%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP211-1 : 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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:31:49 PM UTC 2026
% Result : Unsatisfiable 17.97s 8.77s
% Output : CNFRefutation 17.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 39
% Syntax : Number of formulae : 456 ( 167 unt; 10 def)
% Number of atoms : 1597 ( 791 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 556 ( 169 ~; 387 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 5 ( 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 : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 131 ( 0 sgn 131 !; 0 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c4)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c5)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X1,sk_c7)
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(reorient_equations,[],[f55]) ).
fof(f57,plain,
! [X2,X3,X0,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f56]) ).
fof(f58,plain,
! [X2,X3,X0,X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f57]) ).
tcf(c_78,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_79,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_81,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_84,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 )
| ( multiply(sk_c8,multiply(X3,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_351,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_106]) ).
tcf(c_352,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_106]) ).
tcf(c_353,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_106]) ).
tcf(c_354,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_355,definition,
iPr_def_13 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_356,definition,
iPr_def_14 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_357,definition,
iPr_def_15 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_358,definition,
iPr_def_16 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_359,definition,
iPr_def_17 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_360,definition,
iPr_def_18 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_361,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_362,definition,
iPr_def_20 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_363,definition,
iPr_def_21 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_364,definition,
iPr_def_22 = multiply(sk_c1,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_365,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_354]) ).
tcf(c_366,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_353]) ).
tcf(c_368,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_352]) ).
tcf(c_369,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_351]) ).
tcf(c_370,negated_conjecture,
( ( iPr_def_14 = sk_c8 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105,c_356,c_355]) ).
tcf(c_371,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104,c_357]) ).
tcf(c_372,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103,c_358]) ).
tcf(c_373,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102,c_359]) ).
tcf(c_374,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_13 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101,c_360]) ).
tcf(c_375,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100,c_361]) ).
tcf(c_376,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_378,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95,c_362]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_385,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_90,c_363]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_389,negated_conjecture,
( ( iPr_def_21 = sk_c2 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_85,c_364]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_392,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_393,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_395,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_396,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_592,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_370,c_373]) ).
tcf(c_602,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_374,c_373]) ).
tcf(c_634,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_375,c_357]) ).
tcf(c_635,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_374,c_357]) ).
tcf(c_636,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_373,c_357]) ).
tcf(c_649,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,sk_c6) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_370,c_358]) ).
tcf(c_685,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_378,c_357]) ).
tcf(c_710,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_19) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_379,c_357]) ).
tcf(c_785,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_395]) ).
tcf(c_788,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_396]) ).
tcf(c_827,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = inverse(X0) )
| ( sk_c8 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_396]) ).
tcf(c_833,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_788]) ).
tcf(c_877,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_396]) ).
tcf(c_883,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c3) )
| ( inverse(X0) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_833]) ).
tcf(c_897,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_360,c_79]) ).
tcf(c_898,plain,
multiply(iPr_def_14,sk_c5) = identity,
inference(superposition,[status(thm)],[c_356,c_79]) ).
tcf(c_899,plain,
multiply(iPr_def_21,sk_c1) = identity,
inference(superposition,[status(thm)],[c_363,c_79]) ).
tcf(c_900,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_361,c_79]) ).
tcf(c_905,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_385,c_364]) ).
tcf(c_928,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_387,c_364]) ).
tcf(c_938,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_388,c_364]) ).
tcf(c_953,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_389,c_364]) ).
tcf(c_978,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_390,c_357]) ).
tcf(c_979,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_390,c_375]) ).
tcf(c_1012,plain,
! [X0: $i] :
( ( sk_c8 = inverse(X0) )
| ( sk_c8 != iPr_def_19 )
| ( inverse(X0) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_827]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_19 )
| ( inverse(X0) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_877]) ).
tcf(c_1074,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_393,c_378]) ).
tcf(c_1076,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_393,c_357]) ).
tcf(c_1130,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_394,c_379]) ).
tcf(c_1133,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_394,c_357]) ).
tcf(c_1193,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_592,c_393]) ).
tcf(c_1194,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_592,c_390]) ).
tcf(c_1196,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_20 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_592,c_383]) ).
tcf(c_1197,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_592,c_380]) ).
tcf(c_1255,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_364,c_80]) ).
tcf(c_1256,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_359,c_80]) ).
tcf(c_1257,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c6,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_358,c_80]) ).
tcf(c_1258,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_357,c_80]) ).
tcf(c_1259,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_362,c_80]) ).
tcf(c_1260,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c7,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_355,c_80]) ).
tcf(c_1262,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1264,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_897,c_80]) ).
tcf(c_1265,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_898,c_80]) ).
tcf(c_1266,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_899,c_80]) ).
tcf(c_1267,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_900,c_80]) ).
