%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP303-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 01:32:46 PM UTC 2026
% Result : Unsatisfiable 8.85s 19.54s
% Output : CNFRefutation 8.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 37
% Syntax : Number of formulae : 525 ( 117 unt; 10 def)
% Number of atoms : 2181 ( 994 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 912 ( 321 ~; 591 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 101 !; 0 ?; 87 :)
% 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,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = inverse(sk_c4)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
multiply(sk_c6,sk_c7) = sk_c5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
sk_c5 = multiply(sk_c6,sk_c7),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X1,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| sk_c5 != multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(reorient_equations,[],[f47]) ).
tcf(c_74,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_77,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_81,negated_conjecture,
multiply(sk_c6,sk_c7) = sk_c5,
inference(cnf_transformation,[],[f14]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_98,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X3,sk_c5) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(global_subsumption_just,[status(thm)],[c_98,c_81,c_98]) ).
tcf(c_104,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(renaming,[status(thm)],[c_103]) ).
tcf(c_312,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_104]) ).
tcf(c_313,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_104]) ).
tcf(c_314,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_104]) ).
tcf(c_315,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_104]) ).
tcf(c_316,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c7,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_104]) ).
tcf(c_317,definition,
iPr_def_14 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_318,definition,
iPr_def_15 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_319,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_320,definition,
iPr_def_17 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_321,definition,
iPr_def_18 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_322,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_323,definition,
iPr_def_20 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_324,definition,
iPr_def_21 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_325,definition,
iPr_def_22 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_326,definition,
iPr_def_23 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_327,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_316,c_317]) ).
tcf(c_328,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_315]) ).
tcf(c_329,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_314]) ).
tcf(c_330,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_313]) ).
tcf(c_331,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_312]) ).
tcf(c_332,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97,c_319,c_318]) ).
tcf(c_333,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96,c_320]) ).
tcf(c_334,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_321]) ).
tcf(c_335,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94,c_322]) ).
tcf(c_336,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93,c_323]) ).
tcf(c_337,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_338,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_339,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_340,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89,c_324]) ).
tcf(c_341,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_342,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_343,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_344,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85,c_325]) ).
tcf(c_345,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_346,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_347,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_348,negated_conjecture,
iPr_def_23 = sk_c5,
inference(demodulation,[status(thm)],[c_81,c_326]) ).
tcf(c_349,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_350,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_351,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_352,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_353,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_354,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_543,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_334,c_335]) ).
tcf(c_591,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_336,c_317]) ).
tcf(c_610,plain,
multiply(sk_c4,iPr_def_23) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_318,c_348]) ).
tcf(c_617,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_333,c_323]) ).
tcf(c_618,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_332,c_323]) ).
tcf(c_651,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_340,c_317]) ).
tcf(c_681,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_341,c_317]) ).
tcf(c_683,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_341,c_337]) ).
tcf(c_708,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_342,c_317]) ).
tcf(c_709,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_342,c_338]) ).
tcf(c_727,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_14 != X0 )
| ( sk_c5 != X0 ) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_739,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_343,c_339]) ).
tcf(c_740,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_343,c_317]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i] :
( ( sk_c5 = X0 )
| ( sk_c5 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_758,plain,
! [X0: $i] :
( ( sk_c5 = X0 )
| ( sk_c5 != sk_c5 )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_757]) ).
tcf(c_759,plain,
sk_c5 = sk_c5,
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_768,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_344,c_323]) ).
tcf(c_772,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_344,c_332]) ).
tcf(c_791,plain,
( ( sk_c5 = iPr_def_23 )
| ( iPr_def_23 != sk_c5 )
| ( sk_c5 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_758]) ).
tcf(c_799,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_345,c_323]) ).
tcf(c_816,plain,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_14 != iPr_def_23 )
| ( sk_c5 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_727]) ).
tcf(c_837,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(iPr_def_18,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_346,c_317]) ).
tcf(c_882,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_23 != X0 )
| ( iPr_def_14 != X0 ) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_883,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_23 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_882]) ).
tcf(c_887,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_890,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_346,c_325]) ).
tcf(c_891,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_343,c_325]) ).
tcf(c_892,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_342,c_325]) ).
tcf(c_893,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_341,c_325]) ).
tcf(c_894,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_340,c_325]) ).
tcf(c_895,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_339,c_325]) ).
tcf(c_896,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_338,c_325]) ).
tcf(c_897,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_337,c_325]) ).
tcf(c_898,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_336,c_325]) ).
tcf(c_940,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_345,c_326]) ).
tcf(c_942,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_333,c_326]) ).
tcf(c_943,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_332,c_326]) ).
tcf(c_951,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c6,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_337,c_326]) ).
tcf(c_1000,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_353]) ).
tcf(c_1001,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_1008,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_23 = X0 )
| ( iPr_def_23 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_1011,plain,
! [X0: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != sk_c5 )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_887]) ).
tcf(c_1013,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_322,c_75]) ).
tcf(c_1014,plain,
multiply(iPr_def_17,sk_c4) = identity,
inference(superposition,[status(thm)],[c_320,c_75]) ).
