%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG363-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p 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 : Fri Sep 25 12:54:06 PM UTC 2026
% Result : Unsatisfiable 2.01s 1.75s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 27
% Syntax : Number of formulae : 100 ( 52 unt; 0 def)
% Number of atoms : 156 ( 59 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 119 ( 63 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 116 ( 0 sgn 116 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
fof(f172,axiom,
! [X0,X1] :
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
fof(f173,plain,
! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X1
| c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(reorient_equations,[],[f172]) ).
fof(f287,axiom,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_1) ).
fof(f288,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(reorient_equations,[],[f287]) ).
fof(f299,axiom,
! [X0] : c_lessequals(c_Complex_ORe(X0),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_0) ).
fof(f300,axiom,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).
fof(f301,axiom,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_2) ).
fof(f302,axiom,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__add__cancel_0) ).
fof(f522,axiom,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
fof(f550,axiom,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__le__add__iff_0) ).
fof(f559,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).
fof(f571,axiom,
! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__Re__le__cmod_0) ).
fof(f576,axiom,
! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_s(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r_0) ).
fof(f584,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__one__gt__zero_0) ).
fof(f590,axiom,
! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f607,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f629,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f630,axiom,
! [X0] : c_lessequals(X0,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
fof(f650,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
fof(f660,axiom,
! [X0] :
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f661,plain,
! [X0] :
( c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(reorient_equations,[],[f660]) ).
fof(f672,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| X0 = X1
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
fof(f698,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f721,axiom,
! [X0,X1] :
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).
fof(f759,axiom,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f761,axiom,
! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f766,axiom,
! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(X0)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f767,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f792,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f806,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
tcf(c_747,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f767]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| ( X0 = X1 )
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f672]) ).
tcf(c_749,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f607]) ).
tcf(c_766,plain,
! [X0: $i,X1: $i] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f559]) ).
tcf(c_773,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f550]) ).
tcf(c_781,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f288]) ).
tcf(c_782,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f650]) ).
tcf(c_784,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
inference(cnf_transformation,[],[f522]) ).
tcf(c_787,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f698]) ).
tcf(c_789,plain,
! [X0: $i] : c_lessequals(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f630]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f629]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f721]) ).
tcf(c_798,plain,
! [X0: $i] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f584]) ).
tcf(c_802,plain,
! [X0: $i,X1: $i] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f302]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f301]) ).
tcf(c_804,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_805,plain,
! [X0: $i] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(X0)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f766]) ).
tcf(c_807,plain,
! [X0: $i] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X0),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f571]) ).
tcf(c_808,plain,
! [X0: $i] : c_lessequals(c_Complex_ORe(X0),c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f299]) ).
tcf(c_809,plain,
! [X0: $i] : c_lessequals(c_RealVector_Onorm__class_Onorm(v_s(X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f576]) ).
tcf(c_814,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 )
| ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) ) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_856,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f792]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f761]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f759]) ).
tcf(c_867,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f590]) ).
tcf(c_913,plain,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f806]) ).
tcf(c_917,plain,
! [X0: $i] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oone__class_Oone(X0) )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f661]) ).
tcf(c_1116,plain,
! [X0: $i] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oone__class_Oone(X0) )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(prop_impl_just,[status(thm)],[c_917]) ).
tcf(c_1174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_867]) ).
tcf(c_1184,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_858]) ).
tcf(c_1186,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(prop_impl_just,[status(thm)],[c_859]) ).
tcf(c_1238,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(prop_impl_just,[status(thm)],[c_747]) ).
tcf(c_1683,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(backward_subsumption_resolution,[status(thm)],[c_1238,c_805]) ).
tcf(c_3428,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1184,c_856]) ).
tcf(c_3429,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0,
inference(unflattening,[status(thm)],[c_3428]) ).
tcf(c_3434,plain,
! [X0: $i,X1: $i] :
( ( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1186,c_856]) ).
tcf(c_3435,plain,
! [X0: $i] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
inference(unflattening,[status(thm)],[c_3434]) ).
tcf(c_3446,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1174,c_856]) ).
tcf(c_3447,plain,
! [X0: $i,X1: $i] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_3446]) ).
tcf(c_4021,plain,
! [X0: $i] :
( ( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oone__class_Oone(X0) )
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1116,c_913]) ).
tcf(c_4022,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_4021]) ).
tcf(c_7371,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_3435,c_781]) ).
tcf(c_7416,plain,
! [X0: $i] : c_lessequals(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_789,c_795]) ).
tcf(c_7534,plain,
! [X0: $i] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_798,c_749]) ).
tcf(c_8067,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Complex_ORe(X1),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_808,c_790]) ).
