%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 12:55:38 PM UTC 2026
% Result : Unsatisfiable 2.25s 1.27s
% Output : CNFRefutation 2.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 63 ( 63 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X0,X1] : ifeq2(class_OrderedGroup_Ocomm__monoid__add(X0),true,c_plus(c_0,X1,X0),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(X1,c_minus(X2,X3,X0),X0),true,c_lessequals(c_plus(X1,X3,X0),X2,X0),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
fof(f5,plain,
! [X2,X3,X0,X1] : true = ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(X1,c_minus(X2,X3,X0),X0),true,c_lessequals(c_plus(X1,X3,X0),X2,X0),true),true),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(c_plus(X1,X2,X0),X3,X0),true,c_lessequals(X1,c_minus(X3,X2,X0),X0),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f7,plain,
! [X2,X3,X0,X1] : true = ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(c_plus(X1,X2,X0),X3,X0),true,c_lessequals(X1,c_minus(X3,X2,X0),X0),true),true),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] : ifeq(class_Orderings_Oorder(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X2,X3,X0),true,c_lessequals(X1,X3,X0),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f9,plain,
! [X2,X3,X0,X1] : true = ifeq(class_Orderings_Oorder(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X2,X3,X0),true,c_lessequals(X1,X3,X0),true),true),true),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f11,plain,
true = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f13,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f15,plain,
true != c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0] : ifeq(class_Orderings_Olinorder(X0),true,class_Orderings_Oorder(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f17,plain,
! [X0] : true = ifeq(class_Orderings_Olinorder(X0),true,class_Orderings_Oorder(X0),true),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f19,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Olinorder(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f21,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Olinorder(X0),true),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f23,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f25,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(reorient_equations,[],[f24]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ifeq2(class_OrderedGroup_Ocomm__monoid__add(X0),true,c_plus(c_0,X1,X0),X1) = X1,
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(X1,c_minus(X2,X3,X0),X0),true,c_lessequals(c_plus(X1,X3,X0),X2,X0),true),true) = true,
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(c_plus(X1,X2,X0),X3,X0),true,c_lessequals(X1,c_minus(X3,X2,X0),X0),true),true) = true,
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : ifeq(class_Orderings_Oorder(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X2,X3,X0),true,c_lessequals(X1,X3,X0),true),true),true) = true,
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
inference(cnf_transformation,[],[f11]) ).
tcf(c_70,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
inference(cnf_transformation,[],[f13]) ).
tcf(c_71,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
inference(cnf_transformation,[],[f15]) ).
tcf(c_72,plain,
! [X0: $i] : ifeq(class_Orderings_Olinorder(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(cnf_transformation,[],[f17]) ).
tcf(c_73,plain,
! [X0: $i] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true) = true,
inference(cnf_transformation,[],[f19]) ).
tcf(c_74,plain,
! [X0: $i] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Olinorder(X0),true) = true,
inference(cnf_transformation,[],[f21]) ).
tcf(c_75,plain,
! [X0: $i] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true) = true,
inference(cnf_transformation,[],[f23]) ).
tcf(c_76,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(cnf_transformation,[],[f25]) ).
tcf(c_237,plain,
ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true) = true,
inference(superposition,[status(thm)],[c_76,c_73]) ).
tcf(c_238,plain,
class_OrderedGroup_Ocomm__monoid__add(t_b) = true,
inference(demodulation,[status(thm)],[c_237,c_64]) ).
tcf(c_241,plain,
ifeq(true,true,class_Orderings_Olinorder(t_b),true) = true,
inference(superposition,[status(thm)],[c_76,c_74]) ).
tcf(c_242,plain,
ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true) = true,
inference(superposition,[status(thm)],[c_76,c_75]) ).
tcf(c_243,plain,
! [X0: $i] : ifeq2(true,true,c_plus(c_0,X0,t_b),X0) = X0,
inference(superposition,[status(thm)],[c_238,c_65]) ).
tcf(c_245,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = true,
inference(superposition,[status(thm)],[c_69,c_66]) ).
tcf(c_246,plain,
class_Orderings_Olinorder(t_b) = true,
inference(demodulation,[status(thm)],[c_241,c_64]) ).
tcf(c_248,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = true,
inference(superposition,[status(thm)],[c_246,c_72]) ).
tcf(c_249,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(demodulation,[status(thm)],[c_242,c_64]) ).
tcf(c_253,plain,
class_Orderings_Oorder(t_b) = true,
inference(demodulation,[status(thm)],[c_248,c_64]) ).