tcf(c_1015,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_324,c_75]) ).
tcf(c_1016,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_319,c_75]) ).
tcf(c_1037,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_347,c_325]) ).
tcf(c_1038,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c6 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_347,c_346]) ).
tcf(c_1108,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_349,c_348]) ).
tcf(c_1141,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_350,c_348]) ).
tcf(c_1152,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1141,c_1108]) ).
tcf(c_1153,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1141,c_326]) ).
tcf(c_1174,plain,
( ( iPr_def_23 = iPr_def_23 )
| ( iPr_def_23 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_1011]) ).
tcf(c_1177,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_351,c_348]) ).
tcf(c_1226,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_23 != sk_c5 )
| ( iPr_def_14 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_882]) ).
tcf(c_1242,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_352,c_348]) ).
tcf(c_1260,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1242,c_1177]) ).
tcf(c_1292,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_327,c_348]) ).
tcf(c_1325,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_22 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_325,c_328]) ).
tcf(c_1326,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_74,c_328]) ).
tcf(c_1327,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_75,c_328]) ).
tcf(c_1345,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_22 )
| ( sk_c7 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_1325,c_324]) ).
tcf(c_1473,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,iPr_def_23) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_329,c_348]) ).
tcf(c_1485,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_15 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_610,c_1473]) ).
tcf(c_1486,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_17 )
| ( sk_c6 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1485,c_320]) ).
tcf(c_1522,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_323,c_330]) ).
tcf(c_1523,plain,
( ~ iPr_def_11
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_74,c_330]) ).
tcf(c_1524,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_75,c_330]) ).
tcf(c_1534,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_16 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_1522,c_319]) ).
tcf(c_1617,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c7) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_317,c_331]) ).
tcf(c_1618,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_18 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_321,c_331]) ).
tcf(c_1619,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_323,c_331]) ).
tcf(c_1620,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_74,c_331]) ).
tcf(c_1631,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1619,c_319]) ).
tcf(c_1635,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_19 )
| ( sk_c7 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_1618,c_322]) ).
tcf(c_1705,plain,
! [X0: $i] :
( ( iPr_def_14 = X0 )
| ( iPr_def_14 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1001]) ).
tcf(c_1706,plain,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c6 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1705]) ).
tcf(c_1737,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_321,c_76]) ).
tcf(c_1739,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_325,c_76]) ).
tcf(c_1742,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_75,c_76]) ).
tcf(c_1745,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1013,c_76]) ).
tcf(c_1746,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1014,c_76]) ).
tcf(c_1747,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1015,c_76]) ).
tcf(c_1748,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1016,c_76]) ).
tcf(c_1754,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1748,c_74]) ).
tcf(c_1755,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1747,c_74]) ).
tcf(c_1756,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1746,c_74]) ).
tcf(c_1757,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1745,c_74]) ).
tcf(c_1786,plain,
! [X0: $i] :
( ( iPr_def_23 = X0 )
| ( iPr_def_23 != iPr_def_23 )
| ( X0 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1008]) ).
tcf(c_1788,plain,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_23 != iPr_def_23 )
| ( sk_c6 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1786]) ).
tcf(c_1836,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_543,c_326]) ).
tcf(c_1839,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_543,c_323]) ).
tcf(c_2005,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_683,c_326]) ).
tcf(c_2218,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_739,c_709]) ).
tcf(c_2320,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_772,c_333]) ).
tcf(c_2425,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_16 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1038,c_543]) ).
tcf(c_2431,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1038,c_326]) ).
tcf(c_2432,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1038,c_323]) ).
tcf(c_2688,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_332,c_591]) ).
tcf(c_3111,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1152,c_1292]) ).
tcf(c_3162,plain,
multiply(iPr_def_16,iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_323,c_1754]) ).
tcf(c_3177,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_325,c_1755]) ).
tcf(c_3190,plain,
multiply(iPr_def_17,iPr_def_15) = iPr_def_23,
inference(superposition,[status(thm)],[c_610,c_1756]) ).
tcf(c_3213,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_617,c_1754]) ).
tcf(c_3214,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3213,c_3162]) ).
tcf(c_3224,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c2,multiply(iPr_def_16,X0)) = multiply(iPr_def_20,X0) ) ),
inference(superposition,[status(thm)],[c_618,c_76]) ).
tcf(c_3225,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_618,c_1754]) ).
tcf(c_3226,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3225,c_3162]) ).
tcf(c_3288,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_344,c_651]) ).
tcf(c_3294,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3288,c_3177]) ).
tcf(c_3331,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_543,c_681]) ).
tcf(c_3334,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_345,c_681]) ).
tcf(c_3341,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3334,c_3177]) ).
tcf(c_3388,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_14 )
| ( inverse(iPr_def_21) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_708,c_331]) ).
tcf(c_3453,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_14 )
| ( inverse(iPr_def_21) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_740,c_331]) ).
tcf(c_3526,plain,
multiply(iPr_def_19,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_321,c_1757]) ).
