%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP183-1 : 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 : n011.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 01:31:43 PM UTC 2026
% Result : Unsatisfiable 11.73s 7.39s
% Output : CNFRefutation 51.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 18
% Syntax : Number of formulae : 180 ( 180 unt; 4 def)
% Number of atoms : 483 ( 179 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 : 6 ( 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 : 153 ( 0 sgn 153 !; 0 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
fof(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,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p20) ).
fof(f18,plain,
identity != greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),
inference(reorient_equations,[],[f17]) ).
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_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,
greatest_lower_bound(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_134,definition,
iPr_def_10 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_135,definition,
iPr_def_11 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_136,definition,
iPr_def_12 = inverse(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_137,definition,
iPr_def_13 = greatest_lower_bound(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_138,negated_conjecture,
iPr_def_13 != identity,
inference(demodulation,[status(thm)],[c_80,c_135,c_136,c_134,c_137]) ).
tcf(c_139,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_140,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_141,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_142,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_143,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_144,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_145,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_146,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_147,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,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_151,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_152,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_153,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,
multiply(iPr_def_12,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_136,c_140]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_140,c_139]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_238,c_141]) ).
tcf(c_240,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(iPr_def_11,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_237,c_139]) ).
tcf(c_241,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(iPr_def_11,X0)) = X0,
inference(demodulation,[status(thm)],[c_240,c_141]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_141,c_142]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(multiply(X0,X1),X1) = multiply(greatest_lower_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_141,c_142]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(X1,identity),X0),
inference(demodulation,[status(thm)],[c_247,c_153]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_141,c_143]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] : least_upper_bound(multiply(X0,X1),X1) = multiply(least_upper_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_141,c_143]) ).
tcf(c_259,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_140,c_143]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
inference(demodulation,[status(thm)],[c_258,c_152]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : multiply(least_upper_bound(X0,inverse(X1)),X1) = least_upper_bound(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_259,c_152]) ).
tcf(c_267,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_140,c_144]) ).
tcf(c_269,plain,
! [X0: $i] : greatest_lower_bound(identity,multiply(iPr_def_12,X0)) = multiply(iPr_def_12,greatest_lower_bound(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_237,c_144]) ).
tcf(c_271,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_140,c_144]) ).
tcf(c_276,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_271,c_153]) ).
tcf(c_279,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_140,c_145]) ).
tcf(c_281,plain,
! [X0: $i] : least_upper_bound(identity,multiply(iPr_def_12,X0)) = multiply(iPr_def_12,least_upper_bound(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_237,c_145]) ).
tcf(c_293,plain,
least_upper_bound(a,iPr_def_11) = a,
inference(superposition,[status(thm)],[c_135,c_147]) ).
tcf(c_297,plain,
least_upper_bound(iPr_def_10,iPr_def_13) = iPr_def_10,
inference(superposition,[status(thm)],[c_137,c_147]) ).
tcf(c_300,plain,
least_upper_bound(iPr_def_11,a) = a,
inference(demodulation,[status(thm)],[c_293,c_152]) ).
tcf(c_315,plain,
! [X0: $i] : least_upper_bound(a,least_upper_bound(identity,X0)) = least_upper_bound(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_134,c_150]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(least_upper_bound(X0,X1),X2)) = greatest_lower_bound(X0,X2),
inference(superposition,[status(thm)],[c_146,c_151]) ).
tcf(c_332,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_10,greatest_lower_bound(iPr_def_12,X0)) = greatest_lower_bound(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_137,c_151]) ).
tcf(c_338,plain,
greatest_lower_bound(iPr_def_11,a) = iPr_def_11,
inference(superposition,[status(thm)],[c_300,c_146]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_152,c_146]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_153,c_147]) ).
tcf(c_416,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_140,c_239]) ).
tcf(c_418,plain,
multiply(inverse(iPr_def_12),identity) = iPr_def_11,
inference(superposition,[status(thm)],[c_237,c_239]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_239,c_239]) ).
tcf(c_430,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_416,c_419]) ).
tcf(c_431,plain,
inverse(iPr_def_12) = iPr_def_11,
inference(demodulation,[status(thm)],[c_418,c_430]) ).
tcf(c_1271,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(identity,X1)),
inference(superposition,[status(thm)],[c_430,c_144]) ).
tcf(c_1279,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_430,c_140]) ).
tcf(c_1307,plain,
greatest_lower_bound(identity,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_134,c_348]) ).
