%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 01:31:44 PM UTC 2026
% Result : Unsatisfiable 8.38s 1.80s
% Output : CNFRefutation 8.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 82 ( 82 unt; 6 def)
% Number of atoms : 168 ( 81 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 90 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
fof(f9,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
fof(f15,axiom,
! [X2,X0,X1] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22a) ).
fof(f18,plain,
multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)) != least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))),
inference(reorient_equations,[],[f17]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(X0,greatest_lower_bound(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_72,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(cnf_transformation,[],[f15]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_80,negated_conjecture,
least_upper_bound(least_upper_bound(multiply(a,b),identity),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_96,negated_conjecture,
least_upper_bound(identity,least_upper_bound(multiply(a,b),multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)))) != multiply(least_upper_bound(a,identity),least_upper_bound(b,identity)),
inference(theory_normalisation,[status(thm)],[c_80,c_70,c_68,c_71,c_69]) ).
tcf(c_134,definition,
iPr_def_10 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_135,definition,
iPr_def_11 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_136,definition,
iPr_def_12 = least_upper_bound(b,identity),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_137,definition,
iPr_def_13 = multiply(iPr_def_11,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_138,definition,
iPr_def_14 = least_upper_bound(iPr_def_10,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_139,definition,
iPr_def_15 = least_upper_bound(identity,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_140,negated_conjecture,
iPr_def_15 != iPr_def_13,
inference(demodulation,[status(thm)],[c_96,c_136,c_135,c_137,c_134,c_138,c_139]) ).
tcf(c_143,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_151,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(least_upper_bound(X0,X1),X2) = least_upper_bound(X0,least_upper_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(X1,least_upper_bound(X0,X2)),
inference(superposition,[status(thm)],[c_152,c_154]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_143,c_144]) ).
tcf(c_273,plain,
greatest_lower_bound(b,iPr_def_12) = b,
inference(superposition,[status(thm)],[c_136,c_148]) ).
tcf(c_279,plain,
greatest_lower_bound(iPr_def_12,b) = b,
inference(demodulation,[status(thm)],[c_273,c_155]) ).
tcf(c_285,plain,
least_upper_bound(identity,a) = iPr_def_11,
inference(demodulation,[status(thm)],[c_135,c_154]) ).
tcf(c_286,plain,
least_upper_bound(iPr_def_14,identity) = iPr_def_15,
inference(demodulation,[status(thm)],[c_139,c_154]) ).
tcf(c_287,plain,
least_upper_bound(iPr_def_13,iPr_def_10) = iPr_def_14,
inference(demodulation,[status(thm)],[c_138,c_154]) ).
tcf(c_290,plain,
greatest_lower_bound(identity,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_285,c_148]) ).
tcf(c_291,plain,
greatest_lower_bound(iPr_def_11,identity) = identity,
inference(demodulation,[status(thm)],[c_290,c_155]) ).
tcf(c_292,plain,
greatest_lower_bound(iPr_def_14,iPr_def_15) = iPr_def_14,
inference(superposition,[status(thm)],[c_286,c_148]) ).
tcf(c_296,plain,
! [X0: $i] : multiply(least_upper_bound(a,X0),b) = least_upper_bound(iPr_def_10,multiply(X0,b)),
inference(superposition,[status(thm)],[c_134,c_145]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_143,c_145]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] : least_upper_bound(multiply(X0,X1),X1) = multiply(least_upper_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_143,c_145]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
inference(demodulation,[status(thm)],[c_302,c_154]) ).
tcf(c_354,plain,
! [X0: $i] : multiply(iPr_def_11,least_upper_bound(iPr_def_12,X0)) = least_upper_bound(iPr_def_13,multiply(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_137,c_147]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,least_upper_bound(X0,X1)) = least_upper_bound(X0,X1),
inference(superposition,[status(thm)],[c_151,c_152]) ).
tcf(c_401,plain,
least_upper_bound(iPr_def_12,b) = iPr_def_12,
inference(superposition,[status(thm)],[c_279,c_149]) ).
tcf(c_403,plain,
! [X0: $i] : least_upper_bound(iPr_def_13,least_upper_bound(iPr_def_10,X0)) = least_upper_bound(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_287,c_152]) ).
tcf(c_404,plain,
greatest_lower_bound(iPr_def_13,iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_287,c_148]) ).
tcf(c_405,plain,
greatest_lower_bound(iPr_def_14,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_404,c_155]) ).
tcf(c_466,plain,
! [X0: $i] : least_upper_bound(b,least_upper_bound(X0,identity)) = least_upper_bound(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_136,c_233]) ).
tcf(c_625,plain,
least_upper_bound(iPr_def_14,iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_405,c_149]) ).
tcf(c_706,plain,
multiply(greatest_lower_bound(identity,iPr_def_11),iPr_def_12) = greatest_lower_bound(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_137,c_248]) ).
tcf(c_716,plain,
greatest_lower_bound(iPr_def_13,iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_706,c_155,c_143,c_291]) ).
