%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP281-1 : 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 : n017.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 01:32:43 PM UTC 2026
% Result : Unsatisfiable 22.48s 9.29s
% Output : CNFRefutation 26.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 42
% Syntax : Number of formulae : 486 ( 195 unt; 11 def)
% Number of atoms : 1701 ( 822 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 581 ( 177 ~; 404 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn 119 !; 0 ?; 99 :)
% 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_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = inverse(sk_c4)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c5)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c6 = multiply(sk_c7,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X2)
| multiply(X2,sk_c8) != X1
| sk_c7 != multiply(sk_c8,X1)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c6 != multiply(sk_c7,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(equality_resolution,[],[f66]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_413,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(sk_c8,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c8,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_413,c_415,c_414]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_417,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_418]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110,c_421]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105,c_422]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100,c_423]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95,c_424]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_460,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_679,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_430,c_431]) ).
tcf(c_691,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_432,c_433]) ).
tcf(c_713,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c8,iPr_def_18) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_431,c_414]) ).
tcf(c_723,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_18,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_431,c_415]) ).
tcf(c_735,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_434,c_416]) ).
tcf(c_738,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_431,c_419]) ).
tcf(c_759,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_22,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_440,c_415]) ).
tcf(c_760,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c8,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_440,c_414]) ).
tcf(c_804,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_442,c_419]) ).
tcf(c_864,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_445,c_419]) ).
tcf(c_889,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_433,c_421]) ).
tcf(c_895,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != X0 )
| ( sk_c6 != X0 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_900,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_438,c_422]) ).
tcf(c_901,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_437,c_422]) ).
tcf(c_903,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c8,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_435,c_422]) ).
tcf(c_929,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_939,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_940,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_418,c_84]) ).
tcf(c_941,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_942,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_959,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_446,c_445]) ).
tcf(c_994,plain,
( ( iPr_def_14 = sk_c6 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c6 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_895]) ).
tcf(c_1016,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_447,c_424]) ).
tcf(c_1017,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c3) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_447,c_422]) ).
tcf(c_1020,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_447,c_414]) ).
tcf(c_1045,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_448,c_424]) ).
tcf(c_1046,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c3) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_448,c_422]) ).
tcf(c_1049,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_448,c_414]) ).
tcf(c_1080,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_929]) ).
tcf(c_1118,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( sk_c7 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_450,c_440]) ).
tcf(c_1119,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_450,c_419]) ).
tcf(c_1173,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_451,c_441]) ).
tcf(c_1175,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_451,c_419]) ).
tcf(c_1230,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_452,c_442]) ).
tcf(c_1267,plain,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c6 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1080]) ).
tcf(c_1268,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_1286,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_453,c_443]) ).
tcf(c_1290,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_453,c_419]) ).
tcf(c_1350,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_455,c_416]) ).
tcf(c_1460,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c5,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_458,c_416]) ).
tcf(c_1544,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_679,c_421]) ).
tcf(c_1585,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_691,c_448]) ).
tcf(c_1586,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_691,c_447]) ).
tcf(c_1685,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_959,c_424]) ).
tcf(c_1818,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_16 )
| ( sk_c6 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_455,c_425]) ).
tcf(c_1822,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_17 )
| ( iPr_def_14 != iPr_def_15 )
| ( sk_c6 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_434,c_425]) ).
tcf(c_1911,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_16 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_416,c_427]) ).
tcf(c_1913,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_427]) ).
tcf(c_1926,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_18 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1911,c_418]) ).
tcf(c_1991,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_2014,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_424,c_428]) ).
tcf(c_2017,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_84,c_428]) ).
tcf(c_2032,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2014,c_423]) ).
tcf(c_2134,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_14 )
| ( inverse(sk_c8) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_414,c_429]) ).
tcf(c_2135,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_419,c_429]) ).
tcf(c_2154,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2135,c_420]) ).
tcf(c_2314,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_426]) ).
tcf(c_2414,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1173,c_1118]) ).
tcf(c_2622,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_19 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1286,c_1230]) ).
tcf(c_2810,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2811,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2812,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_2813,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_416,c_85]) ).
tcf(c_2814,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_424,c_85]) ).
tcf(c_2815,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c3,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_422,c_85]) ).
tcf(c_2816,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_421,c_85]) ).
tcf(c_2818,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2821,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_939,c_85]) ).
tcf(c_2822,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_940,c_85]) ).
tcf(c_2823,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_941,c_85]) ).
tcf(c_2824,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_942,c_85]) ).
tcf(c_2830,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2824,c_83]) ).
tcf(c_2831,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2823,c_83]) ).
tcf(c_2832,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2822,c_83]) ).
tcf(c_2833,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2821,c_83]) ).
tcf(c_2901,plain,
multiply(iPr_def_17,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_421,c_2830]) ).
tcf(c_2904,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2901,c_85]) ).
tcf(c_2910,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_424,c_2831]) ).
tcf(c_2913,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_24,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2910,c_85]) ).
tcf(c_3130,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_18,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_433,c_723]) ).
tcf(c_3370,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c5,multiply(iPr_def_15,X0)) = multiply(iPr_def_16,X0) ) ),
inference(superposition,[status(thm)],[c_735,c_85]) ).
tcf(c_3378,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c4,multiply(iPr_def_18,X0)) = multiply(iPr_def_19,X0) ) ),
inference(superposition,[status(thm)],[c_738,c_85]) ).
tcf(c_3382,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c6,
inference(superposition,[status(thm)],[c_416,c_2832]) ).
