%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW227+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:11:46 PM UTC 2026
% Result : Theorem 57.85s 9.07s
% Output : CNFRefutation 57.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 79 ( 56 unt; 0 def)
% Number of atoms : 112 ( 42 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 63 ( 30 ~; 23 |; 1 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_minus__minus,axiom,
! [X11,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ouminus__class_Ouminus(X3,c_Groups_Ouminus__class_Ouminus(X3,X11)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_inverse__inverse__eq,axiom,
! [X11,X3] :
( class_Rings_Odivision__ring__inverse__zero(X3)
=> c_Rings_Oinverse__class_Oinverse(X3,c_Rings_Oinverse__class_Oinverse(X3,X11)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
fof(fact_Bit0__def,axiom,
! [X10] : c_Int_OBit0(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Suc__eq__plus1,axiom,
! [X38] : c_Nat_OSuc(X38) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_Bit1__def,axiom,
! [X10] : c_Int_OBit1(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_real__diff__def,axiom,
! [X33,X27] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X27,X33) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X27,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X33)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X32,X11,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X11,X32) = c_Groups_Oplus__class_Oplus(X3,X32,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_inverse__eq__divide,axiom,
! [X11,X3] :
( class_Rings_Odivision__ring(X3)
=> c_Rings_Oinverse__class_Oinverse(X3,X11) = c_Rings_Oinverse__class_Odivide(X3,c_Groups_Oone__class_Oone(X3),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(fact_inverse__divide,axiom,
! [X29,X11,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> c_Rings_Oinverse__class_Oinverse(X3,c_Rings_Oinverse__class_Odivide(X3,X11,X29)) = c_Rings_Oinverse__class_Odivide(X3,X29,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__divide) ).
fof(fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096) ).
fof(fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).
fof(fact_add__Pls__right,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Int_OPls) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_real__norm__def,axiom,
! [X27] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X27) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_nat__add__assoc,axiom,
! [X10,X38,X37] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X38),X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X10)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(fact_inverse__positive__iff__positive,axiom,
! [X26,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Rings_Oinverse__class_Oinverse(X3,X26))
<=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X26) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(fact_e2,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_e2) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(c_0_23,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_24,plain,
! [X2216,X2217] :
( c_Groups_Ouminus__class_Ouminus(X2217,c_Groups_Ouminus__class_Ouminus(X2217,X2216)) = X2216
| ~ class_Groups_Ogroup__add(X2217) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])])]) ).
fof(c_0_25,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_26,plain,
! [X1417,X1418] :
( c_Rings_Oinverse__class_Oinverse(X1418,c_Rings_Oinverse__class_Oinverse(X1418,X1417)) = X1417
| ~ class_Rings_Odivision__ring__inverse__zero(X1418) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])])]) ).
fof(c_0_27,plain,
! [X138] : c_Int_OBit0(X138) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X138,X138),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_28,plain,
! [X1330] : c_Nat_OSuc(X1330) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1330,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_29,plain,
! [X108] : c_Int_OBit1(X108) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X108),X108),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_30,plain,
! [X426,X427] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X427,X426) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X427,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X426)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
cnf(c_0_31,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(c_0_33,plain,
! [X2576,X2577,X2578] :
( c_Groups_Oplus__class_Oplus(X2578,X2577,X2576) = c_Groups_Oplus__class_Oplus(X2578,X2576,X2577)
| ~ class_Rings_Ocomm__semiring__1(X2578) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])])]) ).
fof(c_0_34,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
fof(c_0_35,plain,
! [X1717,X1718] :
( c_Rings_Oinverse__class_Oinverse(X1718,X1717) = c_Rings_Oinverse__class_Odivide(X1718,c_Groups_Oone__class_Oone(X1718),X1717)
| ~ class_Rings_Odivision__ring(X1718) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__divide])])]) ).
cnf(c_0_36,plain,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Oinverse(X1,X2)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).
fof(c_0_38,plain,
! [X1890,X1891,X1892] :
( c_Rings_Oinverse__class_Oinverse(X1892,c_Rings_Oinverse__class_Odivide(X1892,X1891,X1890)) = c_Rings_Oinverse__class_Odivide(X1892,X1890,X1891)
| ~ class_Fields_Ofield__inverse__zero(X1892) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__divide])])]) ).
fof(c_0_39,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))) ),
inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096])]) ).
cnf(c_0_40,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),
inference(split_conjunct,[status(thm)],[fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096]) ).
cnf(c_0_41,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_42,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_43,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_29]) ).
