%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP170-3 : 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 : n002.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 01:31:39 PM UTC 2026
% Result : Unsatisfiable 9.15s 2.18s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 85 ( 85 unt; 5 def)
% Number of atoms : 151 ( 84 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 : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 105 ( 0 sgn 105 !; 0 ?; 79 :)
% 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(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/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/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) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03c_1) ).
fof(f18,plain,
b = least_upper_bound(a,b),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
least_upper_bound(c,d) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p03c_2) ).
fof(f20,plain,
d = least_upper_bound(c,d),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p03c) ).
fof(f22,plain,
multiply(a,c) != greatest_lower_bound(multiply(a,c),multiply(b,d)),
inference(reorient_equations,[],[f21]) ).
tcf(c_67,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_68,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_72,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_73,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] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_79,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_81,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_82,plain,
least_upper_bound(a,b) = b,
inference(cnf_transformation,[],[f18]) ).
tcf(c_83,plain,
least_upper_bound(c,d) = d,
inference(cnf_transformation,[],[f20]) ).
tcf(c_84,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
inference(cnf_transformation,[],[f22]) ).
tcf(c_141,definition,
iPr_def_10 = multiply(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_142,definition,
iPr_def_11 = multiply(b,d),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_143,definition,
iPr_def_12 = greatest_lower_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_144,definition,
iPr_def_13 = least_upper_bound(c,d),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_145,definition,
iPr_def_14 = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_146,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_84,c_142,c_141,c_143]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_148,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_149,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_150,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_81]) ).
tcf(c_152,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_79]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_158,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_73]) ).
tcf(c_159,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_72]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_162,plain,
iPr_def_13 = d,
inference(demodulation,[status(thm)],[c_83,c_144]) ).
tcf(c_163,plain,
iPr_def_14 = b,
inference(demodulation,[status(thm)],[c_82,c_145]) ).
tcf(c_243,plain,
multiply(iPr_def_14,iPr_def_13) = iPr_def_11,
inference(demodulation,[status(thm)],[c_142,c_162,c_163]) ).
tcf(c_244,plain,
least_upper_bound(c,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_144,c_162]) ).
tcf(c_245,plain,
least_upper_bound(iPr_def_13,c) = iPr_def_13,
inference(theory_normalisation,[status(thm)],[c_244,c_158,c_160,c_159,c_161]) ).
tcf(c_246,plain,
least_upper_bound(a,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_145,c_163]) ).
tcf(c_247,plain,
least_upper_bound(iPr_def_14,a) = iPr_def_14,
inference(theory_normalisation,[status(thm)],[c_246,c_158,c_160,c_159,c_161]) ).
tcf(c_248,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_158,c_160]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
inference(superposition,[status(thm)],[c_159,c_161]) ).
tcf(c_264,plain,
least_upper_bound(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_143,c_155]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_160,c_154]) ).
tcf(c_272,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_148,c_147]) ).
tcf(c_279,plain,
! [X0: $i] : least_upper_bound(iPr_def_14,least_upper_bound(a,X0)) = least_upper_bound(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_247,c_158]) ).
tcf(c_287,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(iPr_def_11,X0)) = greatest_lower_bound(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_143,c_159]) ).
tcf(c_294,plain,
! [X0: $i] : multiply(greatest_lower_bound(a,X0),c) = greatest_lower_bound(iPr_def_10,multiply(X0,c)),
inference(superposition,[status(thm)],[c_141,c_150]) ).
tcf(c_359,plain,
! [X0: $i] : multiply(iPr_def_14,greatest_lower_bound(iPr_def_13,X0)) = greatest_lower_bound(iPr_def_11,multiply(iPr_def_14,X0)),
inference(superposition,[status(thm)],[c_243,c_152]) ).
tcf(c_451,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_248,c_154]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_249,c_155]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_272,c_149]) ).
tcf(c_683,plain,
greatest_lower_bound(c,iPr_def_13) = c,
inference(superposition,[status(thm)],[c_245,c_266]) ).
tcf(c_710,plain,
multiply(inverse(a),iPr_def_10) = c,
inference(superposition,[status(thm)],[c_141,c_511]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_511,c_511]) ).