tcf(c_3383,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_735,c_2832]) ).
tcf(c_3392,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3382,c_85]) ).
tcf(c_3394,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_419,c_2833]) ).
tcf(c_3395,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_738,c_2833]) ).
tcf(c_3400,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3394,c_85]) ).
tcf(c_3509,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_22,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0) ) ),
inference(superposition,[status(thm)],[c_759,c_85]) ).
tcf(c_3596,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c8,multiply(iPr_def_22,X0)) = multiply(iPr_def_14,X0) ) ),
inference(superposition,[status(thm)],[c_760,c_85]) ).
tcf(c_4047,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_864,c_2833]) ).
tcf(c_4048,plain,
( ( sk_c7 = iPr_def_16 )
| ( sk_c8 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_4047,c_3394]) ).
tcf(c_4161,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_889,c_2830]) ).
tcf(c_4162,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_4161,c_2901]) ).
tcf(c_4267,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_448,c_900]) ).
tcf(c_4309,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_447,c_901]) ).
tcf(c_4833,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_452,c_1020]) ).
tcf(c_4846,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4833,c_2910]) ).
tcf(c_5345,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_453,c_1049]) ).
tcf(c_5359,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5345,c_2910]) ).
tcf(c_5449,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1119,c_2833]) ).
tcf(c_5450,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_5449,c_3394]) ).
tcf(c_5583,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1175,c_2833]) ).
tcf(c_5584,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5583,c_3394]) ).
tcf(c_5740,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5359,c_4846]) ).
tcf(c_6217,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_5740,c_424]) ).
tcf(c_6511,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1290,c_2833]) ).
tcf(c_6512,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6511,c_3394]) ).
tcf(c_6677,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1350,c_2832]) ).
tcf(c_6678,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6677,c_3382]) ).
tcf(c_6713,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1460,c_2832]) ).
tcf(c_6714,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6713,c_3382]) ).
tcf(c_8311,plain,
multiply(sk_c8,iPr_def_15) = multiply(iPr_def_14,sk_c8),
inference(superposition,[status(thm)],[c_415,c_2810]) ).
tcf(c_8550,plain,
multiply(sk_c7,iPr_def_14) = multiply(iPr_def_15,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2811]) ).
tcf(c_8551,plain,
multiply(sk_c7,iPr_def_22) = multiply(iPr_def_15,sk_c3),
inference(superposition,[status(thm)],[c_422,c_2811]) ).
tcf(c_8571,plain,
multiply(sk_c7,multiply(iPr_def_14,sk_c8)) = multiply(iPr_def_15,iPr_def_15),
inference(superposition,[status(thm)],[c_8311,c_2811]) ).
tcf(c_8786,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_15,iPr_def_22) = multiply(iPr_def_22,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_440,c_8550]) ).
tcf(c_9119,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_19,sk_c8),
inference(superposition,[status(thm)],[c_415,c_2812]) ).
tcf(c_9200,plain,
multiply(iPr_def_20,multiply(iPr_def_19,sk_c8)) = iPr_def_15,
inference(superposition,[status(thm)],[c_9119,c_2833]) ).
tcf(c_9228,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_24,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2814]) ).
tcf(c_9229,plain,
multiply(sk_c1,iPr_def_22) = multiply(iPr_def_24,sk_c3),
inference(superposition,[status(thm)],[c_422,c_2814]) ).
tcf(c_9612,plain,
( ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(iPr_def_22,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_2815,c_426]) ).
tcf(c_9657,plain,
multiply(sk_c2,iPr_def_22) = multiply(iPr_def_21,sk_c3),
inference(superposition,[status(thm)],[c_422,c_2816]) ).
tcf(c_9677,plain,
multiply(sk_c2,multiply(iPr_def_14,sk_c8)) = multiply(iPr_def_21,iPr_def_15),
inference(superposition,[status(thm)],[c_8311,c_2816]) ).
tcf(c_10359,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1586,c_1585]) ).
tcf(c_10642,plain,
( ( sk_c6 = iPr_def_15 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3383,c_3382]) ).
tcf(c_10669,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3395,c_3394]) ).
tcf(c_10857,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_24,sk_c7) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_6217,c_9228]) ).
tcf(c_11549,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2818,c_83]) ).
tcf(c_11554,plain,
multiply(inverse(sk_c8),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_414,c_11549]) ).
tcf(c_11555,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_11549]) ).
tcf(c_11559,plain,
multiply(inverse(sk_c8),iPr_def_22) = sk_c3,
inference(superposition,[status(thm)],[c_422,c_11549]) ).
tcf(c_11561,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_11549]) ).
tcf(c_11562,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_11549]) ).
tcf(c_11563,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_85,c_11549]) ).
tcf(c_11679,plain,
multiply(inverse(sk_c8),multiply(iPr_def_14,sk_c8)) = iPr_def_15,
inference(superposition,[status(thm)],[c_8311,c_11549]) ).
tcf(c_11690,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2833,c_11549]) ).
tcf(c_11691,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2832,c_11549]) ).
tcf(c_11692,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2831,c_11549]) ).
tcf(c_11693,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2830,c_11549]) ).
tcf(c_11732,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11549,c_11549]) ).
tcf(c_12779,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11562,c_11732]) ).
tcf(c_12790,plain,
multiply(sk_c4,sk_c7) = multiply(iPr_def_19,identity),
inference(superposition,[status(thm)],[c_12779,c_2812]) ).
tcf(c_12791,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_12779,c_2810]) ).