fof(c_0_44,plain,
! [X134] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X134,c_Int_OPls) = X134,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_45,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_46,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_47,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_48,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(c_0_49,plain,
! [X149] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X149) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X149),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_50,plain,
! [X906,X907,X908] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X908,X907),X906) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X908,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X907,X906)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
cnf(c_0_51,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_34]) ).
cnf(c_0_52,plain,
( ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_53,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
fof(c_0_54,plain,
! [X1982,X1983] :
( ( ~ class_Fields_Olinordered__field__inverse__zero(X1983)
| c_Orderings_Oord__class_Oless(X1983,c_Groups_Ozero__class_Ozero(X1983),c_Rings_Oinverse__class_Oinverse(X1983,X1982))
| ~ c_Orderings_Oord__class_Oless(X1983,c_Groups_Ozero__class_Ozero(X1983),X1982) )
& ( ~ class_Fields_Olinordered__field__inverse__zero(X1983)
| c_Orderings_Oord__class_Oless(X1983,c_Groups_Ozero__class_Ozero(X1983),X1982)
| ~ c_Orderings_Oord__class_Oless(X1983,c_Groups_Ozero__class_Ozero(X1983),c_Rings_Oinverse__class_Oinverse(X1983,X1982)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])])]) ).
cnf(c_0_55,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_56,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_57,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(c_0_58,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[fact_e2]) ).
cnf(c_0_59,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_60,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43]),c_0_43]) ).
cnf(c_0_61,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_62,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_63,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_64,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_65,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_66,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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)],[c_0_51,c_0_41]),c_0_42]),c_0_43]),c_0_43]) ).
cnf(c_0_67,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_68,plain,
( ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Oinverse(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_69,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).
cnf(c_0_70,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
cnf(c_0_71,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),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_58,c_0_41]),c_0_43]),c_0_43]) ).
cnf(c_0_72,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____)))))) ),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_41]),c_0_41]),c_0_41]),c_0_42]),c_0_42]),c_0_43]),c_0_43]),c_0_43]),c_0_43]),c_0_43]),c_0_43]) ).
cnf(c_0_73,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____))))),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
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_61]),c_0_61]),c_0_61]),c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_74,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),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(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)],[inference(rw,[status(thm)],[c_0_66,c_0_65]),c_0_67]),c_0_62]),c_0_63]),c_0_64]),c_0_61]),c_0_61]),c_0_61]),c_0_61]) ).
cnf(c_0_75,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_76,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))),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(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_71,c_0_62]),c_0_63]),c_0_64]),c_0_61]),c_0_61]),c_0_61]),c_0_61]) ).
cnf(c_0_77,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,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_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_s____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p,v_z____)))))),
inference(sr,[status(thm)],[inference(cn,[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)],[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)],[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)],[inference(rw,[status(thm)],[c_0_72,c_0_65]),c_0_61]),c_0_61]),c_0_61]),c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_69]),c_0_61]),c_0_61]),c_0_61]),c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_61]),c_0_61]),c_0_61]),c_0_61]),c_0_62]),c_0_63]),c_0_64]),c_0_65]),c_0_73])]),c_0_74]) ).
cnf(c_0_78,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW227+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 09:40:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 57.85/9.07 % Version: 3.5.1
% 57.85/9.07 % Preprocessing class: FMLSSMSMSSSNFFN.
% 57.85/9.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 57.85/9.07 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 57.85/9.07 % Starting new_bool_3 with 600s (2) cores
% 57.85/9.07 % Starting new_bool_1 with 600s (2) cores
% 57.85/9.07 % Starting sh5l with 300s (1) cores
% 57.85/9.07 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with pid 768168 completed with status 0
% 57.85/9.07 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d
% 57.85/9.07 % Preprocessing class: FMLSSMSMSSSNFFN.
% 57.85/9.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 57.85/9.07 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 57.85/9.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 57.85/9.07 % No SInE strategy applied
% 57.85/9.07 % Search class: FGHSM-SMLM31-DFFFFFNN
% 57.85/9.07 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 57.85/9.07 % Starting SubtermCWHack with 82s (1) cores
% 57.85/9.07 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 91s (1) cores
% 57.85/9.07 % Starting SAT001_MinMin_p005000_rr_RG with 89s (1) cores
% 57.85/9.07 % SubtermCWHack with pid 768203 completed with status 0
% 57.85/9.07 % Result found by SubtermCWHack
% 57.85/9.07 % Preprocessing class: FMLSSMSMSSSNFFN.