tcf(c_3597,plain,
( ( iPr_def_14 = iPr_def_20 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_3294,c_336]) ).
tcf(c_3709,plain,
( ( iPr_def_14 = iPr_def_20 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_3341,c_337]) ).
tcf(c_3820,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_20,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_2218,c_1015]) ).
tcf(c_4184,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_14 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_3709,c_3597]) ).
tcf(c_4282,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_768,c_1754]) ).
tcf(c_4283,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4282,c_3162]) ).
tcf(c_4346,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_799,c_1754]) ).
tcf(c_4347,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_4346,c_3162]) ).
tcf(c_4426,plain,
( ( sk_c6 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_14 )
| ( inverse(iPr_def_18) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_837,c_331]) ).
tcf(c_4547,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_890,c_1755]) ).
tcf(c_4548,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4547,c_3177]) ).
tcf(c_4708,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_892,c_1755]) ).
tcf(c_4709,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4708,c_3177]) ).
tcf(c_4726,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_893,c_1755]) ).
tcf(c_4727,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_4726,c_3177]) ).
tcf(c_4800,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_894,c_1755]) ).
tcf(c_4801,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_4800,c_3177]) ).
tcf(c_4812,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_895,c_1755]) ).
tcf(c_4813,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4812,c_3177]) ).
tcf(c_4824,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_896,c_1755]) ).
tcf(c_4825,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4824,c_3177]) ).
tcf(c_4836,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_897,c_1755]) ).
tcf(c_4837,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4836,c_3177]) ).
tcf(c_4848,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_898,c_1755]) ).
tcf(c_4849,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4848,c_3177]) ).
tcf(c_4926,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_22,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_337,c_940]) ).
tcf(c_5195,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_335,c_942]) ).
tcf(c_5196,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_18) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_334,c_942]) ).
tcf(c_5232,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_336,c_943]) ).
tcf(c_5237,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5232,c_3162]) ).
tcf(c_5524,plain,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c5 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_727]) ).
tcf(c_7047,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1037,c_1755]) ).
tcf(c_7048,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_7047,c_3177]) ).
tcf(c_8678,plain,
multiply(sk_c3,iPr_def_23) = multiply(iPr_def_18,sk_c7),
inference(superposition,[status(thm)],[c_326,c_1737]) ).
tcf(c_9215,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_22,sk_c6),
inference(superposition,[status(thm)],[c_317,c_1739]) ).
tcf(c_10324,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1742,c_74]) ).
tcf(c_10331,plain,
multiply(inverse(sk_c6),iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_326,c_10324]) ).
tcf(c_10334,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_74,c_10324]) ).
tcf(c_10335,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_75,c_10324]) ).
tcf(c_10437,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1756,c_10324]) ).
tcf(c_10438,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1755,c_10324]) ).
tcf(c_10439,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1754,c_10324]) ).
tcf(c_10462,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_10324,c_10324]) ).
tcf(c_10913,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_354]) ).
tcf(c_11000,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c6 )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_10331,c_1473]) ).
tcf(c_11127,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_10335,c_10462]) ).
tcf(c_11145,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_11127,c_10334]) ).
tcf(c_12140,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_2320,c_345]) ).
tcf(c_13729,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_10437,c_10324]) ).
tcf(c_13730,plain,
multiply(sk_c4,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_10437,c_11127]) ).
tcf(c_14806,plain,
inverse(iPr_def_17) = sk_c4,
inference(demodulation,[status(thm)],[c_13730,c_11127]) ).
tcf(c_14810,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_23) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_2005,c_13729]) ).
tcf(c_14811,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_23) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1153,c_13729]) ).
tcf(c_14816,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_5196,c_13729]) ).
tcf(c_14817,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_5195,c_13729]) ).
tcf(c_14822,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_14817,c_610]) ).
tcf(c_14825,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_14816,c_610]) ).
tcf(c_14831,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_14811,c_610]) ).
tcf(c_14834,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_14810,c_610]) ).
tcf(c_14980,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_14822,c_323]) ).
tcf(c_15378,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_14825,c_951]) ).
tcf(c_15418,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_14825,c_323]) ).
tcf(c_15517,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_15378,c_3162]) ).
tcf(c_16943,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_14831,c_1177]) ).
tcf(c_17090,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_14834,c_739]) ).
tcf(c_17091,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_14834,c_709]) ).
tcf(c_17845,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_16943,c_1292]) ).
tcf(c_19109,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_345,c_317]) ).
tcf(c_19110,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_344,c_317]) ).
tcf(c_19215,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_341,c_19109]) ).
tcf(c_19257,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_340,c_19110]) ).
tcf(c_19297,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c6 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_347,c_346]) ).
tcf(c_19460,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_352,c_348]) ).
tcf(c_19747,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_324,c_75]) ).
tcf(c_19826,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_323,c_330]) ).
tcf(c_19843,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_16 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_19826,c_319]) ).
tcf(c_19900,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_323,c_331]) ).
tcf(c_19917,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_19900,c_319]) ).
tcf(c_20362,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_19747,c_76]) ).