tcf(c_865,plain,
! [X0: $i] : greatest_lower_bound(a,least_upper_bound(iPr_def_14,X0)) = a,
inference(superposition,[status(thm)],[c_279,c_451]) ).
tcf(c_949,plain,
greatest_lower_bound(iPr_def_13,c) = c,
inference(theory_normalisation,[status(thm)],[c_683,c_158,c_160,c_159,c_161]) ).
tcf(c_1973,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_715,c_511]) ).
tcf(c_2579,plain,
multiply(a,c) = iPr_def_10,
inference(superposition,[status(thm)],[c_710,c_1973]) ).
tcf(c_4491,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,multiply(least_upper_bound(iPr_def_14,X0),c)) = multiply(a,c),
inference(superposition,[status(thm)],[c_865,c_294]) ).
tcf(c_4665,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,multiply(least_upper_bound(iPr_def_14,X0),c)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4491,c_2579]) ).
tcf(c_5648,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_14,c)) = iPr_def_10,
inference(superposition,[status(thm)],[c_507,c_4665]) ).
tcf(c_5707,plain,
greatest_lower_bound(iPr_def_11,multiply(iPr_def_14,c)) = multiply(iPr_def_14,c),
inference(superposition,[status(thm)],[c_949,c_359]) ).
tcf(c_6140,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_14,c)) = greatest_lower_bound(iPr_def_12,multiply(iPr_def_14,c)),
inference(superposition,[status(thm)],[c_5707,c_287]) ).
tcf(c_6287,plain,
greatest_lower_bound(iPr_def_12,multiply(iPr_def_14,c)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_6140,c_5648]) ).
tcf(c_6442,plain,
least_upper_bound(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_6287,c_155]) ).
tcf(c_6677,plain,
least_upper_bound(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_6442,c_158,c_160,c_159,c_161]) ).
tcf(c_6678,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_6677,c_264]) ).
tcf(c_6846,plain,
$false,
inference(superposition,[status(thm)],[c_6678,c_146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 14:00:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running UEQ theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 9.15/2.18 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 9.15/2.18 % SZS status Started for theBenchmark.p
% 9.15/2.18 % SZS status Unsatisfiable for theBenchmark.p
% 9.15/2.18
% 9.15/2.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.15/2.18
% 9.15/2.18 % ------ iProver source info
% 9.15/2.18
% 9.15/2.18 % git: date: 2026-07-19 20:42:38 +0200
% 9.15/2.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.15/2.18 % git: non_committed_changes: false
% 9.15/2.18
% 9.15/2.18 % ------ Parsing...% successful
% 9.15/2.18
% 9.15/2.18
% 9.15/2.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 9.15/2.18
% 9.15/2.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 9.15/2.18
% 9.15/2.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 9.15/2.18
% 9.15/2.18 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 9.15/2.18 % ------ Proving...
% 9.15/2.18 % ------ Problem Properties
% 9.15/2.18
% 9.15/2.18 %
% 9.15/2.18 % clauses 23
% 9.15/2.18 % conjectures 1
% 9.15/2.18 % EPR 3
% 9.15/2.18 % Horn 23
% 9.15/2.18 % unary 23
% 9.15/2.18 % binary 0
% 9.15/2.18 % lits 23
% 9.15/2.18 % lits eq 23
% 9.15/2.18 % fd_pure 0
% 9.15/2.18 % fd_pseudo 0
% 9.15/2.18 % fd_cond 0
% 9.15/2.18 % fd_pseudo_cond 0
% 9.15/2.18 % AC symbols 2
% 9.15/2.18
% 9.15/2.18 % ------ Input Options Time Limit: Unbounded
% 9.15/2.18
% 9.15/2.18
% 9.15/2.18 % ------
% 9.15/2.18 % Current options:
% 9.15/2.18 % ------
% 9.15/2.18
% 9.15/2.18
% 9.15/2.18 %
% 9.15/2.18
% 9.15/2.18 % ------ Proving...
% 9.15/2.18 %
% 9.15/2.18
% 9.15/2.18 % SZS status Unsatisfiable for theBenchmark.p
% 9.15/2.18
% 9.15/2.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.15/2.18
% 9.15/2.18
%------------------------------------------------------------------------------