%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP191-2 : 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 : n020.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 01:31:46 PM UTC 2026
% Result : Unsatisfiable 6.30s 1.95s
% Output : CNFRefutation 6.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 73 unt; 4 def)
% Number of atoms : 126 ( 72 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 88 !; 0 ?; 64 :)
% 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(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,axiom,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p39d_1) ).
fof(f18,plain,
b = greatest_lower_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p39d) ).
fof(f20,plain,
inverse(b) != least_upper_bound(inverse(a),inverse(b)),
inference(reorient_equations,[],[f19]) ).
tcf(c_66,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_71,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_72,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_75,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,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_79,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_81,plain,
greatest_lower_bound(a,b) = b,
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
inference(cnf_transformation,[],[f20]) ).
tcf(c_138,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_139,definition,
iPr_def_11 = inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_140,definition,
iPr_def_12 = least_upper_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_141,definition,
iPr_def_13 = greatest_lower_bound(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_142,negated_conjecture,
iPr_def_12 != iPr_def_11,
inference(demodulation,[status(thm)],[c_82,c_139,c_138,c_140]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_144,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_145,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_147,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_79]) ).
tcf(c_149,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_77]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_154,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_72]) ).
tcf(c_155,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_71]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_158,plain,
iPr_def_13 = b,
inference(demodulation,[status(thm)],[c_81,c_141]) ).
tcf(c_240,plain,
inverse(iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_139,c_158]) ).
tcf(c_241,plain,
least_upper_bound(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_140,c_155,c_157,c_154,c_156]) ).
tcf(c_242,plain,
greatest_lower_bound(a,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_141,c_158]) ).
tcf(c_243,plain,
greatest_lower_bound(iPr_def_13,a) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_242,c_155,c_157,c_154,c_156]) ).
tcf(c_254,plain,
multiply(iPr_def_10,a) = identity,
inference(superposition,[status(thm)],[c_138,c_144]) ).
tcf(c_255,plain,
multiply(iPr_def_11,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_240,c_144]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_157,c_151]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_144,c_143]) ).
tcf(c_433,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_267,c_145]) ).
tcf(c_497,plain,
! [X0: $i] : least_upper_bound(identity,multiply(X0,a)) = multiply(least_upper_bound(iPr_def_10,X0),a),
inference(superposition,[status(thm)],[c_254,c_147]) ).
tcf(c_607,plain,
! [X0: $i] : least_upper_bound(identity,multiply(iPr_def_11,X0)) = multiply(iPr_def_11,least_upper_bound(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_255,c_149]) ).
tcf(c_645,plain,
least_upper_bound(a,iPr_def_13) = a,
inference(superposition,[status(thm)],[c_243,c_264]) ).
tcf(c_656,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(iPr_def_13,X0)) = X0,
inference(superposition,[status(thm)],[c_240,c_433]) ).
tcf(c_658,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_144,c_433]) ).
tcf(c_662,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_433,c_433]) ).
tcf(c_875,plain,
least_upper_bound(iPr_def_13,a) = a,
inference(theory_normalisation,[status(thm)],[c_645,c_155,c_157,c_154,c_156]) ).
tcf(c_1447,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),X0) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_656,c_433]) ).
tcf(c_1853,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(iPr_def_11,X0)) = X0,
inference(superposition,[status(thm)],[c_1447,c_433]) ).
tcf(c_2036,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_662,c_144]) ).
tcf(c_2038,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_662,c_658]) ).
tcf(c_2510,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_2036,c_143]) ).
tcf(c_4546,plain,
multiply(least_upper_bound(iPr_def_10,iPr_def_11),a) = multiply(iPr_def_11,least_upper_bound(iPr_def_13,a)),
inference(superposition,[status(thm)],[c_607,c_497]) ).
tcf(c_4655,plain,
multiply(least_upper_bound(iPr_def_11,iPr_def_10),a) = multiply(iPr_def_11,least_upper_bound(iPr_def_13,a)),
inference(theory_normalisation,[status(thm)],[c_4546,c_155,c_157,c_154,c_156]) ).