tcf(c_1320,plain,
greatest_lower_bound(iPr_def_13,iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_297,c_348]) ).
tcf(c_1332,plain,
greatest_lower_bound(iPr_def_10,iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_1320,c_153]) ).
tcf(c_1333,plain,
greatest_lower_bound(iPr_def_10,identity) = identity,
inference(demodulation,[status(thm)],[c_1307,c_153]) ).
tcf(c_1534,plain,
greatest_lower_bound(identity,multiply(inverse(a),identity)) = multiply(inverse(a),iPr_def_11),
inference(superposition,[status(thm)],[c_135,c_267]) ).
tcf(c_1551,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_11),a)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_338,c_267]) ).
tcf(c_1553,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_10),iPr_def_13)) = multiply(inverse(iPr_def_10),iPr_def_13),
inference(superposition,[status(thm)],[c_1332,c_267]) ).
tcf(c_1554,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_10),identity)) = multiply(inverse(iPr_def_10),identity),
inference(superposition,[status(thm)],[c_1333,c_267]) ).
tcf(c_1578,plain,
greatest_lower_bound(identity,inverse(iPr_def_10)) = inverse(iPr_def_10),
inference(demodulation,[status(thm)],[c_1554,c_430]) ).
tcf(c_1579,plain,
greatest_lower_bound(identity,multiply(iPr_def_12,a)) = identity,
inference(demodulation,[status(thm)],[c_1551,c_140,c_136]) ).
tcf(c_1580,plain,
greatest_lower_bound(identity,inverse(a)) = multiply(inverse(a),iPr_def_11),
inference(demodulation,[status(thm)],[c_1534,c_430]) ).
tcf(c_1651,plain,
! [X0: $i] : multiply(greatest_lower_bound(identity,inverse(a)),X0) = multiply(inverse(a),multiply(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_1580,c_139]) ).
tcf(c_1843,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_12),iPr_def_10)) = multiply(inverse(iPr_def_12),iPr_def_13),
inference(superposition,[status(thm)],[c_137,c_276]) ).
tcf(c_1853,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_13),iPr_def_10)) = multiply(inverse(iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_1332,c_276]) ).
tcf(c_1856,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(iPr_def_10)),identity)) = multiply(inverse(inverse(iPr_def_10)),inverse(iPr_def_10)),
inference(superposition,[status(thm)],[c_1578,c_276]) ).
tcf(c_1859,plain,
multiply(inverse(multiply(inverse(iPr_def_10),iPr_def_13)),multiply(inverse(iPr_def_10),iPr_def_13)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(iPr_def_10),iPr_def_13)),identity)),
inference(superposition,[status(thm)],[c_1553,c_276]) ).
tcf(c_1860,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(iPr_def_12,a)),identity)) = multiply(inverse(multiply(iPr_def_12,a)),identity),
inference(superposition,[status(thm)],[c_1579,c_276]) ).
tcf(c_1884,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_13),iPr_def_10)) = identity,
inference(demodulation,[status(thm)],[c_1853,c_140]) ).
tcf(c_1886,plain,
greatest_lower_bound(identity,multiply(iPr_def_11,iPr_def_10)) = multiply(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_1843,c_431]) ).
tcf(c_1889,plain,
multiply(iPr_def_10,inverse(iPr_def_10)) = identity,
inference(demodulation,[status(thm)],[c_1856,c_153,c_419,c_430,c_1333]) ).
tcf(c_1890,plain,
greatest_lower_bound(identity,inverse(multiply(iPr_def_12,a))) = inverse(multiply(iPr_def_12,a)),
inference(demodulation,[status(thm)],[c_1860,c_430]) ).
tcf(c_1898,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(iPr_def_10),iPr_def_13))) = identity,
inference(demodulation,[status(thm)],[c_1859,c_140,c_430]) ).
tcf(c_1912,plain,
least_upper_bound(identity,multiply(inverse(a),identity)) = multiply(inverse(a),iPr_def_10),
inference(superposition,[status(thm)],[c_134,c_279]) ).
tcf(c_1928,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_11),a)) = multiply(inverse(iPr_def_11),a),
inference(superposition,[status(thm)],[c_300,c_279]) ).
tcf(c_1956,plain,
least_upper_bound(identity,multiply(iPr_def_12,a)) = multiply(iPr_def_12,a),
inference(demodulation,[status(thm)],[c_1928,c_136]) ).
tcf(c_1957,plain,
least_upper_bound(identity,inverse(a)) = multiply(inverse(a),iPr_def_10),
inference(demodulation,[status(thm)],[c_1912,c_430]) ).