tcf(c_12794,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_12779,c_2811]) ).
tcf(c_12795,plain,
multiply(sk_c7,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_12779,c_3400]) ).
tcf(c_12796,plain,
multiply(sk_c6,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_12779,c_3392]) ).
tcf(c_12797,plain,
multiply(sk_c5,sk_c6) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_12779,c_2813]) ).
tcf(c_12798,plain,
multiply(sk_c8,identity) = multiply(iPr_def_23,iPr_def_24),
inference(superposition,[status(thm)],[c_12779,c_2913]) ).
tcf(c_12799,plain,
multiply(sk_c8,sk_c3) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_12779,c_2815]) ).
tcf(c_12800,plain,
multiply(sk_c8,identity) = multiply(iPr_def_17,iPr_def_21),
inference(superposition,[status(thm)],[c_12779,c_2904]) ).
tcf(c_12805,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12779,c_11561]) ).
tcf(c_12806,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_12800,c_2901]) ).
tcf(c_12807,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_12799,c_422]) ).
tcf(c_12809,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_12797,c_416]) ).
tcf(c_12810,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_12796,c_3382]) ).
tcf(c_12811,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_12795,c_3394]) ).
tcf(c_12812,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_12794,c_415]) ).
tcf(c_12815,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_12791,c_414]) ).
tcf(c_12816,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_12790,c_419]) ).
tcf(c_12882,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c7 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_430,c_1926]) ).
tcf(c_12940,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_12 ),
inference(forward_subsumption_resolution,[status(thm)],[c_12882,c_10669]) ).
tcf(c_13207,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_448,c_2032]) ).
tcf(c_13256,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_13207,c_6512,c_13207]) ).
tcf(c_13488,plain,
( ( sk_c8 = iPr_def_14 )
| ~ iPr_def_10
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_4846,c_2154]) ).
tcf(c_13492,plain,
( ( iPr_def_22 = iPr_def_24 )
| ~ iPr_def_10
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1230,c_2154]) ).
tcf(c_13499,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_10
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_432,c_2154]) ).
tcf(c_13574,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_13499,c_4162,c_13499]) ).
tcf(c_13917,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_20)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c4,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11690,c_426]) ).
tcf(c_13919,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_11690,c_84]) ).
tcf(c_13922,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_20)) != sk_c8 )
| ( multiply(sk_c4,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11690,c_429]) ).
tcf(c_13924,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_11690,c_11549]) ).
tcf(c_13925,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_11690,c_12779]) ).
tcf(c_13931,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( inverse(inverse(iPr_def_20)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_13922,c_419]) ).
tcf(c_13978,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(superposition,[status(thm)],[c_13919,c_2833]) ).
tcf(c_13983,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_13925,c_12779]) ).
tcf(c_13999,plain,
multiply(sk_c4,sk_c7) = iPr_def_19,
inference(superposition,[status(thm)],[c_3394,c_13924]) ).
tcf(c_14285,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_11691,c_84]) ).
tcf(c_14289,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11691,c_427]) ).
tcf(c_14290,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_11691,c_11549]) ).
tcf(c_14291,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_11691,c_12779]) ).
tcf(c_14292,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_16 )
| ( inverse(inverse(iPr_def_18)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_14289,c_416]) ).
tcf(c_14310,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(superposition,[status(thm)],[c_14285,c_2832]) ).
tcf(c_14313,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_14291,c_12779]) ).
tcf(c_14317,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c6 != iPr_def_15 )
| ( sk_c7 = iPr_def_16 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1818,c_425,c_994,c_1267,c_1268,c_1991,c_2032,c_4048,c_5450,c_6678]) ).
tcf(c_14318,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_16 )
| ( sk_c6 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_14317]) ).
tcf(c_14342,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_16 )
| ( iPr_def_14 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_455,c_14318]) ).
tcf(c_14548,plain,
( ~ iPr_def_10
| ( inverse(sk_c8) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_2134,c_2134,c_5359,c_13488]) ).
tcf(c_14936,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c8)),multiply(X0,iPr_def_14)) = sk_c7,
inference(superposition,[status(thm)],[c_414,c_11563]) ).
tcf(c_14937,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c7)),multiply(X0,iPr_def_15)) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_11563]) ).
tcf(c_14940,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c5)),multiply(X0,iPr_def_16)) = sk_c6,
inference(superposition,[status(thm)],[c_416,c_11563]) ).
tcf(c_14942,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c8)),multiply(X0,iPr_def_22)) = sk_c3,
inference(superposition,[status(thm)],[c_422,c_11563]) ).
tcf(c_15006,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_16 )
| ( multiply(inverse(multiply(X0,sk_c8)),multiply(X0,iPr_def_22)) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_903,c_11563]) ).
tcf(c_15017,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_20)),multiply(X0,identity)) = sk_c4,
inference(superposition,[status(thm)],[c_939,c_11563]) ).
tcf(c_15018,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_18)),multiply(X0,identity)) = sk_c5,
inference(superposition,[status(thm)],[c_940,c_11563]) ).
tcf(c_15019,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_23)),multiply(X0,identity)) = sk_c1,
inference(superposition,[status(thm)],[c_941,c_11563]) ).
tcf(c_15020,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_17)),multiply(X0,identity)) = sk_c2,
inference(superposition,[status(thm)],[c_942,c_11563]) ).
tcf(c_15048,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(multiply(X0,sk_c5)),multiply(X0,iPr_def_16)) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1460,c_11563]) ).