tcf(c_20363,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_20362,c_74]) ).
tcf(c_21130,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_325,c_20363]) ).
tcf(c_21188,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_19215,c_21130]) ).
tcf(c_21228,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_21188,c_341]) ).
tcf(c_22204,plain,
multiply(sk_c1,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_10438,c_75]) ).
tcf(c_22211,plain,
multiply(sk_c1,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_10438,c_11127]) ).
tcf(c_22235,plain,
( ( identity = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_894,c_22204]) ).
tcf(c_22236,plain,
( ( identity = iPr_def_22 )
| ( sk_c6 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_893,c_22204]) ).
tcf(c_22237,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_892,c_22204]) ).
tcf(c_22238,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_891,c_22204]) ).
tcf(c_22310,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_19257,c_21130]) ).
tcf(c_22341,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_19 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_22310,c_19460]) ).
tcf(c_22351,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_22310,c_340]) ).
tcf(c_22394,plain,
inverse(iPr_def_21) = sk_c1,
inference(demodulation,[status(thm)],[c_22211,c_11127]) ).
tcf(c_22396,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( inverse(iPr_def_20) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_17091,c_22394]) ).
tcf(c_22397,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( inverse(iPr_def_20) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_17090,c_22394]) ).
tcf(c_22399,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_20) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_2218,c_22394]) ).
tcf(c_22774,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_22351,c_21228]) ).
tcf(c_22946,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_12140,c_772]) ).
tcf(c_24107,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22236,c_22235]) ).
tcf(c_24124,plain,
( ( identity = iPr_def_22 )
| ( multiply(inverse(iPr_def_17),iPr_def_23) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_22236,c_10331]) ).
tcf(c_24194,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_24124,c_610,c_14806]) ).
tcf(c_24726,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22238,c_22237]) ).
tcf(c_24994,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_22946,c_4926]) ).
tcf(c_25027,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_24994,c_3162]) ).
tcf(c_25117,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_17 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_24107,c_74]) ).
tcf(c_25169,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_24194,c_22237]) ).
tcf(c_27090,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_24726,c_11145]) ).
tcf(c_27092,plain,
! [X0: $i] :
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_24726,c_74]) ).
tcf(c_27137,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_25169,c_11145]) ).
tcf(c_27139,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_25169,c_74]) ).
tcf(c_27154,plain,
multiply(sk_c2,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_10439,c_75]) ).
tcf(c_27160,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_10439,c_10324]) ).
tcf(c_27161,plain,
multiply(sk_c2,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_10439,c_11127]) ).
tcf(c_27177,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1839,c_27154]) ).
tcf(c_27178,plain,
( ( identity = iPr_def_20 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_618,c_27154]) ).
tcf(c_27535,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_27177,c_24726]) ).
tcf(c_27539,plain,
! [X0: $i] :
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_27177,c_74]) ).
tcf(c_27662,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( identity = iPr_def_20 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_27178,c_333]) ).
tcf(c_28191,plain,
inverse(iPr_def_16) = sk_c2,
inference(demodulation,[status(thm)],[c_27161,c_11127]) ).
tcf(c_28294,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_16 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_27535,c_2425]) ).
tcf(c_29729,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( identity = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_27662,c_323]) ).
tcf(c_29742,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_29729,c_27154]) ).
tcf(c_29968,plain,
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1326,c_11145]) ).
tcf(c_30015,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_342,c_29968]) ).
tcf(c_30016,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_341,c_29968]) ).
tcf(c_30017,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_340,c_29968]) ).
tcf(c_30398,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_29742,c_24107]) ).
tcf(c_30598,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_30398,c_22946]) ).
tcf(c_30863,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_30598,c_4184]) ).
tcf(c_31526,plain,
( ~ iPr_def_11
| ( sk_c6 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1523,c_11145]) ).
tcf(c_31571,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_11
| ( identity != iPr_def_22 )
| ( sk_c7 != sk_c6 ) ),
inference(superposition,[status(thm)],[c_345,c_31526]) ).
tcf(c_31572,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11
| ( identity != iPr_def_22 )
| ( sk_c7 != sk_c6 ) ),
inference(superposition,[status(thm)],[c_344,c_31526]) ).
tcf(c_32157,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1620,c_11145]) ).
tcf(c_32201,plain,
( ( sk_c6 = iPr_def_22 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_19 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_347,c_32157]) ).
tcf(c_32203,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_343,c_32157]) ).
tcf(c_32204,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_10
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_342,c_32157]) ).
tcf(c_33513,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_28294,c_22399]) ).
tcf(c_33517,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_33513,c_28191]) ).
tcf(c_35336,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_16) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_2425,c_27090]) ).
tcf(c_35339,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c2 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_35336,c_28191]) ).
tcf(c_35386,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c1 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_35339,c_33517]) ).
tcf(c_35539,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_35386,c_324]) ).
tcf(c_35540,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c2 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_35539,c_28191]) ).
tcf(c_35593,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c1 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_35540,c_33517]) ).
tcf(c_35603,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_35540,c_2432]) ).
