%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW217+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 : n018.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 32.19s 5.34s
% Output : CNFRefutation 32.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 60 ( 20 unt; 0 def)
% Number of atoms : 135 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 41 ~; 57 |; 11 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn 57 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dme) ).
fof(f8,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A_Iw_A_N_Az_J_A_K_Acmod_A_Ipoly_Acs_A_Iw_A_N_Az_J_J_A_060_061_Ad_A_K_Am_096) ).
fof(f120,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
=> X1 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(f121,axiom,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(f122,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(f132,axiom,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
<=> ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(f184,axiom,
~ ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_Ad_A_060_A1_059_Ad_A_060_Ae_A_P_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(f1260,conjecture,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1261,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(negated_conjecture,[status(cth)],[f1260]) ).
fof(f1262,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(flattening,[],[f1261]) ).
fof(f1306,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ),
inference(ennf_transformation,[],[f121]) ).
fof(f1307,plain,
! [X0,X1,X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ),
inference(flattening,[],[f1306]) ).
fof(f1308,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X1 = X0 ),
inference(ennf_transformation,[],[f120]) ).
fof(f1309,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X1 = X0 ),
inference(flattening,[],[f1308]) ).
fof(f1312,plain,
? [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
inference(ennf_transformation,[],[f184]) ).
fof(f1313,plain,
? [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
inference(flattening,[],[f1312]) ).
fof(f1695,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(nnf_transformation,[],[f132]) ).
fof(f1696,plain,
! [X0,X1] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| ( X1 != X0
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) )
& ( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
inference(flattening,[],[f1695]) ).
fof(f1699,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK1)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_e,v_m____)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f1313]) ).
fof(f1825,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(cnf_transformation,[],[f1262]) ).
fof(f1917,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
inference(cnf_transformation,[],[f8]) ).
fof(f1938,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f1696]) ).
fof(f1939,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f1696]) ).
fof(f1940,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f1696]) ).
fof(f1944,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f1945,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X0) ),
inference(cnf_transformation,[],[f1307]) ).
fof(f1946,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f1309]) ).
fof(f1952,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1699]) ).
fof(f1959,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
inference(cnf_transformation,[],[f5]) ).
fof(f2706,plain,
! [X1] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_resolution,[],[f1938]) ).
tcf(c_49,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),v_e),
inference(cnf_transformation,[],[f1825]) ).
tcf(c_137,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)),
inference(cnf_transformation,[],[f1917]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| ( X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f1940]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f1939]) ).
tcf(c_158,plain,
! [X0: $i] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[],[f2706]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f1944]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f1945]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1) ),
inference(cnf_transformation,[],[f1946]) ).
tcf(c_170,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1952]) ).
tcf(c_177,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
inference(cnf_transformation,[],[f1959]) ).
tcf(c_30191,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(superposition,[status(thm)],[c_170,c_157]) ).
tcf(c_30216,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e),
inference(superposition,[status(thm)],[c_177,c_157]) ).
tcf(c_31293,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_162,c_156]) ).
tcf(c_32893,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X1)
| ( X0 = X1 ) ),
inference(superposition,[status(thm)],[c_31293,c_156]) ).
tcf(c_33693,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(superposition,[status(thm)],[c_30191,c_163]) ).
tcf(c_33876,plain,
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____)) ),
inference(superposition,[status(thm)],[c_30216,c_164]) ).
tcf(c_34022,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(superposition,[status(thm)],[c_162,c_33693]) ).
tcf(c_41771,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ) ),
inference(superposition,[status(thm)],[c_32893,c_49]) ).
tcf(c_41814,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ) ),
inference(superposition,[status(thm)],[c_41771,c_157]) ).
tcf(c_41822,plain,
! [X0: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,X0)
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))),X0) ),
inference(superposition,[status(thm)],[c_41814,c_163]) ).
tcf(c_41864,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ) ),
inference(superposition,[status(thm)],[c_34022,c_41822]) ).
tcf(c_42654,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = sK1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ) ),
inference(superposition,[status(thm)],[c_41864,c_156]) ).
tcf(c_95496,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ) ),
inference(superposition,[status(thm)],[c_137,c_41822]) ).
tcf(c_95763,plain,
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____),v_e) ),
inference(superposition,[status(thm)],[c_95496,c_164]) ).
tcf(c_95772,plain,
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95763,c_30216]) ).
tcf(c_95953,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e ) ),
inference(superposition,[status(thm)],[c_95772,c_137]) ).
tcf(c_96023,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,sK1,v_e)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_e,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = sK1 )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)))) = v_e ) ),
inference(superposition,[status(thm)],[c_95772,c_42654]) ).
tcf(c_97662,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_da____),v_m____) = v_e,
inference(global_subsumption_just,[status(thm)],[c_96023,c_33876,c_95953]) ).
tcf(c_97675,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_e,v_e),
inference(demodulation,[status(thm)],[c_177,c_97662]) ).
tcf(c_97676,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_97675,c_158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW217+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 21:48:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 32.19/5.34 % SZS status Started for theBenchmark.p
% 32.19/5.34 % SZS status Theorem for theBenchmark.p
% 32.19/5.34
% 32.19/5.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 32.19/5.34
% 32.19/5.34 % ------ iProver source info
% 32.19/5.34
% 32.19/5.34 % git: date: 2026-07-19 20:42:38 +0200
% 32.19/5.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 32.19/5.34 % git: non_committed_changes: false
% 32.19/5.34
% 32.19/5.34 % ------ Parsing...
% 32.19/5.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 32.19/5.34
% 32.19/5.34 % ------ Preprocessing... sup_sim: 66 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 32.19/5.34
% 32.19/5.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 32.19/5.34
% 32.19/5.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 32.19/5.34 % ------ Proving...
% 32.19/5.34 % ------ Problem Properties
% 32.19/5.34
% 32.19/5.34 %
% 32.19/5.34 % clauses 552
% 32.19/5.34 % conjectures 1
% 32.19/5.34 % EPR 37
% 32.19/5.34 % Horn 462
% 32.19/5.34 % unary 162
% 32.19/5.34 % binary 233
% 32.19/5.34 % lits 1139
% 32.19/5.34 % lits eq 389
% 32.19/5.34 % fd_pure 0
% 32.19/5.34 % fd_pseudo 0
% 32.19/5.34 % fd_cond 54
% 32.19/5.34 % fd_pseudo_cond 29
% 32.19/5.34 % AC symbols 0
% 32.19/5.34
% 32.19/5.34 % ------ Schedule dynamic 5 is on
% 32.19/5.34
% 32.19/5.34 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 32.19/5.34
% 32.19/5.34
% 32.19/5.34 % ------
% 32.19/5.34 % Current options:
% 32.19/5.34 % ------
% 32.19/5.34
% 32.19/5.34
% 32.19/5.34 %
% 32.19/5.34
% 32.19/5.34 % ------ Proving...
% 32.19/5.34 %
% 32.19/5.34
% 32.19/5.34 % SZS status Theorem for theBenchmark.p
% 32.19/5.34
% 32.19/5.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 32.19/5.34
% 32.19/5.34
%------------------------------------------------------------------------------