%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP179-1 : 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 : n012.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 01:31:41 PM UTC 2026
% Result : Unsatisfiable 22.10s 3.59s
% Output : CNFRefutation 22.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 139 ( 139 unt; 5 def)
% Number of atoms : 293 ( 138 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 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 : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 153 ( 0 sgn 153 !; 0 ?; 124 :)
% 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(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,negated_conjecture,
inverse(least_upper_bound(a,b)) != greatest_lower_bound(inverse(a),inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p10) ).
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_77,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_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,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(least_upper_bound(a,b)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_134,definition,
iPr_def_10 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_135,definition,
iPr_def_11 = inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_136,definition,
iPr_def_12 = greatest_lower_bound(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_137,definition,
iPr_def_13 = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_138,definition,
iPr_def_14 = inverse(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_139,negated_conjecture,
iPr_def_12 != iPr_def_14,
inference(demodulation,[status(thm)],[c_80,c_137,c_138,c_135,c_134,c_136]) ).
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_143,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] : greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,greatest_lower_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_77]) ).
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_237,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_152,c_154]) ).
tcf(c_243,plain,
multiply(iPr_def_10,a) = identity,
inference(superposition,[status(thm)],[c_134,c_141]) ).
tcf(c_244,plain,
multiply(iPr_def_11,b) = identity,
inference(superposition,[status(thm)],[c_135,c_141]) ).
tcf(c_245,plain,
multiply(iPr_def_14,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_138,c_141]) ).
tcf(c_249,plain,
greatest_lower_bound(a,iPr_def_13) = a,
inference(superposition,[status(thm)],[c_137,c_147]) ).
tcf(c_251,plain,
greatest_lower_bound(iPr_def_13,a) = a,
inference(theory_normalisation,[status(thm)],[c_249,c_151,c_153,c_152,c_154]) ).
tcf(c_259,plain,
least_upper_bound(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_136,c_148]) ).
tcf(c_268,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_272,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_286,plain,
greatest_lower_bound(b,iPr_def_13) = b,
inference(superposition,[status(thm)],[c_137,c_268]) ).
tcf(c_296,plain,
greatest_lower_bound(iPr_def_13,b) = b,
inference(theory_normalisation,[status(thm)],[c_286,c_151,c_153,c_152,c_154]) ).
tcf(c_326,plain,
least_upper_bound(iPr_def_11,iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_136,c_272]) ).
tcf(c_582,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_141,c_140]) ).
tcf(c_583,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_243,c_140]) ).
tcf(c_584,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(b,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_244,c_140]) ).
tcf(c_585,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_13,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_245,c_140]) ).
tcf(c_586,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_13,X0)) = X0,
inference(demodulation,[status(thm)],[c_585,c_142]) ).
tcf(c_587,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(b,X0)) = X0,
inference(demodulation,[status(thm)],[c_584,c_142]) ).
tcf(c_588,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(a,X0)) = X0,
inference(demodulation,[status(thm)],[c_583,c_142]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_582,c_142]) ).
tcf(c_618,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_142,c_589]) ).
tcf(c_619,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_141,c_589]) ).
tcf(c_625,plain,
! [X0: $i] : multiply(inverse(iPr_def_10),X0) = multiply(a,X0),
inference(superposition,[status(thm)],[c_588,c_589]) ).
tcf(c_626,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),X0) = multiply(b,X0),
inference(superposition,[status(thm)],[c_587,c_589]) ).
tcf(c_627,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_586,c_589]) ).
tcf(c_628,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_589,c_589]) ).
tcf(c_677,plain,
! [X0: $i] : multiply(a,multiply(iPr_def_10,X0)) = X0,
inference(superposition,[status(thm)],[c_625,c_589]) ).
tcf(c_721,plain,
! [X0: $i] : multiply(b,multiply(iPr_def_11,X0)) = X0,
inference(superposition,[status(thm)],[c_626,c_589]) ).
tcf(c_765,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_627,c_589]) ).
tcf(c_813,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_619,c_628]) ).
tcf(c_827,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_628,c_141]) ).
tcf(c_828,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_628,c_589]) ).
tcf(c_876,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_813,c_618]) ).