tcf(c_35623,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_35603,c_3177]) ).
tcf(c_36525,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_35623,c_1836]) ).
tcf(c_36565,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_20,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_35623,c_317]) ).
tcf(c_36574,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c6 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_36525,c_3162]) ).
tcf(c_36963,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_36574,c_1038]) ).
tcf(c_37216,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_36963,c_1260]) ).
tcf(c_37355,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_14980,c_27154]) ).
tcf(c_37370,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( inverse(iPr_def_20) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_37355,c_11145]) ).
tcf(c_37757,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_37216,c_27090]) ).
tcf(c_37760,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_37216,c_27535]) ).
tcf(c_38491,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_15418,c_27154]) ).
tcf(c_38506,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( inverse(iPr_def_20) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_38491,c_11145]) ).
tcf(c_38508,plain,
! [X0: $i] :
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_38491,c_74]) ).
tcf(c_38705,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_37760,c_22399]) ).
tcf(c_40917,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c1 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_37370,c_22397]) ).
tcf(c_40965,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( inverse(iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_40917,c_324]) ).
tcf(c_42201,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c1 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_40965,c_22397]) ).
tcf(c_42377,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_42201,c_325]) ).
tcf(c_42542,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c1 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_38506,c_22396]) ).
tcf(c_42590,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_42542,c_325]) ).
tcf(c_42838,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_30015,c_1345,c_4548,c_4709]) ).
tcf(c_42868,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_30016,c_1345,c_4347,c_4727]) ).
tcf(c_42874,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_17845,c_42868]) ).
tcf(c_42911,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_30017,c_1345,c_4283,c_4801]) ).
tcf(c_43332,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_38705,c_75]) ).
tcf(c_43333,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c1 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_38705,c_37757]) ).
tcf(c_43336,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c6) = identity ) ),
inference(light_normalisation,[status(thm)],[c_43332,c_9215]) ).
tcf(c_43368,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_43333,c_35593]) ).
tcf(c_43680,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_31571,c_1534,c_3214,c_4837]) ).
tcf(c_43710,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_31572,c_1534,c_3226,c_4849]) ).
tcf(c_44260,plain,
( ( sk_c6 = iPr_def_22 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_32201,c_1635,c_4548,c_7048]) ).
tcf(c_44268,plain,
( ( sk_c7 != identity )
| ( sk_c6 != iPr_def_21 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_32203,c_1635,c_32203,c_32204]) ).
tcf(c_44269,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != identity ) ),
inference(renaming,[status(thm)],[c_44268]) ).
tcf(c_44313,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_10
| ( identity != iPr_def_21 )
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_343,c_44269]) ).
tcf(c_44314,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_10
| ( identity != iPr_def_21 )
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_342,c_44269]) ).
tcf(c_47763,plain,
( ( sk_c6 != iPr_def_21 )
| ( identity != iPr_def_21 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_44313,c_1635,c_44313,c_44314]) ).
tcf(c_47764,plain,
( ~ iPr_def_10
| ( identity != iPr_def_21 )
| ( sk_c6 != iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_47763]) ).
tcf(c_48101,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_25117,c_940]) ).
tcf(c_49070,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_27092,c_2431]) ).
tcf(c_49439,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_27139,c_940]) ).
tcf(c_49595,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_27539,c_3820]) ).
tcf(c_50916,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_49595,c_35593]) ).
tcf(c_53474,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_23 )
| ( X0 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_10913]) ).
tcf(c_53479,plain,
( ( sk_c7 = sk_c6 )
| ( sk_c6 != iPr_def_23 )
| ( sk_c7 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_53474]) ).
tcf(c_60070,plain,
( ( iPr_def_18 = iPr_def_19 )
| ~ iPr_def_11
| ( iPr_def_16 != iPr_def_22 )
| ( sk_c7 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_19297,c_19843]) ).
tcf(c_62651,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_36565,c_27539]) ).
tcf(c_62755,plain,
( ( iPr_def_18 = iPr_def_19 )
| ~ iPr_def_10
| ( iPr_def_14 != iPr_def_21 )
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_62651,c_47764]) ).
tcf(c_63633,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_3224,c_27160]) ).
tcf(c_63678,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_63633,c_591]) ).
tcf(c_63692,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_63633,c_2688]) ).
tcf(c_65386,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_19917,c_1635,c_1631,c_4813,c_4825]) ).
tcf(c_65392,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_10
| ( iPr_def_14 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_22310,c_65386]) ).
tcf(c_65400,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_10
| ( iPr_def_16 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_343,c_65386]) ).
tcf(c_65401,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_10
| ( iPr_def_16 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_342,c_65386]) ).
tcf(c_65504,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_10913]) ).
tcf(c_65510,plain,
( ( sk_c7 = sk_c6 )
| ( sk_c6 != iPr_def_14 )
| ( sk_c7 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_65504]) ).
tcf(c_66988,plain,
( ( iPr_def_16 != iPr_def_21 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_65400,c_1635,c_65401,c_65400]) ).
tcf(c_66989,plain,
( ~ iPr_def_10
| ( iPr_def_16 != iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_66988]) ).
