%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP167-4 : 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 : n003.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 01:31:38 PM UTC 2026
% Result : Unsatisfiable 41.73s 15.31s
% Output : CNFRefutation 41.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 21
% Syntax : Number of formulae : 149 ( 149 unt; 3 def)
% Number of atoms : 323 ( 148 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 5 ( 5 ~; 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 125 !; 0 ?; 89 :)
% 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,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_1) ).
fof(f18,plain,
identity = inverse(identity),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19_3) ).
fof(f21,negated_conjecture,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p19) ).
tcf(c_68,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_73,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_74,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] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_78,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] : least_upper_bound(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,least_upper_bound(X1,X2)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_80,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] : least_upper_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(least_upper_bound(X0,X2),X1),
inference(cnf_transformation,[],[f15]) ).
tcf(c_82,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_83,plain,
inverse(identity) = identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_86,negated_conjecture,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != a,
inference(cnf_transformation,[],[f21]) ).
tcf(c_104,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(theory_normalisation,[status(thm)],[c_86,c_73,c_71,c_74,c_72]) ).
tcf(c_149,definition,
iPr_def_10 = least_upper_bound(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_150,definition,
iPr_def_11 = greatest_lower_bound(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_151,definition,
iPr_def_12 = multiply(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_152,negated_conjecture,
iPr_def_12 != a,
inference(demodulation,[status(thm)],[c_104,c_150,c_149,c_151]) ).
tcf(c_246,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_84,c_69]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_71,c_77]) ).
tcf(c_255,plain,
least_upper_bound(identity,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_150,c_77]) ).
tcf(c_256,plain,
least_upper_bound(iPr_def_11,identity) = identity,
inference(theory_normalisation,[status(thm)],[c_255,c_74,c_72,c_73,c_71]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_72,c_78]) ).
tcf(c_268,plain,
greatest_lower_bound(identity,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_149,c_78]) ).
tcf(c_270,plain,
greatest_lower_bound(iPr_def_10,identity) = identity,
inference(theory_normalisation,[status(thm)],[c_268,c_74,c_72,c_73,c_71]) ).
tcf(c_272,plain,
greatest_lower_bound(iPr_def_11,identity) = iPr_def_11,
inference(superposition,[status(thm)],[c_256,c_78]) ).
tcf(c_274,plain,
least_upper_bound(iPr_def_10,identity) = iPr_def_10,
inference(superposition,[status(thm)],[c_270,c_77]) ).
tcf(c_306,plain,
! [X0: $i] : inverse(multiply(identity,X0)) = multiply(inverse(X0),identity),
inference(superposition,[status(thm)],[c_83,c_85]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_312,plain,
! [X0: $i] : multiply(inverse(X0),identity) = inverse(X0),
inference(light_normalisation,[status(thm)],[c_306,c_68]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_69,c_70]) ).
tcf(c_329,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_151,c_70]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_246,c_70]) ).
tcf(c_353,plain,
! [X0: $i] : greatest_lower_bound(identity,greatest_lower_bound(a,X0)) = greatest_lower_bound(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_150,c_73]) ).
tcf(c_355,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,greatest_lower_bound(identity,X0)) = greatest_lower_bound(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_272,c_73]) ).
tcf(c_380,plain,
! [X0: $i] : least_upper_bound(identity,least_upper_bound(a,X0)) = least_upper_bound(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_149,c_74]) ).
tcf(c_460,plain,
greatest_lower_bound(a,iPr_def_10) = a,
inference(superposition,[status(thm)],[c_149,c_264]) ).
tcf(c_470,plain,
greatest_lower_bound(iPr_def_10,a) = a,
inference(theory_normalisation,[status(thm)],[c_460,c_74,c_72,c_73,c_71]) ).
tcf(c_526,plain,
! [X0: $i] : multiply(iPr_def_10,least_upper_bound(iPr_def_11,X0)) = least_upper_bound(iPr_def_12,multiply(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_151,c_79]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_68,c_81]) ).
tcf(c_663,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(multiply(X0,X1),identity),
inference(superposition,[status(thm)],[c_69,c_81]) ).
tcf(c_676,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(identity,multiply(X0,X1)),
inference(theory_normalisation,[status(thm)],[c_663,c_74,c_72,c_73,c_71]) ).
tcf(c_727,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_68,c_82]) ).