tcf(c_1269,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1267,c_78]) ).
tcf(c_1270,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1266,c_78]) ).
tcf(c_1271,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1265,c_78]) ).
tcf(c_1272,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1264,c_78]) ).
tcf(c_1299,plain,
( ( inverse(sk_c3) = iPr_def_19 )
| ( iPr_def_19 != inverse(sk_c3) )
| ( inverse(sk_c3) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_883]) ).
tcf(c_1300,plain,
inverse(sk_c3) = inverse(sk_c3),
inference(instantiation,[status(thm)],[c_785]) ).
tcf(c_1322,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_602,c_394]) ).
tcf(c_1323,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_22 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_602,c_393]) ).
tcf(c_1325,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_20 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_602,c_384]) ).
tcf(c_1326,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_20 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_602,c_383]) ).
tcf(c_1328,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_19 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_602,c_379]) ).
tcf(c_1329,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_19 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_602,c_378]) ).
tcf(c_1673,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c3) )
| ( X0 != iPr_def_19 )
| ( inverse(sk_c3) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1055]) ).
tcf(c_1674,plain,
( ( sk_c8 = inverse(sk_c3) )
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c3) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1012]) ).
tcf(c_1991,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_396]) ).
tcf(c_2141,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_17 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_359,c_369]) ).
tcf(c_2143,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_13 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_355,c_369]) ).
tcf(c_2154,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( sk_c8 != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2143,c_361]) ).
tcf(c_2161,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_18 )
| ( sk_c8 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2141,c_360]) ).
tcf(c_2255,plain,
( ~ iPr_def_12
| ( inverse(inverse(sk_c8)) != sk_c8 )
| ( multiply(sk_c8,identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_79,c_366]) ).
tcf(c_2722,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1074,c_979]) ).
tcf(c_3045,plain,
( ( iPr_def_19 = iPr_def_22 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1130,c_1074]) ).
tcf(c_3165,plain,
multiply(iPr_def_19,iPr_def_13) = sk_c7,
inference(superposition,[status(thm)],[c_355,c_1269]) ).
tcf(c_3171,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_13,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3165,c_80]) ).
tcf(c_3173,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c2,
inference(superposition,[status(thm)],[c_364,c_1270]) ).
tcf(c_3176,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3173,c_80]) ).
tcf(c_3178,plain,
multiply(iPr_def_14,iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_357,c_1271]) ).
tcf(c_3181,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_15,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3178,c_80]) ).
tcf(c_3183,plain,
multiply(iPr_def_18,iPr_def_17) = sk_c7,
inference(superposition,[status(thm)],[c_359,c_1272]) ).
tcf(c_3186,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_17,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3183,c_80]) ).
tcf(c_3193,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_634,c_1271]) ).
tcf(c_3194,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3193,c_3178]) ).
tcf(c_3205,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_635,c_1271]) ).
tcf(c_3206,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3205,c_3178]) ).
tcf(c_3217,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_636,c_1271]) ).
tcf(c_3218,plain,
( ( sk_c8 = iPr_def_17 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3217,c_3178]) ).
tcf(c_3302,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_371,c_649]) ).
tcf(c_3303,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,multiply(sk_c6,X0)) = multiply(iPr_def_16,X0) ) ),
inference(superposition,[status(thm)],[c_649,c_80]) ).
tcf(c_3304,plain,
( ( sk_c8 = iPr_def_16 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_3302,c_3178]) ).
tcf(c_4262,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_685,c_1271]) ).
tcf(c_4263,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_4262,c_3178]) ).
tcf(c_4311,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_710,c_1271]) ).
tcf(c_4312,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4311,c_3178]) ).
tcf(c_5477,plain,
( ( sk_c8 = iPr_def_14 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_978,c_1271]) ).
tcf(c_5478,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5477,c_3178]) ).
tcf(c_5859,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1076,c_1271]) ).
tcf(c_5860,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5859,c_3178]) ).
tcf(c_5909,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1133,c_1271]) ).
tcf(c_5910,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5909,c_3178]) ).
tcf(c_5981,plain,
multiply(sk_c1,iPr_def_20) = multiply(iPr_def_22,sk_c7),
inference(superposition,[status(thm)],[c_362,c_1255]) ).
tcf(c_6457,plain,
multiply(sk_c5,iPr_def_16) = multiply(iPr_def_15,sk_c6),
inference(superposition,[status(thm)],[c_358,c_1258]) ).
tcf(c_7708,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1194,c_1193]) ).
tcf(c_8138,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1197,c_1196]) ).
tcf(c_8436,plain,
( ( identity = inverse(sk_c3) )
| ( identity != iPr_def_19 )
| ( inverse(sk_c3) != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1673]) ).
