%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA023-2 : 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 12:55:39 PM UTC 2026
% Result : Unsatisfiable 2.09s 1.32s
% Output : CNFRefutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 61 ( 24 unt; 5 def)
% Number of atoms : 144 ( 20 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 110 ( 57 ~; 53 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 84 ( 0 sgn 84 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( c_plus(c_0,X1,X0) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_plus(X1,X3,X0),X2,X0)
| ~ c_lessequals(X1,c_minus(X2,X3,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X1,c_minus(X3,X2,X0),X0)
| ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f5,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f7,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f9,axiom,
! [X0] :
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f10,axiom,
! [X0] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f11,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f12,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( c_plus(c_0,X1,X0) = X1 )
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_plus(X0,X2,X3),X1,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X0,c_minus(X1,X2,X3),X3) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_minus(X3,X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_plus(X0,X1,X2),X3,X2) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_64,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,[],[f4]) ).
tcf(c_65,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(cnf_transformation,[],[f6]) ).
tcf(c_67,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_69,plain,
! [X0: $i] :
( class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
! [X0: $i] :
( class_Orderings_Olinorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f12]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_plus(c_0,X2,X1) = X2 )
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_61]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i] :
( ( c_plus(c_0,X1,X0) = X1 )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_176]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] :
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_68]) ).
tcf(c_188,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_187]) ).
tcf(c_198,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_188,c_72]) ).
tcf(c_199,plain,
class_Orderings_Oorder(t_b),
inference(unflattening,[status(thm)],[c_198]) ).
tcf(c_203,plain,
! [X0: $i,X1: $i] :
( ( c_plus(c_0,X1,X0) = X1 )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_177,c_72]) ).
tcf(c_204,plain,
! [X0: $i] : c_plus(c_0,X0,t_b) = X0,
inference(unflattening,[status(thm)],[c_203]) ).
tcf(c_209,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_72]) ).
tcf(c_210,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(unflattening,[status(thm)],[c_209]) ).
tcf(c_217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_199]) ).
tcf(c_218,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(unflattening,[status(thm)],[c_217]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_plus(X1,X3,X0),X2,X0)
| ~ c_lessequals(X1,c_minus(X2,X3,X0),X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_210]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_plus(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,c_minus(X1,X2,t_b),t_b) ),
inference(unflattening,[status(thm)],[c_231]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,c_minus(X3,X2,X0),X0)
| ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_210]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,c_minus(X2,X1,t_b),t_b)
| ~ c_lessequals(c_plus(X0,X1,t_b),X2,t_b) ),
inference(unflattening,[status(thm)],[c_240]) ).
tcf(c_295,definition,
iPr_def_10 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_296,definition,
iPr_def_11 = v_g(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_297,definition,
iPr_def_12 = c_minus(iPr_def_10,iPr_def_11,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_298,definition,
iPr_def_13 = v_k(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_299,definition,
iPr_def_14 = c_minus(iPr_def_13,iPr_def_11,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,c_minus(X2,X1,t_b),t_b)
| ~ c_lessequals(c_plus(X0,X1,t_b),X2,t_b) ),
inference(demodulation,[status(thm)],[c_241]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_plus(X0,X2,t_b),X1,t_b)
| ~ c_lessequals(X0,c_minus(X1,X2,t_b),t_b) ),
inference(demodulation,[status(thm)],[c_232]) ).
tcf(c_302,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_218]) ).
tcf(c_303,plain,
! [X0: $i] : c_plus(c_0,X0,t_b) = X0,
inference(demodulation,[status(thm)],[c_204]) ).
tcf(c_304,negated_conjecture,
~ c_lessequals(c_0,iPr_def_12,t_b),
inference(demodulation,[status(thm)],[c_67,c_296,c_295,c_297]) ).
tcf(c_305,negated_conjecture,
c_lessequals(iPr_def_13,iPr_def_10,t_b),
inference(demodulation,[status(thm)],[c_66,c_298]) ).