tcf(c_778,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_84,c_312]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
inference(superposition,[status(thm)],[c_778,c_80]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X0,X1)) = multiply(X0,least_upper_bound(identity,X1)),
inference(superposition,[status(thm)],[c_778,c_79]) ).
tcf(c_864,plain,
multiply(iPr_def_12,inverse(iPr_def_11)) = multiply(iPr_def_10,identity),
inference(superposition,[status(thm)],[c_246,c_329]) ).
tcf(c_957,plain,
! [X0: $i] : greatest_lower_bound(identity,greatest_lower_bound(X0,a)) = greatest_lower_bound(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_71,c_353]) ).
tcf(c_960,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(a,X0)) = greatest_lower_bound(identity,a),
inference(superposition,[status(thm)],[c_78,c_353]) ).
tcf(c_970,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(a,X0)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_960,c_150]) ).
tcf(c_1025,plain,
! [X0: $i] : least_upper_bound(least_upper_bound(a,X0),iPr_def_11) = least_upper_bound(a,X0),
inference(superposition,[status(thm)],[c_970,c_252]) ).
tcf(c_1028,plain,
! [X0: $i] : least_upper_bound(iPr_def_11,least_upper_bound(X0,a)) = least_upper_bound(a,X0),
inference(theory_normalisation,[status(thm)],[c_1025,c_74,c_72,c_73,c_71]) ).
tcf(c_1229,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(identity,X0)) = greatest_lower_bound(iPr_def_11,identity),
inference(superposition,[status(thm)],[c_78,c_355]) ).
tcf(c_1241,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(identity,X0)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_1229,c_272]) ).
tcf(c_1453,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,greatest_lower_bound(a,X0)) = least_upper_bound(identity,a),
inference(superposition,[status(thm)],[c_77,c_380]) ).
tcf(c_1460,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(iPr_def_10,X0)) = iPr_def_11,
inference(superposition,[status(thm)],[c_380,c_1241]) ).
tcf(c_1464,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,greatest_lower_bound(a,X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1453,c_149]) ).
tcf(c_1541,plain,
! [X0: $i] : greatest_lower_bound(greatest_lower_bound(a,X0),iPr_def_10) = greatest_lower_bound(a,X0),
inference(superposition,[status(thm)],[c_1464,c_264]) ).
tcf(c_1544,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(X0,a)) = greatest_lower_bound(a,X0),
inference(theory_normalisation,[status(thm)],[c_1541,c_74,c_72,c_73,c_71]) ).
tcf(c_6242,plain,
multiply(inverse(iPr_def_10),iPr_def_12) = multiply(identity,iPr_def_11),
inference(superposition,[status(thm)],[c_151,c_328]) ).
tcf(c_6494,plain,
inverse(multiply(identity,iPr_def_11)) = multiply(inverse(iPr_def_12),iPr_def_10),
inference(superposition,[status(thm)],[c_6242,c_307]) ).
tcf(c_7139,plain,
multiply(inverse(iPr_def_12),iPr_def_10) = inverse(iPr_def_11),
inference(superposition,[status(thm)],[c_68,c_6494]) ).
tcf(c_7317,plain,
multiply(iPr_def_12,inverse(iPr_def_11)) = multiply(identity,iPr_def_10),
inference(superposition,[status(thm)],[c_7139,c_330]) ).
tcf(c_7320,plain,
multiply(identity,iPr_def_10) = multiply(iPr_def_10,identity),
inference(light_normalisation,[status(thm)],[c_7317,c_864]) ).
tcf(c_8594,plain,
! [X0: $i] : greatest_lower_bound(multiply(identity,X0),multiply(iPr_def_10,identity)) = multiply(identity,greatest_lower_bound(X0,iPr_def_10)),
inference(superposition,[status(thm)],[c_7320,c_80]) ).
tcf(c_8602,plain,
! [X0: $i] : greatest_lower_bound(multiply(iPr_def_10,identity),multiply(identity,X0)) = multiply(identity,greatest_lower_bound(X0,iPr_def_10)),
inference(theory_normalisation,[status(thm)],[c_8594,c_74,c_72,c_73,c_71]) ).
tcf(c_8603,plain,
! [X0: $i] : multiply(identity,greatest_lower_bound(X0,iPr_def_10)) = greatest_lower_bound(multiply(iPr_def_10,identity),X0),
inference(light_normalisation,[status(thm)],[c_8602,c_68]) ).