tcf(c_8653,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( iPr_def_13 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_7708,c_2722]) ).
tcf(c_8926,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1323,c_1322]) ).
tcf(c_9227,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1262,c_78]) ).
tcf(c_9234,plain,
multiply(inverse(sk_c8),iPr_def_16) = sk_c6,
inference(superposition,[status(thm)],[c_358,c_9227]) ).
tcf(c_9236,plain,
multiply(inverse(sk_c2),iPr_def_20) = sk_c7,
inference(superposition,[status(thm)],[c_362,c_9227]) ).
tcf(c_9238,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_78,c_9227]) ).
tcf(c_9239,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_9227]) ).
tcf(c_9315,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1272,c_9227]) ).
tcf(c_9316,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_1271,c_9227]) ).
tcf(c_9317,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1270,c_9227]) ).
tcf(c_9318,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1269,c_9227]) ).
tcf(c_9319,plain,
multiply(inverse(iPr_def_19),sk_c7) = iPr_def_13,
inference(superposition,[status(thm)],[c_3165,c_9227]) ).
tcf(c_9327,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_9227,c_9227]) ).
tcf(c_9786,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_9239,c_9327]) ).
tcf(c_9804,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_9786,c_9238]) ).
tcf(c_9866,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1326,c_1325]) ).
tcf(c_10177,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1329,c_1328]) ).
tcf(c_12140,plain,
multiply(sk_c7,identity) = multiply(iPr_def_19,iPr_def_13),
inference(superposition,[status(thm)],[c_9786,c_3171]) ).
tcf(c_12586,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_9315,c_79]) ).
tcf(c_12591,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_9315,c_9786]) ).
tcf(c_12817,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_12591,c_9786]) ).
tcf(c_12820,plain,
( ~ iPr_def_11
| ( multiply(iPr_def_18,sk_c4) != sk_c8 )
| ( multiply(inverse(iPr_def_18),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_12817,c_368]) ).
tcf(c_12822,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_17 )
| ( sk_c8 != identity ) ),
inference(light_normalisation,[status(thm)],[c_12820,c_359,c_897,c_12817]) ).
tcf(c_12890,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_9316,c_9227]) ).
tcf(c_12891,plain,
multiply(sk_c5,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_9316,c_9786]) ).
tcf(c_13078,plain,
inverse(iPr_def_14) = sk_c5,
inference(demodulation,[status(thm)],[c_12891,c_9786]) ).
tcf(c_13528,plain,
multiply(sk_c1,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_9317,c_79]) ).
tcf(c_13532,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_9317,c_9227]) ).
tcf(c_13543,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_953,c_13528]) ).
tcf(c_13544,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_938,c_13528]) ).
tcf(c_13545,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_928,c_13528]) ).
tcf(c_13546,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_905,c_13528]) ).
tcf(c_13602,plain,
multiply(sk_c1,sk_c2) = iPr_def_22,
inference(superposition,[status(thm)],[c_3173,c_13532]) ).
tcf(c_13917,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_13544,c_13543]) ).
tcf(c_14217,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_13545,c_359]) ).
tcf(c_14305,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_13546,c_13544]) ).
tcf(c_14350,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_14,sk_c6) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_13546,c_358]) ).
tcf(c_14554,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_13917,c_9804]) ).
tcf(c_14556,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_13917,c_78]) ).
tcf(c_14575,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_14305,c_9804]) ).
tcf(c_14577,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_14305,c_78]) ).
tcf(c_14867,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_9318,c_9227]) ).
tcf(c_14868,plain,
multiply(sk_c3,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_9318,c_9786]) ).
tcf(c_14949,plain,
inverse(iPr_def_19) = sk_c3,
inference(demodulation,[status(thm)],[c_14868,c_9786]) ).
tcf(c_14952,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(iPr_def_13) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_10177,c_14949]) ).
tcf(c_14953,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( inverse(iPr_def_13) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_8653,c_14949]) ).
tcf(c_14955,plain,
( ~ iPr_def_11
| ( multiply(iPr_def_19,sk_c3) != sk_c8 )
| ( multiply(inverse(iPr_def_19),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14949,c_368]) ).
tcf(c_14963,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_13 )
| ( sk_c8 != identity ) ),
inference(light_normalisation,[status(thm)],[c_14955,c_355,c_900,c_14949]) ).
tcf(c_14971,plain,
multiply(sk_c3,sk_c7) = iPr_def_13,
inference(superposition,[status(thm)],[c_3165,c_14867]) ).
tcf(c_15335,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(iPr_def_13) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_8926,c_14554]) ).
tcf(c_15338,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(iPr_def_19) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_3045,c_14554]) ).
tcf(c_15348,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c3 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_15338,c_14949]) ).