tcf(c_66994,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_10
| ( iPr_def_14 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_22774,c_66989]) ).
tcf(c_78753,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_340,c_42377]) ).
tcf(c_79029,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_341,c_42590]) ).
tcf(c_79040,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_42590,c_38508]) ).
tcf(c_79197,plain,
( ( iPr_def_15 = iPr_def_18 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_14 )
| ( inverse(iPr_def_22) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_79040,c_1617]) ).
tcf(c_79280,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_79040,c_325]) ).
tcf(c_79283,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_18 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_79040,c_342]) ).
tcf(c_79287,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_79040,c_317]) ).
tcf(c_83429,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c6 = identity ) ),
inference(superposition,[status(thm)],[c_43336,c_27092]) ).
tcf(c_83533,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c6 = iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_22341,c_348,c_883,c_1000,c_1174,c_1706,c_1788,c_5237,c_63678]) ).
tcf(c_85631,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_10462,c_75]) ).
tcf(c_85638,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_10462,c_11127]) ).
tcf(c_85639,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_85638,c_11127]) ).
tcf(c_85694,plain,
( ~ iPr_def_11
| ( sk_c7 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1524,c_85639]) ).
tcf(c_85695,plain,
( ~ iPr_def_13
| ( sk_c6 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1327,c_85639]) ).
tcf(c_85702,plain,
inverse(inverse(sk_c6)) = sk_c6,
inference(instantiation,[status(thm)],[c_85639]) ).
tcf(c_85741,plain,
inverse(sk_c2) = iPr_def_16,
inference(superposition,[status(thm)],[c_28191,c_85639]) ).
tcf(c_85783,plain,
sk_c6 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_78753,c_327,c_348,c_759,c_791,c_816,c_3294,c_11000,c_42911,c_43710,c_63692,c_63678,c_65392,c_65510,c_83533,c_85702]) ).
tcf(c_85856,plain,
( ~ iPr_def_10
| ( iPr_def_15 != iPr_def_21 )
| ( identity != iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_47764,c_85783]) ).
tcf(c_85879,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(demodulation,[status(thm)],[c_43680,c_85783]) ).
tcf(c_85885,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_13 ),
inference(demodulation,[status(thm)],[c_42868,c_85783]) ).
tcf(c_85971,plain,
multiply(inverse(iPr_def_15),iPr_def_23) = sk_c7,
inference(demodulation,[status(thm)],[c_10331,c_85783]) ).
tcf(c_85978,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_22,iPr_def_15),
inference(demodulation,[status(thm)],[c_9215,c_85783]) ).
tcf(c_86044,plain,
multiply(iPr_def_19,iPr_def_18) = iPr_def_15,
inference(demodulation,[status(thm)],[c_3526,c_85783]) ).
tcf(c_86065,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != iPr_def_15 )
| ( multiply(X0,iPr_def_15) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_330,c_85783]) ).
tcf(c_86067,plain,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_328,c_85783]) ).
tcf(c_86072,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_345,c_85783]) ).
tcf(c_86076,plain,
multiply(sk_c2,iPr_def_15) = iPr_def_20,
inference(demodulation,[status(thm)],[c_323,c_85783]) ).
tcf(c_86077,plain,
multiply(sk_c3,iPr_def_15) = iPr_def_18,
inference(demodulation,[status(thm)],[c_321,c_85783]) ).
tcf(c_86078,plain,
multiply(sk_c7,iPr_def_15) = iPr_def_14,
inference(demodulation,[status(thm)],[c_317,c_85783]) ).
tcf(c_86082,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_334,c_85783]) ).
tcf(c_86728,plain,
iPr_def_15 = iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_86072,c_327,c_348,c_759,c_791,c_816,c_1486,c_3111,c_3294,c_11000,c_25027,c_30863,c_42911,c_43710,c_48101,c_53479,c_63692,c_63678,c_65392,c_65510,c_66994,c_83533,c_85702,c_85885,c_85879]) ).
tcf(c_86793,plain,
inverse(iPr_def_15) = sk_c4,
inference(demodulation,[status(thm)],[c_14806,c_86728]) ).
tcf(c_86807,plain,
multiply(iPr_def_15,iPr_def_15) = iPr_def_23,
inference(demodulation,[status(thm)],[c_3190,c_86728]) ).
tcf(c_87013,plain,
iPr_def_18 = iPr_def_19,
inference(global_subsumption_just,[status(thm)],[c_3331,c_327,c_348,c_759,c_791,c_816,c_1260,c_2425,c_11000,c_35623,c_36574,c_43368,c_49070,c_50916,c_53479,c_60070,c_62755,c_83429,c_85702,c_85695]) ).
tcf(c_87151,plain,
inverse(sk_c3) = iPr_def_18,
inference(demodulation,[status(thm)],[c_322,c_87013]) ).
tcf(c_87204,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_79029,c_3341,c_11000,c_15517,c_27137,c_42874,c_43680,c_49439,c_53479,c_79197,c_85702]) ).
