%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP167-1 : 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 : n026.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 5.82s 4.17s
% Output : CNFRefutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 116 ( 116 unt; 3 def)
% Number of atoms : 195 ( 115 equ)
% Maximal formula atoms : 1 ( 1 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 154 !; 0 ?; 118 :)
% 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(f10,axiom,
! [X0] : greatest_lower_bound(X0,X0) = X0,
file('/export/starexec/sandbox2/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/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(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(f17,axiom,
! [X0] : positive_part(X0) = least_upper_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_1) ).
fof(f18,axiom,
! [X0] : negative_part(X0) = greatest_lower_bound(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_2) ).
fof(f19,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_3) ).
fof(f20,axiom,
! [X2,X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lat4_4) ).
fof(f21,negated_conjecture,
a != multiply(positive_part(a),negative_part(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lat4) ).
fof(f22,plain,
a != multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)),
inference(definition_unfolding,[],[f21,f17,f18]) ).
tcf(c_69,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_74,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_75,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_76,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_77,plain,
! [X0: $i] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[],[f10]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f11]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[],[f12]) ).
tcf(c_81,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_82,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_84,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,[],[f19]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2)) = greatest_lower_bound(X0,least_upper_bound(X1,X2)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_86,negated_conjecture,
multiply(least_upper_bound(a,identity),greatest_lower_bound(a,identity)) != a,
inference(cnf_transformation,[],[f22]) ).
tcf(c_145,definition,
iPr_def_10 = least_upper_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_146,definition,
iPr_def_11 = greatest_lower_bound(a,identity),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_147,definition,
iPr_def_12 = multiply(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_148,negated_conjecture,
iPr_def_12 != a,
inference(demodulation,[status(thm)],[c_86,c_146,c_145,c_147]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_150,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_151,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_153,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_82]) ).
tcf(c_154,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_81]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_158,plain,
! [X0: $i] : greatest_lower_bound(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_159,plain,
! [X0: $i] : least_upper_bound(X0,X0) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_160,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_75]) ).
tcf(c_161,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_74]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(greatest_lower_bound(X0,X1),greatest_lower_bound(X0,X2)) = greatest_lower_bound(X0,least_upper_bound(X1,X2)),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_165,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_84]) ).
tcf(c_241,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_160,c_162]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,greatest_lower_bound(X0,X2)),
inference(superposition,[status(thm)],[c_161,c_163]) ).
tcf(c_248,plain,
greatest_lower_bound(a,iPr_def_10) = a,
inference(superposition,[status(thm)],[c_145,c_156]) ).
tcf(c_251,plain,
least_upper_bound(a,iPr_def_11) = a,
inference(superposition,[status(thm)],[c_146,c_157]) ).
tcf(c_253,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_162,c_156]) ).
tcf(c_255,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_163,c_157]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_150,c_149]) ).
tcf(c_264,plain,
! [X0: $i] : least_upper_bound(a,least_upper_bound(identity,X0)) = least_upper_bound(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_145,c_160]) ).
tcf(c_272,plain,
! [X0: $i] : greatest_lower_bound(a,greatest_lower_bound(identity,X0)) = greatest_lower_bound(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_146,c_161]) ).
tcf(c_283,plain,
! [X0: $i] : least_upper_bound(a,least_upper_bound(X0,identity)) = least_upper_bound(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_145,c_241]) ).
tcf(c_295,plain,
! [X0: $i] : greatest_lower_bound(a,greatest_lower_bound(X0,identity)) = greatest_lower_bound(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_146,c_242]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i,X2: $i] : least_upper_bound(X0,greatest_lower_bound(X1,greatest_lower_bound(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_242,c_157]) ).
tcf(c_354,plain,
! [X0: $i,X1: $i] : least_upper_bound(multiply(X0,X1),X1) = multiply(least_upper_bound(X0,identity),X1),
inference(superposition,[status(thm)],[c_151,c_153]) ).
