 52 ( 39 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 17 ~; 8 |; 3 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 37 (; 29 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f51651,plain,
$false,
inference(trivial_inequality_removal,[],[f51284]) ).
fof(f51284,plain,
v_na____ != v_na____,
inference(superposition,[],[f19525,f51282]) ).
fof(f51282,plain,
v_na____ = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK81(v_na____),sK81(v_na____))),
inference(forward_demodulation,[],[f51281,f5682]) ).
fof(f5682,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f4061,f5651]) ).
fof(f5651,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f3987,f3973]) ).
fof(f3973,plain,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f735]) ).
fof(f735,axiom,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',fact_One__nat__def) ).
fof(f3987,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(cnf_transformation,[],[f45]) ).
fof(f45,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',fact_semiring__norm_I115_J) ).
fof(f4061,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1251]) ).
fof(f1251,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(rectify,[],[f406]) ).
fof(f406,axiom,
! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X20),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',fact_nat__mult__2__right) ).
fof(f51281,plain,
v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,sK81(v_na____),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(forward_demodulation,[],[f51259,f4218]) ).
fof(f4218,plain,
! [X0,X1] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1),
inference(cnf_transformation,[],[f1357]) ).
fof(f1357,plain,
! [X0,X1] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X0,X1),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X12,X9] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X9,X12) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X12,X9),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',fact_nat__mult__commute) ).
fof(f51259,plain,
v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK81(v_na____))),
inference(resolution,[],[f5710,f3944]) ).
fof(f3944,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',fact_o) ).
fof(f5710,plain,
! [X0] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK81(X0))) = X0 ),
inference(forward_demodulation,[],[f4106,f3973]) ).
fof(f4106,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),sK81(X0))) = X0
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f3211]) ).
fof(f3211,plain,
! [X0] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) != X0 )
& ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),sK81(X0))) = X0
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f3209,f3210]) ).
fof(f3210,plain,
! [X0] :
( ? [X2] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) = X0
=> c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),sK81(X0))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3209,plain,
! [X0] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) != X0 )
& ( ? [X2] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) = X0
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
inference(rectify,[],[f3208]) ).
fof(f3208,plain,
! [X0] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
| ! [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) != X0 )
& ( ? [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) = X0
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1295]) ).
fof(f1295,plain,
! [X0] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X0)
<=> ? [X1] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)) = X0 ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X14] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14)
<=> ? [X23] : c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X23)) = X14 ),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',fact_odd__nat__equiv__def2) ).
fof(f19525,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0)),
inference(superposition,[],[f5653,f5681]) ).
fof(f5681,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(forward_demodulation,[],[f4060,f5651]) ).
fof(f4060,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1250]) ).
fof(f1250,plain,
! [X0] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f407]) ).
fof(f407,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X20) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',fact_nat__mult__2) ).
fof(f5653,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
inference(backward_demodulation,[],[f3753,f5651]) ).
fof(f3753,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
inference(cnf_transformation,[],[f2079]) ).
fof(f2079,plain,
! [X0] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
inference(ennf_transformation,[],[f1188]) ).
fof(f1188,plain,
~ ? [X0] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X0)),
inference(rectify,[],[f1187]) ).
fof(f1187,negated_conjecture,
~ ? [X22] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),
inference(negated_conjecture,[],[f1186]) ).
fof(f1186,conjecture,
? [X22] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X22)),
file('/export/starexec/sandbox/tmp/tmp.kNrkV8fSvu/Vampire---4.8_19196',conj_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.24 % Problem : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.25 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.25/0.47 % Computer : n004.cluster.edu
% 0.25/0.47 % Model : x86_64 x86_64
% 0.25/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.47 % Memory : 8042.1875MB
% 0.25/0.47 % OS : Linux 3.10.0-693.el7.x86_64
% 0.25/0.47 % CPULimit : 300
% 0.25/0.47 % WCLimit : 300
% 0.25/0.47 % DateTime : Wed Aug 30 16:36:37 EDT 2023
% 0.25/0.47 % CPUTime :
% 0.32/0.53 % (19561)Running in auto input_syntax mode. Trying TPTP
% 0.32/0.59 % (19584)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.32/0.59 % (19580)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.32/0.59 % (19579)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.32/0.59 % (19582)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.32/0.59 % (19581)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.32/0.59 % (19583)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.32/0.59 % (19585)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 1.34/0.79 TRYING [1]
% 1.91/0.81 TRYING [2]
% 3.17/1.00 TRYING [1]
% 3.46/1.04 TRYING [2]
% 5.12/1.29 TRYING [3]
% 6.29/1.44 TRYING [1]
% 6.29/1.45 TRYING [3]
% 6.29/1.49 % (19584)First to succeed.
% 6.29/1.50 % (19584)Refutation found. Thanks to Tanya!
% 6.29/1.50 % SZS status Theorem for Vampire---4
% 6.29/1.50 % SZS output start Proof for Vampire---4
% See solution above
% 6.29/1.50 % (19584)------------------------------
% 6.29/1.50 % (19584)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 6.29/1.50 % (19584)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 6.29/1.50 % (19584)Termination reason: Refutation
% 6.29/1.50
% 6.29/1.50 % (19584)Memory used [KB]: 23666
% 6.29/1.50 % (19584)Time elapsed: 0.909 s
% 6.29/1.50 % (19584)------------------------------
% 6.29/1.50 % (19584)------------------------------
% 6.29/1.50 % (19561)Success in time 1.014 s
% 6.29/1.50 % Vampire---4.8 exiting
%------------------------------------------------------------------------------