tcf(c_877,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_813,c_628]) ).
tcf(c_880,plain,
multiply(iPr_def_13,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_813,c_627]) ).
tcf(c_884,plain,
inverse(iPr_def_14) = iPr_def_13,
inference(demodulation,[status(thm)],[c_880,c_813]) ).
tcf(c_887,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_877,c_813]) ).
tcf(c_923,plain,
inverse(iPr_def_13) = iPr_def_14,
inference(superposition,[status(thm)],[c_884,c_887]) ).
tcf(c_984,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_827,c_140]) ).
tcf(c_1146,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(superposition,[status(thm)],[c_984,c_589]) ).
tcf(c_1163,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X0))) = multiply(X1,identity),
inference(superposition,[status(thm)],[c_984,c_828]) ).
tcf(c_1171,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_1163,c_813]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(demodulation,[status(thm)],[c_1146,c_813]) ).
tcf(c_1878,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(X0,iPr_def_13)) = multiply(greatest_lower_bound(iPr_def_14,X0),iPr_def_13),
inference(superposition,[status(thm)],[c_245,c_143]) ).
tcf(c_1890,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,X1),inverse(X0)) = greatest_lower_bound(identity,multiply(X1,inverse(X0))),
inference(superposition,[status(thm)],[c_827,c_143]) ).
tcf(c_2163,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(iPr_def_10,X0)) = multiply(iPr_def_10,greatest_lower_bound(a,X0)),
inference(superposition,[status(thm)],[c_243,c_145]) ).
tcf(c_2164,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(iPr_def_11,X0)) = multiply(iPr_def_11,greatest_lower_bound(b,X0)),
inference(superposition,[status(thm)],[c_244,c_145]) ).
tcf(c_2299,plain,
! [X0: $i] : least_upper_bound(identity,multiply(iPr_def_14,X0)) = multiply(iPr_def_14,least_upper_bound(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_245,c_146]) ).
tcf(c_2365,plain,
! [X0: $i] : least_upper_bound(a,least_upper_bound(b,X0)) = least_upper_bound(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_137,c_151]) ).
tcf(c_4428,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(X0,iPr_def_11)) = greatest_lower_bound(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_136,c_237]) ).
tcf(c_4619,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_1171,c_589]) ).
tcf(c_4789,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_1172,c_589]) ).
tcf(c_4793,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),inverse(inverse(X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_1172,c_1172]) ).
tcf(c_4805,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),multiply(X0,X1))) = inverse(X1),
inference(demodulation,[status(thm)],[c_4793,c_4789]) ).
tcf(c_4806,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),X0) = inverse(X1),
inference(demodulation,[status(thm)],[c_4805,c_4619]) ).
tcf(c_19183,plain,
multiply(greatest_lower_bound(iPr_def_14,iPr_def_10),iPr_def_13) = multiply(iPr_def_10,greatest_lower_bound(a,iPr_def_13)),
inference(superposition,[status(thm)],[c_2163,c_1878]) ).
tcf(c_19205,plain,
multiply(greatest_lower_bound(iPr_def_10,iPr_def_14),iPr_def_13) = multiply(iPr_def_10,greatest_lower_bound(iPr_def_13,a)),
inference(theory_normalisation,[status(thm)],[c_19183,c_151,c_153,c_152,c_154]) ).
tcf(c_19206,plain,
multiply(greatest_lower_bound(iPr_def_10,iPr_def_14),iPr_def_13) = identity,
inference(demodulation,[status(thm)],[c_19205,c_243,c_251]) ).
tcf(c_19328,plain,
multiply(inverse(identity),greatest_lower_bound(iPr_def_10,iPr_def_14)) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_19206,c_4806]) ).
tcf(c_19356,plain,
greatest_lower_bound(iPr_def_10,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_19328,c_142,c_876,c_923]) ).
tcf(c_19389,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(iPr_def_14,X0)) = greatest_lower_bound(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_19356,c_152]) ).
tcf(c_20149,plain,
greatest_lower_bound(iPr_def_14,iPr_def_11) = greatest_lower_bound(iPr_def_14,iPr_def_12),
inference(superposition,[status(thm)],[c_19389,c_4428]) ).
