%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP181-3 : 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 : n012.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 01:31:42 PM UTC 2026
% Result : Unsatisfiable 10.63s 6.26s
% Output : CNFRefutation 10.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 20
% Syntax : Number of formulae : 196 ( 196 unt; 4 def)
% Number of atoms : 461 ( 195 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 8 ( 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; 4 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 127 !; 0 ?; 96 :)
% 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(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,axiom,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_1) ).
fof(f18,axiom,
least_upper_bound(a,c) = least_upper_bound(b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_2) ).
fof(f20,axiom,
! [X0,X1] : inverse(least_upper_bound(X0,X1)) = greatest_lower_bound(inverse(X0),inverse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12x_4) ).
fof(f21,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p12x) ).
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_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_80,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_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_83,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_84,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(b,c),
inference(cnf_transformation,[],[f17]) ).
tcf(c_85,plain,
least_upper_bound(a,c) = least_upper_bound(b,c),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(inverse(X0),inverse(X1)) = inverse(least_upper_bound(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
tcf(c_88,negated_conjecture,
a != b,
inference(cnf_transformation,[],[f21]) ).
tcf(c_152,definition,
iPr_def_10 = least_upper_bound(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_153,definition,
iPr_def_11 = least_upper_bound(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_154,definition,
iPr_def_12 = greatest_lower_bound(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_155,definition,
iPr_def_13 = greatest_lower_bound(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_156,negated_conjecture,
a != b,
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_157,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_158,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_159,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_160,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_83]) ).
tcf(c_162,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_163,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_80]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_168,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_169,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_170,plain,
! [X0: $i,X1: $i] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(inverse(X0),inverse(X1)) = inverse(least_upper_bound(X0,X1)),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_174,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_85,c_153,c_152]) ).
tcf(c_175,plain,
iPr_def_12 = iPr_def_13,
inference(demodulation,[status(thm)],[c_84,c_155,c_154]) ).
tcf(c_263,plain,
least_upper_bound(b,c) = iPr_def_10,
inference(demodulation,[status(thm)],[c_153,c_174]) ).
tcf(c_264,plain,
least_upper_bound(c,b) = iPr_def_10,
inference(theory_normalisation,[status(thm)],[c_263,c_169,c_171,c_168,c_170]) ).
tcf(c_265,plain,
greatest_lower_bound(b,c) = iPr_def_12,
inference(demodulation,[status(thm)],[c_155,c_175]) ).
tcf(c_266,plain,
greatest_lower_bound(c,b) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_265,c_169,c_171,c_168,c_170]) ).
tcf(c_267,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_169,c_171]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_158,c_157]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_275,c_159]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(X0,multiply(X1,X0)) = multiply(greatest_lower_bound(identity,X1),X0),
inference(superposition,[status(thm)],[c_159,c_160]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(multiply(X0,X1),identity),
inference(superposition,[status(thm)],[c_158,c_160]) ).
tcf(c_285,plain,
! [X0: $i,X1: $i] : multiply(greatest_lower_bound(X0,inverse(X1)),X1) = greatest_lower_bound(identity,multiply(X0,X1)),
inference(demodulation,[status(thm)],[c_282,c_171]) ).
tcf(c_296,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_158,c_162]) ).
tcf(c_299,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_158,c_162]) ).
tcf(c_302,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_299,c_171]) ).
tcf(c_308,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(superposition,[status(thm)],[c_158,c_163]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(demodulation,[status(thm)],[c_308,c_170]) ).
tcf(c_318,plain,
least_upper_bound(a,iPr_def_12) = a,
inference(superposition,[status(thm)],[c_154,c_165]) ).
tcf(c_322,plain,
least_upper_bound(c,iPr_def_12) = c,
inference(superposition,[status(thm)],[c_266,c_165]) ).
tcf(c_326,plain,
least_upper_bound(iPr_def_12,c) = c,
inference(demodulation,[status(thm)],[c_322,c_170]) ).
tcf(c_327,plain,
least_upper_bound(iPr_def_12,a) = a,
inference(demodulation,[status(thm)],[c_318,c_170]) ).
tcf(c_365,plain,
greatest_lower_bound(iPr_def_12,a) = iPr_def_12,
inference(superposition,[status(thm)],[c_327,c_164]) ).
