%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP183-3 : 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 : 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 01:31:43 PM UTC 2026
% Result : Unsatisfiable 20.61s 8.75s
% Output : CNFRefutation 20.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 82 unt; 4 def)
% Number of atoms : 151 ( 81 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 0 sgn 100 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
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(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(f17,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_20x) ).
fof(f18,plain,
identity != greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)),
inference(reorient_equations,[],[f17]) ).
tcf(c_65,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
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_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_80,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(inverse(a),identity)) != identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_96,negated_conjecture,
greatest_lower_bound(least_upper_bound(a,identity),least_upper_bound(identity,inverse(a))) != identity,
inference(theory_normalisation,[status(thm)],[c_80,c_70,c_68,c_71,c_69]) ).
tcf(c_135,definition,
iPr_def_10 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_136,definition,
iPr_def_11 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_137,definition,
iPr_def_12 = least_upper_bound(identity,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_138,definition,
iPr_def_13 = greatest_lower_bound(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_139,negated_conjecture,
iPr_def_13 != identity,
inference(demodulation,[status(thm)],[c_96,c_136,c_137,c_135,c_138]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_141,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_142,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_144,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_146,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_147,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_148,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,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_152,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(demodulation,[status(thm)],[c_70]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_234,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_151,c_153]) ).
tcf(c_241,plain,
multiply(iPr_def_11,a) = identity,
inference(superposition,[status(thm)],[c_136,c_141]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_141,c_140]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_242,c_142]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] : least_upper_bound(multiply(X0,X1),X1) = multiply(least_upper_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_142,c_144]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
inference(demodulation,[status(thm)],[c_263,c_153]) ).
tcf(c_277,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_241,c_140]) ).
tcf(c_280,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(a,X0)) = X0,
inference(demodulation,[status(thm)],[c_277,c_142]) ).
tcf(c_291,plain,
greatest_lower_bound(identity,iPr_def_12) = identity,
inference(superposition,[status(thm)],[c_137,c_147]) ).
tcf(c_292,plain,
greatest_lower_bound(iPr_def_12,identity) = identity,
inference(demodulation,[status(thm)],[c_291,c_154]) ).
tcf(c_297,plain,
least_upper_bound(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(superposition,[status(thm)],[c_138,c_148]) ).
tcf(c_299,plain,
least_upper_bound(iPr_def_11,identity) = iPr_def_12,
inference(demodulation,[status(thm)],[c_137,c_153]) ).
tcf(c_304,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_153,c_147]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_154,c_148]) ).
tcf(c_340,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_141,c_146]) ).
tcf(c_387,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(iPr_def_12,X0)) = greatest_lower_bound(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_138,c_152]) ).
tcf(c_470,plain,
! [X0: $i] : least_upper_bound(iPr_def_11,least_upper_bound(X0,identity)) = least_upper_bound(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_299,c_234]) ).
tcf(c_530,plain,
multiply(inverse(iPr_def_11),identity) = a,
inference(superposition,[status(thm)],[c_241,c_243]) ).
tcf(c_532,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),X0) = multiply(a,X0),
inference(superposition,[status(thm)],[c_280,c_243]) ).
tcf(c_698,plain,
greatest_lower_bound(identity,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_135,c_304]) ).
tcf(c_719,plain,
greatest_lower_bound(iPr_def_10,identity) = identity,
inference(demodulation,[status(thm)],[c_698,c_154]) ).
tcf(c_764,plain,
least_upper_bound(iPr_def_12,iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_138,c_311]) ).
tcf(c_1819,plain,
! [X0: $i] : least_upper_bound(X0,multiply(a,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_135,c_266]) ).
tcf(c_2265,plain,
greatest_lower_bound(iPr_def_10,identity) = greatest_lower_bound(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_292,c_387]) ).
tcf(c_2276,plain,
greatest_lower_bound(iPr_def_13,identity) = identity,
inference(demodulation,[status(thm)],[c_2265,c_719]) ).
tcf(c_2551,plain,
least_upper_bound(iPr_def_13,identity) = iPr_def_13,
inference(superposition,[status(thm)],[c_2276,c_148]) ).
tcf(c_2562,plain,
! [X0: $i] : least_upper_bound(iPr_def_13,least_upper_bound(identity,X0)) = least_upper_bound(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_2551,c_151]) ).
