%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP344-1 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:17 PM UTC 2026
% Result : Unsatisfiable 10.68s 2.79s
% Output : CNFRefutation 15.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 32
% Syntax : Number of formulae : 497 ( 131 unt; 9 def)
% Number of atoms : 2000 ( 875 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 876 ( 345 ~; 531 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 111 !; 0 ?; 97 :)
% 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,
multiply(sk_c6,sk_c7) = sk_c5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c5 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c6 = inverse(sk_c3)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c5 = inverse(sk_c4)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = inverse(sk_c2) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = inverse(sk_c3)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c5 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c5 = multiply(sk_c4,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c6) != sk_c5
| inverse(X3) != sk_c5
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( sk_c5 != multiply(X3,sk_c6)
| sk_c5 != inverse(X3)
| sk_c6 != inverse(X2)
| sk_c7 != multiply(X2,sk_c6)
| sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1)
| sk_c7 != multiply(X0,sk_c6)
| inverse(X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(reorient_equations,[],[f38]) ).
tcf(c_70,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_73,negated_conjecture,
multiply(sk_c6,sk_c7) = sk_c5,
inference(cnf_transformation,[],[f5]) ).
tcf(c_74,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_75,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_76,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_77,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_78,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_79,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_80,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_81,negated_conjecture,
( ( multiply(sk_c4,sk_c6) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_83,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c3) = sk_c6 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c4,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_90,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c5 ) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_73,c_90]) ).
tcf(c_96,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c5 )
| ( inverse(X2) != sk_c6 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X3,sk_c6) != sk_c5 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(renaming,[status(thm)],[c_95]) ).
tcf(c_268,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_96]) ).
tcf(c_269,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_96]) ).
tcf(c_270,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_96]) ).
tcf(c_271,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_96]) ).
tcf(c_272,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_96]) ).
tcf(c_273,definition,
iPr_def_14 = multiply(sk_c4,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_274,definition,
iPr_def_15 = multiply(sk_c2,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_275,definition,
iPr_def_16 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_276,definition,
iPr_def_17 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_277,definition,
iPr_def_18 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_278,definition,
iPr_def_19 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_279,definition,
iPr_def_20 = multiply(sk_c1,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_280,definition,
iPr_def_21 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_281,definition,
iPr_def_22 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_282,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_272]) ).
tcf(c_283,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_271]) ).
tcf(c_284,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c6) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_270]) ).
tcf(c_285,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_269]) ).
tcf(c_286,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_268]) ).
tcf(c_287,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_89,c_274,c_273]) ).
tcf(c_288,negated_conjecture,
( ( iPr_def_16 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88,c_275]) ).
tcf(c_289,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87,c_276]) ).
tcf(c_290,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86,c_277]) ).
tcf(c_291,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_85,c_278]) ).
tcf(c_292,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_293,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_294,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_295,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_81,c_279]) ).
tcf(c_296,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_297,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_298,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_299,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_77,c_280]) ).
tcf(c_300,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_16 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_301,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_302,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_303,negated_conjecture,
iPr_def_22 = sk_c5,
inference(demodulation,[status(thm)],[c_73,c_281]) ).
tcf(c_304,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_305,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_310,plain,
sk_c6 = sk_c6,
inference(instantiation,[status(thm)],[c_304]) ).
tcf(c_459,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_287,c_303]) ).
tcf(c_466,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_288,c_303]) ).
tcf(c_488,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_291,c_303]) ).
tcf(c_500,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_488,c_459]) ).
tcf(c_503,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_292,c_303]) ).
tcf(c_514,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_503,c_466]) ).
tcf(c_533,plain,
multiply(sk_c2,iPr_def_22) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_274,c_303]) ).
tcf(c_551,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_17) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_289,c_279]) ).
tcf(c_571,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_293,c_279]) ).
tcf(c_590,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_295,c_303]) ).
tcf(c_601,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_296,c_303]) ).
tcf(c_640,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_299,c_303]) ).
tcf(c_656,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_640,c_590]) ).
tcf(c_664,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_300,c_303]) ).
tcf(c_679,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_664,c_601]) ).
tcf(c_686,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_503,c_281]) ).
tcf(c_687,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_19,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_488,c_281]) ).
tcf(c_688,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_289,c_281]) ).
tcf(c_697,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c6,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_294,c_281]) ).
tcf(c_747,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_280,c_71]) ).
tcf(c_748,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_276,c_71]) ).
tcf(c_749,plain,
multiply(iPr_def_16,sk_c4) = identity,
inference(superposition,[status(thm)],[c_275,c_71]) ).
tcf(c_750,plain,
multiply(iPr_def_19,sk_c2) = identity,
inference(superposition,[status(thm)],[c_278,c_71]) ).
tcf(c_777,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_301,c_281]) ).
tcf(c_779,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c6 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_301,c_297]) ).
tcf(c_807,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_302,c_281]) ).
tcf(c_808,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_302,c_298]) ).
tcf(c_830,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_281,c_72]) ).
tcf(c_832,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_273,c_72]) ).
tcf(c_833,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c6,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_279,c_72]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_71,c_72]) ).
tcf(c_837,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_533,c_72]) ).
tcf(c_851,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_747,c_72]) ).
tcf(c_852,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_851,c_70]) ).
tcf(c_854,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_748,c_72]) ).
tcf(c_855,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_854,c_70]) ).
tcf(c_862,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_749,c_72]) ).
tcf(c_863,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_862,c_70]) ).
tcf(c_865,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_750,c_72]) ).
tcf(c_866,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_865,c_70]) ).
