TSTP Solution File: ALG426-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG426-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n014.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 : Sun May 5 04:30:23 EDT 2024
% Result : Unsatisfiable 51.88s 7.76s
% Output : Refutation 51.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 47 ( 27 unt; 0 def)
% Number of atoms : 72 ( 52 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f273588,plain,
$false,
inference(trivial_inequality_removal,[],[f273587]) ).
fof(f273587,plain,
v_q != v_q,
inference(superposition,[],[f730,f270918]) ).
fof(f270918,plain,
v_p = v_q,
inference(equality_resolution,[],[f262595]) ).
fof(f262595,plain,
! [X0] :
( c_Complex_Oii != X0
| v_p = v_q ),
inference(superposition,[],[f554,f262560]) ).
fof(f262560,plain,
! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| v_p = v_q ),
inference(superposition,[],[f262451,f156515]) ).
fof(f156515,plain,
! [X0,X1] : c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1,
inference(resolution,[],[f156514,f659]) ).
fof(f659,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f156514,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1 ),
inference(equality_resolution,[],[f91955]) ).
fof(f91955,plain,
! [X2,X0,X1] :
( c_Polynomial_OpCons(X2,X0,tc_Complex_Ocomplex) != X1
| c_Polynomial_Osynthetic__div(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(forward_demodulation,[],[f91906,f1321]) ).
fof(f1321,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(forward_demodulation,[],[f1319,f560]) ).
fof(f560,axiom,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pe_0) ).
fof(f1319,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(resolution,[],[f552,f668]) ).
fof(f668,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f552,axiom,
! [X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
fof(f91906,plain,
! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Polynomial_OpCons(X2,X0,tc_Complex_Ocomplex)
| c_Polynomial_Osynthetic__div(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[],[f446,f1326]) ).
fof(f1326,plain,
! [X0] : v_p = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1324,f560]) ).
fof(f1324,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(resolution,[],[f561,f659]) ).
fof(f561,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
fof(f446,axiom,
! [X0,X6,X9,X4,X5] :
( c_HOL_Oplus__class_Oplus(X4,c_Polynomial_Osmult(X5,X6,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X9,X6,X0)
| c_Polynomial_Osynthetic__div(X4,X5,X0) = X6
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_1) ).
fof(f262451,plain,
! [X0,X1] :
( v_p = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ),
inference(superposition,[],[f24021,f262439]) ).
fof(f262439,plain,
! [X0] :
( c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex) = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,v_q,tc_Complex_Ocomplex)),v_p,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ),
inference(superposition,[],[f262201,f729]) ).
fof(f729,plain,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X4,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X4),tc_Complex_Ocomplex)
| c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X4),v_p,tc_Complex_Ocomplex) = X4 ),
inference(forward_demodulation,[],[f558,f560]) ).
fof(f558,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X4,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X4),tc_Complex_Ocomplex)
| c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X4),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_1) ).
fof(f262201,plain,
! [X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_q,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X1,
inference(forward_demodulation,[],[f262200,f840]) ).
fof(f840,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0,
inference(resolution,[],[f513,f678]) ).
fof(f678,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f513,axiom,
! [X2,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f262200,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_q,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f261938,f884]) ).
fof(f884,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[],[f357,f651]) ).
fof(f651,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f357,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f261938,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_q,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(superposition,[],[f82518,f572]) ).
fof(f572,axiom,
! [X8] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q,X8,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f82518,plain,
! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[],[f453,f659]) ).
fof(f453,axiom,
! [X2,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X2,X4,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X8,c_Polynomial_Opoly(X4,X8,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
fof(f24021,plain,
! [X0,X1] : v_p = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),
inference(resolution,[],[f23999,f659]) ).
fof(f23999,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| v_p = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(forward_demodulation,[],[f23989,f560]) ).
fof(f23989,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(trivial_inequality_removal,[],[f23974]) ).
fof(f23974,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
inference(superposition,[],[f426,f3318]) ).
fof(f3318,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f3316,f560]) ).
fof(f3316,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(resolution,[],[f264,f690]) ).
fof(f690,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f264,axiom,
! [X2,X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
fof(f426,axiom,
! [X0,X4,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Odegree(X4,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(X4,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).
fof(f554,axiom,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__not__zero_0) ).
fof(f730,plain,
v_p != v_q,
inference(superposition,[],[f573,f560]) ).
fof(f573,axiom,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ALG426-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 19:56:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (24747)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.41 % (24750)WARNING: value z3 for option sas not known
% 0.14/0.41 % (24748)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.41 % (24751)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.41 % (24752)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)
% 0.14/0.41 % (24753)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)
% 0.14/0.41 % (24754)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)
% 0.14/0.41 % (24750)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)
% 0.14/0.41 % (24749)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.48 TRYING [1]
% 0.21/0.49 TRYING [2]
% 2.46/0.73 TRYING [1]
% 2.46/0.73 TRYING [3]
% 2.76/0.77 TRYING [2]
% 8.21/1.54 TRYING [1]
% 8.21/1.55 TRYING [2]
% 9.21/1.77 TRYING [3]
% 10.19/1.90 TRYING [3]
% 11.31/2.01 TRYING [4]
% 18.82/3.08 TRYING [4]
% 46.43/7.03 TRYING [4]
% 51.67/7.75 % (24753)First to succeed.
% 51.67/7.76 % (24753)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24747"
% 51.88/7.76 % (24753)Refutation found. Thanks to Tanya!
% 51.88/7.76 % SZS status Unsatisfiable for theBenchmark
% 51.88/7.76 % SZS output start Proof for theBenchmark
% See solution above
% 51.88/7.77 % (24753)------------------------------
% 51.88/7.77 % (24753)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 51.88/7.77 % (24753)Termination reason: Refutation
% 51.88/7.77
% 51.88/7.77 % (24753)Memory used [KB]: 71821
% 51.88/7.77 % (24753)Time elapsed: 7.349 s
% 51.88/7.77 % (24753)Instructions burned: 21029 (million)
% 51.88/7.77 % (24747)Success in time 7.317 s
%------------------------------------------------------------------------------