%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP167-2 : 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 : n018.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 01:31:37 PM UTC 2026
% Result : Unsatisfiable 14.45s 4.75s
% Output : CNFRefutation 14.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 23
% Syntax : Number of formulae : 118 ( 118 unt; 4 def)
% Number of atoms : 237 ( 117 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 6 ( 6 ~; 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn 139 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
fof(f6,axiom,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
fof(f7,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
fof(f8,axiom,
! [X2,X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
fof(f11,axiom,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
fof(f12,axiom,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
fof(f13,axiom,
! [X2,X0,X1] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
fof(f14,axiom,
! [X2,X0,X1] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
fof(f16,axiom,
! [X2,X0,X1] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
fof(f17,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_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',lat4_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_3) ).
fof(f21,axiom,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
fof(f22,axiom,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_5) ).
fof(f23,axiom,
! [X2,X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_6) ).
fof(f25,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
fof(f26,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(definition_unfolding,[],[f25,f21,f22]) ).
tcf(c_72,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_73,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_77,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_78,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_81,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_83,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_84,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_86,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_87,plain,
inverse(identity) = identity,
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2)) = least_upper_bound(X0,greatest_lower_bound(X1,X2)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_92,negated_conjecture,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != a,
inference(cnf_transformation,[],[f26]) ).
tcf(c_112,negated_conjecture,
multiply(least_upper_bound(identity,a),greatest_lower_bound(identity,a)) != a,
inference(theory_normalisation,[status(thm)],[c_92,c_77,c_75,c_78,c_76]) ).
tcf(c_161,definition,
iPr_def_10 = least_upper_bound(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_162,definition,
iPr_def_11 = greatest_lower_bound(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_163,definition,
iPr_def_12 = multiply(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_164,definition,
iPr_def_13 = inverse(identity),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_165,negated_conjecture,
iPr_def_12 != a,
inference(demodulation,[status(thm)],[c_112,c_162,c_161,c_163]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_167,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_168,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_169,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_86]) ).
tcf(c_171,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_84]) ).
tcf(c_172,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_83]) ).
tcf(c_173,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_178,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_77]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X0,X2)) = least_upper_bound(X0,greatest_lower_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_184,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_185,plain,
iPr_def_13 = identity,
inference(demodulation,[status(thm)],[c_87,c_164]) ).
tcf(c_281,plain,
inverse(iPr_def_13) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_164,c_185]) ).
tcf(c_282,plain,
least_upper_bound(iPr_def_13,a) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_161,c_185]) ).
tcf(c_283,plain,
greatest_lower_bound(iPr_def_13,a) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_162,c_185]) ).
tcf(c_284,plain,
! [X0: $i] : multiply(iPr_def_13,X0) = X0,
inference(light_normalisation,[status(thm)],[c_168,c_185]) ).
tcf(c_285,plain,
! [X0: $i] : multiply(iPr_def_10,multiply(iPr_def_11,X0)) = multiply(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_163,c_166]) ).
tcf(c_288,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_167,c_185]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(iPr_def_13,X1),
inference(superposition,[status(thm)],[c_288,c_166]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_290,c_284]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(iPr_def_13,X1),X0),
inference(superposition,[status(thm)],[c_284,c_169]) ).
tcf(c_335,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = iPr_def_13,
inference(superposition,[status(thm)],[c_184,c_288]) ).
tcf(c_339,plain,
greatest_lower_bound(iPr_def_13,iPr_def_10) = iPr_def_13,
inference(superposition,[status(thm)],[c_282,c_173]) ).
tcf(c_343,plain,
least_upper_bound(iPr_def_13,iPr_def_11) = iPr_def_13,
inference(superposition,[status(thm)],[c_283,c_174]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_179,c_173]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_180,c_174]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(iPr_def_13,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_288,c_171]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(multiply(inverse(X0),X1),iPr_def_13),
inference(superposition,[status(thm)],[c_288,c_171]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),greatest_lower_bound(X1,X0)) = greatest_lower_bound(iPr_def_13,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[c_365,c_180]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(iPr_def_13,multiply(inverse(X0),X1)),
inference(superposition,[status(thm)],[c_288,c_172]) ).
tcf(c_435,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_13,greatest_lower_bound(iPr_def_10,X0)) = greatest_lower_bound(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_339,c_178]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,X1),inverse(X1)) = greatest_lower_bound(multiply(X0,inverse(X1)),iPr_def_13),
inference(superposition,[status(thm)],[c_335,c_169]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,X1),inverse(X1)) = greatest_lower_bound(iPr_def_13,multiply(X0,inverse(X1))),
inference(demodulation,[status(thm)],[c_453,c_180]) ).