tcf(c_874,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_18 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_277,c_283]) ).
tcf(c_875,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_273,c_283]) ).
tcf(c_876,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_279,c_283]) ).
tcf(c_877,plain,
( ~ iPr_def_13
| ( sk_c6 != sk_c7 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_70,c_283]) ).
tcf(c_889,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_21 )
| ( sk_c7 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_876,c_280]) ).
tcf(c_893,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_16 )
| ( sk_c7 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_875,c_275]) ).
tcf(c_897,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_18 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_874,c_276]) ).
tcf(c_958,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != iPr_def_22 )
| ( multiply(X0,sk_c6) != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_284,c_303]) ).
tcf(c_969,plain,
( ~ iPr_def_12
| ( iPr_def_14 != iPr_def_22 )
| ( inverse(sk_c4) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_273,c_958]) ).
tcf(c_970,plain,
( ~ iPr_def_12
| ( iPr_def_20 != iPr_def_22 )
| ( inverse(sk_c1) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_279,c_958]) ).
tcf(c_983,plain,
( ~ iPr_def_12
| ( iPr_def_21 != iPr_def_22 )
| ( iPr_def_20 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_970,c_280]) ).
tcf(c_987,plain,
( ~ iPr_def_12
| ( iPr_def_16 != iPr_def_22 )
| ( iPr_def_14 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_969,c_275]) ).
tcf(c_1037,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_16 )
| ( iPr_def_16 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_1045,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,iPr_def_22) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_285,c_303]) ).
tcf(c_1058,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_15 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_533,c_1045]) ).
tcf(c_1059,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_19 )
| ( sk_c6 != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1058,c_278]) ).
tcf(c_1077,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_1084,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_18 )
| ( inverse(sk_c3) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_277,c_286]) ).
tcf(c_1088,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_71,c_286]) ).
tcf(c_1107,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_18 )
| ( sk_c6 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1084,c_276]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_21 )
| ( iPr_def_21 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_1208,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,iPr_def_17) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_779,c_286]) ).
tcf(c_1211,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_779,c_281]) ).
tcf(c_1416,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_500,c_514]) ).
tcf(c_1450,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_679,c_656]) ).
tcf(c_1487,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_304]) ).
tcf(c_1490,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_279,c_852]) ).
tcf(c_1493,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_20,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1490,c_72]) ).
tcf(c_1503,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_277,c_855]) ).
tcf(c_1526,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_18,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1503,c_72]) ).
tcf(c_1533,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_21,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_551,c_852]) ).
tcf(c_1534,plain,
( ( sk_c6 = iPr_def_17 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1533,c_1490]) ).
tcf(c_1545,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(iPr_def_21,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_571,c_852]) ).
tcf(c_1546,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1545,c_1490]) ).
tcf(c_1607,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_290,c_688]) ).
tcf(c_1609,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_1607,c_1503]) ).
tcf(c_1736,plain,
multiply(iPr_def_16,iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_273,c_863]) ).
tcf(c_1820,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_1914,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_17,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_779,c_697]) ).
tcf(c_1924,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1914,c_1503]) ).
tcf(c_2137,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,iPr_def_22) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_1609,c_286]) ).
tcf(c_2142,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1609,c_279]) ).
tcf(c_2144,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1609,c_273]) ).
tcf(c_2147,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1609,c_289]) ).
tcf(c_2198,plain,
! [X0: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != sk_c5 )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_1077]) ).
tcf(c_2351,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_2653,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_19,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_664,c_686]) ).
tcf(c_2657,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_601,c_686]) ).
tcf(c_2701,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_19,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_640,c_687]) ).
tcf(c_2705,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_590,c_687]) ).
tcf(c_3216,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( iPr_def_16 != sk_c5 )
| ( iPr_def_14 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_2198]) ).
tcf(c_3275,plain,
( ~ iPr_def_10
| ( inverse(sk_c3) != sk_c6 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_286]) ).
tcf(c_3280,plain,
multiply(sk_c4,iPr_def_22) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_281,c_832]) ).
tcf(c_3341,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_19 )
| ( iPr_def_19 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_3342,plain,
( ( sk_c6 = iPr_def_19 )
| ( iPr_def_19 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_3341]) ).
tcf(c_3647,plain,
multiply(sk_c1,iPr_def_22) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_281,c_833]) ).
tcf(c_3815,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_17,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_808,c_1211]) ).
tcf(c_3827,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c6 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_3815,c_1503]) ).
tcf(c_3884,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_17 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_3827,c_779]) ).
tcf(c_3892,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3827,c_273]) ).
tcf(c_3900,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3892,c_3280]) ).
tcf(c_4048,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_3884,c_656]) ).
tcf(c_4346,plain,
! [X0: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != sk_c5 )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_1820]) ).
tcf(c_4348,plain,
! [X0: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1820]) ).
tcf(c_4493,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_835,c_70]) ).
tcf(c_4498,plain,
multiply(inverse(sk_c6),iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_281,c_4493]) ).
tcf(c_4502,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_70,c_4493]) ).
tcf(c_4503,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_71,c_4493]) ).
tcf(c_4534,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(inverse(sk_c6),iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_807,c_4493]) ).
tcf(c_4535,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(inverse(sk_c6),iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_777,c_4493]) ).
tcf(c_4552,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_852,c_4493]) ).
tcf(c_4553,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_855,c_4493]) ).
tcf(c_4554,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_863,c_4493]) ).
tcf(c_4555,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_866,c_4493]) ).
tcf(c_4567,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_4493,c_4493]) ).
