%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWW212+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n002.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 35.76s 8.81s
% Output : CNFRefutation 35.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 11 unt; 1 def)
% Number of atoms : 103 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 103 ( 53 ~; 37 |; 6 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-5 aty)
% Number of variables : 93 ( 0 sgn 83 !; 10 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
! [X0,X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> hAPP(c_RealVector_Onorm__class_Onorm(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)) = hAPP(c_RealVector_Onorm__class_Onorm(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(f17,axiom,
c_SEQ_Osubseq(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hs) ).
fof(f94,axiom,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ? [X1] :
! [X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),X2))),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Be_O_A0_A_060_Ae_A_061_061_062_AEX_AN_O_AALL_An_062_061N_O_Acmod_A_Is_A_I_If_Ao_Ag_J_An_J_A_N_AComplex_Ax_Ay_J_A_060_Ae_096) ).
fof(f1188,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1274,conjecture,
? [X0] :
( ? [X1] :
! [X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
=> ? [X3] :
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,X4))),X1)),X2) ) )
& c_SEQ_Osubseq(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f1275,negated_conjecture,
~ ? [X0] :
( ? [X1] :
! [X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
=> ? [X3] :
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,X4))),X1)),X2) ) )
& c_SEQ_Osubseq(X0) ),
inference(negated_conjecture,[status(cth)],[f1274]) ).
fof(f1289,plain,
! [X0,X1,X2] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| hAPP(c_RealVector_Onorm__class_Onorm(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)) = hAPP(c_RealVector_Onorm__class_Onorm(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X0),X1)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f1414,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ? [X1] :
! [X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),X2))),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),X0) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f2516,plain,
! [X0] :
( ! [X1] :
? [X2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
& ! [X3] :
? [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,X4))),X1)),X2) ) )
| ~ c_SEQ_Osubseq(X0) ),
inference(ennf_transformation,[],[f1275]) ).
fof(f2580,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ! [X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(X0),X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),X2))),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X1,sK17(X0))],[f1414]) ).
fof(f2885,plain,
! [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK58(X0,X1))
& ! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK59(X0,X1,X3))
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,sK59(X0,X1,X3)))),X1)),sK58(X0,X1)) ) )
| ~ c_SEQ_Osubseq(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58,sK59]),skolemize(X2,sK58(X0,X1)),skolemize(X4,sK59(X0,X1,X3))],[f2516]) ).
fof(f2902,plain,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X2)
| hAPP(c_RealVector_Onorm__class_Onorm(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)) = hAPP(c_RealVector_Onorm__class_Onorm(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X0),X1)) ),
inference(cnf_transformation,[],[f1289]) ).
fof(f2908,plain,
c_SEQ_Osubseq(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),
inference(cnf_transformation,[],[f17]) ).
fof(f3022,plain,
! [X2,X0] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(X0),X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),X2))),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),X0) ),
inference(cnf_transformation,[],[f2580]) ).
fof(f4504,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1188]) ).
fof(f4590,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK58(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f2885]) ).
fof(f4591,plain,
! [X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,sK59(X0,X1,X3))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f2885]) ).
fof(f4592,plain,
! [X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,sK59(X0,X1,X3)))),X1)),sK58(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f2885]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X0),X1),X2)) = hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X0),X2),X1)) )
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(cnf_transformation,[],[f2902]) ).
tcf(c_71,plain,
c_SEQ_Osubseq(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),
inference(cnf_transformation,[],[f2908]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),X1))),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(X0),X1) ),
inference(cnf_transformation,[],[f3022]) ).
tcf(c_1624,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f4504]) ).
tcf(c_1710,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_SEQ_Osubseq(X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,sK59(X0,X1,X2)))),X1)),sK58(X0,X1)) ),
inference(cnf_transformation,[],[f4592]) ).
tcf(c_1711,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK59(X0,X2,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f4591]) ).
tcf(c_1712,negated_conjecture,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK58(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f4590]) ).
tcf(c_2673,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X0),X1),X2)) = hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X0),X2),X1)) )
| ~ class_RealVector_Oreal__normed__vector(X0) ),
inference(prop_impl_just,[status(thm)],[c_65]) ).
tcf(c_33218,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X0),X1),X2)) = hAPP(c_RealVector_Onorm__class_Onorm(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X0),X2),X1)) )
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_2673,c_1624]) ).
tcf(c_33219,plain,
! [X0: $i,X1: $i] : hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),X0),X1)) = hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),X1),X0)),
inference(unflattening,[status(thm)],[c_33218]) ).
tcf(c_38777,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,sK59(X0,X1,X2)))),X1)),sK58(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(prop_impl_just,[status(thm)],[c_1710]) ).
tcf(c_38778,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_SEQ_Osubseq(X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(v_s,hAPP(X0,sK59(X0,X1,X2)))),X1)),sK58(X0,X1)) ),
inference(renaming,[status(thm)],[c_38777]) ).
tcf(c_51997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_SEQ_Osubseq(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),X0),hAPP(v_s,hAPP(X1,sK59(X1,X0,X2))))),sK58(X1,X0)) ),
inference(demodulation,[status(thm)],[c_38778,c_33219]) ).