tcf(c_379,plain,
greatest_lower_bound(iPr_def_12,c) = iPr_def_12,
inference(superposition,[status(thm)],[c_326,c_164]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] : greatest_lower_bound(multiply(X0,X1),multiply(X2,X1)) = multiply(greatest_lower_bound(X2,X0),X1),
inference(superposition,[status(thm)],[c_171,c_160]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] : greatest_lower_bound(inverse(X0),inverse(X1)) = inverse(least_upper_bound(X1,X0)),
inference(superposition,[status(thm)],[c_172,c_171]) ).
tcf(c_499,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_158,c_276]) ).
tcf(c_501,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_276,c_276]) ).
tcf(c_512,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_499,c_501]) ).
tcf(c_1238,plain,
greatest_lower_bound(identity,multiply(inverse(a),c)) = multiply(inverse(a),iPr_def_12),
inference(superposition,[status(thm)],[c_154,c_296]) ).
tcf(c_1248,plain,
greatest_lower_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),iPr_def_12),
inference(superposition,[status(thm)],[c_266,c_296]) ).
tcf(c_1256,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_12),a)) = multiply(inverse(iPr_def_12),iPr_def_12),
inference(superposition,[status(thm)],[c_365,c_296]) ).
tcf(c_1258,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_12),c)) = multiply(inverse(iPr_def_12),iPr_def_12),
inference(superposition,[status(thm)],[c_379,c_296]) ).
tcf(c_1282,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_12),c)) = identity,
inference(demodulation,[status(thm)],[c_1258,c_158]) ).
tcf(c_1283,plain,
greatest_lower_bound(identity,multiply(inverse(iPr_def_12),a)) = identity,
inference(demodulation,[status(thm)],[c_1256,c_158]) ).
tcf(c_1329,plain,
least_upper_bound(identity,multiply(inverse(a),iPr_def_12)) = identity,
inference(superposition,[status(thm)],[c_1238,c_165]) ).
tcf(c_1336,plain,
least_upper_bound(identity,multiply(inverse(c),iPr_def_12)) = identity,
inference(superposition,[status(thm)],[c_1248,c_165]) ).
tcf(c_1437,plain,
greatest_lower_bound(identity,multiply(inverse(b),c)) = multiply(inverse(b),iPr_def_12),
inference(superposition,[status(thm)],[c_266,c_302]) ).
tcf(c_1438,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(greatest_lower_bound(X0,X1)),greatest_lower_bound(X0,greatest_lower_bound(X2,X1))) = greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(X0,X1)),X2)),
inference(superposition,[status(thm)],[c_267,c_302]) ).
tcf(c_1445,plain,
greatest_lower_bound(identity,multiply(inverse(a),iPr_def_12)) = multiply(inverse(a),iPr_def_12),
inference(superposition,[status(thm)],[c_365,c_302]) ).
tcf(c_1449,plain,
multiply(inverse(multiply(inverse(a),c)),multiply(inverse(a),iPr_def_12)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(a),c)),identity)),
inference(superposition,[status(thm)],[c_1238,c_302]) ).
tcf(c_1450,plain,
multiply(inverse(multiply(inverse(c),b)),multiply(inverse(c),iPr_def_12)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(c),b)),identity)),
inference(superposition,[status(thm)],[c_1248,c_302]) ).
tcf(c_1453,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(iPr_def_12),a)),identity)) = multiply(inverse(multiply(inverse(iPr_def_12),a)),identity),
inference(superposition,[status(thm)],[c_1283,c_302]) ).
tcf(c_1454,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(iPr_def_12),c)),identity)) = multiply(inverse(multiply(inverse(iPr_def_12),c)),identity),
inference(superposition,[status(thm)],[c_1282,c_302]) ).
tcf(c_1480,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(iPr_def_12),c))) = inverse(multiply(inverse(iPr_def_12),c)),
inference(demodulation,[status(thm)],[c_1454,c_512]) ).
tcf(c_1481,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(iPr_def_12),a))) = inverse(multiply(inverse(iPr_def_12),a)),
inference(demodulation,[status(thm)],[c_1453,c_512]) ).
tcf(c_1490,plain,
multiply(inverse(multiply(inverse(c),b)),multiply(inverse(c),iPr_def_12)) = greatest_lower_bound(identity,inverse(multiply(inverse(c),b))),
inference(demodulation,[status(thm)],[c_1450,c_512]) ).
tcf(c_1491,plain,
multiply(inverse(multiply(inverse(a),c)),multiply(inverse(a),iPr_def_12)) = greatest_lower_bound(identity,inverse(multiply(inverse(a),c))),
inference(demodulation,[status(thm)],[c_1449,c_512]) ).
tcf(c_1510,plain,
least_upper_bound(identity,multiply(inverse(b),iPr_def_12)) = identity,
inference(superposition,[status(thm)],[c_1437,c_165]) ).