tcf(c_4809,plain,
( ~ iPr_def_11
| ( sk_c6 != sk_c7 )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_4498,c_1045]) ).
tcf(c_4987,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_4503,c_4567]) ).
tcf(c_5004,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_4987,c_4502]) ).
tcf(c_5012,plain,
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( sk_c6 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_877,c_5004]) ).
tcf(c_5790,plain,
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1208,c_779,c_808,c_1107]) ).
tcf(c_5840,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_10
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_4498,c_2137]) ).
tcf(c_6684,plain,
! [X0: $i] :
( ( X0 = iPr_def_21 )
| ( iPr_def_21 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1154]) ).
tcf(c_6919,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_2142,c_3647]) ).
tcf(c_6986,plain,
multiply(sk_c1,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_4552,c_71]) ).
tcf(c_6989,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_4552,c_4493]) ).
tcf(c_7017,plain,
multiply(sk_c1,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_4552,c_4987]) ).
tcf(c_7317,plain,
inverse(iPr_def_21) = sk_c1,
inference(demodulation,[status(thm)],[c_7017,c_4987]) ).
tcf(c_8038,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_2144,c_3280]) ).
tcf(c_8278,plain,
multiply(sk_c3,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_4553,c_71]) ).
tcf(c_8309,plain,
multiply(sk_c3,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_4553,c_4987]) ).
tcf(c_9145,plain,
inverse(iPr_def_17) = sk_c3,
inference(demodulation,[status(thm)],[c_8309,c_4987]) ).
tcf(c_9260,plain,
multiply(sk_c4,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_4554,c_71]) ).
tcf(c_9263,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_4554,c_4493]) ).
tcf(c_9293,plain,
multiply(sk_c4,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_4554,c_4987]) ).
tcf(c_9651,plain,
( ~ iPr_def_10
| ( inverse(sk_c2) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_286]) ).
tcf(c_10247,plain,
inverse(iPr_def_16) = sk_c4,
inference(demodulation,[status(thm)],[c_9293,c_4987]) ).
tcf(c_10265,plain,
multiply(sk_c4,sk_c6) = iPr_def_14,
inference(superposition,[status(thm)],[c_1736,c_9263]) ).
tcf(c_10310,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c6 )
| ( multiply(sk_c2,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_4555,c_286]) ).
tcf(c_10313,plain,
multiply(sk_c2,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_4555,c_71]) ).
tcf(c_10316,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_4555,c_4493]) ).
tcf(c_10346,plain,
multiply(sk_c2,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_4555,c_4987]) ).
tcf(c_10708,plain,
( ~ iPr_def_10
| ( multiply(sk_c2,sk_c6) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_10310,c_83,c_82,c_3275,c_9651]) ).
tcf(c_10722,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_10
| ( multiply(sk_c2,iPr_def_19) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_293,c_10708]) ).
tcf(c_10745,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_10
| ( sk_c7 != identity ) ),
inference(light_normalisation,[status(thm)],[c_10722,c_10313]) ).
tcf(c_10883,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_22 != sk_c5 )
| ( iPr_def_16 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_4346]) ).
tcf(c_11382,plain,
inverse(iPr_def_19) = sk_c2,
inference(demodulation,[status(thm)],[c_10346,c_4987]) ).
tcf(c_11391,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_15) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_1416,c_11382]) ).
tcf(c_11397,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_22) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_686,c_10316]) ).
tcf(c_11400,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_2701,c_10316]) ).
tcf(c_11401,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_2653,c_10316]) ).
tcf(c_11403,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2705,c_10316]) ).
tcf(c_11404,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_2657,c_10316]) ).
tcf(c_11421,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_11404,c_533]) ).
tcf(c_11424,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_11403,c_533]) ).
tcf(c_11430,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_11401,c_533]) ).
tcf(c_11433,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_11400,c_533]) ).
tcf(c_11439,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_11397,c_533]) ).
tcf(c_12115,plain,
( ( iPr_def_15 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_11424,c_11421]) ).
tcf(c_12517,plain,
( ( iPr_def_16 = iPr_def_14 )
| ( iPr_def_16 != iPr_def_16 )
| ( iPr_def_14 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_4348]) ).
tcf(c_12906,plain,
( ( iPr_def_15 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_11433,c_11430]) ).
tcf(c_13189,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( iPr_def_15 = iPr_def_18 )
| ( sk_c6 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_11439,c_294]) ).
tcf(c_13211,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_13189,c_310,c_292,c_303,c_3342,c_10883]) ).
tcf(c_13776,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_15) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_12906,c_7317]) ).
tcf(c_14933,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4534,c_4498]) ).
tcf(c_14991,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c6 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_4535,c_4498]) ).
tcf(c_15336,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c1 = sk_c2 ) ),
inference(superposition,[status(thm)],[c_13776,c_11391]) ).
tcf(c_15413,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_15336,c_533]) ).
tcf(c_15414,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(sk_c1) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_15336,c_278]) ).
tcf(c_15415,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_15414,c_280]) ).
tcf(c_15418,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_15413,c_3647]) ).
tcf(c_15720,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_10
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_301,c_10745]) ).
tcf(c_15764,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_15415,c_1450]) ).
tcf(c_16280,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_298,c_889]) ).
tcf(c_16281,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_297,c_889]) ).
tcf(c_16282,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_601,c_889]) ).
tcf(c_16283,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_590,c_889]) ).
tcf(c_16392,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(forward_subsumption_resolution,[status(thm)],[c_16280,c_14933]) ).
tcf(c_16399,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_282,c_16392]) ).