tcf(c_15148,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),multiply(X0,identity)) = iPr_def_20,
inference(superposition,[status(thm)],[c_13919,c_11563]) ).
tcf(c_15150,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c5)),multiply(X0,identity)) = iPr_def_18,
inference(superposition,[status(thm)],[c_14285,c_11563]) ).
tcf(c_15162,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c5)),X0) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_15150,c_12779]) ).
tcf(c_15163,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),X0) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_15148,c_12779]) ).
tcf(c_15164,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_17)),X0) = sk_c2,
inference(light_normalisation,[status(thm)],[c_15020,c_12779]) ).
tcf(c_15165,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_23)),X0) = sk_c1,
inference(light_normalisation,[status(thm)],[c_15019,c_12779]) ).
tcf(c_15166,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_18)),X0) = sk_c5,
inference(light_normalisation,[status(thm)],[c_15018,c_12779]) ).
tcf(c_15167,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_20)),X0) = sk_c4,
inference(light_normalisation,[status(thm)],[c_15017,c_12779]) ).
tcf(c_17538,plain,
multiply(inverse(identity),multiply(inverse(sk_c8),iPr_def_14)) = sk_c7,
inference(superposition,[status(thm)],[c_84,c_14936]) ).
tcf(c_17571,plain,
multiply(inverse(multiply(inverse(iPr_def_14),sk_c8)),identity) = sk_c7,
inference(superposition,[status(thm)],[c_84,c_14936]) ).
tcf(c_17601,plain,
multiply(identity,sk_c7) = sk_c7,
inference(light_normalisation,[status(thm)],[c_17538,c_11554,c_12805]) ).
tcf(c_17815,plain,
multiply(sk_c5,sk_c6) = iPr_def_16,
inference(superposition,[status(thm)],[c_3382,c_14290]) ).
tcf(c_17982,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_11692,c_84]) ).
tcf(c_17991,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_11692,c_11549]) ).
tcf(c_17992,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_11692,c_12779]) ).
tcf(c_18018,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( identity = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1685,c_17982]) ).
tcf(c_18019,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1045,c_17982]) ).
tcf(c_18020,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1016,c_17982]) ).
tcf(c_18174,plain,
multiply(iPr_def_23,identity) = iPr_def_23,
inference(superposition,[status(thm)],[c_17982,c_2831]) ).
tcf(c_18203,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_12
| ( sk_c7 != identity )
| ( inverse(inverse(iPr_def_14)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_458,c_1913]) ).
tcf(c_19081,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_18020,c_18019]) ).
tcf(c_19087,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_10
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_18020,c_2154]) ).
tcf(c_19117,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_19,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_18020,c_903]) ).
tcf(c_19565,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_17992,c_12779]) ).
tcf(c_19659,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_22) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_1046,c_17991]) ).
tcf(c_19660,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_22) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_1017,c_17991]) ).
tcf(c_19664,plain,
multiply(sk_c1,sk_c8) = iPr_def_24,
inference(superposition,[status(thm)],[c_2910,c_17991]) ).
tcf(c_19670,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_4309,c_17991]) ).
tcf(c_19671,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_4267,c_17991]) ).
tcf(c_19685,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_24,sk_c3) = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_19671,c_9229]) ).
tcf(c_19688,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_24,sk_c3) = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_19670,c_9229]) ).
tcf(c_19708,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_24,sk_c3) = sk_c3 ) ),
inference(light_normalisation,[status(thm)],[c_19660,c_9229]) ).
tcf(c_19711,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_24,sk_c3) = sk_c3 ) ),
inference(light_normalisation,[status(thm)],[c_19659,c_9229]) ).
tcf(c_19774,plain,
inverse(multiply(inverse(iPr_def_14),sk_c8)) = sk_c7,
inference(demodulation,[status(thm)],[c_17571,c_12779]) ).
tcf(c_19794,plain,
multiply(sk_c7,multiply(inverse(iPr_def_14),sk_c8)) = identity,
inference(superposition,[status(thm)],[c_19774,c_84]) ).
tcf(c_19796,plain,
multiply(sk_c7,multiply(inverse(iPr_def_14),iPr_def_14)) = sk_c7,
inference(superposition,[status(thm)],[c_19774,c_14936]) ).
tcf(c_19855,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c7,multiply(inverse(iPr_def_14),iPr_def_14)) = identity ) ),
inference(superposition,[status(thm)],[c_5740,c_19794]) ).
tcf(c_19902,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_19855,c_19796]) ).
tcf(c_20476,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19081,c_83]) ).
tcf(c_20574,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_19902,c_443]) ).
tcf(c_20575,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_19902,c_442]) ).
tcf(c_20683,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_17)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c2,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11693,c_426]) ).
tcf(c_20685,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_11693,c_84]) ).
tcf(c_20694,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_11693,c_11549]) ).
tcf(c_20695,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_11693,c_12779]) ).
tcf(c_20709,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_17)) != sk_c8 )
| ( multiply(sk_c8,iPr_def_21) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_20683,c_421]) ).
tcf(c_20714,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( identity = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1544,c_20685]) ).
tcf(c_20754,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c2)),multiply(X0,identity)) = iPr_def_17,
inference(superposition,[status(thm)],[c_20685,c_11563]) ).
tcf(c_20758,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c2)),X0) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_20754,c_12779]) ).
tcf(c_22271,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_20575,c_20574]) ).
tcf(c_22472,plain,
( ( iPr_def_21 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_20714,c_18018]) ).
