%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG371-1 : 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 : n019.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 12:54:07 PM UTC 2026
% Result : Unsatisfiable 10.63s 12.44s
% Output : CNFRefutation 10.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 15 unt; 0 def)
% Number of atoms : 52 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 29 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f456,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(f460,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(f464,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f478,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(f494,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(f501,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
fof(f512,negated_conjecture,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f513,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f573,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
tcf(c_553,negated_conjecture,
c_HOL_Oord__class_Oless(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(cnf_transformation,[],[f512]) ).
tcf(c_554,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f513]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f494]) ).
tcf(c_559,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,[],[f478]) ).
tcf(c_560,plain,
! [X0: $i] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f464]) ).
tcf(c_561,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,[],[f460]) ).
tcf(c_562,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,[],[f456]) ).
tcf(c_579,plain,
! [X0: $i,X1: $i] :
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_682,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f573]) ).
tcf(c_4101,plain,
! [X0: $i,X1: $i] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X1,X0),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( X0 != tc_Complex_Ocomplex ) ),
inference(resolution_lifted,[status(thm)],[c_579,c_682]) ).
tcf(c_4102,plain,
! [X0: $i] : ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(unflattening,[status(thm)],[c_4101]) ).
tcf(c_13079,plain,
c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_553,c_561]) ).
tcf(c_13276,plain,
( ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_13079,c_558]) ).
tcf(c_13305,plain,
! [X0: $i] :
( c_lessequals(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_554,c_562]) ).
tcf(c_13399,plain,
! [X0: $i] :
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex),X0,tc_RealDef_Oreal)
| ( c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = X0 )
| ~ c_lessequals(v_r,X0,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_13305,c_559]) ).
tcf(c_13504,plain,
( ( c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) )
| ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_13399,c_4102]) ).
tcf(c_13505,plain,
c_RealVector_Onorm__class_Onorm(v_x,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[status(thm)],[c_13504,c_13079]) ).
tcf(c_13517,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_554,c_13505]) ).
tcf(c_13518,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r,
inference(backward_subsumption_resolution,[status(thm)],[c_13276,c_13517]) ).
tcf(c_13542,plain,
c_HOL_Oord__class_Oless(v_r,v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_553,c_13518]) ).
tcf(c_13543,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13542,c_560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG371-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.43 % Computer : n019.cluster.edu
% 0.15/10.43 % Model : x86_64 x86_64
% 0.15/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.43 % Memory : 8046.5625MB
% 0.15/10.43 % OS : Linux 6.8.0-71-generic
% 0.15/10.43 % CPULimit : 300
% 0.15/10.43 % WCLimit : 300
% 0.15/10.43 % DateTime : Fri Sep 25 05:30:01 UTC 2026
% 0.15/10.44 % CPUTime :
% 0.15/10.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.49 Running first-order theorem proving
% 0.15/10.50 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
% 0.20/10.51
% 0.20/10.51 % ======== iProver multi-core TPTP/SMT =========
% 0.20/10.51
% 0.20/10.51 % Detected problem language: tptp
% 0.20/10.52 % Proving...
% 10.63/12.44 % SZS status Started for theBenchmark.p
% 10.63/12.44 % SZS status Unsatisfiable for theBenchmark.p
% 10.63/12.44
% 10.63/12.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.63/12.44
% 10.63/12.44 % ------ iProver source info
% 10.63/12.44
% 10.63/12.44 % git: date: 2026-07-19 20:42:38 +0200
% 10.63/12.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.63/12.44 % git: non_committed_changes: false
% 10.63/12.44
% 10.63/12.44 % ------ Parsing...% successful
% 10.63/12.44
% 10.63/12.44
% 10.63/12.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.63/12.44
% 10.63/12.44 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 32 sf_s rm: 8 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 10.63/12.44
% 10.63/12.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.63/12.44
% 10.63/12.44 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.63/12.44 % ------ Proving...
% 10.63/12.44 % ------ Problem Properties
% 10.63/12.44
% 10.63/12.44 %
% 10.63/12.44 % clauses 187
% 10.63/12.44 % conjectures 3
% 10.63/12.44 % EPR 8
% 10.63/12.44 % Horn 126
% 10.63/12.44 % unary 57
% 10.63/12.44 % binary 30
% 10.63/12.44 % lits 463
% 10.63/12.44 % lits eq 112
% 10.63/12.44 % fd_pure 0
% 10.63/12.44 % fd_pseudo 0
% 10.63/12.44 % fd_cond 26
% 10.63/12.44 % fd_pseudo_cond 5
% 10.63/12.44 % AC symbols 0
% 10.63/12.44
% 10.63/12.44 % ------ Schedule dynamic 5 is on
% 10.63/12.44
% 10.63/12.44 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.63/12.44
% 10.63/12.44
% 10.63/12.44 % ------
% 10.63/12.44 % Current options:
% 10.63/12.44 % ------
% 10.63/12.44
% 10.63/12.44
% 10.63/12.44 %
% 10.63/12.44
% 10.63/12.44 % ------ Proving...
% 10.63/12.44 %
% 10.63/12.44
% 10.63/12.44 % SZS status Unsatisfiable for theBenchmark.p
% 10.63/12.44
% 10.63/12.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.63/12.44
% 10.63/12.44
%------------------------------------------------------------------------------