tcf(c_15687,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( inverse(iPr_def_13) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_7708,c_14575]) ).
tcf(c_15692,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( inverse(iPr_def_19) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_2722,c_14575]) ).
tcf(c_15699,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c3 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_15692,c_14949]) ).
tcf(c_16677,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c5,iPr_def_16) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_14350,c_12890]) ).
tcf(c_18952,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c3 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_15335,c_14952]) ).
tcf(c_19025,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_19,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_18952,c_900]) ).
tcf(c_19032,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_19025,c_3165]) ).
tcf(c_21247,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(sk_c2,identity) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_19032,c_362]) ).
tcf(c_21476,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c3 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_15687,c_14953]) ).
tcf(c_21511,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(iPr_def_19,iPr_def_13) = identity ) ),
inference(superposition,[status(thm)],[c_21476,c_900]) ).
tcf(c_21518,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_21511,c_3165]) ).
tcf(c_22905,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(sk_c2,identity) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_21518,c_362]) ).
tcf(c_24785,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c2 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_21247,c_9786]) ).
tcf(c_24817,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_24785,c_364]) ).
tcf(c_24821,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_24817,c_5981]) ).
tcf(c_28440,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c2 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_22905,c_9786]) ).
tcf(c_28472,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_28440,c_364]) ).
tcf(c_28476,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_28472,c_5981]) ).
tcf(c_31094,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,sk_c6) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_370,c_358]) ).
tcf(c_31096,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c8,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_376,c_358]) ).
tcf(c_31274,plain,
multiply(iPr_def_14,sk_c5) = identity,
inference(superposition,[status(thm)],[c_356,c_79]) ).
tcf(c_31462,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_13 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_355,c_369]) ).
tcf(c_31472,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 )
| ( sk_c8 != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_31462,c_361]) ).
tcf(c_31523,plain,
( ~ iPr_def_12
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,iPr_def_15) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_357,c_366]) ).
tcf(c_31544,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_14 )
| ( multiply(sk_c8,iPr_def_15) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_31523,c_356]) ).
tcf(c_32025,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_31274,c_80]) ).
tcf(c_32026,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_32025,c_78]) ).
tcf(c_32913,plain,
multiply(iPr_def_14,iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_357,c_32026]) ).
tcf(c_33205,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_371,c_31094]) ).
tcf(c_33207,plain,
( ( sk_c8 = iPr_def_16 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_33205,c_32913]) ).
tcf(c_33414,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_33207,c_374]) ).
tcf(c_33508,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_13 = iPr_def_18 )
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_33414,c_374]) ).
tcf(c_33937,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(X0)),multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(superposition,[status(thm)],[c_9327,c_80]) ).
tcf(c_33938,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_9327,c_79]) ).
tcf(c_33942,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_9327,c_9227]) ).
tcf(c_33943,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_9327,c_9786]) ).
tcf(c_33944,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_33943,c_9786]) ).
tcf(c_33969,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(inverse(X0),sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_368,c_33938]) ).
tcf(c_33974,plain,
inverse(inverse(sk_c8)) = sk_c8,
inference(instantiation,[status(thm)],[c_33944]) ).
tcf(c_35534,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_33938,c_80]) ).
tcf(c_35537,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( inverse(iPr_def_22) = identity ) ),
inference(superposition,[status(thm)],[c_33938,c_14577]) ).
tcf(c_35538,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(iPr_def_22) = identity ) ),
inference(superposition,[status(thm)],[c_33938,c_14556]) ).
tcf(c_35539,plain,
multiply(sk_c2,inverse(iPr_def_22)) = multiply(iPr_def_21,identity),
inference(superposition,[status(thm)],[c_33938,c_3176]) ).
tcf(c_35542,plain,
multiply(sk_c7,inverse(iPr_def_17)) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_33938,c_3186]) ).
tcf(c_35543,plain,
multiply(iPr_def_13,inverse(sk_c7)) = multiply(sk_c3,identity),
inference(superposition,[status(thm)],[c_33938,c_1260]) ).
tcf(c_35544,plain,
multiply(iPr_def_20,inverse(sk_c7)) = multiply(sk_c2,identity),
inference(superposition,[status(thm)],[c_33938,c_1259]) ).
tcf(c_35545,plain,
multiply(iPr_def_17,inverse(sk_c7)) = multiply(sk_c4,identity),
inference(superposition,[status(thm)],[c_33938,c_1256]) ).
tcf(c_35547,plain,
multiply(iPr_def_16,inverse(sk_c6)) = multiply(sk_c8,identity),
inference(superposition,[status(thm)],[c_33938,c_1257]) ).
tcf(c_35553,plain,
multiply(iPr_def_15,inverse(sk_c8)) = multiply(sk_c5,identity),
inference(superposition,[status(thm)],[c_33938,c_1258]) ).