tcf(c_494,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = multiply(inverse(X1),X0),
inference(superposition,[status(thm)],[c_184,c_183]) ).
tcf(c_495,plain,
! [X0: $i] : inverse(multiply(iPr_def_13,X0)) = multiply(inverse(X0),iPr_def_13),
inference(superposition,[status(thm)],[c_281,c_183]) ).
tcf(c_507,plain,
! [X0: $i] : multiply(inverse(X0),iPr_def_13) = inverse(X0),
inference(demodulation,[status(thm)],[c_495,c_284]) ).
tcf(c_586,plain,
! [X0: $i] : least_upper_bound(iPr_def_13,greatest_lower_bound(a,X0)) = greatest_lower_bound(iPr_def_10,least_upper_bound(iPr_def_13,X0)),
inference(superposition,[status(thm)],[c_282,c_182]) ).
tcf(c_639,plain,
greatest_lower_bound(a,iPr_def_10) = a,
inference(superposition,[status(thm)],[c_282,c_349]) ).
tcf(c_640,plain,
greatest_lower_bound(iPr_def_11,iPr_def_13) = iPr_def_11,
inference(superposition,[status(thm)],[c_343,c_349]) ).
tcf(c_647,plain,
greatest_lower_bound(iPr_def_13,iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_640,c_180]) ).
tcf(c_648,plain,
greatest_lower_bound(iPr_def_10,a) = a,
inference(demodulation,[status(thm)],[c_639,c_180]) ).
tcf(c_917,plain,
least_upper_bound(a,iPr_def_11) = a,
inference(superposition,[status(thm)],[c_283,c_355]) ).
tcf(c_931,plain,
least_upper_bound(iPr_def_11,a) = a,
inference(demodulation,[status(thm)],[c_917,c_179]) ).
tcf(c_1254,plain,
! [X0: $i] : multiply(X0,iPr_def_13) = X0,
inference(superposition,[status(thm)],[c_184,c_507]) ).
tcf(c_1276,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(iPr_def_13,X1)),
inference(superposition,[status(thm)],[c_1254,c_171]) ).
tcf(c_1287,plain,
multiply(iPr_def_10,iPr_def_11) = multiply(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_1254,c_285]) ).
tcf(c_1291,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1287,c_1254]) ).
tcf(c_3851,plain,
greatest_lower_bound(iPr_def_13,multiply(inverse(a),iPr_def_13)) = multiply(inverse(a),iPr_def_11),
inference(superposition,[status(thm)],[c_283,c_375]) ).
tcf(c_3862,plain,
greatest_lower_bound(iPr_def_13,multiply(inverse(iPr_def_11),iPr_def_13)) = multiply(inverse(iPr_def_11),iPr_def_11),
inference(superposition,[status(thm)],[c_647,c_375]) ).
tcf(c_3904,plain,
greatest_lower_bound(iPr_def_13,inverse(iPr_def_11)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_3862,c_288,c_1254]) ).
tcf(c_3905,plain,
multiply(inverse(a),iPr_def_11) = greatest_lower_bound(iPr_def_13,inverse(a)),
inference(demodulation,[status(thm)],[c_3851,c_1254]) ).
tcf(c_5776,plain,
! [X0: $i] : greatest_lower_bound(X0,multiply(inverse(iPr_def_11),X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_3904,c_296]) ).
tcf(c_5779,plain,
! [X0: $i] : greatest_lower_bound(X0,multiply(inverse(iPr_def_11),X0)) = X0,
inference(demodulation,[status(thm)],[c_5776,c_284]) ).
tcf(c_11222,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_13,inverse(a))) = multiply(iPr_def_11,inverse(a)),
inference(superposition,[status(thm)],[c_283,c_459]) ).
tcf(c_11241,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_10,inverse(a))) = multiply(a,inverse(a)),
inference(superposition,[status(thm)],[c_648,c_459]) ).
tcf(c_11318,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_10,inverse(a))) = iPr_def_13,
inference(demodulation,[status(thm)],[c_11241,c_335]) ).
tcf(c_11319,plain,
multiply(iPr_def_11,inverse(a)) = greatest_lower_bound(iPr_def_13,inverse(a)),
inference(demodulation,[status(thm)],[c_11222,c_284]) ).
tcf(c_24249,plain,
greatest_lower_bound(iPr_def_10,least_upper_bound(iPr_def_13,multiply(inverse(iPr_def_11),a))) = least_upper_bound(iPr_def_13,a),
inference(superposition,[status(thm)],[c_5779,c_586]) ).