tcf(c_1511,plain,
multiply(inverse(multiply(inverse(b),c)),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(b),c)),identity)),
inference(superposition,[status(thm)],[c_1437,c_302]) ).
tcf(c_1516,plain,
multiply(inverse(multiply(inverse(b),c)),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(identity,inverse(multiply(inverse(b),c))),
inference(demodulation,[status(thm)],[c_1511,c_512]) ).
tcf(c_1535,plain,
! [X0: $i] : greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(a),iPr_def_12),X0)) = greatest_lower_bound(multiply(inverse(a),iPr_def_12),X0),
inference(superposition,[status(thm)],[c_1445,c_169]) ).
tcf(c_1651,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(a),iPr_def_12)),identity)) = multiply(inverse(multiply(inverse(a),iPr_def_12)),identity),
inference(superposition,[status(thm)],[c_1329,c_311]) ).
tcf(c_1652,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(c),iPr_def_12)),identity)) = multiply(inverse(multiply(inverse(c),iPr_def_12)),identity),
inference(superposition,[status(thm)],[c_1336,c_311]) ).
tcf(c_1680,plain,
least_upper_bound(identity,inverse(multiply(inverse(c),iPr_def_12))) = inverse(multiply(inverse(c),iPr_def_12)),
inference(demodulation,[status(thm)],[c_1652,c_512]) ).
tcf(c_1681,plain,
least_upper_bound(identity,inverse(multiply(inverse(a),iPr_def_12))) = inverse(multiply(inverse(a),iPr_def_12)),
inference(demodulation,[status(thm)],[c_1651,c_512]) ).
tcf(c_1860,plain,
least_upper_bound(identity,multiply(inverse(multiply(inverse(b),iPr_def_12)),identity)) = multiply(inverse(multiply(inverse(b),iPr_def_12)),identity),
inference(superposition,[status(thm)],[c_1510,c_311]) ).
tcf(c_1865,plain,
least_upper_bound(identity,inverse(multiply(inverse(b),iPr_def_12))) = inverse(multiply(inverse(b),iPr_def_12)),
inference(demodulation,[status(thm)],[c_1860,c_512]) ).
tcf(c_1932,plain,
multiply(inverse(inverse(multiply(inverse(iPr_def_12),c))),inverse(multiply(inverse(iPr_def_12),c))) = greatest_lower_bound(identity,multiply(inverse(inverse(multiply(inverse(iPr_def_12),c))),identity)),
inference(superposition,[status(thm)],[c_1480,c_302]) ).
tcf(c_1937,plain,
multiply(inverse(iPr_def_12),multiply(c,inverse(multiply(inverse(iPr_def_12),c)))) = identity,
inference(demodulation,[status(thm)],[c_1932,c_157,c_501,c_512,c_1282]) ).
tcf(c_1942,plain,
multiply(inverse(inverse(multiply(inverse(iPr_def_12),a))),inverse(multiply(inverse(iPr_def_12),a))) = greatest_lower_bound(identity,multiply(inverse(inverse(multiply(inverse(iPr_def_12),a))),identity)),
inference(superposition,[status(thm)],[c_1481,c_302]) ).
tcf(c_1947,plain,
multiply(inverse(iPr_def_12),multiply(a,inverse(multiply(inverse(iPr_def_12),a)))) = identity,
inference(demodulation,[status(thm)],[c_1942,c_157,c_501,c_512,c_1283]) ).
tcf(c_1970,plain,
multiply(inverse(inverse(multiply(inverse(c),b))),greatest_lower_bound(identity,inverse(multiply(inverse(c),b)))) = multiply(inverse(c),iPr_def_12),
inference(superposition,[status(thm)],[c_1490,c_276]) ).
tcf(c_1994,plain,
multiply(inverse(c),multiply(b,greatest_lower_bound(identity,inverse(multiply(inverse(c),b))))) = multiply(inverse(c),iPr_def_12),
inference(demodulation,[status(thm)],[c_1970,c_157,c_501]) ).
tcf(c_2051,plain,
multiply(inverse(inverse(multiply(inverse(a),c))),greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))) = multiply(inverse(a),iPr_def_12),
inference(superposition,[status(thm)],[c_1491,c_276]) ).
tcf(c_2062,plain,
greatest_lower_bound(multiply(inverse(a),iPr_def_12),greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))) = multiply(greatest_lower_bound(identity,inverse(multiply(inverse(a),c))),multiply(inverse(a),iPr_def_12)),
inference(superposition,[status(thm)],[c_1491,c_278]) ).