% 57.85/9.07 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 57.85/9.07 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 900s (3) cores
% 57.85/9.07 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 57.85/9.07 % No SInE strategy applied
% 57.85/9.07 % Search class: FGHSM-SMLM31-DFFFFFNN
% 57.85/9.07 % Scheduled 7 strats onto 3 cores with 900 seconds (900 total)
% 57.85/9.07 % Starting SubtermCWHack with 82s (1) cores
% 57.85/9.07 % Preprocessing time : 0.035 s
% 57.85/9.07
% 57.85/9.07 % Proof found!
% 57.85/9.07 % SZS status Theorem
% 57.85/9.07 % SZS output start CNFRefutation
% See solution above
% 57.85/9.07 % Parsed axioms : 1171
% 57.85/9.07 % Removed by relevancy pruning/SinE : 0
% 57.85/9.07 % Initial clauses : 1749
% 57.85/9.07 % Removed in clause preprocessing : 79
% 57.85/9.07 % Initial clauses in saturation : 1670
% 57.85/9.07 % Processed clauses : 33176
% 57.85/9.07 % ...of these trivial : 1223
% 57.85/9.07 % ...subsumed : 24550
% 57.85/9.07 % ...remaining for further processing : 7403
% 57.85/9.07 % Other redundant clauses eliminated : 788
% 57.85/9.07 % Clauses deleted for lack of memory : 0
% 57.85/9.07 % Backward-subsumed : 262
% 57.85/9.07 % Backward-rewritten : 373
% 57.85/9.07 % Generated clauses : 229825
% 57.85/9.07 % ...of the previous two non-redundant : 182250
% 57.85/9.07 % ...aggressively subsumed : 0
% 57.85/9.07 % Contextual simplify-reflections : 6
% 57.85/9.07 % Paramodulations : 229000
% 57.85/9.07 % Factorizations : 28
% 57.85/9.07 % NegExts : 0
% 57.85/9.07 % Equation resolutions : 819
% 57.85/9.07 % Disequality decompositions : 0
% 57.85/9.07 % Total rewrite steps : 184823
% 57.85/9.07 % ...of those cached : 175693
% 57.85/9.07 % Propositional unsat checks : 0
% 57.85/9.07 % Propositional check models : 0
% 57.85/9.07 % Propositional check unsatisfiable : 0
% 57.85/9.07 % Propositional clauses : 0
% 57.85/9.07 % Propositional clauses after purity: 0
% 57.85/9.07 % Propositional unsat core size : 0
% 57.85/9.07 % Propositional preprocessing time : 0.000
% 57.85/9.07 % Propositional encoding time : 0.000
% 57.85/9.07 % Propositional solver time : 0.000
% 57.85/9.07 % Success case prop preproc time : 0.000
% 57.85/9.07 % Success case prop encoding time : 0.000
% 57.85/9.07 % Success case prop solver time : 0.000
% 57.85/9.07 % Current number of processed clauses : 6639
% 57.85/9.07 % Positive orientable unit clauses : 1515
% 57.85/9.07 % Positive unorientable unit clauses: 23
% 57.85/9.07 % Negative unit clauses : 1333
% 57.85/9.07 % Non-unit-clauses : 3768
% 57.85/9.07 % Current number of unprocessed clauses: 149566
% 57.85/9.07 % ...number of literals in the above : 409708
% 57.85/9.07 % Current number of archived formulas : 0
% 57.85/9.07 % Current number of archived clauses : 638
% 57.85/9.07 % Clause-clause subsumption calls (NU) : 1224167
% 57.85/9.07 % Rec. Clause-clause subsumption calls : 879073
% 57.85/9.07 % Non-unit clause-clause subsumptions : 9094
% 57.85/9.07 % Unit Clause-clause subsumption calls : 215320
% 57.85/9.07 % Rewrite failures with RHS unbound : 0
% 57.85/9.07 % BW rewrite match attempts : 53073
% 57.85/9.07 % BW rewrite match successes : 274
% 57.85/9.07 % Condensation attempts : 0
% 57.85/9.07 % Condensation successes : 0
% 57.85/9.07 % Termbank termtop insertions : 3622963
% 57.85/9.07 % Search garbage collected termcells : 20282
% 57.85/9.07
% 57.85/9.07 % -------------------------------------------------
% 57.85/9.07 % User time : 7.820 s
% 57.85/9.07 % System time : 0.243 s
% 57.85/9.07 % Total time : 8.063 s
% 57.85/9.07 % Maximum resident set size: 9792 pages
% 57.85/9.07
% 57.85/9.07 % -------------------------------------------------
% 57.85/9.07 % User time : 22.970 s
% 57.85/9.07 % System time : 0.782 s
% 57.85/9.07 % Total time : 23.752 s
% 57.85/9.07 % Maximum resident set size: 5888 pages
% 57.85/9.07 % E exiting
%------------------------------------------------------------------------------