tcf(c_2044,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(inverse(iPr_def_10),X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1889,c_139]) ).
tcf(c_2059,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(inverse(iPr_def_10),X0)) = X0,
inference(demodulation,[status(thm)],[c_2044,c_141]) ).
tcf(c_2073,plain,
least_upper_bound(identity,iPr_def_11) = identity,
inference(superposition,[status(thm)],[c_135,c_358]) ).
tcf(c_2112,plain,
least_upper_bound(iPr_def_11,identity) = identity,
inference(demodulation,[status(thm)],[c_2073,c_152]) ).
tcf(c_2127,plain,
greatest_lower_bound(iPr_def_11,identity) = iPr_def_11,
inference(superposition,[status(thm)],[c_2112,c_146]) ).
tcf(c_2132,plain,
least_upper_bound(identity,multiply(iPr_def_12,identity)) = multiply(iPr_def_12,identity),
inference(superposition,[status(thm)],[c_2112,c_281]) ).
tcf(c_2133,plain,
least_upper_bound(iPr_def_12,identity) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2132,c_152,c_430]) ).
tcf(c_2201,plain,
least_upper_bound(multiply(inverse(iPr_def_13),iPr_def_10),identity) = multiply(inverse(iPr_def_13),iPr_def_10),
inference(superposition,[status(thm)],[c_1884,c_358]) ).
tcf(c_2206,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_13),iPr_def_10)) = multiply(inverse(iPr_def_13),iPr_def_10),
inference(demodulation,[status(thm)],[c_2201,c_152]) ).
tcf(c_2214,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(iPr_def_11,iPr_def_10)),identity)) = multiply(inverse(multiply(iPr_def_11,iPr_def_10)),multiply(iPr_def_11,iPr_def_13)),
inference(superposition,[status(thm)],[c_1886,c_276]) ).
tcf(c_2219,plain,
multiply(inverse(multiply(iPr_def_11,iPr_def_10)),multiply(iPr_def_11,iPr_def_13)) = greatest_lower_bound(identity,inverse(multiply(iPr_def_11,iPr_def_10))),
inference(demodulation,[status(thm)],[c_2214,c_430]) ).
tcf(c_2224,plain,
multiply(inverse(inverse(multiply(iPr_def_12,a))),inverse(multiply(iPr_def_12,a))) = greatest_lower_bound(identity,multiply(inverse(inverse(multiply(iPr_def_12,a))),identity)),
inference(superposition,[status(thm)],[c_1890,c_276]) ).
tcf(c_2229,plain,
multiply(iPr_def_12,multiply(a,inverse(multiply(iPr_def_12,a)))) = identity,
inference(demodulation,[status(thm)],[c_2224,c_139,c_419,c_430,c_1579]) ).
tcf(c_2285,plain,
least_upper_bound(inverse(multiply(inverse(iPr_def_10),iPr_def_13)),identity) = inverse(multiply(inverse(iPr_def_10),iPr_def_13)),
inference(superposition,[status(thm)],[c_1898,c_358]) ).
tcf(c_2292,plain,
least_upper_bound(identity,inverse(multiply(inverse(iPr_def_10),iPr_def_13))) = inverse(multiply(inverse(iPr_def_10),iPr_def_13)),
inference(demodulation,[status(thm)],[c_2285,c_152]) ).
tcf(c_2494,plain,
greatest_lower_bound(identity,multiply(iPr_def_12,identity)) = multiply(iPr_def_12,iPr_def_11),
inference(superposition,[status(thm)],[c_2127,c_269]) ).
tcf(c_2495,plain,
greatest_lower_bound(iPr_def_12,identity) = identity,
inference(demodulation,[status(thm)],[c_2494,c_153,c_237,c_430]) ).
tcf(c_2504,plain,
! [X0: $i] : least_upper_bound(X0,multiply(iPr_def_12,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_2133,c_263]) ).
tcf(c_2626,plain,
least_upper_bound(a,multiply(iPr_def_12,a)) = least_upper_bound(iPr_def_10,multiply(iPr_def_12,a)),
inference(superposition,[status(thm)],[c_1956,c_315]) ).
tcf(c_2643,plain,
least_upper_bound(iPr_def_10,multiply(iPr_def_12,a)) = multiply(iPr_def_12,a),
inference(demodulation,[status(thm)],[c_2626,c_2504]) ).