tcf(c_13511,plain,
multiply(iPr_def_10,least_upper_bound(iPr_def_11,iPr_def_11)) = least_upper_bound(iPr_def_12,iPr_def_12),
inference(superposition,[status(thm)],[c_151,c_526]) ).
tcf(c_13513,plain,
multiply(iPr_def_10,least_upper_bound(iPr_def_11,identity)) = least_upper_bound(iPr_def_12,iPr_def_10),
inference(superposition,[status(thm)],[c_778,c_526]) ).
tcf(c_13528,plain,
multiply(iPr_def_10,least_upper_bound(iPr_def_11,identity)) = least_upper_bound(iPr_def_10,iPr_def_12),
inference(theory_normalisation,[status(thm)],[c_13513,c_74,c_72,c_73,c_71]) ).
tcf(c_13529,plain,
multiply(iPr_def_10,identity) = least_upper_bound(iPr_def_10,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_13528,c_256]) ).
tcf(c_13530,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(ac_demodulation,[status(thm)],[c_13511,c_75,c_75,c_74,c_72,c_73,c_71]) ).
tcf(c_13563,plain,
greatest_lower_bound(iPr_def_11,multiply(iPr_def_10,identity)) = iPr_def_11,
inference(superposition,[status(thm)],[c_13529,c_1460]) ).
tcf(c_15180,plain,
! [X0: $i] : multiply(least_upper_bound(identity,inverse(X0)),X0) = least_upper_bound(X0,identity),
inference(superposition,[status(thm)],[c_69,c_656]) ).
tcf(c_19304,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,inverse(X0)),X0) = greatest_lower_bound(X0,identity),
inference(superposition,[status(thm)],[c_69,c_727]) ).
tcf(c_23118,plain,
! [X0: $i] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_69,c_816]) ).
tcf(c_23216,plain,
! [X0: $i] : multiply(inverse(X0),greatest_lower_bound(identity,X0)) = greatest_lower_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_23118,c_74,c_72,c_73,c_71]) ).
tcf(c_24694,plain,
! [X0: $i] : multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(inverse(X0),identity),
inference(superposition,[status(thm)],[c_69,c_817]) ).
tcf(c_24801,plain,
! [X0: $i] : multiply(inverse(X0),least_upper_bound(identity,X0)) = least_upper_bound(identity,inverse(X0)),
inference(theory_normalisation,[status(thm)],[c_24694,c_74,c_72,c_73,c_71]) ).
tcf(c_49000,plain,
greatest_lower_bound(identity,multiply(identity,greatest_lower_bound(a,iPr_def_10))) = greatest_lower_bound(iPr_def_11,multiply(iPr_def_10,identity)),
inference(superposition,[status(thm)],[c_8603,c_957]) ).
tcf(c_49209,plain,
greatest_lower_bound(identity,multiply(identity,greatest_lower_bound(iPr_def_10,a))) = greatest_lower_bound(iPr_def_11,multiply(iPr_def_10,identity)),
inference(theory_normalisation,[status(thm)],[c_49000,c_74,c_72,c_73,c_71]) ).
tcf(c_49210,plain,
greatest_lower_bound(identity,multiply(identity,a)) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_49209,c_470,c_13563]) ).
tcf(c_50079,plain,
greatest_lower_bound(identity,a) = iPr_def_11,
inference(superposition,[status(thm)],[c_68,c_49210]) ).
tcf(c_80790,plain,
multiply(inverse(a),iPr_def_11) = greatest_lower_bound(identity,inverse(a)),
inference(superposition,[status(thm)],[c_50079,c_23216]) ).
tcf(c_82271,plain,
multiply(inverse(a),iPr_def_10) = least_upper_bound(identity,inverse(a)),
inference(superposition,[status(thm)],[c_149,c_24801]) ).
tcf(c_83384,plain,
multiply(multiply(inverse(a),iPr_def_10),a) = least_upper_bound(a,identity),
inference(superposition,[status(thm)],[c_82271,c_15180]) ).
tcf(c_83385,plain,
multiply(multiply(inverse(a),iPr_def_10),a) = least_upper_bound(identity,a),
inference(theory_normalisation,[status(thm)],[c_83384,c_74,c_72,c_73,c_71]) ).
tcf(c_83386,plain,
multiply(multiply(inverse(a),iPr_def_10),a) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_83385,c_149]) ).
