TSTP Solution File: ALG380-1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : ALG380-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 Sep 6 16:10:01 EDT 2022
% Result : Unsatisfiable 118.26s 75.75s
% Output : Proof 118.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 50
% Syntax : Number of formulae : 90 ( 32 unt; 20 typ; 0 def)
% Number of atoms : 172 ( 79 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 173 ( 77 ~; 73 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 14 >; 13 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 119 ( 108 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Complex_Orcis_type,type,
c_Complex_Orcis: ( $i * $i ) > $i ).
tff(v_a_type,type,
v_a: $i ).
tff(c_HOL_Oabs__class_Oabs_type,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(tc_RealDef_Oreal_type,type,
tc_RealDef_Oreal: $i ).
tff(v_r_type,type,
v_r: $i ).
tff(c_HOL_Otimes__class_Otimes_type,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
tff(c_HOL_Oinverse__class_Odivide_type,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $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(c_NthRoot_Osqrt_type,type,
c_NthRoot_Osqrt: $i > $i ).
tff(c_HOL_Oplus__class_Oplus_type,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower_type,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(tc_nat_type,type,
tc_nat: $i ).
tff(class_OrderedGroup_Omonoid__mult_type,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(c_lessequals_type,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add__abs_type,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(1,plain,
^ [V_x: $i] :
refl(
( ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x )
<=> ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x )
<=> ! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x )
<=> ! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).
tff(5,plain,
! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [V_x: $i] : ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = V_x )
| ( c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = v_a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = v_a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
v_a = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
tff(13,plain,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
<=> ( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power2__eq__square_0) ).
tff(18,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| ( c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) )
| ~ class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[23,20,13]) ).
tff(25,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
tff(27,plain,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [V_a: $i,T_a: $i] :
refl(
( ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) )
<=> ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) )
<=> ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
tff(32,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) )
<=> ( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [V_a: $i,T_a: $i] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) )
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[37,34,27]) ).
tff(39,plain,
^ [V_x: $i] :
refl(
( ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
<=> ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
<=> ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [V_x: $i] :
rewrite(
( ( ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [V_x: $i] :
( ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) )
<=> ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [V_x: $i] :
( ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__pow2_0) ).
tff(45,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) ) )
<=> ( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [V_x: $i] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = V_x ) )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),
inference(unit_resolution,[status(thm)],[51,48,38]) ).
tff(53,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal),
inference(transitivity,[status(thm)],[53,24]) ).
tff(55,plain,
c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(monotonicity,[status(thm)],[54,10]) ).
tff(56,plain,
c_Complex_Orcis(c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
^ [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] :
refl(
( ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) )
<=> ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) )
<=> ! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) )
<=> ! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rcis__mult_0) ).
tff(61,plain,
! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [V_r2: $i,V_b: $i,V_a: $i,V_r1: $i] : ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(V_r1,V_a),c_Complex_Orcis(V_r2,V_b),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(V_r1,V_r2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) )
| ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) = c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(transitivity,[status(thm)],[65,56]) ).
tff(67,plain,
( ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a) )
<=> ( c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
tff(69,plain,
c_HOL_Otimes__class_Otimes(c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_Complex_Orcis(c_NthRoot_Osqrt(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(v_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_Complex_Ocomplex) != c_Complex_Orcis(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_a),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ALG380-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n027.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Aug 29 16:34:00 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 118.26/75.75 % SZS status Unsatisfiable
% 118.26/75.75 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------