tcf(c_35554,plain,
multiply(sk_c7,inverse(iPr_def_13)) = multiply(iPr_def_19,identity),
inference(superposition,[status(thm)],[c_33938,c_3171]) ).
tcf(c_35883,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_24821,c_14556]) ).
tcf(c_40876,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_28476,c_14577]) ).
tcf(c_41064,plain,
multiply(sk_c2,sk_c7) = iPr_def_20,
inference(superposition,[status(thm)],[c_9236,c_33942]) ).
tcf(c_41109,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_33942,c_366]) ).
tcf(c_41145,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_41109,c_33944]) ).
tcf(c_43082,plain,
( ( iPr_def_14 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_40876,c_41145]) ).
tcf(c_43083,plain,
( ( iPr_def_17 = iPr_def_18 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_35883,c_41145]) ).
tcf(c_43094,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_377,c_41145]) ).
tcf(c_43095,plain,
( ( sk_c8 = iPr_def_13 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_372,c_41145]) ).
tcf(c_44935,plain,
( ( sk_c8 = iPr_def_13 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_43095,c_3304,c_43095]) ).
tcf(c_44941,plain,
( iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_365,c_44935]) ).
tcf(c_44945,plain,
( iPr_def_11
| ( sk_c8 = iPr_def_13 ) ),
inference(global_subsumption_just,[status(thm)],[c_44941,c_365,c_2161,c_3206,c_3218,c_3304,c_43095]) ).
tcf(c_47103,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,multiply(iPr_def_15,X0)) = multiply(iPr_def_16,X0) ) ),
inference(superposition,[status(thm)],[c_371,c_3303]) ).
tcf(c_47114,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_13 )
| ( multiply(sk_c8,X0) = multiply(iPr_def_16,X0) ) ),
inference(light_normalisation,[status(thm)],[c_47103,c_3181]) ).
tcf(c_47316,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( inverse(iPr_def_19) = identity ) ),
inference(superposition,[status(thm)],[c_2722,c_35537]) ).
tcf(c_47330,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c3 = identity ) ),
inference(light_normalisation,[status(thm)],[c_47316,c_14949]) ).
tcf(c_47364,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_47330,c_15699]) ).
tcf(c_47644,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(iPr_def_19) = identity ) ),
inference(superposition,[status(thm)],[c_3045,c_35538]) ).
tcf(c_47661,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c3 = identity ) ),
inference(light_normalisation,[status(thm)],[c_47644,c_14949]) ).
tcf(c_47696,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_47661,c_15348]) ).
tcf(c_47811,plain,
multiply(sk_c2,inverse(iPr_def_22)) = iPr_def_21,
inference(demodulation,[status(thm)],[c_35539,c_9786]) ).
tcf(c_47842,plain,
multiply(iPr_def_22,inverse(iPr_def_22)) = multiply(sk_c1,iPr_def_21),
inference(superposition,[status(thm)],[c_47811,c_1255]) ).
tcf(c_47843,plain,
multiply(iPr_def_22,inverse(iPr_def_22)) = identity,
inference(light_normalisation,[status(thm)],[c_47842,c_13528]) ).
tcf(c_49169,plain,
multiply(sk_c7,inverse(iPr_def_17)) = iPr_def_18,
inference(demodulation,[status(thm)],[c_35542,c_9786]) ).
tcf(c_49194,plain,
multiply(iPr_def_17,inverse(iPr_def_17)) = multiply(sk_c4,iPr_def_18),
inference(superposition,[status(thm)],[c_49169,c_1256]) ).
tcf(c_49195,plain,
multiply(iPr_def_17,inverse(iPr_def_17)) = identity,
inference(light_normalisation,[status(thm)],[c_49194,c_12586]) ).
tcf(c_50210,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_31472,c_2161,c_2154,c_3206,c_3218]) ).
tcf(c_50212,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_50210,c_2161,c_4263,c_4312,c_50210]) ).
tcf(c_50214,plain,
( iPr_def_12
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_365,c_50212]) ).
tcf(c_51603,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(X0,inverse(multiply(sk_c6,X0)))) = multiply(sk_c8,identity),
inference(superposition,[status(thm)],[c_35534,c_1257]) ).
tcf(c_51726,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(X0,inverse(multiply(sk_c6,X0)))) = multiply(iPr_def_16,inverse(sk_c6)),
inference(light_normalisation,[status(thm)],[c_51603,c_35547]) ).
tcf(c_54315,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_2154,c_2161,c_4263,c_4312,c_50210]) ).
tcf(c_54317,plain,
( iPr_def_12
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_365,c_54315]) ).