tcf(c_22524,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_20695,c_12779]) ).
tcf(c_22533,plain,
multiply(sk_c2,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_2901,c_20694]) ).
tcf(c_22682,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_22271,c_83]) ).
tcf(c_23596,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_22472,c_2414]) ).
tcf(c_28976,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,multiply(X1,sk_c5))),multiply(X0,X1)) = iPr_def_18,
inference(superposition,[status(thm)],[c_85,c_15162]) ).
tcf(c_29721,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_20476,c_10857]) ).
tcf(c_30996,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_24,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_29721,c_415]) ).
tcf(c_33978,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,multiply(X1,sk_c4))),multiply(X0,X1)) = iPr_def_20,
inference(superposition,[status(thm)],[c_85,c_15163]) ).
tcf(c_33979,plain,
multiply(inverse(identity),iPr_def_20) = iPr_def_20,
inference(superposition,[status(thm)],[c_939,c_15163]) ).
tcf(c_33997,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_20 )
| ( inverse(inverse(multiply(sk_c6,sk_c4))) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15163,c_427]) ).
tcf(c_34000,plain,
multiply(inverse(iPr_def_20),inverse(multiply(sk_c4,sk_c4))) = iPr_def_20,
inference(superposition,[status(thm)],[c_15163,c_15163]) ).
tcf(c_34002,plain,
multiply(identity,iPr_def_20) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_33979,c_12805]) ).
tcf(c_34005,plain,
multiply(sk_c4,inverse(multiply(sk_c4,sk_c4))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_34000,c_13983]) ).
tcf(c_34046,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,multiply(X1,iPr_def_17))),multiply(X0,X1)) = sk_c2,
inference(superposition,[status(thm)],[c_85,c_15164]) ).
tcf(c_34049,plain,
multiply(inverse(identity),sk_c2) = sk_c2,
inference(superposition,[status(thm)],[c_20685,c_15164]) ).
tcf(c_34071,plain,
multiply(inverse(sk_c2),inverse(multiply(iPr_def_17,iPr_def_17))) = sk_c2,
inference(superposition,[status(thm)],[c_15164,c_15164]) ).
tcf(c_34075,plain,
multiply(identity,sk_c2) = sk_c2,
inference(light_normalisation,[status(thm)],[c_34049,c_12805]) ).
tcf(c_34079,plain,
multiply(iPr_def_17,inverse(multiply(iPr_def_17,iPr_def_17))) = sk_c2,
inference(light_normalisation,[status(thm)],[c_34071,c_417]) ).
tcf(c_35221,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c1 )
| ( inverse(inverse(multiply(sk_c6,iPr_def_23))) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_15165,c_427]) ).
tcf(c_35224,plain,
multiply(inverse(sk_c1),inverse(multiply(iPr_def_17,iPr_def_23))) = sk_c2,
inference(superposition,[status(thm)],[c_15165,c_15164]) ).
tcf(c_35232,plain,
multiply(iPr_def_23,inverse(multiply(iPr_def_17,iPr_def_23))) = sk_c2,
inference(light_normalisation,[status(thm)],[c_35224,c_423]) ).
tcf(c_35831,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_22,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_2622,c_30996]) ).
tcf(c_36083,plain,
multiply(inverse(sk_c5),inverse(multiply(sk_c4,iPr_def_18))) = iPr_def_20,
inference(superposition,[status(thm)],[c_15166,c_15163]) ).
tcf(c_36088,plain,
multiply(iPr_def_18,inverse(multiply(sk_c4,iPr_def_18))) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_36083,c_418]) ).
tcf(c_36293,plain,
multiply(inverse(sk_c1),inverse(multiply(iPr_def_20,iPr_def_23))) = sk_c4,
inference(superposition,[status(thm)],[c_15165,c_15167]) ).
tcf(c_36310,plain,
multiply(inverse(sk_c4),inverse(multiply(iPr_def_23,iPr_def_20))) = sk_c1,
inference(superposition,[status(thm)],[c_15167,c_15165]) ).
tcf(c_36311,plain,
multiply(inverse(sk_c4),inverse(multiply(iPr_def_17,iPr_def_20))) = sk_c2,
inference(superposition,[status(thm)],[c_15167,c_15164]) ).
tcf(c_36312,plain,
multiply(inverse(sk_c4),inverse(multiply(iPr_def_20,iPr_def_20))) = sk_c4,
inference(superposition,[status(thm)],[c_15167,c_15167]) ).
tcf(c_36322,plain,
multiply(iPr_def_20,inverse(multiply(iPr_def_20,iPr_def_20))) = sk_c4,
inference(light_normalisation,[status(thm)],[c_36312,c_420]) ).
tcf(c_36323,plain,
multiply(iPr_def_20,inverse(multiply(iPr_def_17,iPr_def_20))) = sk_c2,
inference(light_normalisation,[status(thm)],[c_36311,c_420]) ).
tcf(c_36324,plain,
multiply(iPr_def_20,inverse(multiply(iPr_def_23,iPr_def_20))) = sk_c1,
inference(light_normalisation,[status(thm)],[c_36310,c_420]) ).
tcf(c_36326,plain,
multiply(iPr_def_23,inverse(multiply(iPr_def_20,iPr_def_23))) = sk_c4,
inference(light_normalisation,[status(thm)],[c_36293,c_423]) ).
tcf(c_38850,plain,
multiply(inverse(iPr_def_14),multiply(sk_c8,iPr_def_15)) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_14937]) ).