tcf(c_2935,plain,
least_upper_bound(a,multiply(inverse(iPr_def_13),iPr_def_10)) = least_upper_bound(iPr_def_10,multiply(inverse(iPr_def_13),iPr_def_10)),
inference(superposition,[status(thm)],[c_2206,c_315]) ).
tcf(c_2950,plain,
multiply(inverse(inverse(multiply(iPr_def_11,iPr_def_10))),greatest_lower_bound(identity,inverse(multiply(iPr_def_11,iPr_def_10)))) = multiply(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_2219,c_239]) ).
tcf(c_2974,plain,
multiply(iPr_def_11,greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,inverse(multiply(iPr_def_11,iPr_def_10))))) = multiply(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_2950,c_139,c_419,c_1271]) ).
tcf(c_3004,plain,
multiply(a,inverse(multiply(iPr_def_12,a))) = multiply(inverse(iPr_def_12),identity),
inference(superposition,[status(thm)],[c_2229,c_239]) ).
tcf(c_3028,plain,
multiply(a,inverse(multiply(iPr_def_12,a))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3004,c_430,c_431]) ).
tcf(c_3193,plain,
least_upper_bound(a,inverse(multiply(inverse(iPr_def_10),iPr_def_13))) = least_upper_bound(iPr_def_10,inverse(multiply(inverse(iPr_def_10),iPr_def_13))),
inference(superposition,[status(thm)],[c_2292,c_315]) ).
tcf(c_4662,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_12,a)) = iPr_def_10,
inference(superposition,[status(thm)],[c_2643,c_146]) ).
tcf(c_5450,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(inverse(iPr_def_13),iPr_def_10))) = multiply(inverse(a),least_upper_bound(iPr_def_10,multiply(inverse(iPr_def_13),iPr_def_10))),
inference(superposition,[status(thm)],[c_2935,c_279]) ).
tcf(c_5671,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,inverse(multiply(iPr_def_11,iPr_def_10)))) = multiply(iPr_def_12,multiply(iPr_def_11,iPr_def_13)),
inference(superposition,[status(thm)],[c_2974,c_241]) ).
tcf(c_5676,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,inverse(multiply(iPr_def_11,iPr_def_10)))) = iPr_def_13,
inference(demodulation,[status(thm)],[c_5671,c_241]) ).
tcf(c_5756,plain,
inverse(multiply(iPr_def_12,a)) = multiply(inverse(a),iPr_def_11),
inference(superposition,[status(thm)],[c_3028,c_239]) ).
tcf(c_5794,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(multiply(iPr_def_12,a)),
inference(demodulation,[status(thm)],[c_1580,c_5756]) ).
tcf(c_5967,plain,
multiply(least_upper_bound(iPr_def_10,inverse(multiply(inverse(iPr_def_10),iPr_def_13))),multiply(inverse(iPr_def_10),iPr_def_13)) = least_upper_bound(identity,multiply(a,multiply(inverse(iPr_def_10),iPr_def_13))),
inference(superposition,[status(thm)],[c_3193,c_264]) ).
tcf(c_5970,plain,
least_upper_bound(identity,multiply(a,multiply(inverse(iPr_def_10),iPr_def_13))) = least_upper_bound(iPr_def_13,identity),
inference(demodulation,[status(thm)],[c_5967,c_152,c_264,c_2059]) ).
tcf(c_6293,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(X1,least_upper_bound(X0,X2))) = greatest_lower_bound(X0,X1),
inference(superposition,[status(thm)],[c_153,c_329]) ).
tcf(c_7396,plain,
greatest_lower_bound(iPr_def_10,identity) = greatest_lower_bound(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_2495,c_332]) ).
tcf(c_7410,plain,
greatest_lower_bound(iPr_def_13,identity) = identity,
inference(demodulation,[status(thm)],[c_7396,c_1333]) ).
tcf(c_7675,plain,
least_upper_bound(iPr_def_13,identity) = iPr_def_13,
inference(superposition,[status(thm)],[c_7410,c_147]) ).
tcf(c_7691,plain,
least_upper_bound(identity,multiply(inverse(iPr_def_13),identity)) = multiply(inverse(iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_7675,c_279]) ).
tcf(c_7701,plain,
least_upper_bound(identity,inverse(iPr_def_13)) = identity,
inference(demodulation,[status(thm)],[c_7691,c_140,c_430]) ).
tcf(c_7714,plain,
! [X0: $i] : least_upper_bound(X0,multiply(inverse(iPr_def_13),X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_7701,c_254]) ).