tcf(c_2075,plain,
multiply(inverse(a),multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(a),c))))) = multiply(inverse(a),iPr_def_12),
inference(demodulation,[status(thm)],[c_2051,c_157,c_501]) ).
tcf(c_2079,plain,
multiply(greatest_lower_bound(identity,inverse(multiply(inverse(a),c))),multiply(inverse(a),iPr_def_12)) = greatest_lower_bound(multiply(inverse(a),iPr_def_12),inverse(multiply(inverse(a),c))),
inference(demodulation,[status(thm)],[c_2062,c_267,c_1535]) ).
tcf(c_2173,plain,
multiply(inverse(inverse(multiply(inverse(b),c))),greatest_lower_bound(identity,inverse(multiply(inverse(b),c)))) = multiply(inverse(b),iPr_def_12),
inference(superposition,[status(thm)],[c_1516,c_276]) ).
tcf(c_2184,plain,
greatest_lower_bound(multiply(inverse(b),iPr_def_12),greatest_lower_bound(identity,inverse(multiply(inverse(b),c)))) = multiply(greatest_lower_bound(identity,inverse(multiply(inverse(b),c))),multiply(inverse(b),iPr_def_12)),
inference(superposition,[status(thm)],[c_1516,c_278]) ).
tcf(c_2197,plain,
multiply(inverse(b),multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(b),c))))) = multiply(inverse(b),iPr_def_12),
inference(demodulation,[status(thm)],[c_2173,c_157,c_501]) ).
tcf(c_2201,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),iPr_def_12),inverse(multiply(inverse(b),c)))) = multiply(greatest_lower_bound(identity,inverse(multiply(inverse(b),c))),multiply(inverse(b),iPr_def_12)),
inference(demodulation,[status(thm)],[c_2184,c_267]) ).
tcf(c_2878,plain,
multiply(inverse(inverse(multiply(inverse(c),iPr_def_12))),inverse(multiply(inverse(c),iPr_def_12))) = least_upper_bound(identity,multiply(inverse(inverse(multiply(inverse(c),iPr_def_12))),identity)),
inference(superposition,[status(thm)],[c_1680,c_311]) ).
tcf(c_2885,plain,
multiply(inverse(c),multiply(iPr_def_12,inverse(multiply(inverse(c),iPr_def_12)))) = identity,
inference(demodulation,[status(thm)],[c_2878,c_157,c_501,c_512,c_1336]) ).
tcf(c_2890,plain,
multiply(inverse(inverse(multiply(inverse(a),iPr_def_12))),inverse(multiply(inverse(a),iPr_def_12))) = least_upper_bound(identity,multiply(inverse(inverse(multiply(inverse(a),iPr_def_12))),identity)),
inference(superposition,[status(thm)],[c_1681,c_311]) ).
tcf(c_2897,plain,
multiply(inverse(a),multiply(iPr_def_12,inverse(multiply(inverse(a),iPr_def_12)))) = identity,
inference(demodulation,[status(thm)],[c_2890,c_157,c_501,c_512,c_1329]) ).
tcf(c_2914,plain,
multiply(inverse(inverse(multiply(inverse(b),iPr_def_12))),inverse(multiply(inverse(b),iPr_def_12))) = least_upper_bound(identity,multiply(inverse(inverse(multiply(inverse(b),iPr_def_12))),identity)),
inference(superposition,[status(thm)],[c_1865,c_311]) ).
tcf(c_2921,plain,
multiply(inverse(b),multiply(iPr_def_12,inverse(multiply(inverse(b),iPr_def_12)))) = identity,
inference(demodulation,[status(thm)],[c_2914,c_157,c_501,c_512,c_1510]) ).
tcf(c_2960,plain,
multiply(c,inverse(multiply(inverse(iPr_def_12),c))) = multiply(inverse(inverse(iPr_def_12)),identity),
inference(superposition,[status(thm)],[c_1937,c_276]) ).
tcf(c_2986,plain,
multiply(c,inverse(multiply(inverse(iPr_def_12),c))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2960,c_501,c_512]) ).
tcf(c_3005,plain,
multiply(a,inverse(multiply(inverse(iPr_def_12),a))) = multiply(inverse(inverse(iPr_def_12)),identity),
inference(superposition,[status(thm)],[c_1947,c_276]) ).
tcf(c_3031,plain,
multiply(a,inverse(multiply(inverse(iPr_def_12),a))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3005,c_501,c_512]) ).
