%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG362-1 : 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 : n012.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 8.08s 1.51s
% Output : CNFRefutation 8.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 27 unt; 0 def)
% Number of atoms : 87 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 38 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 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 : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 65 ( 0 sgn 65 !; 0 ?; 45 :)
% Comments :
%------------------------------------------------------------------------------
fof(f291,axiom,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
fof(f292,axiom,
! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
fof(f684,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
fof(f762,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rp_0) ).
fof(f769,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).
fof(f770,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/sandbox/benchmark/theBenchmark.p',cls_abs__Re__le__cmod_0) ).
fof(f771,axiom,
! [X0] : c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r_0) ).
fof(f772,axiom,
! [X0,X1] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
fof(f778,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/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
fof(f785,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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f808,axiom,
! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f827,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f882,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f915,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
tcf(c_849,negated_conjecture,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),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,[],[f827]) ).
tcf(c_851,plain,
! [X0: $i] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f769]) ).
tcf(c_856,plain,
! [X0: $i] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ( c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ) ),
inference(cnf_transformation,[],[f684]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f808]) ).
tcf(c_861,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,[],[f778]) ).
tcf(c_863,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
inference(cnf_transformation,[],[f772]) ).
tcf(c_881,plain,
! [X0: $i] : c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,X0),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f771]) ).
tcf(c_882,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(cnf_transformation,[],[f762]) ).
tcf(c_885,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,[],[f770]) ).
tcf(c_945,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f882]) ).
tcf(c_954,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,[],[f785]) ).
tcf(c_1018,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f915]) ).
tcf(c_1022,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,X0,X2)
| ~ c_HOL_Oord__class_Oless(X0,X1,X2) ),
inference(cnf_transformation,[],[f292]) ).
tcf(c_1023,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f291]) ).
tcf(c_1298,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_954]) ).
tcf(c_3300,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1023,c_1018]) ).
tcf(c_3301,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_3300]) ).
tcf(c_3364,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ( X0 != tc_RealDef_Oreal ) ),
inference(resolution_lifted,[status(thm)],[c_1022,c_1018]) ).
tcf(c_3365,plain,
! [X0: $i,X1: $i] :
( ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal) ),
inference(unflattening,[status(thm)],[c_3364]) ).
tcf(c_3549,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_1298,c_945]) ).
tcf(c_3550,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_3549]) ).
tcf(c_8356,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_863,c_849]) ).
tcf(c_8421,plain,
! [X0: $i] : ~ c_HOL_Oord__class_Oless(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),X0,tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_851,c_3550]) ).
tcf(c_8422,plain,
! [X0: $i] : c_lessequals(X0,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_3301,c_8421]) ).
tcf(c_8818,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X0),tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X0,tc_Complex_Ocomplex),X1,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_885,c_861]) ).
tcf(c_8828,plain,
! [X0: $i] :
( c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_8356,c_861]) ).
tcf(c_8940,plain,
! [X0: $i] :
( ( c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 )
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_856,c_3365]) ).
tcf(c_9006,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_885,c_8828]) ).
tcf(c_9013,plain,
! [X0: $i] :
( c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),X0,tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_9006,c_861]) ).
tcf(c_9080,plain,
c_lessequals(c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_881,c_9013]) ).
tcf(c_9648,plain,
( ( c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = v_r )
| ~ c_lessequals(v_r,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(superposition,[status(thm)],[c_9080,c_859]) ).
tcf(c_19521,plain,
c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal) = v_r,
inference(superposition,[status(thm)],[c_882,c_8940]) ).
tcf(c_19637,plain,
c_lessequals(v_r,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_19521,c_8422]) ).
tcf(c_20300,plain,
c_lessequals(v_r,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_19637,c_3550]) ).
tcf(c_20301,plain,
c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = v_r,
inference(backward_subsumption_resolution,[status(thm)],[c_9648,c_20300]) ).
tcf(c_20349,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(demodulation,[status(thm)],[c_849,c_20301]) ).
tcf(c_20489,plain,
~ c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v_n____),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
inference(superposition,[status(thm)],[c_8818,c_20349]) ).
tcf(c_20490,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_20489,c_881]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG362-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Fri Sep 25 05:27:35 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.32 Running first-order theorem proving
% 0.02/0.32 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
% 0.02/0.32
% 0.02/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.32
% 0.02/0.32 % Detected problem language: tptp
% 0.02/0.33 % Proving...
% 8.08/1.51 % SZS status Started for theBenchmark.p
% 8.08/1.51 % SZS status Unsatisfiable for theBenchmark.p
% 8.08/1.51
% 8.08/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.08/1.51
% 8.08/1.51 % ------ iProver source info
% 8.08/1.51
% 8.08/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 8.08/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.08/1.51 % git: non_committed_changes: false
% 8.08/1.51
% 8.08/1.51 % ------ Parsing...% successful
% 8.08/1.51
% 8.08/1.51
% 8.08/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.08/1.51
% 8.08/1.51 % ------ Preprocessing... sup_sim: 6 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 8.08/1.51
% 8.08/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.08/1.51
% 8.08/1.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e sf_s rm: 0 0s sf_e
% 8.08/1.51 % ------ Proving...
% 8.08/1.51 % ------ Problem Properties
% 8.08/1.51
% 8.08/1.51 %
% 8.08/1.51 % clauses 224
% 8.08/1.51 % conjectures 1
% 8.08/1.51 % EPR 19
% 8.08/1.51 % Horn 211
% 8.08/1.51 % unary 149
% 8.08/1.51 % binary 54
% 8.08/1.51 % lits 320
% 8.08/1.51 % lits eq 141
% 8.08/1.51 % fd_pure 0
% 8.08/1.51 % fd_pseudo 0
% 8.08/1.51 % fd_cond 8
% 8.08/1.51 % fd_pseudo_cond 9
% 8.08/1.51 % AC symbols 0
% 8.08/1.51
% 8.08/1.51 % ------ Schedule dynamic 5 is on
% 8.08/1.51
% 8.08/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.08/1.51
% 8.08/1.51
% 8.08/1.51 % ------
% 8.08/1.51 % Current options:
% 8.08/1.51 % ------
% 8.08/1.51
% 8.08/1.51
% 8.08/1.51 %
% 8.08/1.51
% 8.08/1.51 % ------ Proving...
% 8.08/1.51 %
% 8.08/1.51
% 8.08/1.51 % SZS status Unsatisfiable for theBenchmark.p
% 8.08/1.51
% 8.08/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.08/1.51
% 8.08/1.51
%------------------------------------------------------------------------------