%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA020-2 : 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 : n008.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 1.71s 16.56s
% Output : CNFRefutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 65 ( 34 unt; 4 def)
% Number of atoms : 138 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 105 ( 56 ~; 49 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 12 ( 10 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 0 sgn 52 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_f(c_0) = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,plain,
c_0 = v_f(c_0),
inference(reorient_equations,[],[f1]) ).
fof(f3,negated_conjecture,
c_less(c_0,v_c,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
v_x = c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,plain,
c_0 = v_x,
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f8,axiom,
! [X0] :
( c_HOL_Oabs(c_0,X0) = c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f9,plain,
! [X0] :
( c_0 = c_HOL_Oabs(c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,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(f11,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(f12,axiom,
! [X2,X0,X1] :
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f13,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f14,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f15,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(f16,plain,
v_x = v_f(v_x),
inference(definition_unfolding,[],[f2,f5,f5]) ).
fof(f17,plain,
c_less(v_x,v_c,t_a),
inference(definition_unfolding,[],[f3,f5]) ).
fof(f18,plain,
! [X0] :
( v_x = c_HOL_Oabs(v_x,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(definition_unfolding,[],[f9,f5,f5]) ).
fof(f19,plain,
! [X0,X1] :
( c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(definition_unfolding,[],[f10,f5]) ).
fof(f20,plain,
! [X2,X0,X1] :
( c_lessequals(v_x,c_times(X2,X1,X0),X0)
| ~ c_lessequals(v_x,X2,X0)
| ~ c_lessequals(v_x,X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(definition_unfolding,[],[f12,f5,f5,f5]) ).
tcf(c_61,negated_conjecture,
v_f(v_x) = v_x,
inference(cnf_transformation,[],[f16]) ).
tcf(c_62,negated_conjecture,
c_less(v_x,v_c,t_a),
inference(cnf_transformation,[],[f17]) ).
tcf(c_63,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[],[f6]) ).
tcf(c_64,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[],[f7]) ).
tcf(c_65,negated_conjecture,
! [X0: $i] :
( ( c_HOL_Oabs(v_x,X0) = v_x )
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_66,negated_conjecture,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_less(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_68,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,c_times(X2,X0,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(v_x,X2,X1)
| ~ c_lessequals(v_x,X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_69,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_70,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_71,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_145,plain,
~ c_lessequals(c_HOL_Oabs(v_x,t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(light_normalisation,[status(thm)],[c_63,c_61]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| ( X2 != t_a )
| ( X1 != v_c )
| ( X0 != v_x ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_62]) ).
tcf(c_165,plain,
( c_lessequals(v_x,v_c,t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(unflattening,[status(thm)],[c_164]) ).
tcf(c_174,plain,
! [X0: $i] :
( c_lessequals(v_x,v_c,t_a)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_165]) ).
tcf(c_175,plain,
( c_lessequals(v_x,v_c,t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a) ),
inference(unflattening,[status(thm)],[c_174]) ).
tcf(c_176,plain,
c_lessequals(v_x,v_c,t_a),
inference(global_subsumption_just,[status(thm)],[c_175,c_64,c_175]) ).
tcf(c_182,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_71]) ).
tcf(c_183,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(unflattening,[status(thm)],[c_182]) ).
tcf(c_187,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_69]) ).
tcf(c_188,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(unflattening,[status(thm)],[c_187]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,c_HOL_Oabs(X1,X0),X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_183]) ).
tcf(c_195,plain,
! [X0: $i] : c_lessequals(v_x,c_HOL_Oabs(X0,t_a),t_a),
inference(unflattening,[status(thm)],[c_194]) ).
tcf(c_200,plain,
! [X0: $i] :
( ( c_HOL_Oabs(v_x,X0) = v_x )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_183]) ).
tcf(c_201,plain,
c_HOL_Oabs(v_x,t_a) = v_x,
inference(unflattening,[status(thm)],[c_200]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(v_x,c_times(X2,X1,X0),X0)
| ~ c_lessequals(v_x,X2,X0)
| ~ c_lessequals(v_x,X1,X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_188]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,c_times(X1,X0,t_a),t_a)
| ~ c_lessequals(v_x,X1,t_a)
| ~ c_lessequals(v_x,X0,t_a) ),
inference(unflattening,[status(thm)],[c_207]) ).
tcf(c_238,plain,
~ c_lessequals(v_x,c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
inference(light_normalisation,[status(thm)],[c_145,c_201]) ).
tcf(c_250,definition,
iPr_def_10 = v_h(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_251,definition,
iPr_def_11 = c_HOL_Oabs(iPr_def_10,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_252,definition,
iPr_def_12 = c_times(v_c,iPr_def_11,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_253,definition,
iPr_def_13 = c_HOL_Oabs(v_x,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_255,plain,
~ c_lessequals(v_x,iPr_def_12,t_a),
inference(demodulation,[status(thm)],[c_238,c_250,c_251,c_252]) ).
tcf(c_256,plain,
! [X0: $i,X1: $i] :
( c_lessequals(v_x,c_times(X1,X0,t_a),t_a)
| ~ c_lessequals(v_x,X1,t_a)
| ~ c_lessequals(v_x,X0,t_a) ),
inference(demodulation,[status(thm)],[c_208]) ).