tcf(c_256,plain,
! [X0: $i] : c_plus(c_0,X0,t_b) = X0,
inference(demodulation,[status(thm)],[c_243,c_63]) ).
tcf(c_262,plain,
ifeq(true,true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true) = true,
inference(light_normalisation,[status(thm)],[c_245,c_249]) ).
tcf(c_263,plain,
c_lessequals(v_g(v_x),v_k(v_x),t_b) = true,
inference(demodulation,[status(thm)],[c_262,c_64,c_256]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,ifeq(c_lessequals(c_plus(X0,X1,t_b),X2,t_b),true,c_lessequals(X0,c_minus(X2,X1,t_b),t_b),true),true) = true,
inference(superposition,[status(thm)],[c_249,c_67]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(c_lessequals(c_plus(X0,X1,t_b),X2,t_b),true,c_lessequals(X0,c_minus(X2,X1,t_b),t_b),true) = true,
inference(demodulation,[status(thm)],[c_276,c_64]) ).
tcf(c_284,plain,
! [X0: $i,X1: $i] : ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_0,c_minus(X1,X0,t_b),t_b),true) = true,
inference(superposition,[status(thm)],[c_256,c_283]) ).
tcf(c_293,plain,
! [X0: $i] : ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X0,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X0,v_f(v_x),t_b),true),true),true) = true,
inference(superposition,[status(thm)],[c_70,c_68]) ).
tcf(c_301,plain,
! [X0: $i] : ifeq(true,true,ifeq(c_lessequals(X0,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X0,v_f(v_x),t_b),true),true),true) = true,
inference(light_normalisation,[status(thm)],[c_293,c_253]) ).
tcf(c_394,plain,
! [X0: $i] : ifeq(c_lessequals(X0,v_k(v_x),t_b),true,c_lessequals(X0,v_f(v_x),t_b),true) = true,
inference(demodulation,[status(thm)],[c_301,c_64]) ).
tcf(c_395,plain,
ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true) = true,
inference(superposition,[status(thm)],[c_263,c_394]) ).
tcf(c_469,plain,
c_lessequals(v_g(v_x),v_f(v_x),t_b) = true,
inference(demodulation,[status(thm)],[c_395,c_64]) ).
tcf(c_474,plain,
ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true) = true,
inference(superposition,[status(thm)],[c_469,c_284]) ).
tcf(c_500,plain,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) = true,
inference(demodulation,[status(thm)],[c_474,c_64]) ).
tcf(c_501,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_500,c_71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 05:46:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running UEQ theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 2.25/1.27 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 2.25/1.27 % SZS status Started for theBenchmark.p
% 2.25/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.25/1.27
% 2.25/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.25/1.27
% 2.25/1.27 % ------ iProver source info
% 2.25/1.27
% 2.25/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.25/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.25/1.27 % git: non_committed_changes: false
% 2.25/1.27
% 2.25/1.27 % ------ Parsing...% successful
% 2.25/1.27
% 2.25/1.27
% 2.25/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.25/1.27
% 2.25/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.25/1.27
% 2.25/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.25/1.27
% 2.25/1.27 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.25/1.27 % ------ Proving...
% 2.25/1.27 % ------ Problem Properties
% 2.25/1.27
% 2.25/1.27 %
% 2.25/1.27 % clauses 14
% 2.25/1.27 % conjectures 4
% 2.25/1.27 % EPR 0
% 2.25/1.27 % Horn 14
% 2.25/1.27 % unary 14
% 2.25/1.27 % binary 0
% 2.25/1.27 % lits 14
% 2.25/1.27 % lits eq 14
% 2.25/1.27 % fd_pure 0
% 2.25/1.27 % fd_pseudo 0
% 2.25/1.27 % fd_cond 0
% 2.25/1.27 % fd_pseudo_cond 0
% 2.25/1.27 % AC symbols 0
% 2.25/1.27
% 2.25/1.27 % ------ Input Options Time Limit: Unbounded
% 2.25/1.27
% 2.25/1.27
% 2.25/1.27 % ------
% 2.25/1.27 % Current options:
% 2.25/1.27 % ------
% 2.25/1.27
% 2.25/1.27
% 2.25/1.27 %
% 2.25/1.27
% 2.25/1.27 % ------ Proving...
% 2.25/1.27 %
% 2.25/1.27
% 2.25/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 2.25/1.27
% 2.25/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.25/1.28
% 2.25/1.28
%------------------------------------------------------------------------------