tcf(c_547,plain,
! [X0: $i] : least_upper_bound(a,greatest_lower_bound(identity,X0)) = greatest_lower_bound(iPr_def_10,least_upper_bound(a,X0)),
inference(superposition,[status(thm)],[c_145,c_165]) ).
tcf(c_599,plain,
least_upper_bound(iPr_def_11,a) = a,
inference(theory_normalisation,[status(thm)],[c_251,c_160,c_162,c_161,c_163]) ).
tcf(c_600,plain,
greatest_lower_bound(iPr_def_10,a) = a,
inference(theory_normalisation,[status(thm)],[c_248,c_160,c_162,c_161,c_163]) ).
tcf(c_603,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_258,c_151]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,multiply(X1,X0)) = multiply(least_upper_bound(X1,identity),X0),
inference(theory_normalisation,[status(thm)],[c_354,c_160,c_162,c_161,c_163]) ).
tcf(c_726,plain,
! [X0: $i] : least_upper_bound(iPr_def_11,greatest_lower_bound(a,X0)) = greatest_lower_bound(a,least_upper_bound(iPr_def_11,X0)),
inference(superposition,[status(thm)],[c_599,c_165]) ).
tcf(c_839,plain,
! [X0: $i] : least_upper_bound(greatest_lower_bound(iPr_def_10,X0),a) = greatest_lower_bound(iPr_def_10,least_upper_bound(X0,a)),
inference(superposition,[status(thm)],[c_600,c_164]) ).
tcf(c_852,plain,
greatest_lower_bound(identity,iPr_def_10) = identity,
inference(superposition,[status(thm)],[c_145,c_253]) ).
tcf(c_888,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_150,c_603]) ).
tcf(c_890,plain,
multiply(inverse(iPr_def_10),iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_147,c_603]) ).
tcf(c_891,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_603,c_603]) ).
tcf(c_973,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(X0,identity)) = greatest_lower_bound(a,identity),
inference(superposition,[status(thm)],[c_253,c_272]) ).
tcf(c_991,plain,
least_upper_bound(identity,iPr_def_10) = least_upper_bound(a,identity),
inference(superposition,[status(thm)],[c_159,c_283]) ).
tcf(c_1049,plain,
greatest_lower_bound(identity,iPr_def_11) = greatest_lower_bound(a,identity),
inference(superposition,[status(thm)],[c_158,c_295]) ).
tcf(c_1071,plain,
! [X0: $i] : least_upper_bound(identity,greatest_lower_bound(iPr_def_11,X0)) = identity,
inference(superposition,[status(thm)],[c_272,c_298]) ).
tcf(c_1105,plain,
greatest_lower_bound(iPr_def_10,identity) = identity,
inference(theory_normalisation,[status(thm)],[c_852,c_160,c_162,c_161,c_163]) ).
tcf(c_1108,plain,
greatest_lower_bound(a,identity) = greatest_lower_bound(iPr_def_11,identity),
inference(theory_normalisation,[status(thm)],[c_1049,c_160,c_162,c_161,c_163]) ).
tcf(c_1109,plain,
greatest_lower_bound(iPr_def_11,identity) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1108,c_146]) ).
tcf(c_1116,plain,
least_upper_bound(a,identity) = least_upper_bound(iPr_def_10,identity),
inference(theory_normalisation,[status(thm)],[c_991,c_160,c_162,c_161,c_163]) ).
tcf(c_1117,plain,
least_upper_bound(iPr_def_10,identity) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1116,c_145]) ).
tcf(c_1127,plain,
! [X0: $i] : greatest_lower_bound(iPr_def_11,least_upper_bound(X0,identity)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_973,c_146]) ).
tcf(c_1146,plain,
! [X0: $i] : least_upper_bound(a,greatest_lower_bound(iPr_def_10,X0)) = greatest_lower_bound(iPr_def_10,least_upper_bound(X0,a)),
inference(theory_normalisation,[status(thm)],[c_839,c_160,c_162,c_161,c_163]) ).
