%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG401-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.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 12:54:11 PM UTC 2026
% Result : Unsatisfiable 84.98s 22.56s
% Output : CNFRefutation 84.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 35 unt; 0 def)
% Number of atoms : 70 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 45 ( 25 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 71 ( 0 sgn 71 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f306,axiom,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
fof(f824,axiom,
! [X2,X3,X0,X1,X4] :
( X4 = c_Polynomial_Opoly(X1,X2,X0)
| c_HOL_Oplus__class_Oplus(X1,c_Polynomial_Osmult(X2,X3,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X4,X3,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
fof(f825,plain,
! [X2,X3,X0,X1,X4] :
( c_Polynomial_Opoly(X1,X2,X0) = X4
| c_HOL_Oplus__class_Oplus(X1,c_Polynomial_Osmult(X2,X3,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X4,X3,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(reorient_equations,[],[f824]) ).
fof(f828,axiom,
! [X0,X1] :
( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
fof(f829,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0)
| ~ class_Ring__and__Field_Oidom(X0) ),
inference(reorient_equations,[],[f828]) ).
fof(f896,axiom,
! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).
fof(f952,axiom,
! [X0] : c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_kas_I4_J_0) ).
fof(f1098,axiom,
! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f1119,axiom,
! [X2,X3,X0,X1] :
( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
fof(f1130,axiom,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1131,plain,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(reorient_equations,[],[f1130]) ).
fof(f1132,axiom,
v_s____ = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f1134,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1242,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1243,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1252,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1267,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
tcf(c_1117,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1134]) ).
tcf(c_1118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X3,X0),X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f1119]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_Polynomial_Opoly(X0,X1,X3) = X4 )
| ~ class_Ring__and__Field_Ocomm__semiring__0(X3)
| ( c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Osmult(X1,X2,X3),tc_Polynomial_Opoly(X3)) != c_Polynomial_OpCons(X4,X2,X3) ) ),
inference(cnf_transformation,[],[f825]) ).
tcf(c_1192,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) )
| ~ class_Ring__and__Field_Oidom(X0) ),
inference(cnf_transformation,[],[f829]) ).
tcf(c_1197,plain,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1131]) ).
tcf(c_1204,plain,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1243]) ).
tcf(c_1205,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1242]) ).
tcf(c_1207,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f896]) ).
tcf(c_1250,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f952]) ).
tcf(c_1287,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f1098]) ).
tcf(c_1319,plain,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1267]) ).
tcf(c_1545,plain,
c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_s____,
inference(cnf_transformation,[],[f1132]) ).
tcf(c_1569,plain,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1252]) ).
tcf(c_1581,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1 )
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_9413,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(light_normalisation,[status(thm)],[c_1250,c_1197]) ).
tcf(c_177544,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1205,c_1287]) ).
tcf(c_177638,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(superposition,[status(thm)],[c_1569,c_1581]) ).
tcf(c_177640,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(X0,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0,
inference(light_normalisation,[status(thm)],[c_177638,c_1545]) ).
tcf(c_177705,plain,
! [X0: $i,X1: $i] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_177544,c_1207]) ).
tcf(c_177774,plain,
! [X0: $i] : c_Polynomial_Osmult(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(superposition,[status(thm)],[c_1319,c_1192]) ).
tcf(c_177776,plain,
! [X0: $i] : c_Polynomial_Osmult(X0,v_s____,tc_Complex_Ocomplex) = v_s____,
inference(light_normalisation,[status(thm)],[c_177774,c_1545]) ).
tcf(c_185943,plain,
! [X0: $i,X1: $i,X2: $i] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[status(thm)],[c_1204,c_1118]) ).
tcf(c_185947,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_9413,c_185943]) ).
tcf(c_185949,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_1117,c_185943]) ).
tcf(c_186085,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_185949,c_177705]) ).
tcf(c_210816,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Opoly(X0,X2,tc_Complex_Ocomplex) = X1 )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_HOL_Oplus__class_Oplus(X0,v_s____,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != c_Polynomial_OpCons(X1,v_s____,tc_Complex_Ocomplex) ) ),
inference(superposition,[status(thm)],[c_177776,c_1126]) ).
