%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA014-2 : 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 12:55:36 PM UTC 2026
% Result : Unsatisfiable 1.93s 1.28s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 59 ( 21 unt; 0 def)
% Number of atoms : 105 ( 55 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 95 ( 49 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?; 72 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f4,axiom,
! [X0,X1] :
( c_times(c_1,X1,X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f5,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_Osemigroup__mult__class_Omult__assoc_0) ).
fof(f6,axiom,
! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7,axiom,
! [X2,X0,X1] :
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f8,axiom,
! [X0,X1] :
( c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f9,plain,
! [X0,X1] :
( c_1 = c_times(c_HOL_Oinverse(X1,X0),X1,X0)
| c_0 = X1
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
fof(f11,axiom,
! [X0] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f12,axiom,
! [X0] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f13,axiom,
! [X0] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f14,axiom,
! [X0] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
tcf(c_62,negated_conjecture,
v_c != c_0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] : ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X0)),t_a),c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),t_a),
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( c_times(c_1,X1,X0) = X1 )
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,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,[],[f5]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) = c_HOL_Oabs(c_times(X1,X2,X0),X0) )
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( ( X1 = c_0 )
| ( c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,plain,
! [X0: $i] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,plain,
! [X0: $i] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,plain,
! [X0: $i] :
( class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_74,plain,
! [X0: $i] :
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_75,plain,
( class_Orderings_Oorder(t_a)
| ~ class_Ring__and__Field_Oordered__field(t_a) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ class_Orderings_Oorder(X2)
| ( X2 != t_a )
| ( c_HOL_Oabs(v_f(v_x(X0)),t_a) != X1 )
| ( c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_67]) ).
tcf(c_183,plain,
! [X0: $i] :
( ~ class_Orderings_Oorder(t_a)
| ( c_HOL_Oabs(v_f(v_x(X0)),t_a) != c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a) ) ),
inference(unflattening,[status(thm)],[c_182]) ).
tcf(c_185,plain,
! [X0: $i] : c_HOL_Oabs(v_f(v_x(X0)),t_a) != c_times(X0,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X0)),t_a),t_a),t_a),
inference(global_subsumption_just,[status(thm)],[c_183,c_64,c_75,c_183]) ).
tcf(c_192,plain,
! [X0: $i] :
( class_Ring__and__Field_Oordered__idom(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_73]) ).
tcf(c_193,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(unflattening,[status(thm)],[c_192]) ).
tcf(c_197,plain,
! [X0: $i] :
( class_Ring__and__Field_Ofield(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_72]) ).
tcf(c_198,plain,
class_Ring__and__Field_Ofield(t_a),
inference(unflattening,[status(thm)],[c_197]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) = c_HOL_Oabs(c_times(X1,X2,X0),X0) )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_193]) ).
tcf(c_205,plain,
! [X0: $i,X1: $i] : c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a) = c_HOL_Oabs(c_times(X0,X1,t_a),t_a),
inference(unflattening,[status(thm)],[c_204]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_times(c_1,X2,X1) = X2 )
| ~ class_Ring__and__Field_Ofield(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_65]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( ( c_times(c_1,X1,X0) = X1 )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_211]) ).
tcf(c_222,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_Ofield(X0)
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_66]) ).
tcf(c_223,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_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_222]) ).
tcf(c_233,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_a ) ),
inference(resolution_lifted,[status(thm)],[c_223,c_198]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(unflattening,[status(thm)],[c_233]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] :
( ( c_times(c_1,X1,X0) = X1 )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_212,c_198]) ).
tcf(c_240,plain,
! [X0: $i] : c_times(c_1,X0,t_a) = X0,
inference(unflattening,[status(thm)],[c_239]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i] :
( ( X1 = c_0 )
| ( c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1 )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_198]) ).
tcf(c_246,plain,
! [X0: $i] :
( ( X0 = c_0 )
| ( c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1 ) ),
inference(unflattening,[status(thm)],[c_245]) ).
tcf(c_274,plain,
! [X0: $i] : c_times(X0,c_HOL_Oabs(c_times(v_c,v_f(v_x(X0)),t_a),t_a),t_a) != c_HOL_Oabs(v_f(v_x(X0)),t_a),
inference(demodulation,[status(thm)],[c_185,c_205]) ).