tcf(c_38854,plain,
multiply(inverse(identity),multiply(inverse(sk_c7),iPr_def_15)) = sk_c8,
inference(superposition,[status(thm)],[c_84,c_14937]) ).
tcf(c_38918,plain,
multiply(inverse(multiply(inverse(iPr_def_15),sk_c7)),identity) = sk_c8,
inference(superposition,[status(thm)],[c_84,c_14937]) ).
tcf(c_38953,plain,
multiply(inverse(iPr_def_14),multiply(iPr_def_14,sk_c8)) = sk_c8,
inference(light_normalisation,[status(thm)],[c_38850,c_8311]) ).
tcf(c_38954,plain,
multiply(identity,sk_c8) = sk_c8,
inference(light_normalisation,[status(thm)],[c_38854,c_11555,c_12805]) ).
tcf(c_39482,plain,
multiply(inverse(iPr_def_17),multiply(inverse(multiply(sk_c7,sk_c2)),iPr_def_15)) = sk_c8,
inference(superposition,[status(thm)],[c_20758,c_14937]) ).
tcf(c_39484,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_17 )
| ( inverse(inverse(multiply(sk_c6,sk_c2))) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_20758,c_427]) ).
tcf(c_39520,plain,
multiply(sk_c2,multiply(inverse(multiply(sk_c7,sk_c2)),iPr_def_15)) = sk_c8,
inference(light_normalisation,[status(thm)],[c_39482,c_22524]) ).
tcf(c_39614,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_15) = multiply(iPr_def_16,identity) ) ),
inference(superposition,[status(thm)],[c_12779,c_3370]) ).
tcf(c_39638,plain,
inverse(multiply(inverse(iPr_def_15),sk_c7)) = sk_c8,
inference(demodulation,[status(thm)],[c_38918,c_12779]) ).
tcf(c_39669,plain,
multiply(sk_c8,multiply(inverse(iPr_def_15),sk_c7)) = identity,
inference(superposition,[status(thm)],[c_39638,c_84]) ).
tcf(c_39784,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,multiply(inverse(iPr_def_15),sk_c7)) = identity ) ),
inference(superposition,[status(thm)],[c_448,c_39669]) ).
tcf(c_39787,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_19,multiply(inverse(iPr_def_15),sk_c7)) = identity ) ),
inference(superposition,[status(thm)],[c_432,c_39669]) ).
tcf(c_39811,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c8,multiply(inverse(iPr_def_15),iPr_def_22)) = identity ) ),
inference(superposition,[status(thm)],[c_443,c_39669]) ).
tcf(c_39812,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c8,multiply(inverse(iPr_def_15),iPr_def_22)) = identity ) ),
inference(superposition,[status(thm)],[c_442,c_39669]) ).
tcf(c_39818,plain,
multiply(inverse(sk_c8),identity) = multiply(inverse(iPr_def_15),sk_c7),
inference(superposition,[status(thm)],[c_39669,c_11549]) ).
tcf(c_39821,plain,
multiply(inverse(multiply(sk_c8,inverse(iPr_def_15))),identity) = sk_c7,
inference(superposition,[status(thm)],[c_39669,c_11563]) ).
tcf(c_39825,plain,
multiply(iPr_def_24,multiply(inverse(iPr_def_15),sk_c7)) = multiply(sk_c1,identity),
inference(superposition,[status(thm)],[c_39669,c_2814]) ).
tcf(c_39826,plain,
multiply(iPr_def_15,multiply(inverse(iPr_def_15),sk_c7)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_39669,c_2811]) ).
tcf(c_40925,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_18) = multiply(iPr_def_19,identity) ) ),
inference(superposition,[status(thm)],[c_12779,c_3378]) ).
tcf(c_40983,plain,
multiply(inverse(iPr_def_24),multiply(sk_c1,iPr_def_22)) = sk_c3,
inference(superposition,[status(thm)],[c_19664,c_14942]) ).
tcf(c_40988,plain,
multiply(inverse(identity),multiply(inverse(sk_c8),iPr_def_22)) = sk_c3,
inference(superposition,[status(thm)],[c_84,c_14942]) ).
tcf(c_41040,plain,
multiply(inverse(multiply(inverse(iPr_def_22),sk_c8)),identity) = sk_c3,
inference(superposition,[status(thm)],[c_84,c_14942]) ).
tcf(c_41091,plain,
multiply(inverse(iPr_def_24),multiply(iPr_def_24,sk_c3)) = sk_c3,
inference(light_normalisation,[status(thm)],[c_40983,c_9229]) ).
tcf(c_41093,plain,
multiply(identity,sk_c3) = sk_c3,
inference(light_normalisation,[status(thm)],[c_40988,c_11559,c_12805]) ).
tcf(c_41400,plain,
inverse(multiply(sk_c4,sk_c4)) = multiply(iPr_def_20,iPr_def_20),
inference(superposition,[status(thm)],[c_34005,c_2833]) ).
tcf(c_41561,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,multiply(inverse(iPr_def_15),iPr_def_24)) = identity ) ),
inference(superposition,[status(thm)],[c_453,c_39784]) ).
tcf(c_41567,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_23,multiply(inverse(iPr_def_15),iPr_def_22)) = identity ) ),
inference(superposition,[status(thm)],[c_443,c_39784]) ).
tcf(c_41882,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_19,multiply(inverse(iPr_def_15),iPr_def_18)) = identity ) ),
inference(superposition,[status(thm)],[c_431,c_39787]) ).