tcf(c_20156,plain,
greatest_lower_bound(iPr_def_11,iPr_def_14) = greatest_lower_bound(iPr_def_12,iPr_def_14),
inference(theory_normalisation,[status(thm)],[c_20149,c_151,c_153,c_152,c_154]) ).
tcf(c_22664,plain,
multiply(greatest_lower_bound(iPr_def_14,iPr_def_11),iPr_def_13) = multiply(iPr_def_11,greatest_lower_bound(b,iPr_def_13)),
inference(superposition,[status(thm)],[c_2164,c_1878]) ).
tcf(c_22688,plain,
multiply(greatest_lower_bound(iPr_def_11,iPr_def_14),iPr_def_13) = multiply(iPr_def_11,greatest_lower_bound(iPr_def_13,b)),
inference(theory_normalisation,[status(thm)],[c_22664,c_151,c_153,c_152,c_154]) ).
tcf(c_22689,plain,
multiply(greatest_lower_bound(iPr_def_11,iPr_def_14),iPr_def_13) = identity,
inference(demodulation,[status(thm)],[c_22688,c_244,c_296]) ).
tcf(c_22786,plain,
multiply(inverse(identity),greatest_lower_bound(iPr_def_11,iPr_def_14)) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_22689,c_4806]) ).
tcf(c_22814,plain,
greatest_lower_bound(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_22786,c_142,c_876,c_923]) ).
tcf(c_22848,plain,
greatest_lower_bound(iPr_def_12,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_20156,c_22814]) ).
tcf(c_24161,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(identity,multiply(least_upper_bound(X0,X1),inverse(X1))) = multiply(X1,inverse(X1)),
inference(superposition,[status(thm)],[c_268,c_1890]) ).
tcf(c_24239,plain,
! [X0: $i,X1: $i] : least_upper_bound(identity,multiply(greatest_lower_bound(X0,X1),inverse(X0))) = identity,
inference(superposition,[status(thm)],[c_1890,c_148]) ).
tcf(c_24260,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(identity,multiply(least_upper_bound(X0,X1),inverse(X1))) = identity,
inference(demodulation,[status(thm)],[c_24161,c_827]) ).
tcf(c_28967,plain,
least_upper_bound(identity,multiply(iPr_def_14,inverse(iPr_def_12))) = identity,
inference(superposition,[status(thm)],[c_22848,c_24239]) ).
tcf(c_29037,plain,
multiply(iPr_def_14,least_upper_bound(iPr_def_13,inverse(iPr_def_12))) = identity,
inference(demodulation,[status(thm)],[c_28967,c_2299]) ).
tcf(c_29123,plain,
least_upper_bound(iPr_def_13,inverse(iPr_def_12)) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_29037,c_765]) ).
tcf(c_29125,plain,
least_upper_bound(iPr_def_13,inverse(iPr_def_12)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_29123,c_813]) ).
tcf(c_30025,plain,
greatest_lower_bound(identity,multiply(iPr_def_10,inverse(iPr_def_12))) = identity,
inference(superposition,[status(thm)],[c_259,c_24260]) ).
tcf(c_30029,plain,
greatest_lower_bound(identity,multiply(iPr_def_11,inverse(iPr_def_12))) = identity,
inference(superposition,[status(thm)],[c_326,c_24260]) ).
tcf(c_30176,plain,
multiply(iPr_def_11,greatest_lower_bound(b,inverse(iPr_def_12))) = identity,
inference(demodulation,[status(thm)],[c_30029,c_2164]) ).
tcf(c_30177,plain,
multiply(iPr_def_10,greatest_lower_bound(a,inverse(iPr_def_12))) = identity,
inference(demodulation,[status(thm)],[c_30025,c_2163]) ).
tcf(c_30653,plain,
greatest_lower_bound(b,inverse(iPr_def_12)) = multiply(b,identity),
inference(superposition,[status(thm)],[c_30176,c_721]) ).
tcf(c_30655,plain,
greatest_lower_bound(b,inverse(iPr_def_12)) = b,
inference(demodulation,[status(thm)],[c_30653,c_813]) ).
tcf(c_30696,plain,
least_upper_bound(inverse(iPr_def_12),b) = inverse(iPr_def_12),
inference(superposition,[status(thm)],[c_30655,c_272]) ).