tcf(c_53834,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____)),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),X1)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(X0),X1) ),
inference(demodulation,[status(thm)],[c_173,c_33219]) ).
tcf(c_66856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),X0),hAPP(v_s,hAPP(X1,sK59(X1,X0,X2))))),sK58(X1,X0))
| ~ c_SEQ_Osubseq(X1) ),
inference(prop_impl_just,[status(thm)],[c_51997]) ).
tcf(c_66857,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_SEQ_Osubseq(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),X0),hAPP(v_s,hAPP(X1,sK59(X1,X0,X2))))),sK58(X1,X0)) ),
inference(renaming,[status(thm)],[c_66856]) ).
tcf(c_94370,definition,
iPr_def_10 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_94371,negated_conjecture,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,iPr_def_10,sK58(X0,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(demodulation,[status(thm)],[c_1712,c_94370]) ).
tcf(c_94372,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,sK59(X0,X2,X1))
| ~ c_SEQ_Osubseq(X0) ),
inference(demodulation,[status(thm)],[c_1711]) ).
tcf(c_116131,plain,
! [X0: $i,X1: $i] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____)),hAPP(v_s,hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),X1)))),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,iPr_def_10,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(X0),X1) ),
inference(light_normalisation,[status(thm)],[c_53834,c_94370]) ).
tcf(c_116149,plain,
! [X0: $i] :
( ~ c_SEQ_Osubseq(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,iPr_def_10,sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),sK59(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____),X0)) ),
inference(superposition,[status(thm)],[c_116131,c_66857]) ).
tcf(c_116154,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),sK59(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____),X0))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,iPr_def_10,sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))) ),
inference(global_subsumption_just,[status(thm)],[c_116149,c_71,c_116149]) ).
tcf(c_116155,plain,
! [X0: $i] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,iPr_def_10,sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK17(sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),sK59(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____),X0)) ),
inference(renaming,[status(thm)],[c_116154]) ).
tcf(c_116161,plain,
( ~ c_SEQ_Osubseq(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,iPr_def_10,sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))) ),
inference(superposition,[status(thm)],[c_94372,c_116155]) ).
tcf(c_116164,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,iPr_def_10,sK58(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____),hAPP(hAPP(c_Complex_Ocomplex_OComplex,v_x____),v_y____))),
inference(global_subsumption_just,[status(thm)],[c_116161,c_71,c_116161]) ).
tcf(c_116166,plain,
~ c_SEQ_Osubseq(c_Fun_Ocomp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat,v_f____,v_ga____)),
inference(superposition,[status(thm)],[c_94371,c_116164]) ).
tcf(c_116167,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_116166,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW212+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n002.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 : Thu Sep 24 21:48:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 35.76/8.81 % SZS status Started for theBenchmark.p
% 35.76/8.81 % SZS status Theorem for theBenchmark.p
% 35.76/8.81
% 35.76/8.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.76/8.81
% 35.76/8.81 % ------ iProver source info
% 35.76/8.81
% 35.76/8.81 % git: date: 2026-07-19 20:42:38 +0200
% 35.76/8.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.76/8.81 % git: non_committed_changes: false
% 35.76/8.81
% 35.76/8.81 % ------ Parsing...
% 35.76/8.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.76/8.81
% 35.76/8.81 % ------ Preprocessing... sup_sim: 36 sf_s rm: 60 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 92 sf_s rm: 23 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 24 0s sf_e pe_s pe_e %
% 35.76/8.81
% 35.76/8.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.76/8.81
% 35.76/8.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 35.76/8.81 % ------ Proving...
% 35.76/8.81 % ------ Problem Properties
% 35.76/8.81
% 35.76/8.81 %
% 35.76/8.81 % clauses 1424
% 35.76/8.81 % conjectures 2
% 35.76/8.81 % EPR 237
% 35.76/8.81 % Horn 1220
% 35.76/8.81 % unary 430
% 35.76/8.81 % binary 481
% 35.76/8.81 % lits 3183
% 35.76/8.81 % lits eq 700
% 35.76/8.81 % fd_pure 0
% 35.76/8.81 % fd_pseudo 0
% 35.76/8.81 % fd_cond 117
% 35.76/8.81 % fd_pseudo_cond 71
% 35.76/8.81 % AC symbols 0
% 35.76/8.81
% 35.76/8.81 % ------ Schedule dynamic 5 is on
% 35.76/8.81
% 35.76/8.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 35.76/8.81
% 35.76/8.81
% 35.76/8.81 % ------
% 35.76/8.81 % Current options:
% 35.76/8.81 % ------
% 35.76/8.81
% 35.76/8.81
% 35.76/8.81 %
% 35.76/8.81
% 35.76/8.81 % ------ Proving...
% 35.76/8.81 %
% 35.76/8.81
% 35.76/8.81 % SZS status Theorem for theBenchmark.p
% 35.76/8.81
% 35.76/8.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.76/8.81
% 35.76/8.81
%------------------------------------------------------------------------------