%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP186-1 : 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 : n004.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 01:31:44 PM UTC 2026
% Result : Unsatisfiable 80.72s 12.77s
% Output : CNFRefutation 80.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 141 ( 141 unt; 6 def)
% Number of atoms : 326 ( 140 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 : 8 ( 6 usr; 7 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 150 ( 0 sgn 150 !; 0 ?; 116 :)
% 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(f9,axiom,
! [X0] : least_upper_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
fof(f10,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
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(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,negated_conjecture,
least_upper_bound(multiply(a,b),identity) != multiply(a,inverse(greatest_lower_bound(a,inverse(b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p23) ).
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_73,plain,
! [X0: $i] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f10]) ).
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,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != least_upper_bound(multiply(a,b),identity),
inference(cnf_transformation,[],[f17]) ).
tcf(c_96,negated_conjecture,
multiply(a,inverse(greatest_lower_bound(a,inverse(b)))) != least_upper_bound(identity,multiply(a,b)),
inference(theory_normalisation,[status(thm)],[c_80,c_70,c_68,c_71,c_69]) ).
tcf(c_135,definition,
iPr_def_10 = inverse(b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_136,definition,
iPr_def_11 = greatest_lower_bound(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_137,definition,
iPr_def_12 = inverse(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_138,definition,
iPr_def_13 = multiply(a,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_139,definition,
iPr_def_14 = multiply(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_140,definition,
iPr_def_15 = least_upper_bound(identity,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_141,negated_conjecture,
iPr_def_13 != iPr_def_15,
inference(demodulation,[status(thm)],[c_96,c_139,c_140,c_135,c_136,c_137,c_138]) ).
tcf(c_142,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_143,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_144,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_145,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_146,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_147,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_148,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_149,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_150,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] : greatest_lower_bound(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_152,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_153,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_154,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_155,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_240,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_153,c_155]) ).
tcf(c_246,plain,
! [X0: $i] : multiply(a,multiply(b,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_139,c_142]) ).
tcf(c_250,plain,
multiply(iPr_def_10,b) = identity,
inference(superposition,[status(thm)],[c_135,c_143]) ).
tcf(c_251,plain,
multiply(iPr_def_12,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_137,c_143]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_143,c_142]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_252,c_144]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_144,c_145]) ).
tcf(c_261,plain,
! [X0: $i] : multiply(greatest_lower_bound(X0,a),b) = greatest_lower_bound(multiply(X0,b),iPr_def_14),
inference(superposition,[status(thm)],[c_139,c_145]) ).
tcf(c_265,plain,
! [X0: $i] : multiply(greatest_lower_bound(X0,a),iPr_def_12) = greatest_lower_bound(multiply(X0,iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_138,c_145]) ).
tcf(c_266,plain,
! [X0: $i] : multiply(greatest_lower_bound(X0,a),iPr_def_12) = greatest_lower_bound(iPr_def_13,multiply(X0,iPr_def_12)),
inference(demodulation,[status(thm)],[c_265,c_156]) ).
tcf(c_268,plain,
! [X0: $i] : multiply(greatest_lower_bound(X0,a),b) = greatest_lower_bound(iPr_def_14,multiply(X0,b)),
inference(demodulation,[status(thm)],[c_261,c_156]) ).
tcf(c_281,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(b,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_250,c_142]) ).
tcf(c_283,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(b,X0)) = X0,
inference(demodulation,[status(thm)],[c_281,c_144]) ).
tcf(c_289,plain,
greatest_lower_bound(identity,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_140,c_149]) ).
tcf(c_290,plain,
greatest_lower_bound(iPr_def_15,identity) = identity,
inference(demodulation,[status(thm)],[c_289,c_156]) ).
tcf(c_294,plain,
least_upper_bound(a,iPr_def_11) = a,
inference(superposition,[status(thm)],[c_136,c_150]) ).
tcf(c_296,plain,
least_upper_bound(iPr_def_11,a) = a,
inference(demodulation,[status(thm)],[c_294,c_155]) ).
tcf(c_297,plain,
least_upper_bound(iPr_def_14,identity) = iPr_def_15,
inference(demodulation,[status(thm)],[c_140,c_155]) ).
tcf(c_300,plain,
greatest_lower_bound(iPr_def_14,iPr_def_15) = iPr_def_14,
inference(superposition,[status(thm)],[c_297,c_149]) ).
tcf(c_301,plain,
greatest_lower_bound(iPr_def_15,iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_300,c_156]) ).
