%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP179-2 : 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 : n013.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 38.50s 6.23s
% Output : CNFRefutation 38.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 19
% Syntax : Number of formulae : 149 ( 149 unt; 4 def)
% Number of atoms : 312 ( 148 equ)
% Maximal formula atoms : 1 ( 2 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 168 ( 0 sgn 168 !; 0 ?; 135 :)
% 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(f9,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',idempotence_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(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(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,
least_upper_bound(inverse(a),identity) != inverse(greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p18) ).
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_72,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
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_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_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,
inverse(greatest_lower_bound(a,identity)) != least_upper_bound(inverse(a),identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_96,negated_conjecture,
inverse(greatest_lower_bound(a,identity)) != least_upper_bound(identity,inverse(a)),
inference(theory_normalisation,[status(thm)],[c_80,c_70,c_68,c_71,c_69]) ).
tcf(c_135,definition,
iPr_def_10 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_136,definition,
iPr_def_11 = inverse(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_137,definition,
iPr_def_12 = inverse(a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_138,definition,
iPr_def_13 = least_upper_bound(identity,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_139,negated_conjecture,
iPr_def_11 != iPr_def_13,
inference(demodulation,[status(thm)],[c_96,c_137,c_138,c_135,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_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_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_150,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_72]) ).
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_12,a) = identity,
inference(superposition,[status(thm)],[c_137,c_141]) ).
tcf(c_242,plain,
multiply(iPr_def_11,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_136,c_141]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_141,c_140]) ).
tcf(c_244,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_243,c_142]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_142,c_143]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_141,c_143]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(multiply(X0,X1),identity),
inference(superposition,[status(thm)],[c_141,c_143]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_251,c_154]) ).
tcf(c_264,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_267,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
inference(demodulation,[status(thm)],[c_264,c_153]) ).
tcf(c_278,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(a,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_241,c_140]) ).
tcf(c_281,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(a,X0)) = X0,
inference(demodulation,[status(thm)],[c_278,c_142]) ).
tcf(c_289,plain,
! [X0: $i] : least_upper_bound(identity,multiply(X0,iPr_def_10)) = multiply(least_upper_bound(iPr_def_11,X0),iPr_def_10),
inference(superposition,[status(thm)],[c_242,c_144]) ).
tcf(c_291,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(iPr_def_10,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_242,c_140]) ).
tcf(c_292,plain,
! [X0: $i] : least_upper_bound(multiply(X0,iPr_def_10),identity) = multiply(least_upper_bound(X0,iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_242,c_144]) ).
tcf(c_294,plain,
! [X0: $i] : multiply(iPr_def_11,multiply(iPr_def_10,X0)) = X0,
inference(demodulation,[status(thm)],[c_291,c_142]) ).
tcf(c_296,plain,
! [X0: $i] : least_upper_bound(identity,multiply(X0,iPr_def_10)) = multiply(least_upper_bound(X0,iPr_def_11),iPr_def_10),
inference(demodulation,[status(thm)],[c_292,c_153]) ).
tcf(c_304,plain,
greatest_lower_bound(identity,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_138,c_147]) ).
tcf(c_305,plain,
greatest_lower_bound(iPr_def_13,identity) = identity,
inference(demodulation,[status(thm)],[c_304,c_154]) ).
tcf(c_312,plain,
least_upper_bound(iPr_def_12,identity) = iPr_def_13,
inference(demodulation,[status(thm)],[c_138,c_153]) ).
tcf(c_317,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_324,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_141,c_145]) ).
tcf(c_326,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(iPr_def_12,X0)) = multiply(iPr_def_12,greatest_lower_bound(a,X0)),
inference(superposition,[status(thm)],[c_241,c_145]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[status(thm)],[c_141,c_145]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[c_329,c_154]) ).
tcf(c_349,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_352,plain,
! [X0: $i] : least_upper_bound(identity,multiply(iPr_def_11,X0)) = multiply(iPr_def_11,least_upper_bound(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_242,c_146]) ).
tcf(c_396,plain,
! [X0: $i] : greatest_lower_bound(a,greatest_lower_bound(identity,X0)) = greatest_lower_bound(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_135,c_152]) ).
tcf(c_423,plain,
least_upper_bound(iPr_def_13,identity) = iPr_def_13,
inference(superposition,[status(thm)],[c_305,c_148]) ).
tcf(c_438,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_472,plain,
! [X0: $i] : least_upper_bound(iPr_def_12,least_upper_bound(X0,identity)) = least_upper_bound(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_312,c_234]) ).
tcf(c_522,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_141,c_244]) ).
tcf(c_524,plain,
multiply(inverse(iPr_def_12),identity) = a,
inference(superposition,[status(thm)],[c_241,c_244]) ).