tcf(c_16423,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_13 ),
inference(forward_subsumption_resolution,[status(thm)],[c_16281,c_14991]) ).
tcf(c_16631,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_4567,c_71]) ).
tcf(c_16665,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_4567,c_4987]) ).
tcf(c_16670,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_16665,c_4987]) ).
tcf(c_16817,plain,
( ~ iPr_def_10
| ( sk_c7 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1088,c_16670]) ).
tcf(c_16822,plain,
inverse(inverse(sk_c6)) = sk_c6,
inference(instantiation,[status(thm)],[c_16670]) ).
tcf(c_17080,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_10
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_302,c_16817]) ).
tcf(c_17184,plain,
( ( identity != iPr_def_21 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_17080,c_1107,c_15720,c_17080]) ).
tcf(c_17185,plain,
( ~ iPr_def_10
| ( identity != iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_17184]) ).
tcf(c_17234,plain,
multiply(iPr_def_22,inverse(sk_c7)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_16631,c_830]) ).
tcf(c_17237,plain,
multiply(sk_c6,inverse(iPr_def_18)) = multiply(iPr_def_17,identity),
inference(superposition,[status(thm)],[c_16631,c_1526]) ).
tcf(c_17242,plain,
multiply(sk_c6,inverse(iPr_def_20)) = multiply(iPr_def_21,identity),
inference(superposition,[status(thm)],[c_16631,c_1493]) ).
tcf(c_17342,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c6 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_294,c_15418]) ).
tcf(c_17767,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c6 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_17342,c_310,c_291,c_292,c_3216,c_3342]) ).
tcf(c_17797,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(inverse(iPr_def_19),iPr_def_22) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_17767,c_4498]) ).
tcf(c_17821,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_19) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_17767,c_283]) ).
tcf(c_17837,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_17797,c_533,c_11382]) ).
tcf(c_18082,plain,
! [X0: $i] :
( ( sk_c6 = sk_c7 )
| ( sk_c7 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_18093,plain,
( ( sk_c6 = iPr_def_16 )
| ( iPr_def_16 != iPr_def_14 )
| ( sk_c6 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_18095,plain,
! [X0: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1077]) ).
tcf(c_18097,plain,
( ( sk_c6 = iPr_def_16 )
| ( iPr_def_16 != iPr_def_22 )
| ( sk_c6 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_1037]) ).
tcf(c_18271,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_13
| ( iPr_def_15 != iPr_def_20 )
| ( sk_c7 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_17837,c_889]) ).
tcf(c_18454,plain,
( ( sk_c7 = iPr_def_21 )
| ( iPr_def_21 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_6684]) ).
tcf(c_18455,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_304]) ).
tcf(c_18886,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_17821,c_299,c_300,c_3216,c_12115,c_18271,c_18454,c_18455]) ).
tcf(c_18892,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_282,c_18886]) ).
tcf(c_19088,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_16282,c_300,c_303,c_10883,c_16282,c_18454,c_18455]) ).
tcf(c_19094,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_282,c_19088]) ).
tcf(c_19102,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_13 ),
inference(forward_subsumption_resolution,[status(thm)],[c_16283,c_640]) ).
tcf(c_19109,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_282,c_19102]) ).
tcf(c_20643,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_273,c_283]) ).
tcf(c_20659,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_16 )
| ( sk_c7 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_20643,c_275]) ).
tcf(c_20750,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,iPr_def_22) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_285,c_303]) ).
tcf(c_20965,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_17,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_289,c_281]) ).
tcf(c_21016,plain,
multiply(iPr_def_17,sk_c3) = identity,
inference(superposition,[status(thm)],[c_276,c_71]) ).
tcf(c_21209,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_290,c_20965]) ).
tcf(c_21232,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_21016,c_72]) ).
tcf(c_21233,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_21232,c_70]) ).
tcf(c_21458,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_277,c_21233]) ).
tcf(c_21469,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_21209,c_21458]) ).
tcf(c_21671,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_21469,c_273]) ).
tcf(c_22543,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_14 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_21671,c_20750]) ).
tcf(c_22560,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_16 )
| ( sk_c6 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_22543,c_275]) ).
tcf(c_23355,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_17 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_897,c_16392]) ).
tcf(c_23445,plain,
multiply(iPr_def_22,inverse(sk_c7)) = sk_c6,
inference(demodulation,[status(thm)],[c_17234,c_4987]) ).
tcf(c_23476,plain,
multiply(inverse(iPr_def_22),sk_c6) = inverse(sk_c7),
inference(superposition,[status(thm)],[c_23445,c_4493]) ).
tcf(c_23478,plain,
multiply(iPr_def_15,inverse(sk_c7)) = multiply(sk_c2,sk_c6),
inference(superposition,[status(thm)],[c_23445,c_837]) ).
tcf(c_23535,plain,
( ~ iPr_def_10
| ( multiply(iPr_def_15,inverse(sk_c7)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_10708,c_23478]) ).
tcf(c_23689,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(inverse(iPr_def_16),sk_c6) = inverse(sk_c7) ) ),
inference(superposition,[status(thm)],[c_679,c_23476]) ).
tcf(c_23713,plain,
( ~ iPr_def_12
| ( inverse(sk_c7) != iPr_def_22 )
| ( inverse(inverse(iPr_def_22)) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_23476,c_958]) ).
tcf(c_23755,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( inverse(sk_c7) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_23689,c_10247,c_10265]) ).
tcf(c_23774,plain,
( ~ iPr_def_12
| ( inverse(sk_c7) != iPr_def_22 ) ),
inference(ground_joinability,[status(thm)],[c_23713,c_16670]) ).