tcf(c_799,plain,
least_upper_bound(iPr_def_13,iPr_def_12) = iPr_def_13,
inference(superposition,[status(thm)],[c_716,c_149]) ).
tcf(c_1605,plain,
! [X0: $i] : least_upper_bound(X0,multiply(a,X0)) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_285,c_297]) ).
tcf(c_2410,plain,
least_upper_bound(b,multiply(a,b)) = least_upper_bound(iPr_def_10,multiply(identity,b)),
inference(superposition,[status(thm)],[c_311,c_296]) ).
tcf(c_2414,plain,
multiply(iPr_def_11,b) = least_upper_bound(iPr_def_10,b),
inference(demodulation,[status(thm)],[c_2410,c_143,c_1605]) ).
tcf(c_4622,plain,
least_upper_bound(iPr_def_13,multiply(iPr_def_11,b)) = multiply(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_401,c_354]) ).
tcf(c_4652,plain,
least_upper_bound(iPr_def_14,b) = iPr_def_13,
inference(demodulation,[status(thm)],[c_4622,c_137,c_403,c_2414]) ).
tcf(c_4808,plain,
least_upper_bound(iPr_def_14,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_4652,c_376]) ).
tcf(c_4815,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_4808,c_625]) ).
tcf(c_4838,plain,
least_upper_bound(iPr_def_14,iPr_def_12) = iPr_def_14,
inference(demodulation,[status(thm)],[c_799,c_4815]) ).
tcf(c_4844,plain,
iPr_def_14 != iPr_def_15,
inference(demodulation,[status(thm)],[c_140,c_4815]) ).
tcf(c_5583,plain,
least_upper_bound(b,iPr_def_15) = least_upper_bound(iPr_def_14,iPr_def_12),
inference(superposition,[status(thm)],[c_286,c_466]) ).
tcf(c_5602,plain,
least_upper_bound(iPr_def_15,b) = iPr_def_14,
inference(demodulation,[status(thm)],[c_5583,c_154,c_4838]) ).
tcf(c_6510,plain,
greatest_lower_bound(iPr_def_15,iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_5602,c_148]) ).
tcf(c_6519,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_6510,c_155,c_292]) ).
tcf(c_6520,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6519,c_4844]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.51 % Computer : n014.cluster.edu
% 0.08/0.51 % Model : x86_64 x86_64
% 0.08/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.51 % Memory : 8046.5625MB
% 0.08/0.51 % OS : Linux 6.8.0-71-generic
% 0.08/0.51 % CPULimit : 300
% 0.08/0.51 % WCLimit : 300
% 0.08/0.51 % DateTime : Wed Sep 23 14:03:19 UTC 2026
% 0.08/0.51 % CPUTime :
% 0.08/0.51 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.55 Running UEQ theorem proving
% 0.08/0.55 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56
% 0.08/0.56 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.56
% 0.08/0.56 % Detected problem language: tptp
% 0.14/0.57 % Proving...
% 8.38/1.80 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.38/1.80 % SZS status Started for theBenchmark.p
% 8.38/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 8.38/1.80
% 8.38/1.80 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.38/1.80
% 8.38/1.80 % ------ iProver source info
% 8.38/1.80
% 8.38/1.80 % git: date: 2026-07-19 20:42:38 +0200
% 8.38/1.80 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.38/1.80 % git: non_committed_changes: false
% 8.38/1.80
% 8.38/1.80 % ------ Parsing...% successful
% 8.38/1.80
% 8.38/1.80
% 8.38/1.80 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.38/1.80
% 8.38/1.80 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.38/1.80
% 8.38/1.80 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.38/1.80
% 8.38/1.80 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.38/1.80 % ------ Proving...
% 8.38/1.80 % ------ Problem Properties
% 8.38/1.80
% 8.38/1.80 %
% 8.38/1.80 % clauses 22
% 8.38/1.80 % conjectures 1
% 8.38/1.80 % EPR 1
% 8.38/1.80 % Horn 22
% 8.38/1.80 % unary 22
% 8.38/1.80 % binary 0
% 8.38/1.80 % lits 22
% 8.38/1.80 % lits eq 22
% 8.38/1.80 % fd_pure 0
% 8.38/1.80 % fd_pseudo 0
% 8.38/1.80 % fd_cond 0
% 8.38/1.80 % fd_pseudo_cond 0
% 8.38/1.80 % AC symbols 2
% 8.38/1.80
% 8.38/1.80 % ------ Input Options Time Limit: Unbounded
% 8.38/1.80
% 8.38/1.80
% 8.38/1.80 % ------
% 8.38/1.80 % Current options:
% 8.38/1.80 % ------
% 8.38/1.80
% 8.38/1.80
% 8.38/1.80 %
% 8.38/1.80
% 8.38/1.80 % ------ Proving...
% 8.38/1.80 %
% 8.38/1.80
% 8.38/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 8.38/1.80
% 8.38/1.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.38/1.80
% 8.38/1.80
%------------------------------------------------------------------------------