TSTP Solution File: SWW210+1 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW210+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n032.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 : 600s
% DateTime : Thu Jul 21 00:10:18 EDT 2022
% Result : Theorem 0.27s 2.46s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 35 unt; 0 def)
% Number of atoms : 154 ( 33 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 118 ( 45 ~; 56 |; 5 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 11 con; 0-3 aty)
% Number of variables : 105 ( 20 sgn 45 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IRe_A_Is_A_If_An_J_J_A_N_Ax_J_A_060_Ae_A_P_A2_096,axiom,
? [X4] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X5))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IRe_A_Is_A_If_An_J_J_A_N_Ax_J_A_060_Ae_A_P_A2_096) ).
fof(fact_Bit0__def,axiom,
! [X17] : c_Int_OBit0(X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X17),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X17] : c_Int_OBit1(X17) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X17),X17),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit1__def) ).
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_1) ).
fof(conj_0,hypothesis,
( ? [X81] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X81,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X5))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> ( ? [X82] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X82,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X5)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
=> v_thesis____ ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).
fof(fact_add__Pls__right,axiom,
! [X17] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Int_OPls) = X17,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Pls__right) ).
fof(fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_096,axiom,
? [X4] :
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X5)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_096) ).
fof(fact_le__iff__add,axiom,
! [X38,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X38)
<=> ? [X57] : X38 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X57) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__le__linear,axiom,
! [X37,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X37)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X40) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_diff__add__inverse,axiom,
! [X40,X37] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X40),X37) = X40,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__is__0__eq,axiom,
! [X38,X39] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X39,X38) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X38) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X40] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X40,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X40,
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_le__refl,axiom,
! [X37] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X37),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_le__refl) ).
fof(fact_le__antisym,axiom,
! [X37,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X40,X37)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X37,X40)
=> X40 = X37 ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_le__antisym) ).
fof(c_0_14,plain,
! [X7] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_0,X7)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X7))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IRe_A_Is_A_If_An_J_J_A_N_Ax_J_A_060_Ae_A_P_A2_096])])]) ).
fof(c_0_15,plain,
! [X18] : c_Int_OBit0(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X18),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_16,plain,
! [X18] : c_Int_OBit1(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18),X18),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_17,negated_conjecture,
~ v_thesis____,
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(c_0_18,hypothesis,
! [X83,X85] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X85,esk2_1(X85))
| v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83,esk1_1(X83)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X85))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X83,esk1_1(X83)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X85,esk2_1(X85))
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X83)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X85))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X83)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])])])])])]) ).
cnf(c_0_19,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_22,plain,
! [X18] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,c_Int_OPls) = X18,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_23,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[c_0_17]) ).
cnf(c_0_24,hypothesis,
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk2_1(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X7] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk3_0,X7)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X7)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096EX_An0_O_AALL_An_062_061n0_O_Aabs_A_IIm_A_Is_A_If_A_Ig_An_J_J_J_A_N_Ay_J_A_060_Ae_A_P_A2_096])])]) ).
cnf(c_0_26,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_27,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk1_1(X1))
| v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk2_1(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,hypothesis,
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk2_1(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_31,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk3_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,plain,
! [X58,X59,X58,X59,X61] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59,X58)
| X58 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X59,esk6_2(X58,X59)) )
& ( X58 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X59,X61)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59,X58) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])])]) ).
cnf(c_0_33,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_34,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk1_1(X1))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,esk2_1(X2)) ),
inference(sr,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk2_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X2)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_29]) ).
cnf(c_0_36,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_20]),c_0_21]),c_0_21]) ).
fof(c_0_37,plain,
! [X41,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X42) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(c_0_38,plain,
! [X41,X42] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X42,X41),X42) = X41,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
cnf(c_0_39,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk6_2(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk2_1(X1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
fof(c_0_41,plain,
( ~ epred1_0
<=> ! [X2] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X2))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(definition) ).
cnf(c_0_42,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk3_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_27]),c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_43,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_45,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk6_2(esk2_1(X1),X1)) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_46,plain,
! [X40,X41,X40,X41] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X40) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X40)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X41,X40) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])])])]) ).
cnf(c_0_47,hypothesis,
( epred1_0
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X1))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(split_equiv,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk3_0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,X1)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,hypothesis,
esk6_2(esk2_1(X1),X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk2_1(X1),X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_51,hypothesis,
( epred1_0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk2_1(X1),esk3_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_52,plain,
! [X41] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X41,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_53,plain,
! [X38] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X38),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
cnf(c_0_54,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X2))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_55,hypothesis,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk2_1(X1),X1)) = esk2_1(X1),
inference(rw,[status(thm)],[c_0_45,c_0_49]) ).
cnf(c_0_56,hypothesis,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,esk2_1(X1),esk3_0) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| epred1_0 ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_58,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_59,plain,
( ~ epred2_0
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
introduced(definition) ).
cnf(c_0_60,hypothesis,
( v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X2))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_20]),c_0_20]),c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_61,hypothesis,
( esk2_1(esk3_0) = esk3_0
| epred1_0 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).
cnf(c_0_62,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk3_0)))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(spm,[status(thm)],[c_0_42,c_0_58]) ).
cnf(c_0_63,hypothesis,
( epred2_0
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk1_1(X1)))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(split_equiv,[status(thm)],[c_0_59]) ).
cnf(c_0_64,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk8_0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,X1))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_65,hypothesis,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_29]),c_0_41]),c_0_59]) ).