tcf(c_257,plain,
iPr_def_13 = v_x,
inference(demodulation,[status(thm)],[c_201,c_253]) ).
tcf(c_258,plain,
! [X0: $i] : c_lessequals(v_x,c_HOL_Oabs(X0,t_a),t_a),
inference(demodulation,[status(thm)],[c_195]) ).
tcf(c_259,plain,
c_lessequals(v_x,v_c,t_a),
inference(demodulation,[status(thm)],[c_176]) ).
tcf(c_410,plain,
! [X0: $i] : c_lessequals(iPr_def_13,c_HOL_Oabs(X0,t_a),t_a),
inference(light_normalisation,[status(thm)],[c_258,c_257]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] :
( c_lessequals(iPr_def_13,c_times(X1,X0,t_a),t_a)
| ~ c_lessequals(iPr_def_13,X1,t_a)
| ~ c_lessequals(iPr_def_13,X0,t_a) ),
inference(light_normalisation,[status(thm)],[c_256,c_257]) ).
tcf(c_415,plain,
c_lessequals(iPr_def_13,v_c,t_a),
inference(light_normalisation,[status(thm)],[c_259,c_257]) ).
tcf(c_416,plain,
~ c_lessequals(iPr_def_13,iPr_def_12,t_a),
inference(light_normalisation,[status(thm)],[c_255,c_257]) ).
tcf(c_419,plain,
c_lessequals(iPr_def_13,iPr_def_11,t_a),
inference(superposition,[status(thm)],[c_251,c_410]) ).
tcf(c_422,plain,
( c_lessequals(iPr_def_13,iPr_def_12,t_a)
| ~ c_lessequals(iPr_def_13,iPr_def_11,t_a)
| ~ c_lessequals(iPr_def_13,v_c,t_a) ),
inference(superposition,[status(thm)],[c_252,c_411]) ).
tcf(c_423,plain,
~ c_lessequals(iPr_def_13,iPr_def_11,t_a),
inference(forward_subsumption_resolution,[status(thm)],[c_422,c_416,c_415]) ).
tcf(c_424,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_423,c_419]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/15.64 % Computer : n008.cluster.edu
% 0.15/15.64 % Model : x86_64 x86_64
% 0.15/15.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/15.64 % Memory : 8046.5625MB
% 0.15/15.64 % OS : Linux 6.8.0-71-generic
% 0.15/15.64 % CPULimit : 300
% 0.15/15.64 % WCLimit : 300
% 0.15/15.64 % DateTime : Fri Sep 25 05:47:09 UTC 2026
% 0.15/15.65 % CPUTime :
% 0.15/15.65 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/15.69 Running first-order theorem proving
% 0.15/15.69 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
% 0.19/15.70
% 0.19/15.70 % ======== iProver multi-core TPTP/SMT =========
% 0.19/15.70
% 0.19/15.70 % Detected problem language: tptp
% 0.19/15.71 % Proving...
% 1.71/16.56 % SZS status Started for theBenchmark.p
% 1.71/16.56 % SZS status Unsatisfiable for theBenchmark.p
% 1.71/16.56
% 1.71/16.56 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.71/16.56
% 1.71/16.56 % ------ iProver source info
% 1.71/16.56
% 1.71/16.56 % git: date: 2026-07-19 20:42:38 +0200
% 1.71/16.56 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.71/16.56 % git: non_committed_changes: false
% 1.71/16.56
% 1.71/16.56 % ------ Parsing...% successful
% 1.71/16.56
% 1.71/16.56
% 1.71/16.56 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.71/16.56
% 1.71/16.56 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 1 sf_s rm: 3 0s sf_e pe_s pe_e %
% 1.71/16.56
% 1.71/16.56 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.71/16.56
% 1.71/16.56 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.71/16.56 % ------ Proving...
% 1.71/16.56 % ------ Problem Properties
% 1.71/16.56
% 1.71/16.56 %
% 1.71/16.56 % clauses 11
% 1.71/16.56 % conjectures 1
% 1.71/16.56 % EPR 4
% 1.71/16.56 % Horn 11
% 1.71/16.56 % unary 10
% 1.71/16.56 % binary 0
% 1.71/16.56 % lits 13
% 1.71/16.56 % lits eq 7
% 1.71/16.56 % fd_pure 0
% 1.71/16.56 % fd_pseudo 0
% 1.71/16.56 % fd_cond 0
% 1.71/16.56 % fd_pseudo_cond 0
% 1.71/16.56 % AC symbols 0
% 1.71/16.56
% 1.71/16.56 % ------ Schedule dynamic 5 is on
% 1.71/16.56
% 1.71/16.56 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.71/16.56
% 1.71/16.56
% 1.71/16.56 % ------
% 1.71/16.56 % Current options:
% 1.71/16.56 % ------
% 1.71/16.56
% 1.71/16.56
% 1.71/16.56 %
% 1.71/16.56
% 1.71/16.56 % ------ Proving...
% 1.71/16.56 %
% 1.71/16.56
% 1.71/16.56 % SZS status Unsatisfiable for theBenchmark.p
% 1.71/16.56
% 1.71/16.56 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.71/16.56
% 1.71/16.56
%------------------------------------------------------------------------------