tcf(c_307,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(inverse(X0),X1),X0) = least_upper_bound(identity,multiply(X1,X0)),
inference(superposition,[status(thm)],[c_143,c_146]) ).
tcf(c_315,plain,
! [X0: $i] : multiply(least_upper_bound(X0,a),iPr_def_12) = least_upper_bound(multiply(X0,iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_138,c_146]) ).
tcf(c_322,plain,
! [X0: $i] : multiply(least_upper_bound(X0,a),iPr_def_12) = least_upper_bound(iPr_def_13,multiply(X0,iPr_def_12)),
inference(demodulation,[status(thm)],[c_315,c_155]) ).
tcf(c_342,plain,
! [X0: $i] : multiply(a,greatest_lower_bound(iPr_def_12,X0)) = greatest_lower_bound(iPr_def_13,multiply(a,X0)),
inference(superposition,[status(thm)],[c_138,c_147]) ).
tcf(c_370,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_143,c_148]) ).
tcf(c_424,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(iPr_def_11,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_251,c_142]) ).
tcf(c_429,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(iPr_def_11,X0)) = X0,
inference(demodulation,[status(thm)],[c_424,c_144]) ).
tcf(c_462,plain,
greatest_lower_bound(iPr_def_10,a) = iPr_def_11,
inference(demodulation,[status(thm)],[c_136,c_156]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_156,c_150]) ).
tcf(c_477,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,greatest_lower_bound(X0,X1)) = greatest_lower_bound(X0,X1),
inference(superposition,[status(thm)],[c_151,c_154]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X1,X0),
inference(superposition,[status(thm)],[c_152,c_240]) ).
tcf(c_511,plain,
! [X0: $i] : least_upper_bound(iPr_def_14,least_upper_bound(X0,identity)) = least_upper_bound(X0,iPr_def_15),
inference(superposition,[status(thm)],[c_297,c_240]) ).
tcf(c_564,plain,
! [X0: $i,X1: $i] : multiply(a,greatest_lower_bound(X0,multiply(b,X1))) = greatest_lower_bound(multiply(a,X0),multiply(iPr_def_14,X1)),
inference(superposition,[status(thm)],[c_246,c_147]) ).
tcf(c_707,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_143,c_253]) ).
tcf(c_715,plain,
! [X0: $i] : multiply(inverse(iPr_def_10),X0) = multiply(b,X0),
inference(superposition,[status(thm)],[c_283,c_253]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_253,c_253]) ).
tcf(c_723,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),greatest_lower_bound(X1,multiply(X0,X2))) = greatest_lower_bound(multiply(inverse(X0),X1),X2),
inference(superposition,[status(thm)],[c_253,c_147]) ).
tcf(c_817,plain,
! [X0: $i,X1: $i] : multiply(inverse(greatest_lower_bound(identity,X0)),greatest_lower_bound(X1,multiply(X0,X1))) = X1,
inference(superposition,[status(thm)],[c_257,c_253]) ).
tcf(c_995,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),X0) = multiply(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_429,c_253]) ).
tcf(c_1069,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_707,c_147]) ).
tcf(c_1072,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(X1,identity)),
inference(demodulation,[status(thm)],[c_1069,c_156,c_716]) ).
tcf(c_1425,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_10,iPr_def_12)) = multiply(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_462,c_266]) ).
tcf(c_1745,plain,
greatest_lower_bound(iPr_def_14,multiply(iPr_def_10,b)) = multiply(iPr_def_11,b),
inference(superposition,[status(thm)],[c_462,c_268]) ).
tcf(c_1763,plain,
multiply(iPr_def_11,b) = greatest_lower_bound(iPr_def_14,identity),
inference(demodulation,[status(thm)],[c_1745,c_250]) ).
tcf(c_1940,plain,
multiply(iPr_def_12,greatest_lower_bound(iPr_def_14,identity)) = b,
inference(superposition,[status(thm)],[c_1763,c_429]) ).
tcf(c_1941,plain,
greatest_lower_bound(iPr_def_12,multiply(iPr_def_12,iPr_def_14)) = b,
inference(demodulation,[status(thm)],[c_1940,c_1072]) ).
tcf(c_2330,plain,
greatest_lower_bound(iPr_def_12,b) = b,
inference(superposition,[status(thm)],[c_1941,c_477]) ).
tcf(c_2332,plain,
least_upper_bound(iPr_def_12,b) = iPr_def_12,
inference(superposition,[status(thm)],[c_1941,c_150]) ).