tcf(c_3115,plain,
multiply(b,greatest_lower_bound(identity,inverse(multiply(inverse(c),b)))) = multiply(inverse(inverse(c)),multiply(inverse(c),iPr_def_12)),
inference(superposition,[status(thm)],[c_1994,c_276]) ).
tcf(c_3141,plain,
multiply(b,greatest_lower_bound(identity,inverse(multiply(inverse(c),b)))) = multiply(c,multiply(inverse(c),iPr_def_12)),
inference(demodulation,[status(thm)],[c_3115,c_501]) ).
tcf(c_3783,plain,
multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))) = multiply(inverse(inverse(a)),multiply(inverse(a),iPr_def_12)),
inference(superposition,[status(thm)],[c_2075,c_276]) ).
tcf(c_3810,plain,
multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))) = multiply(a,multiply(inverse(a),iPr_def_12)),
inference(demodulation,[status(thm)],[c_3783,c_501]) ).
tcf(c_3818,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))),greatest_lower_bound(multiply(inverse(a),iPr_def_12),inverse(multiply(inverse(a),c)))) = multiply(inverse(a),iPr_def_12),
inference(superposition,[status(thm)],[c_2079,c_276]) ).
tcf(c_4770,plain,
multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(b),c)))) = multiply(inverse(inverse(b)),multiply(inverse(b),iPr_def_12)),
inference(superposition,[status(thm)],[c_2197,c_276]) ).
tcf(c_4797,plain,
multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(b),c)))) = multiply(b,multiply(inverse(b),iPr_def_12)),
inference(demodulation,[status(thm)],[c_4770,c_501]) ).
tcf(c_4805,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(inverse(b),c)))),greatest_lower_bound(identity,greatest_lower_bound(multiply(inverse(b),iPr_def_12),inverse(multiply(inverse(b),c))))) = multiply(inverse(b),iPr_def_12),
inference(superposition,[status(thm)],[c_2201,c_276]) ).
tcf(c_4832,plain,
greatest_lower_bound(identity,multiply(inverse(greatest_lower_bound(identity,inverse(multiply(inverse(b),c)))),multiply(inverse(b),iPr_def_12))) = multiply(inverse(b),iPr_def_12),
inference(demodulation,[status(thm)],[c_4805,c_1438]) ).
tcf(c_5854,plain,
multiply(iPr_def_12,inverse(multiply(inverse(c),iPr_def_12))) = multiply(inverse(inverse(c)),identity),
inference(superposition,[status(thm)],[c_2885,c_276]) ).
tcf(c_5882,plain,
multiply(iPr_def_12,inverse(multiply(inverse(c),iPr_def_12))) = c,
inference(demodulation,[status(thm)],[c_5854,c_501,c_512]) ).
tcf(c_5891,plain,
multiply(iPr_def_12,inverse(multiply(inverse(a),iPr_def_12))) = multiply(inverse(inverse(a)),identity),
inference(superposition,[status(thm)],[c_2897,c_276]) ).
tcf(c_5919,plain,
multiply(iPr_def_12,inverse(multiply(inverse(a),iPr_def_12))) = a,
inference(demodulation,[status(thm)],[c_5891,c_501,c_512]) ).
tcf(c_5972,plain,
multiply(iPr_def_12,inverse(multiply(inverse(b),iPr_def_12))) = multiply(inverse(inverse(b)),identity),
inference(superposition,[status(thm)],[c_2921,c_276]) ).
tcf(c_6000,plain,
multiply(iPr_def_12,inverse(multiply(inverse(b),iPr_def_12))) = b,
inference(demodulation,[status(thm)],[c_5972,c_501,c_512]) ).
tcf(c_6098,plain,
inverse(multiply(inverse(iPr_def_12),c)) = multiply(inverse(c),iPr_def_12),
inference(superposition,[status(thm)],[c_2986,c_276]) ).
tcf(c_6122,plain,
multiply(c,multiply(inverse(c),iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_2986,c_6098]) ).
tcf(c_6132,plain,
inverse(multiply(inverse(iPr_def_12),a)) = multiply(inverse(a),iPr_def_12),
inference(superposition,[status(thm)],[c_3031,c_276]) ).
tcf(c_6156,plain,
multiply(a,multiply(inverse(a),iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_3031,c_6132]) ).
tcf(c_6217,plain,
multiply(b,greatest_lower_bound(identity,inverse(multiply(inverse(c),b)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3141,c_6122]) ).
tcf(c_6224,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(c),b))) = multiply(inverse(b),iPr_def_12),
inference(superposition,[status(thm)],[c_6217,c_276]) ).