tcf(c_8072,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,v_r,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_RealVector_Onorm__class_Onorm(v_s(X1),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_809,c_790]) ).
tcf(c_8739,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_766,c_1683]) ).
tcf(c_9510,plain,
! [X0: $i] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_3435,c_802]) ).
tcf(c_9546,plain,
! [X0: $i] : c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),
inference(light_normalisation,[status(thm)],[c_9510,c_3429,c_7371]) ).
tcf(c_10178,plain,
! [X0: $i] :
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) )
| ( c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
inference(superposition,[status(thm)],[c_784,c_814]) ).
tcf(c_10186,plain,
! [X0: $i] : c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_10178,c_782]) ).
tcf(c_10252,plain,
c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_784,c_10186]) ).
tcf(c_11684,plain,
! [X0: $i] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(X0)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_807,c_8072]) ).
tcf(c_11693,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,v_r,tc_RealDef_Oreal)
| ~ c_lessequals(X0,c_Complex_ORe(v_s(X1)),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_8067,c_8072]) ).
tcf(c_11776,plain,
! [X0: $i] : c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_Complex_ORe(v_s(X0)),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_11684,c_804]) ).
tcf(c_12393,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_11776,c_11693]) ).
tcf(c_12414,plain,
( c_lessequals(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(v_r,v_r,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_12393,c_803]) ).
tcf(c_12420,plain,
c_lessequals(c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_12414,c_789]) ).
tcf(c_12429,plain,
( ( c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r )
| ~ c_lessequals(v_r,c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_12420,c_787]) ).
tcf(c_12436,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(forward_subsumption_resolution,[status(thm)],[c_12429,c_7416]) ).
tcf(c_12459,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_12436,c_7534]) ).
tcf(c_13100,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_12459,c_3447]) ).
tcf(c_13104,plain,
c_lessequals(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_13100,c_773]) ).
tcf(c_13121,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(superposition,[status(thm)],[c_13104,c_748]) ).
tcf(c_13125,plain,
c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_13121,c_8739]) ).
tcf(c_13192,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_13125,c_9546]) ).
tcf(c_13202,plain,
c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = v_r,
inference(light_normalisation,[status(thm)],[c_13192,c_4022,c_12436]) ).
tcf(c_13223,plain,
c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) = v_r,
inference(demodulation,[status(thm)],[c_13125,c_13202]) ).
tcf(c_13246,plain,
c_HOL_Ouminus__class_Ouminus(v_r,tc_RealDef_Oreal) != v_r,
inference(demodulation,[status(thm)],[c_10252,c_13202]) ).
tcf(c_13321,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13223,c_13246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG363-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 05:26:38 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.01/1.75 % SZS status Started for theBenchmark.p
% 2.01/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 2.01/1.75
% 2.01/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.01/1.75
% 2.01/1.75 % ------ iProver source info
% 2.01/1.75
% 2.01/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 2.01/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.01/1.75 % git: non_committed_changes: false
% 2.01/1.75
% 2.01/1.75 % ------ Parsing...% successful
% 2.01/1.75
% 2.01/1.75
% 2.01/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.01/1.75
% 2.01/1.75 % ------ Preprocessing... sup_sim: 3 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 2.01/1.75
% 2.01/1.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.01/1.75
% 2.01/1.75 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.01/1.75 % ------ Proving...
% 2.01/1.75 % ------ Problem Properties
% 2.01/1.75
% 2.01/1.75 %
% 2.01/1.75 % clauses 201
% 2.01/1.75 % conjectures 0
% 2.01/1.75 % EPR 8
% 2.01/1.75 % Horn 183
% 2.01/1.75 % unary 93
% 2.01/1.75 % binary 68
% 2.01/1.75 % lits 353
% 2.01/1.75 % lits eq 125
% 2.01/1.75 % fd_pure 0
% 2.01/1.75 % fd_pseudo 0
% 2.01/1.75 % fd_cond 23
% 2.01/1.75 % fd_pseudo_cond 7
% 2.01/1.75 % AC symbols 0
% 2.01/1.75
% 2.01/1.75 % ------ Schedule dynamic 5 is on
% 2.01/1.75
% 2.01/1.75 % ------ no conjectures: strip conj schedule
% 2.01/1.75
% 2.01/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.01/1.75
% 2.01/1.75
% 2.01/1.75 % ------
% 2.01/1.75 % Current options:
% 2.01/1.75 % ------
% 2.01/1.75
% 2.01/1.75
% 2.01/1.75 %
% 2.01/1.75
% 2.01/1.75 % ------ Proving...
% 2.01/1.75 %
% 2.01/1.75
% 2.01/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 2.01/1.75
% 2.01/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.01/1.75
% 2.01/1.75
%------------------------------------------------------------------------------