%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA028-1 : 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 : n026.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 229.93s 36.55s
% Output : CNFRefutation 229.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 44 ( 23 unt; 5 def)
% Number of atoms : 107 ( 12 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 57 ( 30 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 11 ( 9 usr; 6 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn 41 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1439,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_plus(X3,X1,X0),c_plus(X3,X2,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f1440,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X1,X3,X0)
| ~ c_lessequals(c_plus(X1,X2,X0),c_plus(X3,X2,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-1.ax',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f3029,axiom,
! [X0] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f3032,axiom,
! [X0] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/MSC001-0.ax',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f3365,axiom,
! [X2,X0,X1] :
( c_plus(c_minus(X1,X2,X0),X2,X0) = X1
| ~ class_OrderedGroup_Oab__group__add(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__11_0) ).
fof(f3391,negated_conjecture,
! [X0] : c_lessequals(v_g(X0),v_k(X0),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3393,negated_conjecture,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),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(f3394,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tcf(c_3858,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_plus(X3,X0,X2),c_plus(X3,X1,X2),X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f1439]) ).
tcf(c_3859,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,X3,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_lessequals(c_plus(X0,X1,X2),c_plus(X3,X1,X2),X2) ),
inference(cnf_transformation,[],[f1440]) ).
tcf(c_5015,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3029]) ).
tcf(c_5018,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f3032]) ).
tcf(c_5325,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_plus(c_minus(X1,X2,X0),X2,X0) = X1 )
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f3365]) ).
tcf(c_5348,negated_conjecture,
! [X0: $i] : c_lessequals(v_g(X0),v_k(X0),t_b),
inference(cnf_transformation,[],[f3391]) ).
tcf(c_5350,negated_conjecture,
~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[],[f3393]) ).
tcf(c_5351,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f3394]) ).
tcf(c_6928,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__group__add(X0) ),
inference(prop_impl_just,[status(thm)],[c_5018]) ).
tcf(c_6929,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(renaming,[status(thm)],[c_6928]) ).
tcf(c_8728,plain,
! [X0: $i] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) ),
inference(prop_impl_just,[status(thm)],[c_5015]) ).
tcf(c_8729,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(renaming,[status(thm)],[c_8728]) ).
tcf(c_54167,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__group__add(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_5351,c_6929]) ).
tcf(c_54168,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(unflattening,[status(thm)],[c_54167]) ).
tcf(c_54172,plain,
! [X0: $i] :
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_5351,c_8729]) ).
tcf(c_54173,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(unflattening,[status(thm)],[c_54172]) ).
tcf(c_204878,definition,
iPr_def_14 = v_f(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_204879,definition,
iPr_def_15 = v_k(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_204880,definition,
iPr_def_16 = c_minus(iPr_def_14,iPr_def_15,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_204881,definition,
iPr_def_17 = v_g(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_204882,definition,
iPr_def_18 = c_minus(iPr_def_14,iPr_def_17,t_b),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_204918,plain,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b),
inference(demodulation,[status(thm)],[c_54173]) ).
tcf(c_204919,plain,
class_OrderedGroup_Oab__group__add(t_b),
inference(demodulation,[status(thm)],[c_54168]) ).
tcf(c_204936,negated_conjecture,
~ c_lessequals(iPr_def_16,iPr_def_18,t_b),
inference(demodulation,[status(thm)],[c_5350,c_204881,c_204882,c_204879,c_204878,c_204880]) ).
tcf(c_204938,negated_conjecture,
! [X0: $i] : c_lessequals(v_g(X0),v_k(X0),t_b),
inference(demodulation,[status(thm)],[c_5348]) ).
tcf(c_356191,plain,
c_lessequals(v_g(v_x),iPr_def_15,t_b),
inference(superposition,[status(thm)],[c_204879,c_204938]) ).
tcf(c_356193,plain,
c_lessequals(iPr_def_17,iPr_def_15,t_b),
inference(light_normalisation,[status(thm)],[c_356191,c_204881]) ).
tcf(c_385403,plain,
! [X0: $i,X1: $i] : c_plus(c_minus(X0,X1,t_b),X1,t_b) = X0,
inference(superposition,[status(thm)],[c_204919,c_5325]) ).
tcf(c_385724,plain,
c_plus(iPr_def_16,iPr_def_15,t_b) = iPr_def_14,
inference(superposition,[status(thm)],[c_204880,c_385403]) ).