tcf(c_6248,plain,
multiply(b,multiply(inverse(b),iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_6217,c_6224]) ).
tcf(c_6789,plain,
multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(a),c)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_3810,c_6156]) ).
tcf(c_6796,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(a),c))) = multiply(inverse(c),iPr_def_12),
inference(superposition,[status(thm)],[c_6789,c_276]) ).
tcf(c_6823,plain,
greatest_lower_bound(multiply(inverse(a),iPr_def_12),inverse(multiply(inverse(a),c))) = multiply(multiply(inverse(c),iPr_def_12),multiply(inverse(a),iPr_def_12)),
inference(demodulation,[status(thm)],[c_2079,c_6796]) ).
tcf(c_6825,plain,
multiply(inverse(multiply(inverse(a),c)),multiply(inverse(a),iPr_def_12)) = multiply(inverse(c),iPr_def_12),
inference(demodulation,[status(thm)],[c_1491,c_6796]) ).
tcf(c_6827,plain,
greatest_lower_bound(multiply(inverse(a),iPr_def_12),inverse(multiply(inverse(a),c))) = multiply(inverse(c),multiply(iPr_def_12,multiply(inverse(a),iPr_def_12))),
inference(demodulation,[status(thm)],[c_6823,c_157]) ).
tcf(c_6828,plain,
multiply(inverse(multiply(inverse(c),iPr_def_12)),multiply(inverse(c),multiply(iPr_def_12,multiply(inverse(a),iPr_def_12)))) = multiply(inverse(a),iPr_def_12),
inference(light_normalisation,[status(thm)],[c_3818,c_6796,c_6827]) ).
tcf(c_7140,plain,
multiply(c,greatest_lower_bound(identity,inverse(multiply(inverse(b),c)))) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_4797,c_6248]) ).
tcf(c_7147,plain,
greatest_lower_bound(identity,inverse(multiply(inverse(b),c))) = multiply(inverse(c),iPr_def_12),
inference(superposition,[status(thm)],[c_7140,c_276]) ).
tcf(c_7175,plain,
multiply(inverse(multiply(inverse(b),c)),multiply(inverse(b),iPr_def_12)) = multiply(inverse(c),iPr_def_12),
inference(demodulation,[status(thm)],[c_1516,c_7147]) ).
tcf(c_7177,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(inverse(c),iPr_def_12)),multiply(inverse(b),iPr_def_12))) = multiply(inverse(b),iPr_def_12),
inference(light_normalisation,[status(thm)],[c_4832,c_7147]) ).
tcf(c_7185,plain,
multiply(inverse(multiply(inverse(multiply(inverse(c),iPr_def_12)),multiply(inverse(b),iPr_def_12))),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(identity,multiply(inverse(multiply(inverse(multiply(inverse(c),iPr_def_12)),multiply(inverse(b),iPr_def_12))),identity)),
inference(superposition,[status(thm)],[c_7177,c_302]) ).
tcf(c_7193,plain,
multiply(inverse(multiply(inverse(multiply(inverse(c),iPr_def_12)),multiply(inverse(b),iPr_def_12))),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(identity,inverse(multiply(inverse(multiply(inverse(c),iPr_def_12)),multiply(inverse(b),iPr_def_12)))),
inference(demodulation,[status(thm)],[c_7185,c_512]) ).
tcf(c_8180,plain,
inverse(multiply(inverse(c),iPr_def_12)) = multiply(inverse(iPr_def_12),c),
inference(superposition,[status(thm)],[c_5882,c_276]) ).
tcf(c_8207,plain,
multiply(multiply(inverse(iPr_def_12),c),multiply(inverse(c),multiply(iPr_def_12,multiply(inverse(a),iPr_def_12)))) = multiply(inverse(a),iPr_def_12),
inference(demodulation,[status(thm)],[c_6828,c_8180]) ).
tcf(c_8210,plain,
multiply(inverse(iPr_def_12),multiply(c,multiply(inverse(c),multiply(iPr_def_12,multiply(inverse(a),iPr_def_12))))) = multiply(inverse(a),iPr_def_12),
inference(demodulation,[status(thm)],[c_8207,c_157]) ).
tcf(c_8218,plain,
inverse(multiply(inverse(a),iPr_def_12)) = multiply(inverse(iPr_def_12),a),
inference(superposition,[status(thm)],[c_5919,c_276]) ).
tcf(c_8242,plain,
multiply(iPr_def_12,multiply(inverse(iPr_def_12),a)) = a,
inference(demodulation,[status(thm)],[c_5919,c_8218]) ).