tcf(c_525,plain,
multiply(inverse(iPr_def_11),identity) = iPr_def_10,
inference(superposition,[status(thm)],[c_242,c_244]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_244,c_244]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),least_upper_bound(X1,multiply(X0,X2))) = least_upper_bound(multiply(inverse(X0),X1),X2),
inference(superposition,[status(thm)],[c_244,c_146]) ).
tcf(c_617,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),multiply(identity,X0)) = multiply(a,X0),
inference(superposition,[status(thm)],[c_524,c_140]) ).
tcf(c_624,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),X0) = multiply(a,X0),
inference(demodulation,[status(thm)],[c_617,c_142]) ).
tcf(c_633,plain,
multiply(a,identity) = a,
inference(demodulation,[status(thm)],[c_524,c_624]) ).
tcf(c_718,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),X0) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_294,c_244]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,least_upper_bound(X1,least_upper_bound(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_151,c_317]) ).
tcf(c_784,plain,
least_upper_bound(identity,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_135,c_438]) ).
tcf(c_805,plain,
least_upper_bound(iPr_def_10,identity) = identity,
inference(demodulation,[status(thm)],[c_784,c_153]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i] : multiply(inverse(greatest_lower_bound(inverse(X0),X1)),greatest_lower_bound(identity,multiply(X1,X0))) = X0,
inference(superposition,[status(thm)],[c_248,c_244]) ).
tcf(c_1089,plain,
greatest_lower_bound(iPr_def_10,identity) = iPr_def_10,
inference(superposition,[status(thm)],[c_805,c_147]) ).
tcf(c_1111,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(multiply(inverse(inverse(X0)),X1),X0) = multiply(inverse(inverse(X0)),greatest_lower_bound(X1,identity)),
inference(superposition,[status(thm)],[c_522,c_145]) ).
tcf(c_1120,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(X1,identity)),
inference(demodulation,[status(thm)],[c_1111,c_154,c_526]) ).
tcf(c_1152,plain,
multiply(a,iPr_def_12) = identity,
inference(superposition,[status(thm)],[c_624,c_141]) ).
tcf(c_1204,plain,
multiply(greatest_lower_bound(identity,a),iPr_def_12) = greatest_lower_bound(iPr_def_12,identity),
inference(superposition,[status(thm)],[c_1152,c_247]) ).
tcf(c_1210,plain,
multiply(iPr_def_12,identity) = iPr_def_12,
inference(superposition,[status(thm)],[c_1152,c_281]) ).
tcf(c_1212,plain,
greatest_lower_bound(iPr_def_12,identity) = multiply(iPr_def_10,iPr_def_12),
inference(demodulation,[status(thm)],[c_1204,c_154,c_135]) ).
tcf(c_2009,plain,
! [X0: $i] : least_upper_bound(X0,multiply(iPr_def_12,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_312,c_267]) ).
tcf(c_2302,plain,
least_upper_bound(identity,multiply(iPr_def_10,iPr_def_12)) = identity,
inference(superposition,[status(thm)],[c_1212,c_438]) ).
tcf(c_3273,plain,
multiply(inverse(iPr_def_11),greatest_lower_bound(iPr_def_11,identity)) = greatest_lower_bound(identity,iPr_def_10),
inference(superposition,[status(thm)],[c_525,c_324]) ).
tcf(c_3317,plain,
multiply(iPr_def_10,greatest_lower_bound(iPr_def_11,identity)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_3273,c_154,c_718,c_1089]) ).
tcf(c_3409,plain,
multiply(iPr_def_12,greatest_lower_bound(a,identity)) = greatest_lower_bound(identity,iPr_def_12),
inference(superposition,[status(thm)],[c_1210,c_326]) ).
tcf(c_3425,plain,
multiply(iPr_def_10,iPr_def_12) = multiply(iPr_def_12,iPr_def_10),
inference(demodulation,[status(thm)],[c_3409,c_154,c_135,c_1212]) ).
tcf(c_3571,plain,
greatest_lower_bound(iPr_def_11,identity) = multiply(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_3317,c_294]) ).
tcf(c_3572,plain,
greatest_lower_bound(iPr_def_11,identity) = identity,
inference(demodulation,[status(thm)],[c_3571,c_242]) ).
tcf(c_3601,plain,
least_upper_bound(iPr_def_11,identity) = iPr_def_11,
inference(superposition,[status(thm)],[c_3572,c_148]) ).
tcf(c_4547,plain,
! [X0: $i,X1: $i] : least_upper_bound(identity,multiply(inverse(X0),greatest_lower_bound(X1,X0))) = identity,
inference(superposition,[status(thm)],[c_338,c_148]) ).