tcf(c_210825,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex) = X0 )
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ( c_Polynomial_OpCons(X0,v_s____,tc_Complex_Ocomplex) != X1 ) ),
inference(light_normalisation,[status(thm)],[c_210816,c_177640]) ).
tcf(c_210826,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex) = X0 )
| ( c_Polynomial_OpCons(X0,v_s____,tc_Complex_Ocomplex) != X1 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210825,c_1204]) ).
tcf(c_314839,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,v_k____,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(v_a____,v_s____,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,X0,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_185947,c_177705]) ).
tcf(c_332597,plain,
! [X0: $i,X1: $i] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_s____,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0,
inference(equality_resolution,[status(thm)],[c_210826]) ).
tcf(c_332602,plain,
! [X0: $i] : c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,X0,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_314839,c_332597]) ).
tcf(c_332612,plain,
c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_a____,c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(demodulation,[status(thm)],[c_186085,c_332602]) ).
tcf(c_332613,plain,
$false,
inference(ground_joinability,[status(thm)],[c_332612,c_177544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG401-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 05:33:38 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 84.98/22.56 % SZS status Started for theBenchmark.p
% 84.98/22.56 % SZS status Unsatisfiable for theBenchmark.p
% 84.98/22.56
% 84.98/22.56 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 84.98/22.56
% 84.98/22.56 % ------ iProver source info
% 84.98/22.56
% 84.98/22.56 % git: date: 2026-07-19 20:42:38 +0200
% 84.98/22.56 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 84.98/22.56 % git: non_committed_changes: false
% 84.98/22.56
% 84.98/22.56 % ------ Parsing...% successful
% 84.98/22.56
% 84.98/22.56
% 84.98/22.56 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 84.98/22.56
% 84.98/22.56 % ------ Preprocessing... sup_sim: 2 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 84.98/22.56
% 84.98/22.56 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 84.98/22.56
% 84.98/22.56 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 84.98/22.56 % ------ Proving...
% 84.98/22.56 % ------ Problem Properties
% 84.98/22.56
% 84.98/22.56 %
% 84.98/22.56 % clauses 640
% 84.98/22.56 % conjectures 1
% 84.98/22.56 % EPR 29
% 84.98/22.56 % Horn 508
% 84.98/22.56 % unary 195
% 84.98/22.56 % binary 195
% 84.98/22.56 % lits 1445
% 84.98/22.56 % lits eq 481
% 84.98/22.56 % fd_pure 0
% 84.98/22.56 % fd_pseudo 0
% 84.98/22.56 % fd_cond 63
% 84.98/22.56 % fd_pseudo_cond 27
% 84.98/22.56 % AC symbols 0
% 84.98/22.56
% 84.98/22.56 % ------ Schedule dynamic 5 is on
% 84.98/22.56
% 84.98/22.56 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 84.98/22.56
% 84.98/22.56
% 84.98/22.56 % ------
% 84.98/22.56 % Current options:
% 84.98/22.56 % ------
% 84.98/22.56
% 84.98/22.56
% 84.98/22.56 %
% 84.98/22.56
% 84.98/22.56 % ------ Proving...
% 84.98/22.56 % Proof_search_loop: time out after: 4899 full_loop iterations
% 84.98/22.56
% 84.98/22.56 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 84.98/22.56
% 84.98/22.56
% 84.98/22.56 % ------
% 84.98/22.56 % Current options:
% 84.98/22.56 % ------
% 84.98/22.56
% 84.98/22.56
% 84.98/22.56 %
% 84.98/22.56
% 84.98/22.56 % ------ Proving...
% 84.98/22.56 %
% 84.98/22.56
% 84.98/22.56 % SZS status Unsatisfiable for theBenchmark.p
% 84.98/22.56
% 84.98/22.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 84.98/22.56
% 84.98/22.56
%------------------------------------------------------------------------------