tcf(c_282,plain,
! [X0: $i] : c_times(X0,c_HOL_Oabs(c_times(v_c,v_f(v_x(X0)),t_a),t_a),t_a) != c_HOL_Oabs(v_f(v_x(X0)),t_a),
inference(demodulation,[status(thm)],[c_274]) ).
tcf(c_283,plain,
! [X0: $i] :
( ( X0 = c_0 )
| ( c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1 ) ),
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_284,plain,
! [X0: $i] : c_times(c_1,X0,t_a) = X0,
inference(demodulation,[status(thm)],[c_240]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i,X2: $i] : c_times(c_times(X0,X1,t_a),X2,t_a) = c_times(X0,c_times(X1,X2,t_a),t_a),
inference(demodulation,[status(thm)],[c_234]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i] : c_times(c_HOL_Oabs(X0,t_a),c_HOL_Oabs(X1,t_a),t_a) = c_HOL_Oabs(c_times(X0,X1,t_a),t_a),
inference(demodulation,[status(thm)],[c_205]) ).
tcf(c_287,negated_conjecture,
v_c != c_0,
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i] :
( ( X0 = c_0 )
| ( c_times(c_HOL_Oinverse(X0,t_a),c_times(X0,X1,t_a),t_a) = c_times(c_1,X1,t_a) ) ),
inference(superposition,[status(thm)],[c_283,c_285]) ).
tcf(c_355,plain,
! [X0: $i] : c_HOL_Oabs(c_times(X0,c_times(v_c,v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),t_a),t_a) != c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X0,t_a))),t_a),
inference(superposition,[status(thm)],[c_286,c_282]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i] :
( ( X0 = c_0 )
| ( c_times(c_HOL_Oinverse(X0,t_a),c_times(X0,X1,t_a),t_a) = X1 ) ),
inference(demodulation,[status(thm)],[c_347,c_284]) ).
tcf(c_430,plain,
v_c = c_0,
inference(superposition,[status(thm)],[c_360,c_355]) ).
tcf(c_431,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_430,c_287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.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
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 05:46:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.93/1.28 % SZS status Started for theBenchmark.p
% 1.93/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.93/1.28
% 1.93/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.93/1.28
% 1.93/1.28 % ------ iProver source info
% 1.93/1.28
% 1.93/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.93/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.93/1.28 % git: non_committed_changes: false
% 1.93/1.28
% 1.93/1.28 % ------ Parsing...% successful
% 1.93/1.28
% 1.93/1.28
% 1.93/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.93/1.28
% 1.93/1.28 % ------ 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: 3 0s sf_e pe_s pe_e %
% 1.93/1.28
% 1.93/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.93/1.28
% 1.93/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.93/1.28 % ------ Proving...
% 1.93/1.28 % ------ Problem Properties
% 1.93/1.28
% 1.93/1.28 %
% 1.93/1.28 % clauses 6
% 1.93/1.28 % conjectures 1
% 1.93/1.28 % EPR 1
% 1.93/1.28 % Horn 5
% 1.93/1.28 % unary 5
% 1.93/1.28 % binary 1
% 1.93/1.28 % lits 7
% 1.93/1.28 % lits eq 7
% 1.93/1.28 % fd_pure 0
% 1.93/1.28 % fd_pseudo 0
% 1.93/1.28 % fd_cond 1
% 1.93/1.28 % fd_pseudo_cond 0
% 1.93/1.28 % AC symbols 0
% 1.93/1.28
% 1.93/1.28 % ------ Schedule dynamic 5 is on
% 1.93/1.28
% 1.93/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.93/1.28
% 1.93/1.28
% 1.93/1.28 % ------
% 1.93/1.28 % Current options:
% 1.93/1.28 % ------
% 1.93/1.28
% 1.93/1.28
% 1.93/1.28 %
% 1.93/1.28
% 1.93/1.28 % ------ Proving...
% 1.93/1.28 %
% 1.93/1.28
% 1.93/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.93/1.28
% 1.93/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.93/1.28
% 1.93/1.28
%------------------------------------------------------------------------------