tcf(c_4696,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_12),identity)) = multiply(inverse(iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_312,c_349]) ).
tcf(c_4697,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_11),identity)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_3601,c_349]) ).
tcf(c_4749,plain,
multiply(iPr_def_10,iPr_def_11) = identity,
inference(demodulation,[status(thm)],[c_4697,c_153,c_525,c_718,c_805]) ).
tcf(c_4750,plain,
least_upper_bound(a,identity) = multiply(a,iPr_def_13),
inference(demodulation,[status(thm)],[c_4696,c_153,c_624,c_633]) ).
tcf(c_5045,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_4749,c_140]) ).
tcf(c_5062,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,X0)) = X0,
inference(demodulation,[status(thm)],[c_5045,c_142]) ).
tcf(c_5226,plain,
least_upper_bound(iPr_def_11,iPr_def_13) = least_upper_bound(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_3601,c_472]) ).
tcf(c_5243,plain,
least_upper_bound(iPr_def_11,iPr_def_12) = least_upper_bound(iPr_def_13,iPr_def_11),
inference(demodulation,[status(thm)],[c_5226,c_153]) ).
tcf(c_7377,plain,
! [X0: $i] : greatest_lower_bound(identity,least_upper_bound(X0,iPr_def_13)) = identity,
inference(superposition,[status(thm)],[c_423,c_744]) ).
tcf(c_8491,plain,
least_upper_bound(identity,multiply(iPr_def_12,iPr_def_10)) = multiply(least_upper_bound(iPr_def_13,iPr_def_11),iPr_def_10),
inference(superposition,[status(thm)],[c_5243,c_289]) ).
tcf(c_8492,plain,
least_upper_bound(identity,multiply(iPr_def_13,iPr_def_10)) = identity,
inference(demodulation,[status(thm)],[c_8491,c_296,c_2302,c_3425]) ).
tcf(c_8858,plain,
least_upper_bound(identity,multiply(iPr_def_11,multiply(iPr_def_12,iPr_def_10))) = multiply(iPr_def_11,multiply(iPr_def_13,iPr_def_10)),
inference(superposition,[status(thm)],[c_2009,c_352]) ).
tcf(c_8865,plain,
multiply(iPr_def_11,multiply(iPr_def_13,iPr_def_10)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_8858,c_153,c_294,c_312,c_3425]) ).
tcf(c_16049,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_522,c_526]) ).
tcf(c_17538,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_16049,c_526]) ).
tcf(c_17541,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_17538,c_16049]) ).
tcf(c_18000,plain,
least_upper_bound(multiply(inverse(iPr_def_13),identity),iPr_def_10) = multiply(inverse(iPr_def_13),identity),
inference(superposition,[status(thm)],[c_8492,c_533]) ).
tcf(c_18102,plain,
least_upper_bound(iPr_def_10,inverse(iPr_def_13)) = inverse(iPr_def_13),
inference(demodulation,[status(thm)],[c_18000,c_153,c_16049]) ).
tcf(c_22277,plain,
multiply(iPr_def_10,iPr_def_13) = multiply(iPr_def_13,iPr_def_10),
inference(superposition,[status(thm)],[c_8865,c_5062]) ).
tcf(c_24374,plain,
greatest_lower_bound(iPr_def_10,inverse(iPr_def_13)) = iPr_def_10,
inference(superposition,[status(thm)],[c_18102,c_147]) ).
tcf(c_27693,plain,
! [X0: $i] : least_upper_bound(identity,multiply(inverse(least_upper_bound(X0,iPr_def_13)),identity)) = identity,
inference(superposition,[status(thm)],[c_7377,c_4547]) ).
tcf(c_27743,plain,
! [X0: $i] : least_upper_bound(identity,inverse(least_upper_bound(X0,iPr_def_13))) = identity,
inference(demodulation,[status(thm)],[c_27693,c_16049]) ).
tcf(c_36640,plain,
multiply(inverse(greatest_lower_bound(inverse(iPr_def_13),a)),greatest_lower_bound(identity,least_upper_bound(a,identity))) = iPr_def_13,
inference(superposition,[status(thm)],[c_4750,c_818]) ).
tcf(c_36707,plain,
inverse(greatest_lower_bound(a,inverse(iPr_def_13))) = iPr_def_13,
inference(demodulation,[status(thm)],[c_36640,c_154,c_317,c_16049]) ).
tcf(c_38520,plain,
greatest_lower_bound(a,inverse(iPr_def_13)) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_36707,c_17541]) ).
tcf(c_45114,plain,
least_upper_bound(identity,inverse(iPr_def_13)) = identity,
inference(superposition,[status(thm)],[c_150,c_27743]) ).
