TSTP Solution File: SWV632-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n025.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 Sep 29 15:23:54 EDT 2022
% Result : Unsatisfiable 63.36s 40.77s
% Output : Proof 63.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 59
% Syntax : Number of formulae : 121 ( 45 unt; 18 typ; 0 def)
% Number of atoms : 245 ( 142 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 240 ( 106 ~; 96 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 12 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 228 ( 207 !; 0 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(c_HOL_Oone__class_Oone_type,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_Suc_type,type,
c_Suc: $i > $i ).
tff(c_Int_Onumber__class_Onumber__of_type,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(c_Int_OBit0_type,type,
c_Int_OBit0: $i > $i ).
tff(c_Int_OBit1_type,type,
c_Int_OBit1: $i > $i ).
tff(c_Int_OPls_type,type,
c_Int_OPls: $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1_type,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(v_j_type,type,
v_j: $i ).
tff(v_i_type,type,
v_i: $i ).
tff(c_FFT__Mirabelle_Oroot_type,type,
c_FFT__Mirabelle_Oroot: $i > $i ).
tff(v_m_type,type,
v_m: $i ).
tff(1,plain,
( ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) )
<=> ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) )
<=> ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__add__1_0) ).
tff(4,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [V_z: $i] :
refl(
( ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
<=> ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
<=> ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [V_z: $i] :
rewrite(
( ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
<=> ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
<=> ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
<=> ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__2_0) ).
tff(12,plain,
! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ~ ! [V_z: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),V_z,tc_nat) = c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat) )
| ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
^ [V_n: $i,V_m: $i] :
refl(
( ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
<=> ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
<=> ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
tff(22,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ~ ! [V_n: $i,V_m: $i] : ( c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat) )
| ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
tff(30,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [V_a: $i,T_a: $i,V_m: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
<=> ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
<=> ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
tff(35,plain,
! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) )
<=> ( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(40,plain,
( ~ ! [V_a: $i,T_a: $i,V_m: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(unit_resolution,[status(thm)],[40,37,30]) ).
tff(42,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(symmetry,[status(thm)],[41]) ).
tff(43,plain,
^ [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
<=> ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
tff(47,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) )
<=> ( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [V_c: $i,V_b: $i,V_a: $i,T_a: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),
inference(unit_resolution,[status(thm)],[52,49,30]) ).
tff(54,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)),
inference(transitivity,[status(thm)],[54,42,27,17,5]) ).
tff(56,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(monotonicity,[status(thm)],[55]) ).
tff(57,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat) ),
inference(symmetry,[status(thm)],[56]) ).
tff(58,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos2_0) ).
tff(61,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(modus_ponens,[status(thm)],[61,58]) ).
tff(63,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat),
inference(modus_ponens,[status(thm)],[62,57]) ).
tff(64,plain,
^ [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
refl(
( ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
<=> ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
<=> ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
<=> ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
tff(68,plain,
! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) )
<=> ( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [V_rx: $i,T_a: $i,V_ry: $i,V_lx: $i] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| ( c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ( c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),
inference(unit_resolution,[status(thm)],[73,70,30]) ).
tff(75,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),
inference(monotonicity,[status(thm)],[55]) ).
tff(76,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),
inference(transitivity,[status(thm)],[75,74]) ).
tff(77,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat),
inference(monotonicity,[status(thm)],[55]) ).
tff(78,plain,
c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)) = c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(monotonicity,[status(thm)],[78,76]) ).
tff(80,plain,
( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) )
<=> ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(86,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[86,83]) ).
tff(88,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex),
inference(modus_ponens,[status(thm)],[87,82]) ).
tff(89,plain,
^ [V_n: $i,V_d: $i,V_k: $i] :
refl(
( ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
<=> ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
<=> ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [V_n: $i,V_d: $i,V_k: $i] :
rewrite(
( ( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) )
<=> ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [V_n: $i,V_d: $i,V_k: $i] :
( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) )
<=> ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V_n: $i,V_d: $i,V_k: $i] :
( ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).
tff(95,plain,
! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) )
<=> ( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [V_n: $i,V_d: $i,V_k: $i] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_d,tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(V_d,V_n,tc_nat)),c_HOL_Otimes__class_Otimes(V_d,V_k,tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_k,tc_Complex_Ocomplex) ) )
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),tc_nat)
| ( c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_m),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_Complex_Ocomplex) ) ),
inference(unit_resolution,[status(thm)],[101,98]) ).
tff(103,plain,
$false,
inference(unit_resolution,[status(thm)],[102,88,63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV632-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 06:39:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 63.36/40.77 % SZS status Unsatisfiable
% 63.36/40.77 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------