tcf(c_7718,plain,
! [X0: $i] : least_upper_bound(X0,multiply(inverse(iPr_def_13),X0)) = X0,
inference(demodulation,[status(thm)],[c_7714,c_141]) ).
tcf(c_7721,plain,
least_upper_bound(a,multiply(inverse(iPr_def_13),iPr_def_10)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2935,c_7718]) ).
tcf(c_8005,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(iPr_def_12,a)),iPr_def_10)) = multiply(inverse(multiply(iPr_def_12,a)),iPr_def_10),
inference(superposition,[status(thm)],[c_4662,c_276]) ).
tcf(c_9123,plain,
greatest_lower_bound(least_upper_bound(iPr_def_10,multiply(inverse(iPr_def_13),iPr_def_10)),least_upper_bound(identity,multiply(inverse(a),multiply(inverse(iPr_def_13),iPr_def_10)))) = multiply(greatest_lower_bound(inverse(a),identity),least_upper_bound(iPr_def_10,multiply(inverse(iPr_def_13),iPr_def_10))),
inference(superposition,[status(thm)],[c_5450,c_252]) ).
tcf(c_9124,plain,
greatest_lower_bound(least_upper_bound(iPr_def_10,multiply(inverse(iPr_def_13),iPr_def_10)),least_upper_bound(identity,multiply(inverse(a),multiply(inverse(iPr_def_13),iPr_def_10)))) = multiply(greatest_lower_bound(identity,inverse(a)),least_upper_bound(iPr_def_10,multiply(inverse(iPr_def_13),iPr_def_10))),
inference(superposition,[status(thm)],[c_5450,c_243]) ).
tcf(c_9137,plain,
greatest_lower_bound(iPr_def_10,least_upper_bound(identity,multiply(inverse(a),multiply(inverse(iPr_def_13),iPr_def_10)))) = multiply(inverse(a),multiply(iPr_def_11,iPr_def_10)),
inference(demodulation,[status(thm)],[c_9124,c_1651,c_7718]) ).
tcf(c_9138,plain,
greatest_lower_bound(iPr_def_10,least_upper_bound(identity,multiply(inverse(a),multiply(inverse(iPr_def_13),iPr_def_10)))) = multiply(inverse(multiply(iPr_def_12,a)),iPr_def_10),
inference(demodulation,[status(thm)],[c_9123,c_153,c_5794,c_7718]) ).
tcf(c_9278,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_10),multiply(iPr_def_10,inverse(multiply(iPr_def_11,iPr_def_10))))) = multiply(inverse(iPr_def_10),iPr_def_13),
inference(superposition,[status(thm)],[c_5676,c_267]) ).
tcf(c_9289,plain,
greatest_lower_bound(identity,inverse(multiply(iPr_def_11,iPr_def_10))) = multiply(inverse(iPr_def_10),iPr_def_13),
inference(demodulation,[status(thm)],[c_9278,c_239]) ).
tcf(c_9628,plain,
! [X0: $i] : greatest_lower_bound(X0,multiply(inverse(a),X0)) = multiply(inverse(multiply(iPr_def_12,a)),X0),
inference(superposition,[status(thm)],[c_5794,c_243]) ).
tcf(c_10629,plain,
least_upper_bound(identity,multiply(a,multiply(inverse(iPr_def_10),iPr_def_13))) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_5970,c_7675]) ).
tcf(c_14493,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(inverse(iPr_def_13),iPr_def_10))) = multiply(inverse(a),iPr_def_10),
inference(superposition,[status(thm)],[c_7721,c_279]) ).
tcf(c_14509,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(inverse(iPr_def_13),iPr_def_10))) = least_upper_bound(identity,inverse(a)),
inference(demodulation,[status(thm)],[c_14493,c_1957]) ).
tcf(c_15362,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_419,c_430]) ).
tcf(c_15363,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_15362,c_430]) ).
tcf(c_17603,plain,
greatest_lower_bound(identity,multiply(inverse(identity),multiply(inverse(multiply(iPr_def_12,a)),iPr_def_10))) = multiply(inverse(identity),multiply(inverse(multiply(iPr_def_12,a)),iPr_def_10)),
inference(superposition,[status(thm)],[c_8005,c_267]) ).
tcf(c_17628,plain,
greatest_lower_bound(iPr_def_10,least_upper_bound(identity,inverse(a))) = identity,
inference(demodulation,[status(thm)],[c_17603,c_153,c_141,c_1279,c_1333,c_1957,c_6293,c_9628]) ).