tcf(c_1680,plain,
greatest_lower_bound(a,identity) = greatest_lower_bound(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_1105,c_295]) ).
tcf(c_1738,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_888,c_154]) ).
tcf(c_1844,plain,
! [X0: $i] : least_upper_bound(identity,greatest_lower_bound(X0,iPr_def_11)) = identity,
inference(superposition,[status(thm)],[c_163,c_1071]) ).
tcf(c_1865,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,greatest_lower_bound(iPr_def_11,X0)) = least_upper_bound(a,identity),
inference(superposition,[status(thm)],[c_1071,c_264]) ).
tcf(c_1887,plain,
greatest_lower_bound(iPr_def_11,iPr_def_10) = iPr_def_11,
inference(superposition,[status(thm)],[c_145,c_1127]) ).
tcf(c_1926,plain,
greatest_lower_bound(iPr_def_10,iPr_def_11) = iPr_def_11,
inference(theory_normalisation,[status(thm)],[c_1887,c_160,c_162,c_161,c_163]) ).
tcf(c_1947,plain,
greatest_lower_bound(a,identity) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1680,c_1926]) ).
tcf(c_1953,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,greatest_lower_bound(iPr_def_11,X0)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_1865,c_145]) ).
tcf(c_2005,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(inverse(inverse(X0)),X1)) = multiply(inverse(inverse(X0)),greatest_lower_bound(X1,identity)),
inference(theory_normalisation,[status(thm)],[c_1738,c_160,c_162,c_161,c_163]) ).
tcf(c_2006,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X0,X1)) = multiply(X0,greatest_lower_bound(X1,identity)),
inference(demodulation,[status(thm)],[c_2005,c_891]) ).
tcf(c_2189,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,greatest_lower_bound(X0,iPr_def_11)) = least_upper_bound(a,identity),
inference(superposition,[status(thm)],[c_1844,c_264]) ).
tcf(c_2290,plain,
! [X0: $i] : least_upper_bound(iPr_def_10,greatest_lower_bound(X0,iPr_def_11)) = iPr_def_10,
inference(superposition,[status(thm)],[c_163,c_1953]) ).
tcf(c_2379,plain,
least_upper_bound(a,identity) = iPr_def_10,
inference(demodulation,[status(thm)],[c_2189,c_2290]) ).
tcf(c_3056,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_891,c_603]) ).
tcf(c_3372,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_890,c_3056]) ).
tcf(c_14766,plain,
! [X0: $i] : least_upper_bound(a,greatest_lower_bound(identity,X0)) = greatest_lower_bound(iPr_def_10,least_upper_bound(X0,a)),
inference(superposition,[status(thm)],[c_162,c_547]) ).
tcf(c_14854,plain,
! [X0: $i] : least_upper_bound(a,greatest_lower_bound(identity,X0)) = least_upper_bound(a,greatest_lower_bound(iPr_def_10,X0)),
inference(demodulation,[status(thm)],[c_14766,c_1146]) ).
tcf(c_19030,plain,
! [X0: $i] : least_upper_bound(X0,multiply(a,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_2379,c_613]) ).
tcf(c_19032,plain,
! [X0: $i] : least_upper_bound(X0,multiply(iPr_def_10,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_1117,c_613]) ).
tcf(c_29021,plain,
least_upper_bound(iPr_def_11,greatest_lower_bound(a,multiply(a,iPr_def_11))) = greatest_lower_bound(a,multiply(iPr_def_10,iPr_def_11)),
inference(superposition,[status(thm)],[c_19030,c_726]) ).
tcf(c_29239,plain,
greatest_lower_bound(iPr_def_12,a) = iPr_def_12,
inference(demodulation,[status(thm)],[c_29021,c_163,c_1109,c_2006,c_3372,c_19030]) ).