tcf(c_54370,plain,
multiply(iPr_def_13,inverse(sk_c7)) = sk_c3,
inference(demodulation,[status(thm)],[c_35543,c_9786]) ).
tcf(c_54390,plain,
multiply(inverse(iPr_def_13),sk_c3) = inverse(sk_c7),
inference(superposition,[status(thm)],[c_54370,c_9227]) ).
tcf(c_54392,plain,
multiply(sk_c7,inverse(sk_c7)) = multiply(iPr_def_19,sk_c3),
inference(superposition,[status(thm)],[c_54370,c_3171]) ).
tcf(c_54444,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),multiply(sk_c3,X0)) = multiply(inverse(sk_c7),X0),
inference(superposition,[status(thm)],[c_54390,c_80]) ).
tcf(c_54764,plain,
multiply(iPr_def_20,inverse(sk_c7)) = sk_c2,
inference(demodulation,[status(thm)],[c_35544,c_9786]) ).
tcf(c_54766,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_13,inverse(sk_c7)) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_9866,c_54764]) ).
tcf(c_54767,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( multiply(iPr_def_13,inverse(sk_c7)) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_8138,c_54764]) ).
tcf(c_54789,plain,
multiply(inverse(iPr_def_20),sk_c2) = inverse(sk_c7),
inference(superposition,[status(thm)],[c_54764,c_9227]) ).
tcf(c_54828,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c2 = sk_c3 ) ),
inference(light_normalisation,[status(thm)],[c_54767,c_54370]) ).
tcf(c_54831,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c2 = sk_c3 ) ),
inference(light_normalisation,[status(thm)],[c_54766,c_54370]) ).
tcf(c_55476,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),multiply(sk_c2,X0)) = multiply(inverse(sk_c7),X0),
inference(superposition,[status(thm)],[c_54789,c_80]) ).
tcf(c_55665,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c2 = identity ) ),
inference(superposition,[status(thm)],[c_54828,c_47330]) ).
tcf(c_55765,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c2 = identity ) ),
inference(superposition,[status(thm)],[c_54831,c_47661]) ).
tcf(c_57519,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != inverse(sk_c3) )
| ( X0 != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_1991]) ).
tcf(c_57520,plain,
( ( sk_c8 = identity )
| ( identity != inverse(sk_c3) )
| ( sk_c8 != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_57519]) ).
tcf(c_58847,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_55665,c_388]) ).
tcf(c_58849,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_55665,c_385]) ).
tcf(c_60230,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_55765,c_389]) ).
tcf(c_60231,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_55765,c_388]) ).
tcf(c_60689,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_58847,c_361,c_1299,c_1300,c_1674,c_3218,c_4263,c_5860,c_8436,c_14963,c_43082,c_47364,c_50214,c_57520]) ).
tcf(c_61110,plain,
( ( iPr_def_14 = iPr_def_17 )
| ( sk_c8 = iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_58849,c_361,c_1299,c_1300,c_1674,c_3194,c_5478,c_8436,c_12822,c_43082,c_47364,c_50214,c_57520,c_60689]) ).
tcf(c_61198,plain,
iPr_def_14 = iPr_def_17,
inference(superposition,[status(thm)],[c_61110,c_60689]) ).
tcf(c_61307,plain,
multiply(sk_c7,inverse(iPr_def_14)) = iPr_def_18,
inference(demodulation,[status(thm)],[c_49169,c_61198]) ).
tcf(c_61366,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_14217,c_61198]) ).
tcf(c_61410,plain,
multiply(iPr_def_18,iPr_def_14) = sk_c7,
inference(demodulation,[status(thm)],[c_3183,c_61198]) ).
tcf(c_61419,plain,
multiply(sk_c4,sk_c7) = iPr_def_14,
inference(demodulation,[status(thm)],[c_359,c_61198]) ).
tcf(c_61440,plain,
multiply(sk_c7,sk_c5) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_61307,c_13078]) ).
tcf(c_61529,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c8 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_60230,c_361,c_1299,c_1300,c_1674,c_3206,c_4312,c_5910,c_8436,c_14963,c_43083,c_47696,c_50214,c_57520]) ).
tcf(c_61531,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_61529,c_61198]) ).
tcf(c_61704,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c8 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_60231,c_361,c_1299,c_1300,c_1674,c_3218,c_4263,c_5860,c_8436,c_14963,c_43083,c_47696,c_50214,c_57520]) ).
tcf(c_61706,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_61704,c_61198]) ).
tcf(c_61752,plain,
iPr_def_14 = iPr_def_18,
inference(superposition,[status(thm)],[c_61706,c_61531]) ).
tcf(c_61807,plain,
multiply(sk_c7,sk_c5) = iPr_def_14,
inference(demodulation,[status(thm)],[c_61440,c_61752]) ).