tcf(c_41883,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_19,multiply(inverse(iPr_def_15),iPr_def_16)) = identity ) ),
inference(superposition,[status(thm)],[c_430,c_39787]) ).
tcf(c_42081,plain,
inverse(multiply(inverse(iPr_def_22),sk_c8)) = sk_c3,
inference(demodulation,[status(thm)],[c_41040,c_12779]) ).
tcf(c_42106,plain,
multiply(sk_c3,multiply(inverse(iPr_def_22),sk_c8)) = identity,
inference(superposition,[status(thm)],[c_42081,c_84]) ).
tcf(c_42273,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_21,multiply(inverse(iPr_def_22),sk_c8)) = identity ) ),
inference(superposition,[status(thm)],[c_436,c_42106]) ).
tcf(c_42274,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_21,multiply(inverse(iPr_def_22),sk_c8)) = identity ) ),
inference(superposition,[status(thm)],[c_435,c_42106]) ).
tcf(c_42294,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c3,multiply(inverse(iPr_def_22),iPr_def_23)) = identity ) ),
inference(superposition,[status(thm)],[c_448,c_42106]) ).
tcf(c_42302,plain,
multiply(inverse(multiply(sk_c3,inverse(iPr_def_22))),identity) = sk_c8,
inference(superposition,[status(thm)],[c_42106,c_11563]) ).
tcf(c_42450,plain,
inverse(multiply(iPr_def_17,iPr_def_17)) = multiply(sk_c2,sk_c2),
inference(superposition,[status(thm)],[c_34079,c_20694]) ).
tcf(c_43509,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(multiply(sk_c8,inverse(iPr_def_15))),identity) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_39811,c_11563]) ).
tcf(c_43580,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(multiply(sk_c8,inverse(iPr_def_15))),identity) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_39812,c_11563]) ).
tcf(c_44479,plain,
inverse(multiply(iPr_def_17,iPr_def_23)) = multiply(sk_c1,sk_c2),
inference(superposition,[status(thm)],[c_35232,c_17991]) ).
tcf(c_44774,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(multiply(iPr_def_23,inverse(iPr_def_15))),identity) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_41561,c_11563]) ).
tcf(c_44888,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(multiply(iPr_def_23,inverse(iPr_def_15))),identity) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_41567,c_11563]) ).
tcf(c_45142,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(inverse(multiply(iPr_def_19,inverse(iPr_def_15))),identity) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_41882,c_11563]) ).
tcf(c_45171,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(inverse(multiply(iPr_def_19,inverse(iPr_def_15))),identity) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_41883,c_11563]) ).
tcf(c_45448,plain,
inverse(multiply(sk_c4,iPr_def_18)) = multiply(sk_c5,iPr_def_20),
inference(superposition,[status(thm)],[c_36088,c_14290]) ).
tcf(c_45464,plain,
multiply(iPr_def_18,multiply(sk_c5,iPr_def_20)) = iPr_def_20,
inference(demodulation,[status(thm)],[c_36088,c_45448]) ).
tcf(c_46223,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_21,multiply(inverse(iPr_def_21),sk_c8)) = identity ) ),
inference(superposition,[status(thm)],[c_23596,c_42273]) ).
tcf(c_46389,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_21,multiply(inverse(iPr_def_21),sk_c8)) = identity ) ),
inference(superposition,[status(thm)],[c_23596,c_42274]) ).
tcf(c_46699,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(inverse(multiply(sk_c3,inverse(iPr_def_22))),identity) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_42294,c_11563]) ).
tcf(c_48158,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_15,multiply(inverse(iPr_def_15),sk_c7)) = multiply(iPr_def_22,identity) ) ),
inference(superposition,[status(thm)],[c_39669,c_3509]) ).
tcf(c_48216,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c7,identity) = multiply(iPr_def_22,identity) ) ),
inference(light_normalisation,[status(thm)],[c_48158,c_39826]) ).
tcf(c_48967,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(inverse(multiply(sk_c8,multiply(iPr_def_18,sk_c5))),iPr_def_14) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_713,c_28976]) ).
tcf(c_49651,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(inverse(multiply(sk_c8,identity)),iPr_def_14) = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_48967,c_940]) ).
tcf(c_52688,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_20)),multiply(X0,sk_c4)) = inverse(multiply(iPr_def_20,iPr_def_20)),
inference(superposition,[status(thm)],[c_36322,c_11563]) ).
tcf(c_52690,plain,
inverse(multiply(iPr_def_20,iPr_def_20)) = multiply(sk_c4,sk_c4),
inference(superposition,[status(thm)],[c_36322,c_13924]) ).
tcf(c_53522,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(inverse(multiply(iPr_def_18,multiply(iPr_def_20,sk_c4))),iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_3130,c_33978]) ).
tcf(c_53621,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(multiply(X0,iPr_def_20)),multiply(X0,sk_c4))),sk_c4) = iPr_def_20,
inference(superposition,[status(thm)],[c_15167,c_33978]) ).
tcf(c_53730,plain,
multiply(multiply(iPr_def_20,iPr_def_20),sk_c4) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_53621,c_41400,c_52688,c_52690]) ).
tcf(c_53791,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(inverse(multiply(iPr_def_18,identity)),iPr_def_15) = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_53522,c_939]) ).
tcf(c_57421,plain,
inverse(multiply(iPr_def_17,iPr_def_20)) = multiply(sk_c4,sk_c2),
inference(superposition,[status(thm)],[c_36323,c_13924]) ).