tcf(c_8364,plain,
inverse(multiply(inverse(b),iPr_def_12)) = multiply(inverse(iPr_def_12),b),
inference(superposition,[status(thm)],[c_6000,c_276]) ).
tcf(c_8388,plain,
multiply(iPr_def_12,multiply(inverse(iPr_def_12),b)) = b,
inference(demodulation,[status(thm)],[c_6000,c_8364]) ).
tcf(c_9284,plain,
multiply(greatest_lower_bound(identity,inverse(multiply(inverse(a),c))),multiply(inverse(a),iPr_def_12)) = greatest_lower_bound(multiply(inverse(a),iPr_def_12),multiply(inverse(c),iPr_def_12)),
inference(superposition,[status(thm)],[c_6825,c_278]) ).
tcf(c_9303,plain,
multiply(inverse(c),multiply(iPr_def_12,multiply(inverse(a),iPr_def_12))) = multiply(inverse(iPr_def_10),iPr_def_12),
inference(demodulation,[status(thm)],[c_9284,c_157,c_152,c_405,c_412,c_6796]) ).
tcf(c_9936,plain,
multiply(multiply(inverse(c),iPr_def_12),multiply(inverse(b),c)) = greatest_lower_bound(identity,multiply(identity,multiply(inverse(b),c))),
inference(superposition,[status(thm)],[c_7147,c_285]) ).
tcf(c_9938,plain,
multiply(inverse(c),multiply(iPr_def_12,multiply(inverse(b),c))) = multiply(inverse(b),iPr_def_12),
inference(demodulation,[status(thm)],[c_9936,c_159,c_157,c_1437]) ).
tcf(c_9960,plain,
multiply(greatest_lower_bound(identity,inverse(multiply(inverse(b),c))),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(multiply(inverse(b),iPr_def_12),multiply(inverse(c),iPr_def_12)),
inference(superposition,[status(thm)],[c_7175,c_278]) ).
tcf(c_9979,plain,
multiply(inverse(c),multiply(iPr_def_12,multiply(inverse(b),iPr_def_12))) = multiply(inverse(iPr_def_10),iPr_def_12),
inference(demodulation,[status(thm)],[c_9960,c_172,c_170,c_160,c_157,c_264,c_7147]) ).
tcf(c_10084,plain,
multiply(inverse(multiply(multiply(inverse(iPr_def_12),c),multiply(inverse(b),iPr_def_12))),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(identity,inverse(multiply(multiply(inverse(iPr_def_12),c),multiply(inverse(b),iPr_def_12)))),
inference(light_normalisation,[status(thm)],[c_7193,c_8180]) ).
tcf(c_10085,plain,
multiply(inverse(multiply(inverse(iPr_def_12),multiply(c,multiply(inverse(b),iPr_def_12)))),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(identity,inverse(multiply(inverse(iPr_def_12),multiply(c,multiply(inverse(b),iPr_def_12))))),
inference(superposition,[status(thm)],[c_157,c_10084]) ).
tcf(c_12062,plain,
multiply(inverse(iPr_def_12),multiply(c,multiply(inverse(iPr_def_10),iPr_def_12))) = multiply(inverse(a),iPr_def_12),
inference(light_normalisation,[status(thm)],[c_8210,c_9303]) ).
tcf(c_12069,plain,
multiply(inverse(inverse(iPr_def_12)),multiply(inverse(a),iPr_def_12)) = multiply(c,multiply(inverse(iPr_def_10),iPr_def_12)),
inference(superposition,[status(thm)],[c_12062,c_276]) ).
tcf(c_12097,plain,
multiply(c,multiply(inverse(iPr_def_10),iPr_def_12)) = multiply(iPr_def_12,multiply(inverse(a),iPr_def_12)),
inference(demodulation,[status(thm)],[c_12069,c_501]) ).
tcf(c_14806,plain,
multiply(inverse(inverse(c)),multiply(inverse(b),iPr_def_12)) = multiply(iPr_def_12,multiply(inverse(b),c)),
inference(superposition,[status(thm)],[c_9938,c_276]) ).
tcf(c_14836,plain,
multiply(c,multiply(inverse(b),iPr_def_12)) = multiply(iPr_def_12,multiply(inverse(b),c)),
inference(demodulation,[status(thm)],[c_14806,c_501]) ).
tcf(c_14941,plain,
multiply(inverse(inverse(c)),multiply(inverse(iPr_def_10),iPr_def_12)) = multiply(iPr_def_12,multiply(inverse(b),iPr_def_12)),
inference(superposition,[status(thm)],[c_9979,c_276]) ).
