%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA031-2 : 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 : 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 12:55:41 PM UTC 2026
% Result : Unsatisfiable 4.05s 1.50s
% Output : CNFRefutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 51 ( 18 unt; 0 def)
% Number of atoms : 102 ( 23 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 108 ( 57 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 114 ( 0 sgn 114 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_b(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_f(v_x(X0)),t_b),c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,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(f4,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_Omult__ac__1_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( c_times(X1,X2,X0) = c_times(X2,X1,X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
fof(f6,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(f7,axiom,
! [X0] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f8,axiom,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f9,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f10,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
tcf(c_60,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_b(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,negated_conjecture,
! [X0: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_f(v_x(X0)),t_b),c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),t_b),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,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,[],[f3]) ).
tcf(c_63,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,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(X1,X2,X0) = c_times(X2,X1,X0) )
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,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,[],[f6]) ).
tcf(c_66,plain,
! [X0: $i] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_67,plain,
! [X0: $i] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
! [X0: $i] :
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
! [X0: $i] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[],[f11]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_62]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_167]) ).
tcf(c_178,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__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_63]) ).
tcf(c_179,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__idom(X0) ),
inference(unflattening,[status(thm)],[c_178]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_times(X2,X3,X1) = c_times(X3,X2,X1) )
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_64]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(X1,X2,X0) = c_times(X2,X1,X0) )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(unflattening,[status(thm)],[c_189]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_lessequals(c_times(X4,X2,X0),c_times(X4,X3,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X4,X0)
| ~ c_lessequals(X2,X3,X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_68]) ).
tcf(c_201,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__idom(X2)
| ~ c_lessequals(c_0,X3,X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(unflattening,[status(thm)],[c_200]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(X1,X2,X0) = c_times(X2,X1,X0) )
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_190,c_70]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(unflattening,[status(thm)],[c_219]) ).
tcf(c_225,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_b ) ),
inference(resolution_lifted,[status(thm)],[c_179,c_70]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(unflattening,[status(thm)],[c_225]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ( X0 != t_b ) ),
inference(resolution_lifted,[status(thm)],[c_168,c_70]) ).
tcf(c_232,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(unflattening,[status(thm)],[c_231]) ).
tcf(c_237,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_b ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_201]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X2,X0,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(unflattening,[status(thm)],[c_237]) ).
tcf(c_274,plain,
! [X0: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_g(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),t_b),
inference(demodulation,[status(thm)],[c_61,c_220]) ).
tcf(c_285,plain,
! [X0: $i] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_g(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),t_b),
inference(demodulation,[status(thm)],[c_274]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X2,X0,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(demodulation,[status(thm)],[c_238]) ).
tcf(c_287,plain,
! [X0: $i] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),
inference(demodulation,[status(thm)],[c_232]) ).
tcf(c_288,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(demodulation,[status(thm)],[c_226]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(demodulation,[status(thm)],[c_220]) ).
tcf(c_290,negated_conjecture,
! [X0: $i] : c_lessequals(c_HOL_Oabs(v_b(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_434,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(X0,c_times(X1,X2,t_b),t_b) = c_times(X1,c_times(X2,X0,t_b),t_b),
inference(superposition,[status(thm)],[c_288,c_289]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(c_times(X0,X2,t_b),c_times(X2,X1,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X0,X1,t_b) ),
inference(superposition,[status(thm)],[c_289,c_286]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_times(X0,X3,t_b),c_times(X1,c_times(X2,X3,t_b),t_b),t_b)
| ~ c_lessequals(c_0,X3,t_b)
| ~ c_lessequals(X0,c_times(X1,X2,t_b),t_b) ),
inference(superposition,[status(thm)],[c_434,c_441]) ).
tcf(c_2350,plain,
! [X0: $i] :
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b) ),
inference(superposition,[status(thm)],[c_556,c_285]) ).
tcf(c_2351,plain,
! [X0: $i] : ~ c_lessequals(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[status(thm)],[c_2350,c_287]) ).
tcf(c_2431,plain,
$false,
inference(superposition,[status(thm)],[c_290,c_2351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA031-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.58 % Computer : n026.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Fri Sep 25 05:51:26 UTC 2026
% 0.09/0.59 % CPUTime :
% 0.09/0.59 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.62 Running first-order theorem proving
% 0.09/0.62 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
% 0.14/0.64
% 0.14/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.64
% 0.14/0.64 % Detected problem language: tptp
% 0.14/0.65 % Proving...
% 4.05/1.50 % SZS status Started for theBenchmark.p
% 4.05/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.05/1.50
% 4.05/1.50 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.05/1.50
% 4.05/1.50 % ------ iProver source info
% 4.05/1.50
% 4.05/1.50 % git: date: 2026-07-19 20:42:38 +0200
% 4.05/1.50 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.05/1.50 % git: non_committed_changes: false
% 4.05/1.50
% 4.05/1.50 % ------ Parsing...% successful
% 4.05/1.50
% 4.05/1.50
% 4.05/1.50 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.05/1.50
% 4.05/1.50 % ------ 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: 1 sf_s rm: 2 0s sf_e pe_s pe_e %
% 4.05/1.50
% 4.05/1.50 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.05/1.50
% 4.05/1.50 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.05/1.50 % ------ Proving...
% 4.05/1.50 % ------ Problem Properties
% 4.05/1.50
% 4.05/1.50 %
% 4.05/1.50 % clauses 6
% 4.05/1.50 % conjectures 1
% 4.05/1.50 % EPR 0
% 4.05/1.50 % Horn 6
% 4.05/1.50 % unary 5
% 4.05/1.50 % binary 0
% 4.05/1.50 % lits 8
% 4.05/1.50 % lits eq 2
% 4.05/1.50 % fd_pure 0
% 4.05/1.50 % fd_pseudo 0
% 4.05/1.50 % fd_cond 0
% 4.05/1.50 % fd_pseudo_cond 0
% 4.05/1.50 % AC symbols 0
% 4.05/1.50
% 4.05/1.50 % ------ Schedule dynamic 5 is on
% 4.05/1.50
% 4.05/1.50 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.05/1.50
% 4.05/1.50
% 4.05/1.50 % ------
% 4.05/1.50 % Current options:
% 4.05/1.50 % ------
% 4.05/1.50
% 4.05/1.50
% 4.05/1.50 %
% 4.05/1.50
% 4.05/1.50 % ------ Proving...
% 4.05/1.50 %
% 4.05/1.50
% 4.05/1.50 % SZS status Unsatisfiable for theBenchmark.p
% 4.05/1.50
% 4.05/1.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.05/1.50
% 4.05/1.50
%------------------------------------------------------------------------------