cnf(c_0_66,hypothesis,
epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_61]),c_0_62])]) ).
cnf(c_0_67,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk1_1(X1))
| v_thesis____
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X2))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_68,plain,
! [X41,X42] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,X41)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X42)
| X42 = X41 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
cnf(c_0_69,hypothesis,
( epred2_0
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk1_1(X1),esk8_0) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,hypothesis,
~ epred2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).
cnf(c_0_71,hypothesis,
( v_thesis____
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk1_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X2))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_72,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk1_1(X1),esk8_0),
inference(sr,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,hypothesis,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk1_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(X2))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_27]),c_0_27]),c_0_27]),c_0_27]),c_0_29]) ).
cnf(c_0_75,hypothesis,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_s(hAPP(v_f____,hAPP(v_ga____,esk2_1(esk3_0))))),v_y____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_76,hypothesis,
( esk8_0 = esk1_1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk8_0,esk1_1(X1)) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,hypothesis,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,esk1_1(X1)),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_78,hypothesis,
esk1_1(esk8_0) = esk8_0,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_79,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_s(hAPP(v_f____,esk8_0))),v_x____)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e____,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(spm,[status(thm)],[c_0_33,c_0_58]) ).
cnf(c_0_80,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_78]),c_0_79])]),c_0_70]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWW210+1 : TPTP v8.1.0. Released v5.2.0.
% 0.10/0.11 % Command : run_ET %s %d
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Sat Jun 4 10:31:02 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.27/2.46 # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.27/2.46 # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.27/2.46 # Preprocessing time : 0.037 s
% 0.27/2.46
% 0.27/2.46 # Proof found!
% 0.27/2.46 # SZS status Theorem
% 0.27/2.46 # SZS output start CNFRefutation
% See solution above
% 0.27/2.46 # Proof object total steps : 81
% 0.27/2.46 # Proof object clause steps : 50
% 0.27/2.46 # Proof object formula steps : 31
% 0.27/2.46 # Proof object conjectures : 4
% 0.27/2.46 # Proof object clause conjectures : 1
% 0.27/2.46 # Proof object formula conjectures : 3
% 0.27/2.46 # Proof object initial clauses used : 19
% 0.27/2.46 # Proof object initial formulas used : 14
% 0.27/2.46 # Proof object generating inferences : 17
% 0.27/2.46 # Proof object simplifying inferences : 59
% 0.27/2.46 # Training examples: 0 positive, 0 negative
% 0.27/2.46 # Parsed axioms : 1202
% 0.27/2.46 # Removed by relevancy pruning/SinE : 936
% 0.27/2.46 # Initial clauses : 375
% 0.27/2.46 # Removed in clause preprocessing : 14
% 0.27/2.46 # Initial clauses in saturation : 361
% 0.27/2.46 # Processed clauses : 5556
% 0.27/2.46 # ...of these trivial : 340
% 0.27/2.46 # ...subsumed : 2834
% 0.27/2.46 # ...remaining for further processing : 2382
% 0.27/2.46 # Other redundant clauses eliminated : 819
% 0.27/2.46 # Clauses deleted for lack of memory : 0
% 0.27/2.46 # Backward-subsumed : 47
% 0.27/2.46 # Backward-rewritten : 216
% 0.27/2.46 # Generated clauses : 69360
% 0.27/2.46 # ...of the previous two non-trivial : 60611
% 0.27/2.46 # Contextual simplify-reflections : 49
% 0.27/2.46 # Paramodulations : 68101
% 0.27/2.46 # Factorizations : 10
% 0.27/2.46 # Equation resolutions : 1242
% 0.27/2.46 # Current number of processed clauses : 2104
% 0.27/2.46 # Positive orientable unit clauses : 774
% 0.27/2.46 # Positive unorientable unit clauses: 45
% 0.27/2.46 # Negative unit clauses : 89
% 0.27/2.46 # Non-unit-clauses : 1196
% 0.27/2.46 # Current number of unprocessed clauses: 48249
% 0.27/2.46 # ...number of literals in the above : 92835
% 0.27/2.46 # Current number of archived formulas : 0
% 0.27/2.46 # Current number of archived clauses : 269
% 0.27/2.46 # Clause-clause subsumption calls (NU) : 91316
% 0.27/2.46 # Rec. Clause-clause subsumption calls : 88960
% 0.27/2.46 # Non-unit clause-clause subsumptions : 2280
% 0.27/2.46 # Unit Clause-clause subsumption calls : 4675
% 0.27/2.46 # Rewrite failures with RHS unbound : 0
% 0.27/2.46 # BW rewrite match attempts : 19743
% 0.27/2.46 # BW rewrite match successes : 285
% 0.27/2.46 # Condensation attempts : 0
% 0.27/2.46 # Condensation successes : 0
% 0.27/2.46 # Termbank termtop insertions : 2443309
% 0.27/2.46
% 0.27/2.46 # -------------------------------------------------
% 0.27/2.46 # User time : 1.041 s
% 0.27/2.46 # System time : 0.029 s
% 0.27/2.46 # Total time : 1.070 s
% 0.27/2.46 # Maximum resident set size: 61072 pages
% 0.27/23.45 eprover: CPU time limit exceeded, terminating
% 0.27/23.45 eprover: CPU time limit exceeded, terminating
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: CPU time limit exceeded, terminating
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.51 eprover: eprover: No such file or directory
% 0.27/23.51 Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.52 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.52 eprover: No such file or directory
%------------------------------------------------------------------------------