tcf(c_23937,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_12
| ( inverse(iPr_def_21) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_301,c_23774]) ).
tcf(c_23938,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_12
| ( inverse(iPr_def_21) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_664,c_23774]) ).
tcf(c_23939,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_12
| ( inverse(iPr_def_21) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_640,c_23774]) ).
tcf(c_23945,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_12
| ( inverse(iPr_def_18) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_290,c_23774]) ).
tcf(c_23964,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c1 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_23939,c_7317]) ).
tcf(c_23968,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c1 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_23938,c_7317]) ).
tcf(c_23972,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c1 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_23937,c_7317]) ).
tcf(c_24937,plain,
multiply(sk_c6,inverse(iPr_def_18)) = iPr_def_17,
inference(demodulation,[status(thm)],[c_17237,c_4987]) ).
tcf(c_24963,plain,
multiply(inverse(sk_c6),iPr_def_17) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_24937,c_4493]) ).
tcf(c_25306,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(inverse(iPr_def_17),iPr_def_17) = inverse(iPr_def_18) ) ),
inference(superposition,[status(thm)],[c_289,c_24963]) ).
tcf(c_25326,plain,
( ( sk_c6 = iPr_def_15 )
| ( inverse(iPr_def_18) = identity ) ),
inference(light_normalisation,[status(thm)],[c_25306,c_8278,c_9145]) ).
tcf(c_28023,plain,
multiply(sk_c6,inverse(iPr_def_20)) = iPr_def_21,
inference(demodulation,[status(thm)],[c_17242,c_4987]) ).
tcf(c_28026,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_19,inverse(iPr_def_20)) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_17767,c_28023]) ).
tcf(c_28041,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(iPr_def_20)) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_466,c_28023]) ).
tcf(c_28042,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(iPr_def_20)) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_459,c_28023]) ).
tcf(c_28411,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_12
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_25326,c_23945]) ).
tcf(c_28720,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_10
| ( multiply(iPr_def_15,inverse(iPr_def_20)) != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_298,c_23535]) ).
tcf(c_28721,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_10
| ( multiply(iPr_def_15,inverse(iPr_def_20)) != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_297,c_23535]) ).
tcf(c_29187,plain,
( ( multiply(iPr_def_15,inverse(iPr_def_20)) != iPr_def_20 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_28720,c_1107,c_28721,c_28720]) ).
tcf(c_29188,plain,
( ~ iPr_def_10
| ( multiply(iPr_def_15,inverse(iPr_def_20)) != iPr_def_20 ) ),
inference(renaming,[status(thm)],[c_29187]) ).
tcf(c_30097,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(sk_c7)) = multiply(sk_c2,iPr_def_19) ) ),
inference(superposition,[status(thm)],[c_503,c_23478]) ).
tcf(c_30098,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(sk_c7)) = multiply(sk_c2,iPr_def_19) ) ),
inference(superposition,[status(thm)],[c_488,c_23478]) ).
tcf(c_30117,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(sk_c7)) = identity ) ),
inference(light_normalisation,[status(thm)],[c_30098,c_10313]) ).
tcf(c_30120,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(sk_c7)) = identity ) ),
inference(light_normalisation,[status(thm)],[c_30097,c_10313]) ).
tcf(c_30388,plain,
( ( sk_c1 != iPr_def_22 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_23972,c_987,c_23968,c_23964]) ).
tcf(c_30389,plain,
( ~ iPr_def_12
| ( sk_c1 != iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_30388]) ).
tcf(c_30667,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(iPr_def_20)) = identity ) ),
inference(superposition,[status(thm)],[c_590,c_30117]) ).
tcf(c_30963,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_14,sk_c7) = identity ) ),
inference(superposition,[status(thm)],[c_23755,c_71]) ).
tcf(c_30969,plain,
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_12
| ( iPr_def_14 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_23755,c_23774]) ).
tcf(c_32093,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_30963,c_3900]) ).
tcf(c_32189,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_15,inverse(iPr_def_20)) = identity ) ),
inference(superposition,[status(thm)],[c_601,c_30120]) ).
tcf(c_32447,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_14,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_32093,c_70]) ).
tcf(c_33357,plain,
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c6 != sk_c7 )
| ( inverse(iPr_def_14) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_32447,c_283]) ).
tcf(c_33390,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_32447,c_3900]) ).
tcf(c_33658,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_30667,c_28042]) ).
tcf(c_33746,plain,
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_13
| ( iPr_def_14 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_33390,c_23355]) ).
tcf(c_34150,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_33658,c_17185]) ).
tcf(c_34155,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( inverse(iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_33658,c_5004]) ).
tcf(c_34157,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_33658,c_70]) ).
tcf(c_34160,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c1 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_34155,c_7317]) ).
tcf(c_34194,plain,
( iPr_def_12
| iPr_def_11
| ( iPr_def_14 = iPr_def_22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_19109,c_34150]) ).
tcf(c_34473,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_34157,c_747]) ).
tcf(c_34714,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_32189,c_28041]) ).
tcf(c_34865,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_12
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_34473,c_30389]) ).
tcf(c_35430,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_34714,c_17185]) ).
tcf(c_35435,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( inverse(iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_34714,c_5004]) ).
tcf(c_35437,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_34714,c_70]) ).
tcf(c_35440,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c1 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_35435,c_7317]) ).
tcf(c_35459,plain,
( ( iPr_def_20 = iPr_def_21 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_33357,c_4048,c_33746]) ).