tcf(c_30706,plain,
least_upper_bound(b,inverse(iPr_def_12)) = inverse(iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_30696,c_151,c_153,c_152,c_154]) ).
tcf(c_30723,plain,
least_upper_bound(a,inverse(iPr_def_12)) = least_upper_bound(iPr_def_13,inverse(iPr_def_12)),
inference(superposition,[status(thm)],[c_30706,c_2365]) ).
tcf(c_30724,plain,
least_upper_bound(a,inverse(iPr_def_12)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_30723,c_29125]) ).
tcf(c_30777,plain,
greatest_lower_bound(a,inverse(iPr_def_12)) = multiply(a,identity),
inference(superposition,[status(thm)],[c_30177,c_677]) ).
tcf(c_30779,plain,
greatest_lower_bound(a,inverse(iPr_def_12)) = a,
inference(demodulation,[status(thm)],[c_30777,c_813]) ).
tcf(c_30820,plain,
least_upper_bound(inverse(iPr_def_12),a) = inverse(iPr_def_12),
inference(superposition,[status(thm)],[c_30779,c_272]) ).
tcf(c_30830,plain,
least_upper_bound(a,inverse(iPr_def_12)) = inverse(iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_30820,c_151,c_153,c_152,c_154]) ).
tcf(c_30831,plain,
inverse(iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_30830,c_30724]) ).
tcf(c_30864,plain,
inverse(iPr_def_13) = iPr_def_12,
inference(superposition,[status(thm)],[c_30831,c_887]) ).
tcf(c_30879,plain,
iPr_def_12 = iPr_def_14,
inference(demodulation,[status(thm)],[c_138,c_30864]) ).
tcf(c_30880,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_30879,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP179-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 14:00:06 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.33 Running UEQ theorem proving
% 0.03/0.33 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
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.03/0.34 % Detected problem language: tptp
% 0.09/0.34 % Proving...
% 22.10/3.59 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 22.10/3.59 % SZS status Started for theBenchmark.p
% 22.10/3.59 % SZS status Unsatisfiable for theBenchmark.p
% 22.10/3.59
% 22.10/3.59 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.10/3.59
% 22.10/3.59 % ------ iProver source info
% 22.10/3.59
% 22.10/3.59 % git: date: 2026-07-19 20:42:38 +0200
% 22.10/3.59 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.10/3.59 % git: non_committed_changes: false
% 22.10/3.59
% 22.10/3.59 % ------ Parsing...% successful
% 22.10/3.59
% 22.10/3.59
% 22.10/3.59 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.10/3.59
% 22.10/3.59 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.10/3.59
% 22.10/3.59 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.10/3.59
% 22.10/3.59 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 22.10/3.59 % ------ Proving...
% 22.10/3.59 % ------ Problem Properties
% 22.10/3.59
% 22.10/3.59 %
% 22.10/3.59 % clauses 21
% 22.10/3.59 % conjectures 1
% 22.10/3.59 % EPR 1
% 22.10/3.59 % Horn 21
% 22.10/3.59 % unary 21
% 22.10/3.59 % binary 0
% 22.10/3.59 % lits 21
% 22.10/3.59 % lits eq 21
% 22.10/3.59 % fd_pure 0
% 22.10/3.59 % fd_pseudo 0
% 22.10/3.59 % fd_cond 0
% 22.10/3.59 % fd_pseudo_cond 0
% 22.10/3.59 % AC symbols 2
% 22.10/3.59
% 22.10/3.59 % ------ Input Options Time Limit: Unbounded
% 22.10/3.59
% 22.10/3.59
% 22.10/3.59 % ------
% 22.10/3.59 % Current options:
% 22.10/3.59 % ------
% 22.10/3.59
% 22.10/3.59
% 22.10/3.59 %
% 22.10/3.59
% 22.10/3.59 % ------ Proving...
% 22.10/3.59 %
% 22.10/3.59
% 22.10/3.59 % SZS status Unsatisfiable for theBenchmark.p
% 22.10/3.59
% 22.10/3.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.10/3.60
% 22.10/3.60
%------------------------------------------------------------------------------