tcf(c_87240,plain,
multiply(iPr_def_18,iPr_def_18) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_86044,c_87013]) ).
tcf(c_87391,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c2) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_86076,c_86065]) ).
tcf(c_87392,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_18 )
| ( inverse(sk_c3) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_86077,c_86065]) ).
tcf(c_87403,plain,
( ~ iPr_def_11
| ( iPr_def_15 != iPr_def_18 )
| ( sk_c7 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_87392,c_87151]) ).
tcf(c_87407,plain,
( ~ iPr_def_11
| ( iPr_def_15 != iPr_def_16 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_87391,c_85741]) ).
tcf(c_87468,plain,
( ~ iPr_def_13
| ( identity != iPr_def_15 )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_75,c_86067]) ).
tcf(c_87501,plain,
( ~ iPr_def_13
| ( identity != iPr_def_15 ) ),
inference(ground_joinability,[status(thm)],[c_87468,c_85639]) ).
tcf(c_87697,plain,
( ( iPr_def_15 = iPr_def_18 )
| ~ iPr_def_11
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_79040,c_85694]) ).
tcf(c_87712,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_11
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_342,c_85694]) ).
tcf(c_87778,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_87712,c_4825,c_25169,c_86082,c_87407,c_87403,c_87697]) ).
tcf(c_87780,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_87778,c_25169,c_87403,c_87697,c_87778]) ).
tcf(c_87782,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( iPr_def_15 = iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_17845,c_87780]) ).
tcf(c_87783,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( iPr_def_14 != iPr_def_23 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1292,c_87780]) ).
tcf(c_87807,plain,
sk_c7 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_85971,c_610,c_86793]) ).
tcf(c_87810,plain,
multiply(iPr_def_15,iPr_def_15) = iPr_def_14,
inference(demodulation,[status(thm)],[c_86078,c_87807]) ).
tcf(c_87817,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_79283,c_87807]) ).
tcf(c_87820,plain,
( ( iPr_def_15 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(demodulation,[status(thm)],[c_42838,c_87807]) ).
tcf(c_87835,plain,
multiply(sk_c3,iPr_def_23) = multiply(iPr_def_18,iPr_def_15),
inference(demodulation,[status(thm)],[c_8678,c_87807]) ).
tcf(c_87843,plain,
multiply(sk_c1,iPr_def_15) = iPr_def_22,
inference(demodulation,[status(thm)],[c_325,c_87807]) ).
tcf(c_87844,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_342,c_87807]) ).
tcf(c_87884,plain,
iPr_def_14 = iPr_def_23,
inference(demodulation,[status(thm)],[c_86807,c_87810]) ).
tcf(c_87888,plain,
sk_c5 = iPr_def_14,
inference(demodulation,[status(thm)],[c_348,c_87884]) ).
tcf(c_88082,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_87782,c_327,c_1000,c_5524,c_87780,c_87888]) ).
tcf(c_88090,plain,
( iPr_def_12
| iPr_def_10
| ( iPr_def_15 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_88082,c_87820]) ).
tcf(c_88094,plain,
( ( iPr_def_15 = iPr_def_18 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_88090,c_327,c_348,c_759,c_791,c_816,c_1486,c_3294,c_11000,c_42911,c_43710,c_63692,c_63678,c_65392,c_65510,c_83533,c_85702,c_87204,c_88090]) ).
tcf(c_88095,plain,
( iPr_def_10
| ( iPr_def_15 = iPr_def_18 ) ),
inference(renaming,[status(thm)],[c_88094]) ).
tcf(c_88259,plain,
multiply(sk_c3,iPr_def_14) = multiply(iPr_def_18,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_87835,c_87884]) ).
tcf(c_88468,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_87817,c_79280]) ).
tcf(c_88475,plain,
( ( iPr_def_15 = iPr_def_18 )
| ( identity = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_88468,c_22204]) ).
tcf(c_88482,plain,
iPr_def_15 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_79287,c_85856,c_87844,c_88095,c_88475]) ).
tcf(c_88490,plain,
multiply(sk_c3,iPr_def_14) = multiply(iPr_def_15,iPr_def_15),
inference(demodulation,[status(thm)],[c_88259,c_88482]) ).
tcf(c_88499,plain,
inverse(sk_c3) = iPr_def_15,
inference(demodulation,[status(thm)],[c_87151,c_88482]) ).
tcf(c_88500,plain,
multiply(iPr_def_15,iPr_def_15) = iPr_def_15,
inference(demodulation,[status(thm)],[c_87240,c_88482]) ).
tcf(c_88519,plain,
iPr_def_14 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_88500,c_87810]) ).
tcf(c_88520,plain,
multiply(sk_c3,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_88490,c_87810]) ).
tcf(c_88530,plain,
( ~ iPr_def_13
| ( identity != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_87501,c_88519]) ).
tcf(c_88531,plain,
multiply(sk_c1,iPr_def_14) = iPr_def_22,
inference(demodulation,[status(thm)],[c_87843,c_88519]) ).
