%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ANA016-2 : 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 12:55:37 PM UTC 2026
% Result : Unsatisfiable 1.77s 1.28s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 22 unt; 4 def)
% Number of atoms : 97 ( 52 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 62 ( 30 ~; 32 |; 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 : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 63 ( 0 sgn 63 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
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_times(X1,c_HOL_Oinverse(X1,X0),X0) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
fof(f7,plain,
! [X0,X1] :
( c_1 = c_times(X1,c_HOL_Oinverse(X1,X0),X0)
| c_0 = X1
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,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(f9,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(f10,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) ).
tcf(c_58,negated_conjecture,
v_c != c_0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_59,negated_conjecture,
c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a) != v_g(v_x),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( c_times(c_1,X1,X0) = X1 )
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,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_63,plain,
! [X0: $i,X1: $i] :
( ( X1 = c_0 )
| ( c_times(X1,c_HOL_Oinverse(X1,X0),X0) = c_1 )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,plain,
! [X0: $i] :
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_65,plain,
! [X0: $i] :
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_66,plain,
! [X0: $i] :
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_136,plain,
! [X0: $i] :
( class_Ring__and__Field_Ofield(X0)
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_66]) ).
tcf(c_137,plain,
class_Ring__and__Field_Ofield(t_a),
inference(unflattening,[status(thm)],[c_136]) ).
tcf(c_142,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_64,c_61]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( ( c_times(c_1,X1,X0) = X1 )
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(unflattening,[status(thm)],[c_142]) ).
tcf(c_153,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_65,c_62]) ).
tcf(c_154,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_153]) ).
tcf(c_164,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_154,c_137]) ).
tcf(c_165,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_164]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] :
( ( c_times(c_1,X1,X0) = X1 )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_143,c_137]) ).
tcf(c_171,plain,
! [X0: $i] : c_times(c_1,X0,t_a) = X0,
inference(unflattening,[status(thm)],[c_170]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] :
( ( X1 = c_0 )
| ( c_times(X1,c_HOL_Oinverse(X1,X0),X0) = c_1 )
| ( X0 != t_a ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_137]) ).
tcf(c_177,plain,
! [X0: $i] :
( ( X0 = c_0 )
| ( c_times(X0,c_HOL_Oinverse(X0,t_a),t_a) = c_1 ) ),
inference(unflattening,[status(thm)],[c_176]) ).
tcf(c_208,definition,
iPr_def_10 = c_HOL_Oinverse(v_c,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_209,definition,
iPr_def_11 = v_g(v_x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_210,definition,
iPr_def_12 = c_times(iPr_def_10,iPr_def_11,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_211,definition,
iPr_def_13 = c_times(v_c,iPr_def_12,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_212,plain,
! [X0: $i] :
( ( X0 = c_0 )
| ( c_times(X0,c_HOL_Oinverse(X0,t_a),t_a) = c_1 ) ),
inference(demodulation,[status(thm)],[c_177]) ).
tcf(c_213,plain,
! [X0: $i] : c_times(c_1,X0,t_a) = X0,
inference(demodulation,[status(thm)],[c_171]) ).
tcf(c_214,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_165]) ).
tcf(c_215,negated_conjecture,
iPr_def_13 != iPr_def_11,
inference(demodulation,[status(thm)],[c_59,c_209,c_208,c_210,c_211]) ).
tcf(c_216,negated_conjecture,
v_c != c_0,
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_281,plain,
! [X0: $i,X1: $i] :
( ( X0 = c_0 )
| ( c_times(X0,c_times(c_HOL_Oinverse(X0,t_a),X1,t_a),t_a) = c_times(c_1,X1,t_a) ) ),
inference(superposition,[status(thm)],[c_212,c_214]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] :
( ( X0 = c_0 )
| ( c_times(X0,c_times(c_HOL_Oinverse(X0,t_a),X1,t_a),t_a) = X1 ) ),
inference(demodulation,[status(thm)],[c_281,c_213]) ).
tcf(c_351,plain,
! [X0: $i] :
( ( v_c = c_0 )
| ( c_times(v_c,c_times(iPr_def_10,X0,t_a),t_a) = X0 ) ),
inference(superposition,[status(thm)],[c_208,c_296]) ).
tcf(c_354,plain,
! [X0: $i] : c_times(v_c,c_times(iPr_def_10,X0,t_a),t_a) = X0,
inference(forward_subsumption_resolution,[status(thm)],[c_351,c_216]) ).
tcf(c_364,plain,
c_times(v_c,iPr_def_12,t_a) = iPr_def_11,
inference(superposition,[status(thm)],[c_210,c_354]) ).
tcf(c_371,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_211,c_364]) ).
tcf(c_372,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_215,c_371]) ).
tcf(c_373,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA016-2 : 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
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Fri Sep 25 05:47:07 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 0.03/0.41
% 0.03/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.41
% 0.03/0.41 % Detected problem language: tptp
% 0.03/0.43 % Proving...
% 1.77/1.28 % SZS status Started for theBenchmark.p
% 1.77/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/1.28
% 1.77/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.77/1.28
% 1.77/1.28 % ------ iProver source info
% 1.77/1.28
% 1.77/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.77/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.77/1.28 % git: non_committed_changes: false
% 1.77/1.28
% 1.77/1.28 % ------ Parsing...% successful
% 1.77/1.28
% 1.77/1.28
% 1.77/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.77/1.28
% 1.77/1.28 % ------ 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: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.77/1.28
% 1.77/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.77/1.28
% 1.77/1.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.77/1.28 % ------ Proving...
% 1.77/1.28 % ------ Problem Properties
% 1.77/1.28
% 1.77/1.28 %
% 1.77/1.28 % clauses 9
% 1.77/1.28 % conjectures 2
% 1.77/1.28 % EPR 2
% 1.77/1.28 % Horn 8
% 1.77/1.28 % unary 8
% 1.77/1.28 % binary 1
% 1.77/1.28 % lits 10
% 1.77/1.28 % lits eq 10
% 1.77/1.28 % fd_pure 0
% 1.77/1.28 % fd_pseudo 0
% 1.77/1.28 % fd_cond 1
% 1.77/1.28 % fd_pseudo_cond 0
% 1.77/1.28 % AC symbols 0
% 1.77/1.28
% 1.77/1.28 % ------ Schedule dynamic 5 is on
% 1.77/1.28
% 1.77/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.77/1.28
% 1.77/1.28
% 1.77/1.28 % ------
% 1.77/1.28 % Current options:
% 1.77/1.28 % ------
% 1.77/1.28
% 1.77/1.28
% 1.77/1.28 %
% 1.77/1.28
% 1.77/1.28 % ------ Proving...
% 1.77/1.28 %
% 1.77/1.28
% 1.77/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/1.28
% 1.77/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.77/1.28
% 1.77/1.28
%------------------------------------------------------------------------------