tcf(c_14971,plain,
multiply(iPr_def_12,multiply(inverse(a),iPr_def_12)) = multiply(iPr_def_12,multiply(inverse(b),iPr_def_12)),
inference(demodulation,[status(thm)],[c_14941,c_501,c_12097]) ).
tcf(c_14974,plain,
multiply(inverse(multiply(inverse(iPr_def_12),multiply(iPr_def_12,multiply(inverse(b),c)))),multiply(inverse(b),iPr_def_12)) = greatest_lower_bound(identity,inverse(multiply(inverse(iPr_def_12),multiply(iPr_def_12,multiply(inverse(b),c))))),
inference(light_normalisation,[status(thm)],[c_10085,c_14836]) ).
tcf(c_14984,plain,
multiply(inverse(inverse(multiply(inverse(iPr_def_12),multiply(iPr_def_12,multiply(inverse(b),c))))),greatest_lower_bound(identity,inverse(multiply(inverse(iPr_def_12),multiply(iPr_def_12,multiply(inverse(b),c)))))) = multiply(inverse(b),iPr_def_12),
inference(superposition,[status(thm)],[c_14974,c_276]) ).
tcf(c_15014,plain,
multiply(inverse(a),iPr_def_12) = multiply(inverse(b),iPr_def_12),
inference(demodulation,[status(thm)],[c_14984,c_157,c_276,c_501,c_6122,c_7147,c_14971]) ).
tcf(c_15020,plain,
inverse(multiply(inverse(a),iPr_def_12)) = multiply(inverse(iPr_def_12),b),
inference(demodulation,[status(thm)],[c_8364,c_15014]) ).
tcf(c_15031,plain,
multiply(inverse(iPr_def_12),a) = multiply(inverse(iPr_def_12),b),
inference(demodulation,[status(thm)],[c_15020,c_8218]) ).
tcf(c_15034,plain,
multiply(iPr_def_12,multiply(inverse(iPr_def_12),a)) = b,
inference(demodulation,[status(thm)],[c_8388,c_15031]) ).
tcf(c_15036,plain,
a = b,
inference(demodulation,[status(thm)],[c_15034,c_8242]) ).
tcf(c_15037,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15036,c_156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP181-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 14:00:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running UEQ theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 10.63/6.26 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 10.63/6.26 % SZS status Started for theBenchmark.p
% 10.63/6.26 % SZS status Unsatisfiable for theBenchmark.p
% 10.63/6.26
% 10.63/6.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.63/6.26
% 10.63/6.26 % ------ iProver source info
% 10.63/6.26
% 10.63/6.26 % git: date: 2026-07-19 20:42:38 +0200
% 10.63/6.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.63/6.26 % git: non_committed_changes: false
% 10.63/6.26
% 10.63/6.26 % ------ Parsing...% successful
% 10.63/6.26
% 10.63/6.26
% 10.63/6.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.63/6.26
% 10.63/6.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.63/6.26
% 10.63/6.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.63/6.26
% 10.63/6.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.63/6.26 % ------ Proving...
% 10.63/6.26 % ------ Problem Properties
% 10.63/6.26
% 10.63/6.26 %
% 10.63/6.26 % clauses 24
% 10.63/6.26 % conjectures 1
% 10.63/6.26 % EPR 3
% 10.63/6.26 % Horn 24
% 10.63/6.26 % unary 24
% 10.63/6.26 % binary 0
% 10.63/6.26 % lits 24
% 10.63/6.26 % lits eq 24
% 10.63/6.26 % fd_pure 0
% 10.63/6.26 % fd_pseudo 0
% 10.63/6.26 % fd_cond 0
% 10.63/6.26 % fd_pseudo_cond 0
% 10.63/6.26 % AC symbols 2
% 10.63/6.26
% 10.63/6.26 % ------ Input Options Time Limit: Unbounded
% 10.63/6.26
% 10.63/6.26
% 10.63/6.26 % ------
% 10.63/6.26 % Current options:
% 10.63/6.26 % ------
% 10.63/6.26
% 10.63/6.26
% 10.63/6.26 %
% 10.63/6.26
% 10.63/6.26 % ------ Proving...
% 10.63/6.26 %
% 10.63/6.26
% 10.63/6.26 % SZS status Unsatisfiable for theBenchmark.p
% 10.63/6.26
% 10.63/6.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.63/6.26
% 10.63/6.26
%------------------------------------------------------------------------------