tcf(c_385725,plain,
c_plus(iPr_def_18,iPr_def_17,t_b) = iPr_def_14,
inference(superposition,[status(thm)],[c_204882,c_385403]) ).
tcf(c_498201,plain,
! [X0: $i] :
( c_lessequals(c_plus(iPr_def_16,X0,t_b),iPr_def_14,t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(X0,iPr_def_15,t_b) ),
inference(superposition,[status(thm)],[c_385724,c_3858]) ).
tcf(c_498230,plain,
! [X0: $i] :
( c_lessequals(c_plus(iPr_def_16,X0,t_b),iPr_def_14,t_b)
| ~ c_lessequals(X0,iPr_def_15,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_498201,c_204918]) ).
tcf(c_498597,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_18,t_b)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ c_lessequals(c_plus(X0,iPr_def_17,t_b),iPr_def_14,t_b) ),
inference(superposition,[status(thm)],[c_385725,c_3859]) ).
tcf(c_498608,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_18,t_b)
| ~ c_lessequals(c_plus(X0,iPr_def_17,t_b),iPr_def_14,t_b) ),
inference(forward_subsumption_resolution,[status(thm)],[c_498597,c_204918]) ).
tcf(c_524802,plain,
( c_lessequals(iPr_def_16,iPr_def_18,t_b)
| ~ c_lessequals(iPr_def_17,iPr_def_15,t_b) ),
inference(superposition,[status(thm)],[c_498230,c_498608]) ).
tcf(c_524809,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_524802,c_204936,c_356193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA028-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n026.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 05:50:39 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 229.93/36.55 % SZS status Started for theBenchmark.p
% 229.93/36.55 % SZS status Unsatisfiable for theBenchmark.p
% 229.93/36.55
% 229.93/36.55 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 229.93/36.55
% 229.93/36.55 % ------ iProver source info
% 229.93/36.55
% 229.93/36.55 % git: date: 2026-07-19 20:42:38 +0200
% 229.93/36.55 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 229.93/36.55 % git: non_committed_changes: false
% 229.93/36.55
% 229.93/36.55 % ------ Parsing...% successful
% 229.93/36.55
% 229.93/36.55
% 229.93/36.55 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 229.93/36.55
% 229.93/36.55 % ------ Preprocessing... sup_sim: 119 sf_s rm: 81 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e sup_sim: 64 sf_s rm: 44 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 44 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 44 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 44 0s sf_e pe_s pe_e %
% 229.93/36.55
% 229.93/36.55 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 229.93/36.55
% 229.93/36.55 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 229.93/36.55 % ------ Proving...
% 229.93/36.55 % ------ Problem Properties
% 229.93/36.55
% 229.93/36.55 %
% 229.93/36.55 % clauses 1747
% 229.93/36.55 % conjectures 4
% 229.93/36.55 % EPR 246
% 229.93/36.55 % Horn 1539
% 229.93/36.55 % unary 616
% 229.93/36.55 % binary 752
% 229.93/36.55 % lits 3356
% 229.93/36.55 % lits eq 1132
% 229.93/36.55 % fd_pure 0
% 229.93/36.55 % fd_pseudo 0
% 229.93/36.55 % fd_cond 108
% 229.93/36.55 % fd_pseudo_cond 66
% 229.93/36.55 % AC symbols 0
% 229.93/36.55
% 229.93/36.55 % ------ Schedule dynamic 5 is on
% 229.93/36.55
% 229.93/36.55 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 229.93/36.55
% 229.93/36.55
% 229.93/36.55 % ------
% 229.93/36.55 % Current options:
% 229.93/36.55 % ------
% 229.93/36.55
% 229.93/36.55
% 229.93/36.55 %
% 229.93/36.55
% 229.93/36.55 % ------ Proving...
% 229.93/36.55 % Proof_search_loop: time out after: 7933 full_loop iterations
% 229.93/36.55
% 229.93/36.55 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 229.93/36.55
% 229.93/36.55
% 229.93/36.55 % ------
% 229.93/36.55 % Current options:
% 229.93/36.55 % ------
% 229.93/36.55
% 229.93/36.55
% 229.93/36.55 %
% 229.93/36.55
% 229.93/36.55 % ------ Proving...
% 229.93/36.55 %
% 229.93/36.55
% 229.93/36.55 % SZS status Unsatisfiable for theBenchmark.p
% 229.93/36.55
% 229.93/36.55 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 229.93/36.55
% 229.93/36.55
%------------------------------------------------------------------------------