TSTP Solution File: SWW246+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %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 : Tue Apr 30 17:29:16 EDT 2024
% Result : ContradictoryAxioms 1.58s 0.69s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 61 ( 35 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 64 ( 28 ~; 22 |; 4 &)
% ( 5 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 56 ( 52 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9364,plain,
$false,
inference(resolution,[],[f9363,f3677]) ).
fof(f3677,plain,
class_Rings_Oidom(t_a),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,axiom,
class_Rings_Oidom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
fof(f9363,plain,
~ class_Rings_Oidom(t_a),
inference(resolution,[],[f9349,f3785]) ).
fof(f3785,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a) ),
inference(cnf_transformation,[],[f2489]) ).
fof(f2489,plain,
( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))
| ~ class_Rings_Oidom(t_a) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
( class_Rings_Oidom(t_a)
=> ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a,t_a,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C0_C) ).
fof(f9349,plain,
! [X0,X1] : c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))),
inference(trivial_inequality_removal,[],[f9348]) ).
fof(f9348,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) != c_Groups_Ozero__class_Ozero(t_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(forward_demodulation,[],[f9304,f6684]) ).
fof(f6684,plain,
! [X0] : c_Groups_Ozero__class_Ozero(t_a) = hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X0),
inference(resolution,[],[f5088,f3677]) ).
fof(f5088,plain,
! [X2,X0] :
( ~ class_Rings_Oidom(X2)
| c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
inference(equality_resolution,[],[f4512]) ).
fof(f4512,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1
| ~ class_Rings_Oidom(X2) ),
inference(cnf_transformation,[],[f3551]) ).
fof(f3551,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(flattening,[],[f3550]) ).
fof(f3550,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Polynomial_Oorder(X2,X0,X1)
& c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(c_Polynomial_Opoly(X2,X1),X0) ) )
| ~ class_Rings_Oidom(X2) ),
inference(nnf_transformation,[],[f2942]) ).
fof(f2942,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) )
| ~ class_Rings_Oidom(X2) ),
inference(ennf_transformation,[],[f1870]) ).
fof(f1870,plain,
! [X0,X1,X2] :
( class_Rings_Oidom(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = hAPP(c_Polynomial_Opoly(X2,X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X2,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X1 ) ) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X10,X3,X4] :
( class_Rings_Oidom(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Polynomial_Opoly(X4,X3),X10)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Polynomial_Oorder(X4,X10,X3)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).
fof(f9304,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(t_a) != hAPP(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),sK26(c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X0,X1,c_Polynomial_Opoly(t_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) ),
inference(superposition,[],[f4685,f6684]) ).
fof(f4685,plain,
! [X2,X0,X1] :
( hAPP(X0,sK26(X0)) != hAPP(X0,sK27(X0))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
inference(cnf_transformation,[],[f3594]) ).
fof(f3594,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| hAPP(X0,sK26(X0)) != hAPP(X0,sK27(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f3119,f3593]) ).
fof(f3593,plain,
! [X0] :
( ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4)
=> hAPP(X0,sK26(X0)) != hAPP(X0,sK27(X0)) ),
introduced(choice_axiom,[]) ).
fof(f3119,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
| ? [X3,X4] : hAPP(X0,X3) != hAPP(X0,X4) ),
inference(ennf_transformation,[],[f2290]) ).
fof(f2290,plain,
! [X0,X1,X2] :
( ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0) ),
inference(unused_predicate_definition_removal,[],[f1995]) ).
fof(f1995,plain,
! [X0,X1,X2] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X1,X0)
<=> ! [X3,X4] : hAPP(X0,X3) = hAPP(X0,X4) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X1,X14,X4] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X14,X1)
<=> ! [X2,X15] : hAPP(X1,X2) = hAPP(X1,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_constant__def) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW246+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %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 Apr 30 03:28:25 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (21556)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.44 % (21559)WARNING: value z3 for option sas not known
% 0.18/0.44 % (21563)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 theBenchmark for (497ds/0Mi)
% 0.18/0.44 % (21557)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.44 % (21562)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 theBenchmark for (522ds/0Mi)
% 0.18/0.44 % (21558)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.44 % (21559)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 theBenchmark for (569ds/0Mi)
% 0.18/0.44 % (21561)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 theBenchmark for (531ds/0Mi)
% 0.18/0.44 % (21560)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 1.58/0.69 % (21562)First to succeed.
% 1.58/0.69 % (21562)Refutation found. Thanks to Tanya!
% 1.58/0.69 % SZS status ContradictoryAxioms for theBenchmark
% 1.58/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 1.58/0.69 % (21562)------------------------------
% 1.58/0.69 % (21562)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.58/0.69 % (21562)Termination reason: Refutation
% 1.58/0.69
% 1.58/0.69 % (21562)Memory used [KB]: 6495
% 1.58/0.69 % (21562)Time elapsed: 0.255 s
% 1.58/0.69 % (21562)Instructions burned: 505 (million)
% 1.58/0.69 % (21562)------------------------------
% 1.58/0.69 % (21562)------------------------------
% 1.58/0.69 % (21556)Success in time 0.345 s
%------------------------------------------------------------------------------