tcf(c_35465,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_282,c_35459]) ).
tcf(c_35849,plain,
( iPr_def_12
| iPr_def_11
| ( iPr_def_16 = iPr_def_22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_19094,c_35430]) ).
tcf(c_35859,plain,
( ( iPr_def_20 = iPr_def_21 )
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_35465,c_656,c_5790,c_30969,c_35465]) ).
tcf(c_35860,plain,
( iPr_def_11
| ( iPr_def_20 = iPr_def_21 ) ),
inference(renaming,[status(thm)],[c_35859]) ).
tcf(c_36298,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_35437,c_747]) ).
tcf(c_36450,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_12
| ( identity != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_36298,c_30389]) ).
tcf(c_38956,plain,
( ( sk_c6 = sk_c7 )
| ( sk_c7 != iPr_def_16 )
| ( sk_c6 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_18082]) ).
tcf(c_39019,plain,
( ( identity = iPr_def_16 )
| ( iPr_def_16 != iPr_def_14 )
| ( identity != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_18095]) ).
tcf(c_39465,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_19,inverse(iPr_def_19)) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_15764,c_28026]) ).
tcf(c_39478,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( identity = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_39465,c_750,c_11382]) ).
tcf(c_40003,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_39478,c_17185]) ).
tcf(c_40008,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_39478,c_5004]) ).
tcf(c_40010,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_39478,c_70]) ).
tcf(c_40013,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c1 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_40008,c_7317]) ).
tcf(c_40042,plain,
( iPr_def_12
| iPr_def_11
| ( iPr_def_14 = iPr_def_16 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_18892,c_40003]) ).
tcf(c_40088,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_40013,c_279]) ).
tcf(c_40312,plain,
( ( identity != iPr_def_22 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_28411,c_987,c_34865,c_36450]) ).
tcf(c_40313,plain,
( ~ iPr_def_12
| ( identity != iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_40312]) ).
tcf(c_40440,plain,
( ( sk_c7 = iPr_def_16 )
| ( iPr_def_16 != iPr_def_14 )
| ( sk_c7 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_18095]) ).
tcf(c_40620,plain,
iPr_def_20 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_1924,c_679,c_1450,c_1487,c_3827,c_4809,c_12517,c_16822,c_18097,c_33390,c_35860,c_38956,c_40440]) ).
tcf(c_40640,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c1 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_35440,c_40620]) ).
tcf(c_40644,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c1 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_34160,c_40620]) ).
tcf(c_40670,plain,
multiply(sk_c6,inverse(iPr_def_20)) = iPr_def_20,
inference(demodulation,[status(thm)],[c_28023,c_40620]) ).
tcf(c_40672,plain,
( ~ iPr_def_12
| ( iPr_def_20 != iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_983,c_40620]) ).
tcf(c_40714,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_20,X0)) = X0,
inference(demodulation,[status(thm)],[c_6989,c_40620]) ).
tcf(c_40715,plain,
inverse(iPr_def_20) = sk_c1,
inference(demodulation,[status(thm)],[c_7317,c_40620]) ).
tcf(c_40716,plain,
multiply(sk_c1,iPr_def_20) = identity,
inference(demodulation,[status(thm)],[c_6986,c_40620]) ).
tcf(c_40733,plain,
multiply(iPr_def_20,iPr_def_20) = sk_c6,
inference(demodulation,[status(thm)],[c_1490,c_40620]) ).
tcf(c_40806,plain,
( ~ iPr_def_10
| ( multiply(iPr_def_15,sk_c1) != iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_29188,c_40715]) ).
tcf(c_40828,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_20,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_40010,c_40620]) ).
tcf(c_41012,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_20,sk_c6) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_40088,c_40620]) ).
tcf(c_41026,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_17767,c_41012]) ).
tcf(c_41045,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c6 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_41012,c_40828]) ).
tcf(c_41145,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_11
| ( iPr_def_15 != iPr_def_19 )
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_17767,c_1059]) ).
tcf(c_41149,plain,
( ( iPr_def_17 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2147,c_1059]) ).
tcf(c_41153,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_11
| ( iPr_def_15 != iPr_def_19 )
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_293,c_1059]) ).
tcf(c_41157,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_466,c_1059]) ).
tcf(c_41158,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_459,c_1059]) ).
tcf(c_41309,plain,
( ( sk_c6 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_41153,c_1059,c_1534,c_1546]) ).
tcf(c_41337,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(inverse(iPr_def_20),iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_41026,c_4493]) ).
tcf(c_41351,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( identity = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_41337,c_40715,c_40716]) ).
tcf(c_41470,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_41157,c_13211,c_41157]) ).
tcf(c_41476,plain,
( iPr_def_12
| ( iPr_def_16 = iPr_def_22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_35849,c_41470]) ).
tcf(c_41482,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_41158,c_488]) ).
tcf(c_41489,plain,
( iPr_def_12
| ( iPr_def_14 = iPr_def_22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_34194,c_41482]) ).
tcf(c_41594,plain,
multiply(sk_c6,sk_c1) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_40670,c_40715]) ).
tcf(c_42444,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_20659,c_299,c_300,c_893,c_1487,c_3216,c_12115,c_12517,c_18271,c_18454,c_18455,c_40440]) ).
tcf(c_43587,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(iPr_def_20,iPr_def_20) = identity ) ),
inference(superposition,[status(thm)],[c_40640,c_40716]) ).
tcf(c_43615,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c6 = identity ) ),
inference(light_normalisation,[status(thm)],[c_43587,c_40733]) ).
tcf(c_43767,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_2351]) ).