tcf(c_29470,plain,
least_upper_bound(a,iPr_def_12) = a,
inference(superposition,[status(thm)],[c_29239,c_255]) ).
tcf(c_29541,plain,
least_upper_bound(iPr_def_12,a) = a,
inference(theory_normalisation,[status(thm)],[c_29470,c_160,c_162,c_161,c_163]) ).
tcf(c_30645,plain,
least_upper_bound(a,greatest_lower_bound(identity,multiply(iPr_def_10,a))) = greatest_lower_bound(iPr_def_10,multiply(iPr_def_10,a)),
inference(superposition,[status(thm)],[c_19032,c_547]) ).
tcf(c_30775,plain,
a = iPr_def_12,
inference(demodulation,[status(thm)],[c_30645,c_162,c_1947,c_2006,c_3372,c_14854,c_29541]) ).
tcf(c_31008,plain,
$false,
inference(superposition,[status(thm)],[c_30775,c_148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP167-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.78 % Computer : n026.cluster.edu
% 0.10/0.78 % Model : x86_64 x86_64
% 0.10/0.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.78 % Memory : 8046.5625MB
% 0.10/0.78 % OS : Linux 6.8.0-71-generic
% 0.10/0.78 % CPULimit : 300
% 0.10/0.78 % WCLimit : 300
% 0.10/0.78 % DateTime : Wed Sep 23 13:58:25 UTC 2026
% 0.10/0.78 % CPUTime :
% 0.10/0.78 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.82 Running UEQ theorem proving
% 0.15/0.82 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
% 0.15/0.83
% 0.15/0.83 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.83
% 0.15/0.83 % Detected problem language: tptp
% 0.15/0.85 % Proving...
% 5.82/4.17 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 5.82/4.17 % SZS status Started for theBenchmark.p
% 5.82/4.17 % SZS status Unsatisfiable for theBenchmark.p
% 5.82/4.17
% 5.82/4.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 5.82/4.17
% 5.82/4.17 % ------ iProver source info
% 5.82/4.17
% 5.82/4.17 % git: date: 2026-07-19 20:42:38 +0200
% 5.82/4.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 5.82/4.17 % git: non_committed_changes: false
% 5.82/4.17
% 5.82/4.17 % ------ Parsing...% successful
% 5.82/4.17
% 5.82/4.17
% 5.82/4.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 5.82/4.17
% 5.82/4.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 5.82/4.17
% 5.82/4.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 5.82/4.17
% 5.82/4.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 5.82/4.17 % ------ Proving...
% 5.82/4.17 % ------ Problem Properties
% 5.82/4.17
% 5.82/4.17 %
% 5.82/4.17 % clauses 21
% 5.82/4.17 % conjectures 1
% 5.82/4.17 % EPR 1
% 5.82/4.17 % Horn 21
% 5.82/4.17 % unary 21
% 5.82/4.17 % binary 0
% 5.82/4.17 % lits 21
% 5.82/4.17 % lits eq 21
% 5.82/4.17 % fd_pure 0
% 5.82/4.17 % fd_pseudo 0
% 5.82/4.17 % fd_cond 0
% 5.82/4.17 % fd_pseudo_cond 0
% 5.82/4.17 % AC symbols 2
% 5.82/4.17
% 5.82/4.17 % ------ Input Options Time Limit: Unbounded
% 5.82/4.17
% 5.82/4.17
% 5.82/4.17 % ------
% 5.82/4.17 % Current options:
% 5.82/4.17 % ------
% 5.82/4.17
% 5.82/4.17
% 5.82/4.17 %
% 5.82/4.17
% 5.82/4.17 % ------ Proving...
% 5.82/4.17 %
% 5.82/4.17
% 5.82/4.17 % SZS status Unsatisfiable for theBenchmark.p
% 5.82/4.17
% 5.82/4.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 5.82/4.17
% 5.82/4.17
%------------------------------------------------------------------------------