tcf(c_3432,plain,
least_upper_bound(iPr_def_13,multiply(iPr_def_11,iPr_def_12)) = multiply(a,iPr_def_12),
inference(superposition,[status(thm)],[c_296,c_322]) ).
tcf(c_3454,plain,
least_upper_bound(iPr_def_13,multiply(inverse(iPr_def_12),iPr_def_12)) = least_upper_bound(identity,multiply(a,iPr_def_12)),
inference(superposition,[status(thm)],[c_322,c_307]) ).
tcf(c_3455,plain,
least_upper_bound(iPr_def_13,multiply(iPr_def_11,iPr_def_12)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3432,c_138]) ).
tcf(c_3456,plain,
least_upper_bound(iPr_def_13,multiply(iPr_def_11,iPr_def_12)) = least_upper_bound(iPr_def_13,identity),
inference(demodulation,[status(thm)],[c_3454,c_155,c_138,c_995]) ).
tcf(c_5263,plain,
least_upper_bound(multiply(iPr_def_11,iPr_def_12),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_3455,c_506]) ).
tcf(c_5268,plain,
least_upper_bound(iPr_def_13,identity) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5263,c_155,c_3456]) ).
tcf(c_5555,plain,
greatest_lower_bound(iPr_def_13,multiply(a,b)) = multiply(a,b),
inference(superposition,[status(thm)],[c_2330,c_342]) ).
tcf(c_5580,plain,
greatest_lower_bound(iPr_def_14,iPr_def_13) = iPr_def_14,
inference(demodulation,[status(thm)],[c_5555,c_156,c_139]) ).
tcf(c_5860,plain,
least_upper_bound(iPr_def_13,iPr_def_15) = least_upper_bound(iPr_def_14,iPr_def_13),
inference(superposition,[status(thm)],[c_5268,c_511]) ).
tcf(c_5862,plain,
least_upper_bound(iPr_def_14,iPr_def_13) = least_upper_bound(iPr_def_15,iPr_def_13),
inference(demodulation,[status(thm)],[c_5860,c_155]) ).
tcf(c_5871,plain,
least_upper_bound(iPr_def_13,iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_5580,c_470]) ).
tcf(c_5877,plain,
least_upper_bound(iPr_def_15,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5871,c_155,c_5862]) ).
tcf(c_6381,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_12),b)) = multiply(inverse(iPr_def_12),iPr_def_12),
inference(superposition,[status(thm)],[c_2332,c_370]) ).
tcf(c_6415,plain,
multiply(iPr_def_11,iPr_def_12) = identity,
inference(demodulation,[status(thm)],[c_6381,c_470,c_995,c_1763]) ).
tcf(c_6562,plain,
greatest_lower_bound(iPr_def_15,iPr_def_13) = iPr_def_15,
inference(superposition,[status(thm)],[c_5877,c_149]) ).
tcf(c_6606,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_15,greatest_lower_bound(iPr_def_13,X0)) = greatest_lower_bound(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_6562,c_154]) ).
tcf(c_7753,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_10,iPr_def_12)) = identity,
inference(light_normalisation,[status(thm)],[c_1425,c_6415]) ).
tcf(c_15180,plain,
greatest_lower_bound(iPr_def_15,multiply(iPr_def_10,iPr_def_12)) = greatest_lower_bound(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_7753,c_6606]) ).
tcf(c_15210,plain,
greatest_lower_bound(iPr_def_15,multiply(iPr_def_10,iPr_def_12)) = identity,
inference(demodulation,[status(thm)],[c_15180,c_290]) ).
tcf(c_34874,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_707,c_716]) ).
tcf(c_36412,plain,
multiply(b,identity) = inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_34874,c_715]) ).
tcf(c_36422,plain,
inverse(iPr_def_10) = b,
inference(demodulation,[status(thm)],[c_36412,c_34874]) ).
tcf(c_39639,plain,
greatest_lower_bound(multiply(inverse(iPr_def_10),iPr_def_13),iPr_def_12) = multiply(inverse(iPr_def_10),identity),
inference(superposition,[status(thm)],[c_7753,c_723]) ).
tcf(c_39658,plain,
greatest_lower_bound(multiply(inverse(iPr_def_10),iPr_def_15),iPr_def_12) = multiply(inverse(iPr_def_10),identity),
inference(superposition,[status(thm)],[c_15210,c_723]) ).
tcf(c_39831,plain,
greatest_lower_bound(iPr_def_12,multiply(b,iPr_def_15)) = b,
inference(demodulation,[status(thm)],[c_39658,c_156,c_36422,c_34874]) ).