tcf(c_57432,plain,
multiply(iPr_def_20,multiply(sk_c4,sk_c2)) = sk_c2,
inference(demodulation,[status(thm)],[c_36323,c_57421]) ).
tcf(c_57518,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_20,inverse(multiply(iPr_def_17,iPr_def_20))) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_10359,c_36324]) ).
tcf(c_57541,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_20,multiply(sk_c4,sk_c2)) = sk_c1 ) ),
inference(light_normalisation,[status(thm)],[c_57518,c_57421]) ).
tcf(c_58430,plain,
inverse(multiply(iPr_def_20,iPr_def_23)) = multiply(sk_c1,sk_c4),
inference(superposition,[status(thm)],[c_36326,c_17991]) ).
tcf(c_59321,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(inverse(multiply(X0,iPr_def_17)),multiply(X0,iPr_def_22)) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_22682,c_34046]) ).
tcf(c_59417,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(inverse(multiply(sk_c8,multiply(iPr_def_21,iPr_def_17))),iPr_def_22) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_903,c_34046]) ).
tcf(c_64396,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2314,c_12805]) ).
tcf(c_64429,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c8 != identity )
| ( multiply(iPr_def_20,iPr_def_20) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_18019,c_64396]) ).
tcf(c_64767,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c8,multiply(iPr_def_15,iPr_def_22)) = multiply(iPr_def_14,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_8786,c_3596]) ).
tcf(c_64800,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(inverse(multiply(iPr_def_14,sk_c4)),multiply(sk_c8,iPr_def_22)) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_3596,c_33978]) ).
tcf(c_75213,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_64800,c_64767,c_64429,c_59417,c_59321,c_58430,c_57541,c_57432,c_53791,c_53730,c_52690,c_49651,c_48216,c_46699,c_46389,c_46223,c_45464,c_45171,c_45142,c_44888,c_44774,c_44479,c_43580,c_43509,c_42450,c_42302,c_41400,c_41093,c_41091,c_40925,c_39826,c_39825,c_39821,c_39818,c_39614,c_39520,c_39484,c_38953,c_35831,c_35221,c_34075,c_34002,c_33997,c_22533,c_22524,c_20709,c_20685,c_19902,c_19711,c_19708,c_19688,c_19685,c_19664,c_19565,c_19117,c_19087,c_19081,c_18203,c_18174,c_18019,c_18018,c_17992,c_17815,c_15048,c_15006,c_14942,c_14940,c_14548,c_14342,c_14313,c_14310,c_14292,c_13999,c_13983,c_13978,c_13931,c_13917,c_13925,c_13919,c_13574,c_13492,c_13256,c_12940,c_12816,c_12815,c_12812,c_12811,c_12810,c_12809,c_12807,c_12806,c_12800,c_12799,c_12798,c_12796,c_12795,c_12794,c_12791,c_12805,c_17601,c_11679,c_11559,c_11555,c_11554,c_10642,c_9677,c_9657,c_9612,c_9229,c_9228,c_9200,c_8571,c_8551,c_6714,c_5584,c_5450,c_5359,c_4162,c_2622,c_2017,c_1926,c_1822,c_942,c_901,c_900,c_804,c_459,c_439,c_438,c_437,c_436,c_435,c_425,c_423,c_420,c_418,c_417,c_38954]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP281-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n017.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 14:16:35 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 22.48/9.29 % SZS status Started for theBenchmark.p
% 22.48/9.29 % SZS status Unsatisfiable for theBenchmark.p
% 22.48/9.29
% 22.48/9.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.48/9.29
% 22.48/9.29 % ------ iProver source info
% 22.48/9.29
% 22.48/9.29 % git: date: 2026-07-19 20:42:38 +0200
% 22.48/9.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.48/9.29 % git: non_committed_changes: false
% 22.48/9.29
% 22.48/9.29 % ------ Parsing...% successful
% 22.48/9.29
% 22.48/9.29
% 22.48/9.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.48/9.29
% 22.48/9.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.48/9.29
% 22.48/9.29 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.48/9.29
% 22.48/9.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 22.48/9.29 % ------ Proving...
% 22.48/9.29 % ------ Problem Properties
% 22.48/9.29
% 22.48/9.29 %
% 22.48/9.29 % clauses 49
% 22.48/9.29 % conjectures 35
% 22.48/9.29 % EPR 31
% 22.48/9.29 % Horn 18
% 22.48/9.29 % unary 14
% 22.48/9.29 % binary 30
% 22.48/9.29 % lits 92
% 22.48/9.29 % lits eq 84
% 22.48/9.29 % fd_pure 0
% 22.48/9.29 % fd_pseudo 0
% 22.48/9.29 % fd_cond 0
% 22.48/9.29 % fd_pseudo_cond 0
% 22.48/9.29 % AC symbols 0
% 22.48/9.29
% 22.48/9.29 % ------ Schedule dynamic 5 is on
% 22.48/9.29
% 22.48/9.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.48/9.29
% 22.48/9.29
% 22.48/9.29 % ------
% 22.48/9.29 % Current options:
% 22.48/9.29 % ------
% 22.48/9.29
% 22.48/9.29
% 22.48/9.29 %
% 22.48/9.29
% 22.48/9.29 % ------ Proving...
% 22.48/9.29 %
% 22.48/9.29
% 22.48/9.29 % SZS status Unsatisfiable for theBenchmark.p
% 22.48/9.29
% 22.48/9.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.49/9.30
% 26.49/9.30
%------------------------------------------------------------------------------