%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 12:55:37 PM UTC 2026
% Result : Unsatisfiable 3.11s 1.32s
% Output : CNFRefutation 3.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 18 unt; 1 def)
% Number of atoms : 113 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 59 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 121 ( 0 sgn 121 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
fof(f5,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_g(X0),t_a),c_times(v_d,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
! [X0] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X0)),t_a),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,axiom,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f8,axiom,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f9,axiom,
! [X0] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f10,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
fof(f11,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f12,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tcf(c_61,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,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) )
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) = c_HOL_Oabs(c_times(X1,X2,X0),X0) )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X3,X0,X2),c_times(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Opordered__semiring(X2)
| ~ c_lessequals(c_0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_65,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_g(X0),t_a),c_times(v_d,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,negated_conjecture,
! [X0: $i] : ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X0)),t_a),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),
inference(cnf_transformation,[],[f6]) ).
tcf(c_67,plain,
! [X0: $i] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_69,plain,
! [X0: $i] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[],[f12]) ).
tcf(c_178,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_61]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(unflattening,[status(thm)],[c_178]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) )
| ~ class_Ring__and__Field_Ofield(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_62]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_189]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1) = c_HOL_Oabs(c_times(X2,X3,X1),X1) )
| ~ class_Ring__and__Field_Oordered__field(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_63]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) = c_HOL_Oabs(c_times(X1,X2,X0),X0) )
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(unflattening,[status(thm)],[c_200]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1) )
| ~ class_Ring__and__Field_Oordered__field(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_190]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) )
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(unflattening,[status(thm)],[c_211]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_lessequals(c_0,X4,X1)
| ~ c_lessequals(X2,X3,X1)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_64]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X3,X0,X2),c_times(X3,X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ c_lessequals(c_0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_222]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_212,c_72]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(unflattening,[status(thm)],[c_241]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) = c_HOL_Oabs(c_times(X1,X2,X0),X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_201,c_72]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a) = c_HOL_Oabs(c_times(X0,X1,t_a),t_a),
inference(unflattening,[status(thm)],[c_247]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_179,c_72]) ).
tcf(c_254,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(unflattening,[status(thm)],[c_253]) ).
tcf(c_259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_223]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X2,X0,t_a),c_times(X2,X1,t_a),t_a)
| ~ c_lessequals(c_0,X2,t_a)
| ~ c_lessequals(X0,X1,t_a) ),
inference(unflattening,[status(thm)],[c_259]) ).
tcf(c_305,definition,
iPr_def_10 = c_HOL_Oinverse(v_c,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_306,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X2,X0,t_a),c_times(X2,X1,t_a),t_a)
| ~ c_lessequals(c_0,X2,t_a)
| ~ c_lessequals(X0,X1,t_a) ),
inference(demodulation,[status(thm)],[c_260]) ).
tcf(c_307,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_a),t_a),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] : c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a) = c_HOL_Oabs(c_times(X0,X1,t_a),t_a),
inference(demodulation,[status(thm)],[c_248]) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(demodulation,[status(thm)],[c_242]) ).
tcf(c_310,negated_conjecture,
! [X0: $i] : ~ c_lessequals(c_HOL_Oabs(c_times(iPr_def_10,v_g(v_x(X0)),t_a),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),
inference(demodulation,[status(thm)],[c_66,c_305]) ).
tcf(c_311,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_g(X0),t_a),c_times(v_d,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i] : ~ c_lessequals(c_HOL_Oabs(c_times(iPr_def_10,v_g(v_x(c_times(X0,X1,t_a))),t_a),t_a),c_times(X0,c_times(X1,c_HOL_Oabs(v_f(v_x(c_times(X0,X1,t_a))),t_a),t_a),t_a),t_a),
inference(superposition,[status(thm)],[c_309,c_310]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_HOL_Oabs(c_times(X2,X0,t_a),t_a),c_times(c_HOL_Oabs(X2,t_a),X1,t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(X2,t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(X0,t_a),X1,t_a) ),
inference(superposition,[status(thm)],[c_308,c_306]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_HOL_Oabs(c_times(X2,X0,t_a),t_a),c_times(c_HOL_Oabs(X2,t_a),X1,t_a),t_a)
| ~ c_lessequals(c_HOL_Oabs(X0,t_a),X1,t_a) ),
inference(forward_subsumption_resolution,[status(thm)],[c_486,c_307]) ).
tcf(c_542,plain,
! [X0: $i] : ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(iPr_def_10,t_a),X0,t_a))),t_a),c_times(X0,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(iPr_def_10,t_a),X0,t_a))),t_a),t_a),t_a),
inference(superposition,[status(thm)],[c_492,c_463]) ).
tcf(c_655,plain,
$false,
inference(superposition,[status(thm)],[c_311,c_542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 05:46:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 3.11/1.32 % SZS status Started for theBenchmark.p
% 3.11/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.11/1.32
% 3.11/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.11/1.32
% 3.11/1.32 % ------ iProver source info
% 3.11/1.32
% 3.11/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 3.11/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.11/1.32 % git: non_committed_changes: false
% 3.11/1.32
% 3.11/1.32 % ------ Parsing...% successful
% 3.11/1.32
% 3.11/1.32
% 3.11/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.11/1.32
% 3.11/1.32 % ------ 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: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.11/1.32
% 3.11/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.11/1.32
% 3.11/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.11/1.32 % ------ Proving...
% 3.11/1.32 % ------ Problem Properties
% 3.11/1.32
% 3.11/1.32 %
% 3.11/1.32 % clauses 7
% 3.11/1.32 % conjectures 2
% 3.11/1.32 % EPR 0
% 3.11/1.32 % Horn 7
% 3.11/1.32 % unary 6
% 3.11/1.32 % binary 0
% 3.11/1.32 % lits 9
% 3.11/1.32 % lits eq 3
% 3.11/1.32 % fd_pure 0
% 3.11/1.32 % fd_pseudo 0
% 3.11/1.32 % fd_cond 0
% 3.11/1.32 % fd_pseudo_cond 0
% 3.11/1.32 % AC symbols 0
% 3.11/1.32
% 3.11/1.32 % ------ Schedule dynamic 5 is on
% 3.11/1.32
% 3.11/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 3.11/1.32
% 3.11/1.32 % ------
% 3.11/1.32 % Current options:
% 3.11/1.32 % ------
% 3.11/1.32
% 3.11/1.32
% 3.11/1.32 %
% 3.11/1.32
% 3.11/1.32 % ------ Proving...
% 3.11/1.32 %
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% 3.11/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 3.11/1.32
% 3.11/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 3.11/1.32
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