tcf(c_39841,plain,
greatest_lower_bound(iPr_def_12,multiply(b,iPr_def_13)) = b,
inference(demodulation,[status(thm)],[c_39639,c_156,c_36422,c_34874]) ).
tcf(c_55418,plain,
greatest_lower_bound(multiply(a,iPr_def_12),multiply(iPr_def_14,iPr_def_15)) = multiply(a,b),
inference(superposition,[status(thm)],[c_39831,c_564]) ).
tcf(c_55422,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_14,iPr_def_15)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_55418,c_156,c_138,c_139]) ).
tcf(c_58047,plain,
greatest_lower_bound(multiply(a,iPr_def_12),multiply(iPr_def_14,iPr_def_13)) = multiply(a,b),
inference(superposition,[status(thm)],[c_39841,c_564]) ).
tcf(c_58051,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_14,iPr_def_13)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_58047,c_156,c_138,c_139]) ).
tcf(c_84231,plain,
greatest_lower_bound(iPr_def_15,multiply(iPr_def_14,iPr_def_15)) = greatest_lower_bound(iPr_def_15,iPr_def_14),
inference(superposition,[status(thm)],[c_55422,c_6606]) ).
tcf(c_84233,plain,
greatest_lower_bound(iPr_def_15,multiply(iPr_def_14,iPr_def_15)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_84231,c_301]) ).
tcf(c_88325,plain,
multiply(inverse(greatest_lower_bound(identity,iPr_def_14)),iPr_def_14) = iPr_def_13,
inference(superposition,[status(thm)],[c_58051,c_817]) ).
tcf(c_88334,plain,
multiply(inverse(greatest_lower_bound(iPr_def_14,identity)),iPr_def_14) = iPr_def_13,
inference(demodulation,[status(thm)],[c_88325,c_156]) ).
tcf(c_92073,plain,
multiply(inverse(greatest_lower_bound(identity,iPr_def_14)),iPr_def_14) = iPr_def_15,
inference(superposition,[status(thm)],[c_84233,c_817]) ).
tcf(c_92083,plain,
iPr_def_13 = iPr_def_15,
inference(demodulation,[status(thm)],[c_92073,c_156,c_88334]) ).
tcf(c_92084,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_92083,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP186-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Wed Sep 23 14:03:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running UEQ theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 80.72/12.77 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 80.72/12.77 % SZS status Started for theBenchmark.p
% 80.72/12.77 % SZS status Unsatisfiable for theBenchmark.p
% 80.72/12.77
% 80.72/12.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 80.72/12.77
% 80.72/12.77 % ------ iProver source info
% 80.72/12.77
% 80.72/12.77 % git: date: 2026-07-19 20:42:38 +0200
% 80.72/12.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 80.72/12.77 % git: non_committed_changes: false
% 80.72/12.77
% 80.72/12.77 % ------ Parsing...% successful
% 80.72/12.77
% 80.72/12.77
% 80.72/12.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 80.72/12.77
% 80.72/12.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 80.72/12.77
% 80.72/12.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 80.72/12.77
% 80.72/12.77 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 80.72/12.77 % ------ Proving...
% 80.72/12.77 % ------ Problem Properties
% 80.72/12.77
% 80.72/12.77 %
% 80.72/12.77 % clauses 22
% 80.72/12.77 % conjectures 1
% 80.72/12.77 % EPR 1
% 80.72/12.77 % Horn 22
% 80.72/12.77 % unary 22
% 80.72/12.77 % binary 0
% 80.72/12.77 % lits 22
% 80.72/12.77 % lits eq 22
% 80.72/12.77 % fd_pure 0
% 80.72/12.77 % fd_pseudo 0
% 80.72/12.77 % fd_cond 0
% 80.72/12.77 % fd_pseudo_cond 0
% 80.72/12.77 % AC symbols 2
% 80.72/12.77
% 80.72/12.77 % ------ Input Options Time Limit: Unbounded
% 80.72/12.77
% 80.72/12.77
% 80.72/12.77 % ------
% 80.72/12.77 % Current options:
% 80.72/12.77 % ------
% 80.72/12.77
% 80.72/12.77
% 80.72/12.77 %
% 80.72/12.77
% 80.72/12.77 % ------ Proving...
% 80.72/12.77 %
% 80.72/12.77
% 80.72/12.77 % SZS status Unsatisfiable for theBenchmark.p
% 80.72/12.77
% 80.72/12.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 80.72/12.77
% 80.72/12.77
%------------------------------------------------------------------------------