%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW219+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n020.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 : Fri Sep 25 03:29:16 PM UTC 2026
% Result : Theorem 16.22s 13.27s
% Output : CNFRefutation 16.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 61 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 28 ~; 19 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 38 ( 0 sgn 31 !; 7 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
? [X0] :
! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X1)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,X1)),v_r) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) ).
fof(f14,axiom,
! [X0] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).
fof(f192,axiom,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f1266,axiom,
! [X0] :
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,X1)),v_r)
=> ( ! [X1] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X1)))))
=> v_thesis____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1267,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f1268,negated_conjecture,
~ v_thesis____,
inference(negated_conjecture,[status(cth)],[f1267]) ).
fof(f1269,plain,
! [X0] :
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,X1)),v_r)
=> ( ! [X2] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,X2))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X2)))))
=> v_thesis____ ) ),
inference(rectify,[],[f1266]) ).
fof(f1270,plain,
~ v_thesis____,
inference(flattening,[],[f1268]) ).
fof(f1271,plain,
! [X0] :
( ? [X1] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,X1)),v_r)
| ? [X2] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,X2))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X2)))))
| v_thesis____ ),
inference(ennf_transformation,[],[f1269]) ).
fof(f1272,plain,
! [X0] :
( ? [X1] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,X1)),v_r)
| ? [X2] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,X2))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X2)))))
| v_thesis____ ),
inference(flattening,[],[f1271]) ).
fof(f1575,plain,
! [X0] :
( ? [X2] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,X2)),v_r)
| ? [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X1)))))
| v_thesis____ ),
inference(rectify,[],[f1272]) ).
fof(f1576,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(sK0(X0))))))
| v_thesis____ ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0))],[f1575]) ).
fof(f1669,plain,
! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK21,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X1)))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(sK21,X1)),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(X0,sK21)],[f5]) ).
fof(f1757,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(sK0(X0))))))
| v_thesis____ ),
inference(cnf_transformation,[],[f1576]) ).
fof(f1758,plain,
~ v_thesis____,
inference(cnf_transformation,[],[f1270]) ).
fof(f1990,plain,
! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f192]) ).
fof(f2010,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK21,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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(X1))))),
inference(cnf_transformation,[],[f1669]) ).
fof(f2011,plain,
! [X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(sK21,X1)),v_r),
inference(cnf_transformation,[],[f1669]) ).
fof(f2169,plain,
! [X0] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f14]) ).
fof(f2412,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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_Oone__class_Oone(tc_Nat_Onat),sK0(X0))))))
| v_thesis____ ),
inference(definition_unfolding,[],[f1757,f1990]) ).
fof(f2418,plain,
! [X1] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK21,X1))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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_Oone__class_Oone(tc_Nat_Onat),X1))))),
inference(definition_unfolding,[],[f2010,f1990]) ).
fof(f2533,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(definition_unfolding,[],[f2169,f1990]) ).
tcf(c_49,plain,
! [X0: $i] :
( v_thesis____
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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_Oone__class_Oone(tc_Nat_Onat),sK0(X0)))))) ),
inference(cnf_transformation,[],[f2412]) ).
tcf(c_50,negated_conjecture,
~ v_thesis____,
inference(cnf_transformation,[],[f1758]) ).
tcf(c_295,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(sK21,X0)),v_r),
inference(cnf_transformation,[],[f2011]) ).
tcf(c_296,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK21,X0))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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_Oone__class_Oone(tc_Nat_Onat),X0))))),
inference(cnf_transformation,[],[f2418]) ).
tcf(c_449,plain,
! [X0: $i] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f2533]) ).
tcf(c_1140,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),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_Oone__class_Oone(tc_Nat_Onat),sK0(X0)))))) ),
inference(prop_impl_just,[status(thm)],[c_50,c_49]) ).
tcf(c_5978,plain,
! [X0: $i] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK21,X0))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),
inference(light_normalisation,[status(thm)],[c_296,c_449]) ).
tcf(c_6255,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK0(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) ),
inference(demodulation,[status(thm)],[c_1140,c_449]) ).
tcf(c_11426,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK0(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r) ),
inference(prop_impl_just,[status(thm)],[c_6255]) ).
tcf(c_11427,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(X0,sK1(X0))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(X0,sK0(X0)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK0(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) ),
inference(renaming,[status(thm)],[c_11426]) ).
tcf(c_27988,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(sK21,sK1(sK21))),v_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK21,sK0(sK21)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK0(sK21)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) ),
inference(instantiation,[status(thm)],[c_11427]) ).
tcf(c_27989,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(sK21,sK1(sK21))),v_r),
inference(instantiation,[status(thm)],[c_295]) ).
tcf(c_33947,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),hAPP(sK21,sK0(sK21)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK0(sK21)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),
inference(instantiation,[status(thm)],[c_5978]) ).
tcf(c_33948,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_33947,c_27989,c_27988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW219+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/10.38 % Computer : n020.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Thu Sep 24 21:46:44 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.42 Running first-order theorem proving
% 0.15/10.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.43
% 0.15/10.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.43
% 0.15/10.43 % Detected problem language: tptp
% 0.15/10.44 % Proving...
% 16.22/13.27 % SZS status Started for theBenchmark.p
% 16.22/13.27 % SZS status Theorem for theBenchmark.p
% 16.22/13.27
% 16.22/13.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.22/13.27
% 16.22/13.27 % ------ iProver source info
% 16.22/13.27
% 16.22/13.27 % git: date: 2026-07-19 20:42:38 +0200
% 16.22/13.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.22/13.27 % git: non_committed_changes: false
% 16.22/13.27
% 16.22/13.27 % ------ Parsing...
% 16.22/13.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.22/13.27
% 16.22/13.27 % ------ Preprocessing... sup_sim: 56 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 16.22/13.27
% 16.22/13.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 16.22/13.27
% 16.22/13.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.22/13.27 % ------ Proving...
% 16.22/13.27 % ------ Problem Properties
% 16.22/13.27
% 16.22/13.27 %
% 16.22/13.27 % clauses 473
% 16.22/13.27 % conjectures 0
% 16.22/13.27 % EPR 26
% 16.22/13.27 % Horn 412
% 16.22/13.27 % unary 145
% 16.22/13.27 % binary 193
% 16.22/13.27 % lits 982
% 16.22/13.27 % lits eq 295
% 16.22/13.27 % fd_pure 0
% 16.22/13.27 % fd_pseudo 0
% 16.22/13.27 % fd_cond 31
% 16.22/13.27 % fd_pseudo_cond 22
% 16.22/13.27 % AC symbols 0
% 16.22/13.27
% 16.22/13.27 % ------ Schedule dynamic 5 is on
% 16.22/13.27
% 16.22/13.27 % ------ no conjectures: strip conj schedule
% 16.22/13.27
% 16.22/13.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 16.22/13.27
% 16.22/13.27
% 16.22/13.27 % ------
% 16.22/13.27 % Current options:
% 16.22/13.27 % ------
% 16.22/13.27
% 16.22/13.27
% 16.22/13.27 %
% 16.22/13.27
% 16.22/13.27 % ------ Proving...
% 16.22/13.27 %
% 16.22/13.27
% 16.22/13.27 % SZS status Theorem for theBenchmark.p
% 16.22/13.27
% 16.22/13.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.22/13.27
% 16.22/13.27
%------------------------------------------------------------------------------