tcf(c_84168,plain,
multiply(inverse(a),multiply(iPr_def_10,a)) = iPr_def_10,
inference(superposition,[status(thm)],[c_83386,c_70]) ).
tcf(c_84218,plain,
multiply(identity,multiply(iPr_def_10,a)) = multiply(a,iPr_def_10),
inference(superposition,[status(thm)],[c_84168,c_330]) ).
tcf(c_118501,plain,
multiply(multiply(inverse(a),iPr_def_11),a) = greatest_lower_bound(a,identity),
inference(superposition,[status(thm)],[c_80790,c_19304]) ).
tcf(c_118502,plain,
multiply(multiply(inverse(a),iPr_def_11),a) = greatest_lower_bound(identity,a),
inference(theory_normalisation,[status(thm)],[c_118501,c_74,c_72,c_73,c_71]) ).
tcf(c_118503,plain,
multiply(multiply(inverse(a),iPr_def_11),a) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_118502,c_50079]) ).
tcf(c_119591,plain,
multiply(inverse(a),multiply(iPr_def_11,a)) = iPr_def_11,
inference(superposition,[status(thm)],[c_118503,c_70]) ).
tcf(c_119641,plain,
multiply(identity,multiply(iPr_def_11,a)) = multiply(a,iPr_def_11),
inference(superposition,[status(thm)],[c_119591,c_330]) ).
tcf(c_124536,plain,
multiply(a,iPr_def_10) = multiply(iPr_def_10,a),
inference(superposition,[status(thm)],[c_84218,c_68]) ).
tcf(c_124753,plain,
multiply(a,least_upper_bound(identity,iPr_def_10)) = least_upper_bound(a,multiply(iPr_def_10,a)),
inference(superposition,[status(thm)],[c_124536,c_817]) ).
tcf(c_124763,plain,
multiply(greatest_lower_bound(identity,a),iPr_def_10) = greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,a)),
inference(superposition,[status(thm)],[c_124536,c_727]) ).
tcf(c_124774,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,a)) = multiply(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_124763,c_50079]) ).
tcf(c_124779,plain,
multiply(a,least_upper_bound(iPr_def_10,identity)) = least_upper_bound(a,multiply(iPr_def_10,a)),
inference(theory_normalisation,[status(thm)],[c_124753,c_74,c_72,c_73,c_71]) ).
tcf(c_124780,plain,
least_upper_bound(a,multiply(iPr_def_10,a)) = multiply(iPr_def_10,a),
inference(light_normalisation,[status(thm)],[c_124779,c_274,c_124536]) ).
tcf(c_131639,plain,
multiply(multiply(inverse(a),iPr_def_10),a) = least_upper_bound(identity,multiply(identity,a)),
inference(superposition,[status(thm)],[c_82271,c_676]) ).
tcf(c_131702,plain,
least_upper_bound(identity,multiply(identity,a)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_131639,c_83386]) ).
tcf(c_131763,plain,
least_upper_bound(identity,a) = iPr_def_10,
inference(superposition,[status(thm)],[c_68,c_131702]) ).
tcf(c_140845,plain,
multiply(a,iPr_def_11) = multiply(iPr_def_11,a),
inference(superposition,[status(thm)],[c_119641,c_68]) ).
tcf(c_140879,plain,
multiply(a,least_upper_bound(identity,iPr_def_11)) = least_upper_bound(a,multiply(iPr_def_11,a)),
inference(superposition,[status(thm)],[c_140845,c_817]) ).
tcf(c_140891,plain,
multiply(least_upper_bound(identity,a),iPr_def_11) = least_upper_bound(iPr_def_11,multiply(iPr_def_11,a)),
inference(superposition,[status(thm)],[c_140845,c_656]) ).
tcf(c_140908,plain,
least_upper_bound(iPr_def_11,multiply(iPr_def_11,a)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_140891,c_13530,c_131763]) ).
tcf(c_140916,plain,
multiply(a,least_upper_bound(iPr_def_11,identity)) = least_upper_bound(a,multiply(iPr_def_11,a)),
inference(theory_normalisation,[status(thm)],[c_140879,c_74,c_72,c_73,c_71]) ).
tcf(c_140917,plain,
least_upper_bound(a,multiply(iPr_def_11,a)) = multiply(a,identity),
inference(light_normalisation,[status(thm)],[c_140916,c_256]) ).