tcf(c_61808,plain,
multiply(iPr_def_14,iPr_def_14) = sk_c7,
inference(demodulation,[status(thm)],[c_61410,c_61752]) ).
tcf(c_61827,plain,
inverse(iPr_def_14) = sk_c4,
inference(demodulation,[status(thm)],[c_12817,c_61752]) ).
tcf(c_61830,plain,
multiply(sk_c4,iPr_def_14) = identity,
inference(demodulation,[status(thm)],[c_12586,c_61752]) ).
tcf(c_61859,plain,
multiply(iPr_def_14,sk_c4) = identity,
inference(demodulation,[status(thm)],[c_897,c_61752]) ).
tcf(c_61864,plain,
sk_c4 = sk_c5,
inference(demodulation,[status(thm)],[c_13078,c_61827]) ).
tcf(c_61872,plain,
multiply(sk_c4,iPr_def_16) = multiply(iPr_def_15,sk_c6),
inference(demodulation,[status(thm)],[c_6457,c_61864]) ).
tcf(c_61879,plain,
multiply(sk_c4,sk_c8) = iPr_def_15,
inference(demodulation,[status(thm)],[c_357,c_61864]) ).
tcf(c_61947,plain,
multiply(sk_c7,sk_c4) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_61807,c_61864]) ).
tcf(c_61956,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_16,sk_c4) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_372,c_61947]) ).
tcf(c_61957,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c4,
inference(superposition,[status(thm)],[c_61947,c_9227]) ).
tcf(c_61958,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c4,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_61947,c_80]) ).
tcf(c_61973,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_14,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_61808,c_80]) ).
tcf(c_61980,plain,
multiply(inverse(iPr_def_14),identity) = sk_c4,
inference(superposition,[status(thm)],[c_61859,c_9227]) ).
tcf(c_61982,plain,
multiply(iPr_def_14,inverse(sk_c7)) = sk_c4,
inference(light_normalisation,[status(thm)],[c_61980,c_35545,c_61198,c_61827]) ).
tcf(c_62043,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_13546,c_61879]) ).
tcf(c_62082,plain,
! [X0: $i] : multiply(inverse(sk_c7),multiply(iPr_def_14,X0)) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_61957,c_80]) ).
tcf(c_62097,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(inverse(sk_c7),X0)) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_61982,c_80]) ).
tcf(c_62169,plain,
multiply(sk_c7,iPr_def_14) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_61419,c_61958]) ).
tcf(c_62172,plain,
multiply(sk_c7,sk_c4) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_9786,c_61958]) ).
tcf(c_62174,plain,
multiply(sk_c7,identity) = multiply(iPr_def_14,iPr_def_14),
inference(superposition,[status(thm)],[c_61830,c_61958]) ).
tcf(c_62201,plain,
multiply(sk_c7,inverse(sk_c7)) = multiply(iPr_def_14,sk_c4),
inference(superposition,[status(thm)],[c_61982,c_61973]) ).
tcf(c_62290,plain,
multiply(inverse(sk_c7),sk_c7) = multiply(sk_c4,iPr_def_14),
inference(superposition,[status(thm)],[c_61808,c_62082]) ).
tcf(c_62346,plain,
multiply(sk_c4,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_79,c_62097]) ).
tcf(c_62351,plain,
multiply(sk_c4,iPr_def_14) = multiply(iPr_def_14,sk_c4),
inference(superposition,[status(thm)],[c_61957,c_62097]) ).
tcf(c_62602,plain,
( ~ iPr_def_11
| ( sk_c8 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_33969,c_3218,c_12822,c_14963]) ).
tcf(c_62625,plain,
( ( sk_c8 = iPr_def_13 )
| ~ iPr_def_11
| ( identity != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_370,c_62602]) ).
tcf(c_62682,plain,
( ( sk_c8 = iPr_def_13 )
| ( identity != iPr_def_14 ) ),
inference(global_subsumption_just,[status(thm)],[c_62625,c_44945,c_62625]) ).
tcf(c_63060,plain,
( ~ iPr_def_12
| ( multiply(sk_c8,identity) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_2255,c_2255,c_33974]) ).
tcf(c_63197,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,X0) = multiply(iPr_def_16,X0) ) ),
inference(superposition,[status(thm)],[c_370,c_47114]) ).
tcf(c_63332,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,sk_c4) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_63197,c_61956]) ).
tcf(c_63338,plain,
( ( identity = iPr_def_14 )
| ( sk_c8 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_63332,c_61859]) ).
tcf(c_63458,plain,
multiply(inverse(sk_c7),sk_c7) = multiply(inverse(iPr_def_13),iPr_def_13),
inference(superposition,[status(thm)],[c_14971,c_54444]) ).