tcf(c_45185,plain,
greatest_lower_bound(inverse(iPr_def_13),identity) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_45114,c_317]) ).
tcf(c_45205,plain,
greatest_lower_bound(identity,inverse(iPr_def_13)) = inverse(iPr_def_13),
inference(demodulation,[status(thm)],[c_45185,c_154]) ).
tcf(c_48372,plain,
greatest_lower_bound(identity,multiply(identity,iPr_def_13)) = multiply(inverse(iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_45205,c_255]) ).
tcf(c_48377,plain,
greatest_lower_bound(a,inverse(iPr_def_13)) = greatest_lower_bound(iPr_def_10,inverse(iPr_def_13)),
inference(superposition,[status(thm)],[c_45205,c_396]) ).
tcf(c_48384,plain,
inverse(iPr_def_13) = iPr_def_10,
inference(demodulation,[status(thm)],[c_48377,c_24374,c_38520]) ).
tcf(c_48387,plain,
greatest_lower_bound(identity,multiply(identity,iPr_def_13)) = multiply(iPr_def_10,iPr_def_13),
inference(demodulation,[status(thm)],[c_48372,c_48384]) ).
tcf(c_48388,plain,
multiply(iPr_def_13,iPr_def_10) = identity,
inference(demodulation,[status(thm)],[c_48387,c_142,c_305,c_1120,c_22277]) ).
tcf(c_48433,plain,
multiply(iPr_def_11,identity) = iPr_def_13,
inference(demodulation,[status(thm)],[c_8865,c_48388]) ).
tcf(c_48435,plain,
iPr_def_11 = iPr_def_13,
inference(demodulation,[status(thm)],[c_48433,c_16049]) ).
tcf(c_48436,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_48435,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP179-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.80 % Computer : n013.cluster.edu
% 0.09/0.80 % Model : x86_64 x86_64
% 0.09/0.80 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.80 % Memory : 8046.5625MB
% 0.09/0.80 % OS : Linux 6.8.0-71-generic
% 0.09/0.80 % CPULimit : 300
% 0.09/0.80 % WCLimit : 300
% 0.09/0.80 % DateTime : Wed Sep 23 14:00:07 UTC 2026
% 0.09/0.80 % CPUTime :
% 0.09/0.80 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.84 Running UEQ theorem proving
% 0.09/0.84 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
% 0.09/0.85
% 0.09/0.85 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.85
% 0.09/0.85 % Detected problem language: tptp
% 0.09/0.86 % Proving...
% 38.50/6.23 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 38.50/6.23 % SZS status Started for theBenchmark.p
% 38.50/6.23 % SZS status Unsatisfiable for theBenchmark.p
% 38.50/6.23
% 38.50/6.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 38.50/6.23
% 38.50/6.23 % ------ iProver source info
% 38.50/6.23
% 38.50/6.23 % git: date: 2026-07-19 20:42:38 +0200
% 38.50/6.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 38.50/6.23 % git: non_committed_changes: false
% 38.50/6.23
% 38.50/6.23 % ------ Parsing...% successful
% 38.50/6.23
% 38.50/6.23
% 38.50/6.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 38.50/6.23
% 38.50/6.23 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 38.50/6.23
% 38.50/6.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 38.50/6.23
% 38.50/6.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 38.50/6.23 % ------ Proving...
% 38.50/6.23 % ------ Problem Properties
% 38.50/6.23
% 38.50/6.23 %
% 38.50/6.23 % clauses 20
% 38.50/6.23 % conjectures 1
% 38.50/6.23 % EPR 1
% 38.50/6.23 % Horn 20
% 38.50/6.23 % unary 20
% 38.50/6.23 % binary 0
% 38.50/6.24 % lits 20
% 38.50/6.24 % lits eq 20
% 38.50/6.24 % fd_pure 0
% 38.50/6.24 % fd_pseudo 0
% 38.50/6.24 % fd_cond 0
% 38.50/6.24 % fd_pseudo_cond 0
% 38.50/6.24 % AC symbols 2
% 38.50/6.24
% 38.50/6.24 % ------ Input Options Time Limit: Unbounded
% 38.50/6.24
% 38.50/6.24
% 38.50/6.24 % ------
% 38.50/6.24 % Current options:
% 38.50/6.24 % ------
% 38.50/6.24
% 38.50/6.24
% 38.50/6.24 %
% 38.50/6.24
% 38.50/6.24 % ------ Proving...
% 38.50/6.24 %
% 38.50/6.24
% 38.50/6.24 % SZS status Unsatisfiable for theBenchmark.p
% 38.50/6.24
% 38.50/6.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 38.50/6.24
% 38.50/6.24
%------------------------------------------------------------------------------