tcf(c_4656,plain,
multiply(iPr_def_11,a) = multiply(iPr_def_12,a),
inference(demodulation,[status(thm)],[c_4655,c_241,c_875]) ).
tcf(c_4761,plain,
multiply(iPr_def_13,multiply(iPr_def_12,a)) = a,
inference(superposition,[status(thm)],[c_4656,c_1853]) ).
tcf(c_5197,plain,
multiply(iPr_def_13,multiply(multiply(iPr_def_12,a),inverse(a))) = identity,
inference(superposition,[status(thm)],[c_4761,c_2510]) ).
tcf(c_5487,plain,
multiply(iPr_def_13,iPr_def_12) = identity,
inference(demodulation,[status(thm)],[c_5197,c_143,c_2036,c_2038]) ).
tcf(c_5748,plain,
multiply(iPr_def_11,identity) = iPr_def_12,
inference(superposition,[status(thm)],[c_5487,c_656]) ).
tcf(c_5913,plain,
iPr_def_11 = iPr_def_12,
inference(demodulation,[status(thm)],[c_5748,c_2038]) ).
tcf(c_6234,plain,
$false,
inference(superposition,[status(thm)],[c_5913,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.61 % Computer : n020.cluster.edu
% 0.11/0.61 % Model : x86_64 x86_64
% 0.11/0.61 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.61 % Memory : 8046.5625MB
% 0.11/0.61 % OS : Linux 6.8.0-71-generic
% 0.11/0.61 % CPULimit : 300
% 0.11/0.61 % WCLimit : 300
% 0.11/0.61 % DateTime : Wed Sep 23 14:06:51 UTC 2026
% 0.11/0.61 % CPUTime :
% 0.11/0.61 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.65 Running UEQ theorem proving
% 0.16/0.65 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
% 0.16/0.66
% 0.16/0.66 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.66
% 0.16/0.66 % Detected problem language: tptp
% 0.16/0.68 % Proving...
% 6.30/1.95 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 6.30/1.95 % SZS status Started for theBenchmark.p
% 6.30/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 6.30/1.95
% 6.30/1.95 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.30/1.95
% 6.30/1.95 % ------ iProver source info
% 6.30/1.95
% 6.30/1.95 % git: date: 2026-07-19 20:42:38 +0200
% 6.30/1.95 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.30/1.95 % git: non_committed_changes: false
% 6.30/1.95
% 6.30/1.95 % ------ Parsing...% successful
% 6.30/1.95
% 6.30/1.95
% 6.30/1.95 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.30/1.95
% 6.30/1.95 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 6.30/1.95
% 6.30/1.95 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.30/1.95
% 6.30/1.95 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.30/1.95 % ------ Proving...
% 6.30/1.95 % ------ Problem Properties
% 6.30/1.95
% 6.30/1.95 %
% 6.30/1.95 % clauses 21
% 6.30/1.95 % conjectures 1
% 6.30/1.95 % EPR 2
% 6.30/1.95 % Horn 21
% 6.30/1.95 % unary 21
% 6.30/1.95 % binary 0
% 6.30/1.95 % lits 21
% 6.30/1.95 % lits eq 21
% 6.30/1.95 % fd_pure 0
% 6.30/1.95 % fd_pseudo 0
% 6.30/1.95 % fd_cond 0
% 6.30/1.95 % fd_pseudo_cond 0
% 6.30/1.95 % AC symbols 2
% 6.30/1.95
% 6.30/1.95 % ------ Input Options Time Limit: Unbounded
% 6.30/1.95
% 6.30/1.95
% 6.30/1.95 % ------
% 6.30/1.95 % Current options:
% 6.30/1.95 % ------
% 6.30/1.95
% 6.30/1.95
% 6.30/1.95 %
% 6.30/1.95
% 6.30/1.95 % ------ Proving...
% 6.30/1.95 %
% 6.30/1.95
% 6.30/1.95 % SZS status Unsatisfiable for theBenchmark.p
% 6.30/1.95
% 6.30/1.95 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.30/1.96
% 6.30/1.96
%------------------------------------------------------------------------------