tcf(c_141314,plain,
! [X0: $i] : least_upper_bound(iPr_def_11,least_upper_bound(multiply(iPr_def_11,a),X0)) = least_upper_bound(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_140908,c_74]) ).
tcf(c_141328,plain,
multiply(iPr_def_11,least_upper_bound(identity,a)) = iPr_def_12,
inference(superposition,[status(thm)],[c_140908,c_817]) ).
tcf(c_141332,plain,
multiply(iPr_def_11,iPr_def_10) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_141328,c_131763]) ).
tcf(c_143005,plain,
least_upper_bound(a,multiply(iPr_def_11,a)) = least_upper_bound(iPr_def_12,a),
inference(superposition,[status(thm)],[c_141314,c_1028]) ).
tcf(c_143114,plain,
multiply(a,identity) = least_upper_bound(iPr_def_12,a),
inference(light_normalisation,[status(thm)],[c_143005,c_140917]) ).
tcf(c_143255,plain,
greatest_lower_bound(iPr_def_12,multiply(a,identity)) = iPr_def_12,
inference(superposition,[status(thm)],[c_143114,c_78]) ).
tcf(c_144242,plain,
greatest_lower_bound(iPr_def_12,a) = iPr_def_12,
inference(superposition,[status(thm)],[c_778,c_143255]) ).
tcf(c_148329,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,a)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_124774,c_141332]) ).
tcf(c_148334,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(multiply(iPr_def_10,a),X0)) = greatest_lower_bound(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_148329,c_73]) ).
tcf(c_150126,plain,
greatest_lower_bound(a,multiply(iPr_def_10,a)) = a,
inference(superposition,[status(thm)],[c_124780,c_78]) ).
tcf(c_152094,plain,
greatest_lower_bound(a,multiply(iPr_def_10,a)) = greatest_lower_bound(iPr_def_12,a),
inference(superposition,[status(thm)],[c_148334,c_1544]) ).
tcf(c_152173,plain,
a = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_152094,c_144242,c_150126]) ).
tcf(c_152456,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_152,c_152173]) ).
tcf(c_152457,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_152456]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 13:58:05 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running UEQ theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 41.73/15.31 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 41.73/15.31 % SZS status Started for theBenchmark.p
% 41.73/15.31 % SZS status Unsatisfiable for theBenchmark.p
% 41.73/15.31
% 41.73/15.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 41.73/15.31
% 41.73/15.31 % ------ iProver source info
% 41.73/15.31
% 41.73/15.31 % git: date: 2026-07-19 20:42:38 +0200
% 41.73/15.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 41.73/15.31 % git: non_committed_changes: false
% 41.73/15.31
% 41.73/15.31 % ------ Parsing...% successful
% 41.73/15.31
% 41.73/15.31
% 41.73/15.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 41.73/15.31
% 41.73/15.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 41.73/15.31
% 41.73/15.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 41.73/15.31
% 41.73/15.31 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 41.73/15.31 % ------ Proving...
% 41.73/15.31 % ------ Problem Properties
% 41.73/15.31
% 41.73/15.31 %
% 41.73/15.31 % clauses 22
% 41.73/15.31 % conjectures 1
% 41.73/15.31 % EPR 1
% 41.73/15.31 % Horn 22
% 41.73/15.31 % unary 22
% 41.73/15.31 % binary 0
% 41.73/15.31 % lits 22
% 41.73/15.31 % lits eq 22
% 41.73/15.31 % fd_pure 0
% 41.73/15.31 % fd_pseudo 0
% 41.73/15.31 % fd_cond 0
% 41.73/15.31 % fd_pseudo_cond 0
% 41.73/15.31 % AC symbols 2
% 41.73/15.31
% 41.73/15.31 % ------ Input Options Time Limit: Unbounded
% 41.73/15.31
% 41.73/15.31
% 41.73/15.31 % ------
% 41.73/15.31 % Current options:
% 41.73/15.31 % ------
% 41.73/15.31
% 41.73/15.31
% 41.73/15.31 %
% 41.73/15.31
% 41.73/15.31 % ------ Proving...
% 41.73/15.31 %
% 41.73/15.31
% 41.73/15.31 % SZS status Unsatisfiable for theBenchmark.p
% 41.73/15.31
% 41.73/15.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 41.73/15.31
% 41.73/15.31
%------------------------------------------------------------------------------