tcf(c_24281,plain,
greatest_lower_bound(iPr_def_10,multiply(inverse(iPr_def_11),a)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_24249,c_282,c_383,c_931]) ).
tcf(c_35117,plain,
greatest_lower_bound(iPr_def_13,multiply(iPr_def_10,inverse(multiply(inverse(iPr_def_11),a)))) = multiply(iPr_def_10,inverse(multiply(inverse(iPr_def_11),a))),
inference(superposition,[status(thm)],[c_24281,c_459]) ).
tcf(c_35156,plain,
greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,inverse(a))) = iPr_def_13,
inference(demodulation,[status(thm)],[c_35117,c_435,c_494,c_1276,c_3905,c_11318]) ).
tcf(c_37142,plain,
greatest_lower_bound(iPr_def_13,multiply(inverse(iPr_def_10),multiply(iPr_def_10,inverse(a)))) = multiply(inverse(iPr_def_10),iPr_def_13),
inference(superposition,[status(thm)],[c_35156,c_361]) ).
tcf(c_37170,plain,
greatest_lower_bound(iPr_def_13,inverse(a)) = inverse(iPr_def_10),
inference(demodulation,[status(thm)],[c_37142,c_291,c_1254]) ).
tcf(c_41766,plain,
multiply(iPr_def_11,inverse(a)) = inverse(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_11319,c_37170]) ).
tcf(c_41790,plain,
multiply(inverse(iPr_def_11),inverse(iPr_def_10)) = inverse(a),
inference(superposition,[status(thm)],[c_41766,c_291]) ).
tcf(c_41836,plain,
inverse(a) = inverse(iPr_def_12),
inference(demodulation,[status(thm)],[c_41790,c_183,c_1291]) ).
tcf(c_43455,plain,
inverse(inverse(iPr_def_12)) = a,
inference(superposition,[status(thm)],[c_41836,c_184]) ).
tcf(c_43468,plain,
a = iPr_def_12,
inference(demodulation,[status(thm)],[c_43455,c_184]) ).
tcf(c_43551,plain,
iPr_def_12 != iPr_def_12,
inference(demodulation,[status(thm)],[c_165,c_43468]) ).
tcf(c_43552,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_43551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 13:57:49 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running UEQ theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 14.45/4.75 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 14.45/4.75 % SZS status Started for theBenchmark.p
% 14.45/4.75 % SZS status Unsatisfiable for theBenchmark.p
% 14.45/4.75
% 14.45/4.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.45/4.75
% 14.45/4.75 % ------ iProver source info
% 14.45/4.75
% 14.45/4.75 % git: date: 2026-07-19 20:42:38 +0200
% 14.45/4.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.45/4.75 % git: non_committed_changes: false
% 14.45/4.75
% 14.45/4.75 % ------ Parsing...% successful
% 14.45/4.75
% 14.45/4.75
% 14.45/4.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.45/4.75
% 14.45/4.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 14.45/4.75
% 14.45/4.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.45/4.75
% 14.45/4.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 14.45/4.75 % ------ Proving...
% 14.45/4.75 % ------ Problem Properties
% 14.45/4.75
% 14.45/4.75 %
% 14.45/4.75 % clauses 25
% 14.45/4.75 % conjectures 1
% 14.45/4.75 % EPR 2
% 14.45/4.75 % Horn 25
% 14.45/4.75 % unary 25
% 14.45/4.75 % binary 0
% 14.45/4.75 % lits 25
% 14.45/4.75 % lits eq 25
% 14.45/4.75 % fd_pure 0
% 14.45/4.75 % fd_pseudo 0
% 14.45/4.75 % fd_cond 0
% 14.45/4.75 % fd_pseudo_cond 0
% 14.45/4.75 % AC symbols 2
% 14.45/4.75
% 14.45/4.75 % ------ Input Options Time Limit: Unbounded
% 14.45/4.75
% 14.45/4.75
% 14.45/4.75 % ------
% 14.45/4.75 % Current options:
% 14.45/4.75 % ------
% 14.45/4.75
% 14.45/4.75
% 14.45/4.75 %
% 14.45/4.75
% 14.45/4.75 % ------ Proving...
% 14.45/4.75 %
% 14.45/4.75
% 14.45/4.75 % SZS status Unsatisfiable for theBenchmark.p
% 14.45/4.75
% 14.45/4.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.45/4.76
% 14.45/4.76
%------------------------------------------------------------------------------