tcf(c_306,negated_conjecture,
c_lessequals(c_0,iPr_def_14,t_b),
inference(demodulation,[status(thm)],[c_65,c_299]) ).
tcf(c_480,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_10,t_b)
| ~ c_lessequals(X0,iPr_def_13,t_b) ),
inference(superposition,[status(thm)],[c_305,c_302]) ).
tcf(c_500,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_minus(X1,X0,t_b),t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_303,c_300]) ).
tcf(c_512,plain,
! [X0: $i] :
( c_lessequals(c_plus(X0,iPr_def_11,t_b),iPr_def_13,t_b)
| ~ c_lessequals(X0,iPr_def_14,t_b) ),
inference(superposition,[status(thm)],[c_299,c_301]) ).
tcf(c_520,plain,
( c_lessequals(c_0,iPr_def_12,t_b)
| ~ c_lessequals(iPr_def_11,iPr_def_10,t_b) ),
inference(superposition,[status(thm)],[c_297,c_500]) ).
tcf(c_524,plain,
~ c_lessequals(iPr_def_11,iPr_def_10,t_b),
inference(forward_subsumption_resolution,[status(thm)],[c_520,c_304]) ).
tcf(c_546,plain,
( c_lessequals(iPr_def_11,iPr_def_13,t_b)
| ~ c_lessequals(c_0,iPr_def_14,t_b) ),
inference(superposition,[status(thm)],[c_303,c_512]) ).
tcf(c_550,plain,
c_lessequals(iPr_def_11,iPr_def_13,t_b),
inference(forward_subsumption_resolution,[status(thm)],[c_546,c_306]) ).
tcf(c_560,plain,
c_lessequals(iPr_def_11,iPr_def_10,t_b),
inference(superposition,[status(thm)],[c_550,c_480]) ).
tcf(c_561,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_560,c_524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA023-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 05:48:37 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 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...
% 2.09/1.32 % SZS status Started for theBenchmark.p
% 2.09/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.32
% 2.09/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.09/1.32
% 2.09/1.32 % ------ iProver source info
% 2.09/1.32
% 2.09/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 2.09/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.09/1.32 % git: non_committed_changes: false
% 2.09/1.32
% 2.09/1.32 % ------ Parsing...% successful
% 2.09/1.32
% 2.09/1.32
% 2.09/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.09/1.32
% 2.09/1.32 % ------ 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 %
% 2.09/1.32
% 2.09/1.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.09/1.32
% 2.09/1.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.09/1.32 % ------ Proving...
% 2.09/1.32 % ------ Problem Properties
% 2.09/1.32
% 2.09/1.32 %
% 2.09/1.32 % clauses 12
% 2.09/1.32 % conjectures 3
% 2.09/1.32 % EPR 4
% 2.09/1.32 % Horn 12
% 2.09/1.32 % unary 9
% 2.09/1.32 % binary 2
% 2.09/1.32 % lits 16
% 2.09/1.32 % lits eq 6
% 2.09/1.32 % fd_pure 0
% 2.09/1.32 % fd_pseudo 0
% 2.09/1.32 % fd_cond 0
% 2.09/1.32 % fd_pseudo_cond 0
% 2.09/1.32 % AC symbols 0
% 2.09/1.32
% 2.09/1.32 % ------ Schedule dynamic 5 is on
% 2.09/1.32
% 2.09/1.32 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.09/1.32
% 2.09/1.32
% 2.09/1.32 % ------
% 2.09/1.32 % Current options:
% 2.09/1.32 % ------
% 2.09/1.32
% 2.09/1.32
% 2.09/1.32 %
% 2.09/1.32
% 2.09/1.32 % ------ Proving...
% 2.09/1.32 %
% 2.09/1.32
% 2.09/1.32 % SZS status Unsatisfiable for theBenchmark.p
% 2.09/1.32
% 2.09/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.09/1.32
% 2.09/1.32
%------------------------------------------------------------------------------