tcf(c_43769,plain,
( ( sk_c6 = identity )
| ( identity != iPr_def_16 )
| ( sk_c6 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_43767]) ).
tcf(c_43978,plain,
( ( iPr_def_17 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_17767,c_41149]) ).
tcf(c_44020,plain,
( ~ iPr_def_11
| ( iPr_def_14 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_43978,c_1416,c_17767,c_41145]) ).
tcf(c_44021,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_11 ),
inference(renaming,[status(thm)],[c_44020]) ).
tcf(c_44026,plain,
( iPr_def_12
| ( iPr_def_14 = iPr_def_16 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_40042,c_44021]) ).
tcf(c_44108,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(iPr_def_20,iPr_def_20) = identity ) ),
inference(superposition,[status(thm)],[c_40644,c_40716]) ).
tcf(c_44136,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = identity ) ),
inference(light_normalisation,[status(thm)],[c_44108,c_40733]) ).
tcf(c_44284,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c1,iPr_def_20) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_6919,c_40714]) ).
tcf(c_44319,plain,
( ( sk_c7 = identity )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_44284,c_40716]) ).
tcf(c_45383,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(iPr_def_20,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_41045,c_281]) ).
tcf(c_46359,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_19) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_41351,c_5004]) ).
tcf(c_46362,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c2 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_46359,c_11382]) ).
tcf(c_46649,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_45383,c_15418]) ).
tcf(c_48177,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( multiply(identity,sk_c7) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_43615,c_281]) ).
tcf(c_48185,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_43615,c_466]) ).
tcf(c_48514,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( identity = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_44136,c_459]) ).
tcf(c_48876,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c7 != identity )
| ( sk_c6 != identity ) ),
inference(superposition,[status(thm)],[c_44319,c_5012]) ).
tcf(c_49368,plain,
( ( iPr_def_16 = iPr_def_22 )
| ~ iPr_def_12
| ( iPr_def_15 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_48185,c_40313]) ).
tcf(c_49439,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_12
| ( iPr_def_15 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_48514,c_40313]) ).
tcf(c_49463,plain,
iPr_def_14 = iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_46362,c_987,c_44026,c_46649,c_49368,c_49439]) ).
tcf(c_49506,plain,
( ~ iPr_def_12
| ( iPr_def_14 != iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_987,c_49463]) ).
tcf(c_49549,plain,
inverse(iPr_def_14) = sk_c4,
inference(demodulation,[status(thm)],[c_10247,c_49463]) ).
tcf(c_49550,plain,
multiply(sk_c4,iPr_def_14) = identity,
inference(demodulation,[status(thm)],[c_9260,c_49463]) ).
tcf(c_49654,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(identity,sk_c7) = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_48177,c_49463]) ).
tcf(c_49655,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_49654,c_70]) ).
tcf(c_49730,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_49655,c_590]) ).
tcf(c_49785,plain,
iPr_def_14 = iPr_def_22,
inference(global_subsumption_just,[status(thm)],[c_49730,c_40672,c_41489,c_49730]) ).
tcf(c_49839,plain,
( ~ iPr_def_12
| ( inverse(sk_c7) != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_23774,c_49785]) ).
tcf(c_49840,plain,
multiply(inverse(iPr_def_14),sk_c6) = inverse(sk_c7),
inference(demodulation,[status(thm)],[c_23476,c_49785]) ).
tcf(c_49871,plain,
multiply(sk_c4,iPr_def_14) = multiply(iPr_def_14,sk_c7),
inference(demodulation,[status(thm)],[c_3280,c_49785]) ).
tcf(c_49883,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_1609,c_49785]) ).
tcf(c_49893,plain,
multiply(sk_c6,sk_c7) = iPr_def_14,
inference(demodulation,[status(thm)],[c_281,c_49785]) ).
tcf(c_49912,plain,
multiply(iPr_def_14,sk_c7) = identity,
inference(light_normalisation,[status(thm)],[c_49871,c_49550]) ).
tcf(c_49914,plain,
inverse(sk_c7) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_49840,c_10265,c_49549]) ).
tcf(c_49915,plain,
~ iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_49839,c_49914]) ).
tcf(c_50012,plain,
( ( identity = iPr_def_14 )
| ( sk_c6 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_8038,c_49912]) ).
tcf(c_50041,plain,
( iPr_def_13
| iPr_def_11
| iPr_def_10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_282,c_49915]) ).
tcf(c_50079,plain,
( ( sk_c6 = iPr_def_15 )
| ( inverse(iPr_def_18) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_290,c_49914]) ).
tcf(c_50176,plain,
sk_c6 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_50079,c_282,c_1487,c_1609,c_5840,c_12517,c_16822,c_18097,c_22560,c_39019,c_41476,c_43769,c_44319,c_48876,c_49463,c_49506,c_49785,c_50012,c_49883]) ).
tcf(c_50204,plain,
multiply(iPr_def_15,sk_c1) = iPr_def_20,
inference(demodulation,[status(thm)],[c_41594,c_50176]) ).
tcf(c_50207,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(demodulation,[status(thm)],[c_41309,c_50176]) ).
tcf(c_50209,plain,
( ~ iPr_def_11
| ( iPr_def_15 != iPr_def_19 )
| ( iPr_def_15 != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1059,c_50176]) ).
tcf(c_50233,plain,
( ( iPr_def_15 = iPr_def_17 )
| ~ iPr_def_13 ),
inference(demodulation,[status(thm)],[c_16423,c_50176]) ).
