%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 12:55:40 PM UTC 2026
% Result : Unsatisfiable 0.29s 1.07s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 56 ( 23 unt; 7 def)
% Number of atoms : 136 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 55 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 16 ( 14 usr; 8 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 68 ( 0 sgn 68 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f7,axiom,
! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_less(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Omax(X3,X1,X0),X2,X0)
| ~ c_lessequals(X3,X2,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f10,axiom,
! [X2,X0,X1] :
( c_lessequals(X1,X2,X0)
| ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f11,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f12,axiom,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f13,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f14,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
tcf(c_63,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_less(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Orderings_Omax(X3,X0,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X3,X1,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X3,X0,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
! [X0: $i] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_77,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_Ring__and__Field_Oordered__idom(t_b) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_80,plain,
( class_Orderings_Oorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(resolution,[status(thm)],[c_75,c_66]) ).
tcf(c_163,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(resolution,[status(thm)],[c_65,c_153]) ).
tcf(c_168,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(resolution,[status(thm)],[c_65,c_76]) ).
tcf(c_172,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[c_65,c_74]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(resolution,[status(thm)],[c_69,c_72]) ).
tcf(c_197,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[status(thm)],[c_73,c_168]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,t_b)
| c_lessequals(X0,X1,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(resolution,[status(thm)],[c_179,c_172]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Orderings_Omax(X2,X0,t_b),X1,t_b)
| ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[c_70,c_172]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X2,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(resolution,[status(thm)],[c_71,c_197]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X0,t_b)
| c_lessequals(X0,X1,t_b) ),
inference(prop_impl_just,[status(thm)],[c_65,c_77,c_80,c_222]) ).
tcf(c_314,definition,
iPr_def_10 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_315,definition,
iPr_def_11 = v_k(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_316,definition,
iPr_def_12 = c_minus(iPr_def_10,iPr_def_11,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_317,definition,
iPr_def_13 = c_Orderings_Omax(iPr_def_12,c_0,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_318,definition,
iPr_def_14 = v_g(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_319,definition,
iPr_def_15 = c_minus(iPr_def_10,iPr_def_14,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_320,definition,
iPr_def_16 = c_HOL_Oabs(iPr_def_15,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_321,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X2,X0,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_249]) ).
tcf(c_322,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_Orderings_Omax(X2,X0,t_b),X1,t_b)
| ~ c_lessequals(X2,X1,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_233]) ).
tcf(c_323,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(demodulation,[status(thm)],[c_163]) ).
tcf(c_324,negated_conjecture,
~ c_lessequals(iPr_def_13,iPr_def_16,t_b),
inference(demodulation,[status(thm)],[c_64,c_318,c_319,c_320,c_315,c_314,c_316,c_317]) ).
tcf(c_325,negated_conjecture,
~ c_lessequals(c_0,iPr_def_12,t_b),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X0,c_HOL_Oabs(X1,t_b),t_b)
| ~ c_lessequals(X0,c_0,t_b) ),
inference(superposition,[status(thm)],[c_323,c_321]) ).
tcf(c_706,plain,
! [X0: $i] :
( c_lessequals(iPr_def_13,X0,t_b)
| ~ c_lessequals(iPr_def_12,X0,t_b)
| ~ c_lessequals(c_0,X0,t_b) ),
inference(superposition,[status(thm)],[c_317,c_322]) ).
tcf(c_729,plain,
! [X0: $i] :
( c_lessequals(iPr_def_13,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(iPr_def_12,c_HOL_Oabs(X0,t_b),t_b) ),
inference(superposition,[status(thm)],[c_323,c_706]) ).
tcf(c_743,plain,
! [X0: $i] :
( c_lessequals(iPr_def_13,c_HOL_Oabs(X0,t_b),t_b)
| ~ c_lessequals(iPr_def_12,c_0,t_b) ),
inference(superposition,[status(thm)],[c_658,c_729]) ).
tcf(c_752,plain,
( c_lessequals(iPr_def_13,iPr_def_16,t_b)
| ~ c_lessequals(iPr_def_12,c_0,t_b) ),
inference(superposition,[status(thm)],[c_320,c_743]) ).
tcf(c_755,plain,
~ c_lessequals(iPr_def_12,c_0,t_b),
inference(forward_subsumption_resolution,[status(thm)],[c_752,c_324]) ).
tcf(c_821,plain,
c_lessequals(c_0,iPr_def_12,t_b),
inference(superposition,[status(thm)],[c_266,c_755]) ).
tcf(c_827,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_821,c_325]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA029-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 05:50:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.42
% 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...
% 0.29/1.07 % SZS status Started for theBenchmark.p
% 0.29/1.07 % SZS status Unsatisfiable for theBenchmark.p
% 0.29/1.07
% 0.29/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.29/1.07
% 0.29/1.07 % ------ iProver source info
% 0.29/1.07
% 0.29/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.29/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.29/1.07 % git: non_committed_changes: false
% 0.29/1.07
% 0.29/1.07 % ------ Parsing...% successful
% 0.29/1.07
% 0.29/1.07
% 0.29/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.29/1.07
% 0.29/1.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.29/1.07
% 0.29/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.29/1.07
% 0.29/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.29/1.07 % ------ Proving...
% 0.29/1.07 % ------ Problem Properties
% 0.29/1.07
% 0.29/1.07 %
% 0.29/1.07 % clauses 15
% 0.29/1.07 % conjectures 2
% 0.29/1.07 % EPR 4
% 0.29/1.07 % Horn 14
% 0.29/1.07 % unary 10
% 0.29/1.07 % binary 3
% 0.29/1.07 % lits 22
% 0.29/1.07 % lits eq 7
% 0.29/1.07 % fd_pure 0
% 0.29/1.07 % fd_pseudo 0
% 0.29/1.07 % fd_cond 0
% 0.29/1.07 % fd_pseudo_cond 0
% 0.29/1.07 % AC symbols 0
% 0.29/1.07
% 0.29/1.07 % ------ Schedule dynamic 5 is on
% 0.29/1.07
% 0.29/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.29/1.07
% 0.29/1.07
% 0.29/1.07 % ------
% 0.29/1.07 % Current options:
% 0.29/1.07 % ------
% 0.29/1.07
% 0.29/1.07
% 0.29/1.07 %
% 0.29/1.07
% 0.29/1.07 % ------ Proving...
% 0.29/1.07 %
% 0.29/1.07
% 0.29/1.07 % SZS status Unsatisfiable for theBenchmark.p
% 0.29/1.07
% 0.29/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.29/1.07
%------------------------------------------------------------------------------