tcf(c_21611,plain,
multiply(inverse(a),multiply(iPr_def_11,iPr_def_10)) = identity,
inference(light_normalisation,[status(thm)],[c_9137,c_14509,c_17628]) ).
tcf(c_21625,plain,
multiply(inverse(inverse(a)),identity) = multiply(iPr_def_11,iPr_def_10),
inference(superposition,[status(thm)],[c_21611,c_239]) ).
tcf(c_21666,plain,
multiply(iPr_def_11,iPr_def_10) = a,
inference(demodulation,[status(thm)],[c_21625,c_430,c_15363]) ).
tcf(c_21697,plain,
multiply(inverse(multiply(iPr_def_12,a)),iPr_def_10) = identity,
inference(light_normalisation,[status(thm)],[c_9138,c_14509,c_17628]) ).
tcf(c_21711,plain,
multiply(inverse(inverse(multiply(iPr_def_12,a))),identity) = iPr_def_10,
inference(superposition,[status(thm)],[c_21697,c_239]) ).
tcf(c_21744,plain,
multiply(iPr_def_12,a) = iPr_def_10,
inference(demodulation,[status(thm)],[c_21711,c_430,c_15363]) ).
tcf(c_21760,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(iPr_def_10),
inference(demodulation,[status(thm)],[c_5794,c_21744]) ).
tcf(c_21770,plain,
multiply(a,inverse(iPr_def_10)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_3028,c_21744]) ).
tcf(c_22109,plain,
multiply(inverse(iPr_def_10),iPr_def_13) = inverse(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_9289,c_21666,c_21760]) ).
tcf(c_22162,plain,
least_upper_bound(identity,multiply(a,inverse(iPr_def_10))) = iPr_def_13,
inference(superposition,[status(thm)],[c_22109,c_10629]) ).
tcf(c_22168,plain,
identity = iPr_def_13,
inference(demodulation,[status(thm)],[c_22162,c_152,c_2112,c_21770]) ).
tcf(c_22358,plain,
iPr_def_13 != iPr_def_13,
inference(demodulation,[status(thm)],[c_138,c_22168]) ).
tcf(c_22359,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_22358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP183-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:02:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.39 Running UEQ theorem proving
% 0.09/0.39 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
% 0.09/0.40
% 0.09/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.40
% 0.09/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 11.73/7.39 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 11.73/7.39 % SZS status Started for theBenchmark.p
% 11.73/7.39 % SZS status Unsatisfiable for theBenchmark.p
% 11.73/7.39
% 11.73/7.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.73/7.39
% 11.73/7.39 % ------ iProver source info
% 11.73/7.39
% 11.73/7.39 % git: date: 2026-07-19 20:42:38 +0200
% 11.73/7.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.73/7.39 % git: non_committed_changes: false
% 11.73/7.39
% 11.73/7.39 % ------ Parsing...% successful
% 11.73/7.39
% 11.73/7.39
% 11.73/7.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.73/7.39
% 11.73/7.39 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 11.73/7.39
% 11.73/7.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.73/7.39
% 11.73/7.39 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 11.73/7.39 % ------ Proving...
% 11.73/7.39 % ------ Problem Properties
% 11.73/7.39
% 11.73/7.39 %
% 11.73/7.39 % clauses 20
% 11.73/7.39 % conjectures 1
% 11.73/7.39 % EPR 1
% 11.73/7.39 % Horn 20
% 11.73/7.39 % unary 20
% 11.73/7.39 % binary 0
% 11.73/7.39 % lits 20
% 11.73/7.39 % lits eq 20
% 11.73/7.39 % fd_pure 0
% 11.73/7.39 % fd_pseudo 0
% 11.73/7.39 % fd_cond 0
% 11.73/7.39 % fd_pseudo_cond 0
% 11.73/7.39 % AC symbols 2
% 11.73/7.39
% 11.73/7.39 % ------ Input Options Time Limit: Unbounded
% 11.73/7.39
% 11.73/7.39
% 11.73/7.39 % ------
% 11.73/7.39 % Current options:
% 11.73/7.39 % ------
% 11.73/7.39
% 11.73/7.39
% 11.73/7.39 %
% 11.73/7.39
% 11.73/7.39 % ------ Proving...
% 11.73/7.39 %
% 11.73/7.39
% 11.73/7.39 % SZS status Unsatisfiable for theBenchmark.p
% 11.73/7.39
% 11.73/7.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 51.44/7.40
% 51.44/7.40
%------------------------------------------------------------------------------