tcf(c_88535,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_22,iPr_def_14),
inference(demodulation,[status(thm)],[c_85978,c_88519]) ).
tcf(c_88536,plain,
sk_c7 = iPr_def_14,
inference(demodulation,[status(thm)],[c_87807,c_88519]) ).
tcf(c_88542,plain,
sk_c6 = iPr_def_14,
inference(demodulation,[status(thm)],[c_85783,c_88519]) ).
tcf(c_88572,plain,
inverse(sk_c3) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_88499,c_88519]) ).
tcf(c_88573,plain,
multiply(sk_c3,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_88572,c_85631]) ).
tcf(c_88577,plain,
identity = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_88573,c_88520]) ).
tcf(c_88582,plain,
! [X0: $i] : multiply(X0,iPr_def_14) = X0,
inference(demodulation,[status(thm)],[c_11127,c_88577]) ).
tcf(c_88644,plain,
inverse(iPr_def_21) != sk_c7,
inference(global_subsumption_just,[status(thm)],[c_3388,c_348,c_1000,c_1226,c_1635,c_3388,c_3453,c_5524,c_11000,c_65510,c_85702,c_87783,c_87888,c_88542,c_88536,c_88530,c_88577]) ).
tcf(c_88646,plain,
sk_c1 != iPr_def_14,
inference(light_normalisation,[status(thm)],[c_88644,c_22394,c_88536]) ).
tcf(c_88667,plain,
sk_c6 = iPr_def_22,
inference(global_subsumption_just,[status(thm)],[c_4426,c_348,c_1000,c_1226,c_5524,c_11000,c_44260,c_65510,c_85702,c_87783,c_87888,c_88542,c_88536,c_88530,c_88577]) ).
tcf(c_88669,plain,
iPr_def_14 = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_88667,c_88542]) ).
tcf(c_88691,plain,
multiply(sk_c1,iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_88531,c_88535,c_88669]) ).
tcf(c_88692,plain,
sk_c1 = iPr_def_14,
inference(demodulation,[status(thm)],[c_88691,c_88582]) ).
tcf(c_88693,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_88692,c_88646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP303-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/15.60 % Computer : n013.cluster.edu
% 0.10/15.60 % Model : x86_64 x86_64
% 0.10/15.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.60 % Memory : 8046.5625MB
% 0.10/15.60 % OS : Linux 6.8.0-71-generic
% 0.10/15.60 % CPULimit : 300
% 0.10/15.60 % WCLimit : 300
% 0.10/15.60 % DateTime : Wed Sep 23 14:24:43 UTC 2026
% 0.15/15.60 % CPUTime :
% 0.15/15.60 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/15.64 Running first-order theorem proving
% 0.15/15.64 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/15.65
% 0.15/15.65 % ======== iProver multi-core TPTP/SMT =========
% 0.15/15.65
% 0.15/15.65 % Detected problem language: tptp
% 0.15/15.66 % Proving...
% 8.85/19.54 % SZS status Started for theBenchmark.p
% 8.85/19.54 % SZS status Unsatisfiable for theBenchmark.p
% 8.85/19.54
% 8.85/19.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.85/19.54
% 8.85/19.54 % ------ iProver source info
% 8.85/19.54
% 8.85/19.54 % git: date: 2026-07-19 20:42:38 +0200
% 8.85/19.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.85/19.54 % git: non_committed_changes: false
% 8.85/19.54
% 8.85/19.54 % ------ Parsing...% successful
% 8.85/19.54
% 8.85/19.54
% 8.85/19.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.85/19.54
% 8.85/19.54 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.85/19.54
% 8.85/19.54 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.85/19.54
% 8.85/19.54 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.85/19.54 % ------ Proving...
% 8.85/19.54 % ------ Problem Properties
% 8.85/19.54
% 8.85/19.54 %
% 8.85/19.54 % clauses 39
% 8.85/19.54 % conjectures 26
% 8.85/19.54 % EPR 22
% 8.85/19.54 % Horn 18
% 8.85/19.54 % unary 14
% 8.85/19.54 % binary 20
% 8.85/19.54 % lits 71
% 8.85/19.54 % lits eq 63
% 8.85/19.54 % fd_pure 0
% 8.85/19.54 % fd_pseudo 0
% 8.85/19.54 % fd_cond 0
% 8.85/19.54 % fd_pseudo_cond 0
% 8.85/19.54 % AC symbols 0
% 8.85/19.54
% 8.85/19.54 % ------ Schedule dynamic 5 is on
% 8.85/19.54
% 8.85/19.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.85/19.54
% 8.85/19.54
% 8.85/19.54 % ------
% 8.85/19.54 % Current options:
% 8.85/19.54 % ------
% 8.85/19.54
% 8.85/19.54
% 8.85/19.54 %
% 8.85/19.54
% 8.85/19.54 % ------ Proving...
% 8.85/19.54 %
% 8.85/19.54
% 8.85/19.54 % SZS status Unsatisfiable for theBenchmark.p
% 8.85/19.54
% 8.85/19.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.85/19.56
% 8.85/19.56
%------------------------------------------------------------------------------