tcf(c_50264,plain,
multiply(iPr_def_17,iPr_def_18) = iPr_def_15,
inference(demodulation,[status(thm)],[c_1503,c_50176]) ).
tcf(c_50267,plain,
( ( iPr_def_15 = iPr_def_17 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_297,c_50176]) ).
tcf(c_50268,plain,
( ( iPr_def_15 = iPr_def_19 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_294,c_50176]) ).
tcf(c_50271,plain,
multiply(sk_c3,iPr_def_15) = iPr_def_18,
inference(demodulation,[status(thm)],[c_277,c_50176]) ).
tcf(c_50329,plain,
( ~ iPr_def_11
| ( iPr_def_15 != iPr_def_19 ) ),
inference(equality_resolution_simp,[status(thm)],[c_50209]) ).
tcf(c_50389,plain,
~ iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_40806,c_50204]) ).
tcf(c_50390,plain,
( iPr_def_13
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_50041,c_50389]) ).
tcf(c_50402,plain,
iPr_def_15 = iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_50267,c_50390,c_50233,c_50207]) ).
tcf(c_50410,plain,
multiply(sk_c3,iPr_def_15) = identity,
inference(demodulation,[status(thm)],[c_8278,c_50402]) ).
tcf(c_50414,plain,
identity = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_50410,c_50271]) ).
tcf(c_50427,plain,
! [X0: $i] : multiply(X0,iPr_def_18) = X0,
inference(demodulation,[status(thm)],[c_4987,c_50414]) ).
tcf(c_50430,plain,
! [X0: $i] : multiply(iPr_def_18,X0) = X0,
inference(demodulation,[status(thm)],[c_70,c_50414]) ).
tcf(c_50441,plain,
sk_c7 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_50268,c_16399,c_49506,c_49785,c_50389,c_50329,c_50268]) ).
tcf(c_50444,plain,
inverse(iPr_def_18) = iPr_def_14,
inference(demodulation,[status(thm)],[c_49914,c_50441]) ).
tcf(c_50478,plain,
multiply(iPr_def_15,iPr_def_18) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_49893,c_50176,c_50441]) ).
tcf(c_50479,plain,
iPr_def_14 = iPr_def_15,
inference(demodulation,[status(thm)],[c_50478,c_50427]) ).
tcf(c_50483,plain,
iPr_def_14 = iPr_def_17,
inference(demodulation,[status(thm)],[c_50402,c_50479]) ).
tcf(c_50484,plain,
sk_c6 = iPr_def_14,
inference(demodulation,[status(thm)],[c_50176,c_50479]) ).
tcf(c_50494,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_50444,c_4493]) ).
tcf(c_50495,plain,
! [X0: $i] : multiply(iPr_def_14,X0) = X0,
inference(light_normalisation,[status(thm)],[c_50494,c_50430]) ).
tcf(c_50526,plain,
multiply(iPr_def_14,iPr_def_18) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_50264,c_50479,c_50483]) ).
tcf(c_50527,plain,
iPr_def_14 = iPr_def_18,
inference(demodulation,[status(thm)],[c_50526,c_50495]) ).
tcf(c_50532,plain,
sk_c7 = iPr_def_14,
inference(demodulation,[status(thm)],[c_50441,c_50527]) ).
tcf(c_50533,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_50532,c_50484,c_50390,c_49463,c_42444,c_40440,c_38956,c_18093,c_16822,c_12517,c_4809,c_1487]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP344-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:33:48 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 10.68/2.79 % SZS status Started for theBenchmark.p
% 10.68/2.79 % SZS status Unsatisfiable for theBenchmark.p
% 10.68/2.79
% 10.68/2.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.68/2.79
% 10.68/2.79 % ------ iProver source info
% 10.68/2.79
% 10.68/2.79 % git: date: 2026-07-19 20:42:38 +0200
% 10.68/2.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.68/2.79 % git: non_committed_changes: false
% 10.68/2.79
% 10.68/2.79 % ------ Parsing...% successful
% 10.68/2.79
% 10.68/2.79
% 10.68/2.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.68/2.79
% 10.68/2.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.68/2.79
% 10.68/2.79 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.68/2.79
% 10.68/2.79 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.68/2.79 % ------ Proving...
% 10.68/2.79 % ------ Problem Properties
% 10.68/2.79
% 10.68/2.79 %
% 10.68/2.79 % clauses 34
% 10.68/2.79 % conjectures 22
% 10.68/2.79 % EPR 18
% 10.68/2.79 % Horn 17
% 10.68/2.79 % unary 13
% 10.68/2.79 % binary 16
% 10.68/2.79 % lits 61
% 10.68/2.79 % lits eq 53
% 10.68/2.79 % fd_pure 0
% 10.68/2.79 % fd_pseudo 0
% 10.68/2.79 % fd_cond 0
% 10.68/2.79 % fd_pseudo_cond 0
% 10.68/2.79 % AC symbols 0
% 10.68/2.79
% 10.68/2.79 % ------ Schedule dynamic 5 is on
% 10.68/2.79
% 10.68/2.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.68/2.79
% 10.68/2.79
% 10.68/2.79 % ------
% 10.68/2.79 % Current options:
% 10.68/2.79 % ------
% 10.68/2.79
% 10.68/2.79
% 10.68/2.79 %
% 10.68/2.79
% 10.68/2.79 % ------ Proving...
% 10.68/2.79 %
% 10.68/2.79
% 10.68/2.79 % SZS status Unsatisfiable for theBenchmark.p
% 10.68/2.79
% 10.68/2.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.02/2.80
% 15.02/2.80
%------------------------------------------------------------------------------