tcf(c_4344,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_11),identity)) = multiply(inverse(iPr_def_11),iPr_def_12),
inference(superposition,[status(thm)],[c_299,c_340]) ).
tcf(c_4399,plain,
multiply(a,iPr_def_12) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4344,c_153,c_135,c_530,c_532]) ).
tcf(c_5691,plain,
least_upper_bound(iPr_def_11,iPr_def_13) = least_upper_bound(iPr_def_13,iPr_def_12),
inference(superposition,[status(thm)],[c_2551,c_470]) ).
tcf(c_5707,plain,
least_upper_bound(iPr_def_11,iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_5691,c_153,c_764]) ).
tcf(c_6688,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_11),iPr_def_13)) = multiply(inverse(iPr_def_11),iPr_def_12),
inference(superposition,[status(thm)],[c_5707,c_340]) ).
tcf(c_6701,plain,
least_upper_bound(identity,multiply(a,iPr_def_13)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_6688,c_532,c_4399]) ).
tcf(c_16651,plain,
least_upper_bound(iPr_def_13,multiply(a,iPr_def_13)) = least_upper_bound(iPr_def_13,iPr_def_10),
inference(superposition,[status(thm)],[c_6701,c_2562]) ).
tcf(c_16681,plain,
multiply(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(demodulation,[status(thm)],[c_16651,c_153,c_297,c_1819]) ).
tcf(c_18079,plain,
multiply(inverse(iPr_def_10),iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_16681,c_243]) ).
tcf(c_18109,plain,
identity = iPr_def_13,
inference(demodulation,[status(thm)],[c_18079,c_141]) ).
tcf(c_18207,plain,
iPr_def_13 != iPr_def_13,
inference(demodulation,[status(thm)],[c_139,c_18109]) ).
tcf(c_18208,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_18207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP183-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.36 % Computer : n003.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Wed Sep 23 14:04:10 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.39 Running UEQ theorem proving
% 0.10/5.39 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
% 0.14/5.41
% 0.14/5.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.41
% 0.14/5.41 % Detected problem language: tptp
% 0.14/5.42 % Proving...
% 20.61/8.75 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 20.61/8.75 % SZS status Started for theBenchmark.p
% 20.61/8.75 % SZS status Unsatisfiable for theBenchmark.p
% 20.61/8.75
% 20.61/8.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 20.61/8.75
% 20.61/8.75 % ------ iProver source info
% 20.61/8.75
% 20.61/8.75 % git: date: 2026-07-19 20:42:38 +0200
% 20.61/8.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 20.61/8.75 % git: non_committed_changes: false
% 20.61/8.75
% 20.61/8.75 % ------ Parsing...% successful
% 20.61/8.75
% 20.61/8.75
% 20.61/8.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 20.61/8.75
% 20.61/8.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 20.61/8.75
% 20.61/8.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 20.61/8.75
% 20.61/8.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 20.61/8.75 % ------ Proving...
% 20.61/8.75 % ------ Problem Properties
% 20.61/8.75
% 20.61/8.75 %
% 20.61/8.75 % clauses 20
% 20.61/8.75 % conjectures 1
% 20.61/8.75 % EPR 1
% 20.61/8.75 % Horn 20
% 20.61/8.75 % unary 20
% 20.61/8.75 % binary 0
% 20.61/8.75 % lits 20
% 20.61/8.75 % lits eq 20
% 20.61/8.75 % fd_pure 0
% 20.61/8.75 % fd_pseudo 0
% 20.61/8.75 % fd_cond 0
% 20.61/8.75 % fd_pseudo_cond 0
% 20.61/8.75 % AC symbols 2
% 20.61/8.75
% 20.61/8.75 % ------ Input Options Time Limit: Unbounded
% 20.61/8.75
% 20.61/8.75
% 20.61/8.75 % ------
% 20.61/8.75 % Current options:
% 20.61/8.75 % ------
% 20.61/8.75
% 20.61/8.75
% 20.61/8.75 %
% 20.61/8.75
% 20.61/8.75 % ------ Proving...
% 20.61/8.75 %
% 20.61/8.75
% 20.61/8.75 % SZS status Unsatisfiable for theBenchmark.p
% 20.61/8.75
% 20.61/8.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.61/8.75
% 20.61/8.75
%------------------------------------------------------------------------------