%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n015.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 8.33s 1.73s
% Output : CNFRefutation 8.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 77 ( 77 unt; 4 def)
% Number of atoms : 125 ( 76 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 : 94 ( 0 sgn 94 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,axiom,
least_upper_bound(a,b) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p39c_1) ).
fof(f18,plain,
a = least_upper_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p39c) ).
fof(f20,plain,
inverse(a) != greatest_lower_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_76,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_80,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_81,plain,
least_upper_bound(a,b) = a,
inference(cnf_transformation,[],[f18]) ).
tcf(c_82,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
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 = greatest_lower_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_141,definition,
iPr_def_13 = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_142,negated_conjecture,
iPr_def_12 != iPr_def_10,
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_146,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_80]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
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 = a,
inference(demodulation,[status(thm)],[c_81,c_141]) ).
tcf(c_240,plain,
inverse(iPr_def_13) = iPr_def_10,
inference(demodulation,[status(thm)],[c_138,c_158]) ).
tcf(c_241,plain,
greatest_lower_bound(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_140,c_154,c_156,c_155,c_157]) ).
tcf(c_242,plain,
least_upper_bound(iPr_def_13,b) = iPr_def_13,
inference(demodulation,[status(thm)],[c_141,c_158]) ).
tcf(c_252,plain,
multiply(iPr_def_11,b) = identity,
inference(superposition,[status(thm)],[c_139,c_144]) ).
tcf(c_253,plain,
multiply(iPr_def_10,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_240,c_144]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_156,c_150]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_144,c_143]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_265,c_145]) ).
tcf(c_455,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(X0,b)) = multiply(greatest_lower_bound(iPr_def_11,X0),b),
inference(superposition,[status(thm)],[c_252,c_146]) ).
tcf(c_604,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(iPr_def_10,X0)) = multiply(iPr_def_10,greatest_lower_bound(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_253,c_148]) ).
tcf(c_625,plain,
greatest_lower_bound(b,iPr_def_13) = b,
inference(superposition,[status(thm)],[c_242,c_260]) ).
tcf(c_651,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(b,X0)) = X0,
inference(superposition,[status(thm)],[c_139,c_390]) ).
tcf(c_654,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_144,c_390]) ).
tcf(c_657,plain,
multiply(inverse(iPr_def_10),identity) = iPr_def_13,
inference(superposition,[status(thm)],[c_253,c_390]) ).
tcf(c_658,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_390,c_390]) ).
tcf(c_872,plain,
greatest_lower_bound(iPr_def_13,b) = b,
inference(theory_normalisation,[status(thm)],[c_625,c_154,c_156,c_155,c_157]) ).
tcf(c_1419,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),X0) = multiply(b,X0),
inference(superposition,[status(thm)],[c_651,c_390]) ).
tcf(c_1803,plain,
multiply(b,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_1419,c_144]) ).
tcf(c_1804,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,X0)) = X0,
inference(superposition,[status(thm)],[c_1419,c_390]) ).
tcf(c_1857,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_658,c_144]) ).
tcf(c_1859,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_658,c_654]) ).
tcf(c_2500,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_1859,c_654]) ).
tcf(c_2502,plain,
inverse(iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_1859,c_657]) ).
tcf(c_2525,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_1857,c_143]) ).
tcf(c_3684,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(superposition,[status(thm)],[c_2525,c_390]) ).
tcf(c_3816,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(demodulation,[status(thm)],[c_3684,c_1859]) ).
tcf(c_5179,plain,
! [X0: $i] : inverse(multiply(X0,iPr_def_11)) = multiply(b,inverse(X0)),
inference(superposition,[status(thm)],[c_3816,c_1804]) ).
tcf(c_5331,plain,
multiply(greatest_lower_bound(iPr_def_11,iPr_def_10),b) = multiply(iPr_def_10,greatest_lower_bound(iPr_def_13,b)),
inference(superposition,[status(thm)],[c_604,c_455]) ).
tcf(c_5347,plain,
multiply(iPr_def_10,b) = multiply(iPr_def_12,b),
inference(demodulation,[status(thm)],[c_5331,c_241,c_872]) ).
tcf(c_5534,plain,
multiply(b,inverse(multiply(iPr_def_12,b))) = inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_5347,c_3816]) ).
tcf(c_5795,plain,
inverse(iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5534,c_143,c_1803,c_1859,c_2502,c_5179]) ).
tcf(c_6034,plain,
inverse(iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_5795,c_2500]) ).
tcf(c_6536,plain,
iPr_def_10 = iPr_def_12,
inference(superposition,[status(thm)],[c_6034,c_240]) ).
tcf(c_7098,plain,
$false,
inference(superposition,[status(thm)],[c_6536,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:08:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running UEQ theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 8.33/1.73 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.33/1.73 % SZS status Started for theBenchmark.p
% 8.33/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.33/1.73
% 8.33/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.33/1.73
% 8.33/1.73 % ------ iProver source info
% 8.33/1.73
% 8.33/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 8.33/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.33/1.73 % git: non_committed_changes: false
% 8.33/1.73
% 8.33/1.73 % ------ Parsing...% successful
% 8.33/1.73
% 8.33/1.73
% 8.33/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.33/1.73
% 8.33/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.33/1.73
% 8.33/1.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.33/1.73
% 8.33/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.33/1.73 % ------ Proving...
% 8.33/1.73 % ------ Problem Properties
% 8.33/1.73
% 8.33/1.73 %
% 8.33/1.73 % clauses 21
% 8.33/1.73 % conjectures 1
% 8.33/1.73 % EPR 2
% 8.33/1.73 % Horn 21
% 8.33/1.73 % unary 21
% 8.33/1.73 % binary 0
% 8.33/1.73 % lits 21
% 8.33/1.73 % lits eq 21
% 8.33/1.73 % fd_pure 0
% 8.33/1.73 % fd_pseudo 0
% 8.33/1.73 % fd_cond 0
% 8.33/1.73 % fd_pseudo_cond 0
% 8.33/1.73 % AC symbols 2
% 8.33/1.73
% 8.33/1.73 % ------ Input Options Time Limit: Unbounded
% 8.33/1.73
% 8.33/1.73
% 8.33/1.73 % ------
% 8.33/1.73 % Current options:
% 8.33/1.73 % ------
% 8.33/1.73
% 8.33/1.73
% 8.33/1.73 %
% 8.33/1.73
% 8.33/1.73 % ------ Proving...
% 8.33/1.73 %
% 8.33/1.73
% 8.33/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 8.33/1.73
% 8.33/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.33/1.73
% 8.33/1.73
%------------------------------------------------------------------------------