tcf(c_63496,plain,
multiply(inverse(sk_c7),sk_c7) = multiply(inverse(iPr_def_20),iPr_def_20),
inference(superposition,[status(thm)],[c_41064,c_55476]) ).
tcf(c_63516,plain,
multiply(inverse(iPr_def_13),iPr_def_13) = multiply(inverse(iPr_def_20),iPr_def_20),
inference(light_normalisation,[status(thm)],[c_63496,c_63458]) ).
tcf(c_64599,plain,
! [X0: $i] : multiply(multiply(iPr_def_15,sk_c6),X0) = multiply(sk_c4,multiply(iPr_def_16,X0)),
inference(superposition,[status(thm)],[c_61872,c_80]) ).
tcf(c_64626,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_16,X0)) = multiply(iPr_def_15,multiply(sk_c6,X0)),
inference(demodulation,[status(thm)],[c_64599,c_33937,c_33944]) ).
tcf(c_64631,plain,
multiply(iPr_def_15,multiply(sk_c6,identity)) = multiply(sk_c4,iPr_def_16),
inference(superposition,[status(thm)],[c_9786,c_64626]) ).
tcf(c_64642,plain,
multiply(iPr_def_15,multiply(sk_c6,identity)) = multiply(iPr_def_15,sk_c6),
inference(light_normalisation,[status(thm)],[c_64631,c_61872]) ).
tcf(c_64694,plain,
( ( sk_c8 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_16) = multiply(iPr_def_16,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_372,c_62169]) ).
tcf(c_65131,plain,
sk_c8 = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_64694,c_62682,c_63338]) ).
tcf(c_65156,plain,
multiply(sk_c4,iPr_def_13) = iPr_def_15,
inference(demodulation,[status(thm)],[c_61879,c_65131]) ).
tcf(c_65174,plain,
( ( iPr_def_13 = iPr_def_19 )
| ~ iPr_def_12
| ( iPr_def_13 != iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_43094,c_65131]) ).
tcf(c_65189,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_15,X0)) = multiply(iPr_def_13,X0),
inference(demodulation,[status(thm)],[c_3181,c_65131]) ).
tcf(c_65190,plain,
multiply(inverse(iPr_def_13),iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_9234,c_65131]) ).
tcf(c_65229,plain,
( ( iPr_def_13 = iPr_def_19 )
| ( sk_c7 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_377,c_65131]) ).
tcf(c_65232,plain,
( ( iPr_def_13 = iPr_def_19 )
| ( iPr_def_13 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_375,c_65131]) ).
tcf(c_66149,plain,
multiply(iPr_def_16,inverse(sk_c6)) = multiply(iPr_def_13,identity),
inference(light_normalisation,[status(thm)],[c_35547,c_65131]) ).
tcf(c_66150,plain,
multiply(iPr_def_16,inverse(sk_c6)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_66149,c_9786]) ).
tcf(c_66158,plain,
multiply(iPr_def_15,multiply(sk_c6,inverse(sk_c6))) = multiply(sk_c4,iPr_def_13),
inference(superposition,[status(thm)],[c_66150,c_64626]) ).
tcf(c_66159,plain,
multiply(iPr_def_15,multiply(sk_c6,inverse(sk_c6))) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_66158,c_65156]) ).
tcf(c_66621,plain,
sk_c8 = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_33508,c_62682,c_63338]) ).
tcf(c_66651,plain,
( ( iPr_def_13 = iPr_def_19 )
| ( multiply(iPr_def_13,iPr_def_15) = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_31096,c_66621]) ).
tcf(c_67791,plain,
( ~ iPr_def_12
| ( iPr_def_13 != iPr_def_14 )
| ( multiply(iPr_def_13,iPr_def_15) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_31544,c_66621]) ).
tcf(c_67803,plain,
( ( iPr_def_13 = iPr_def_19 )
| ~ iPr_def_12
| ( iPr_def_13 != iPr_def_14 )
| ( sk_c7 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_66651,c_67791]) ).
tcf(c_68851,plain,
multiply(iPr_def_15,inverse(iPr_def_13)) = multiply(sk_c4,identity),
inference(light_normalisation,[status(thm)],[c_35553,c_61864,c_65131]) ).
tcf(c_68852,plain,
multiply(iPr_def_15,inverse(iPr_def_13)) = sk_c4,
inference(demodulation,[status(thm)],[c_68851,c_9786]) ).
tcf(c_68859,plain,
multiply(inverse(iPr_def_15),sk_c4) = inverse(iPr_def_13),
inference(superposition,[status(thm)],[c_68852,c_9227]) ).
tcf(c_68863,plain,
multiply(iPr_def_13,inverse(iPr_def_13)) = multiply(iPr_def_14,sk_c4),
inference(superposition,[status(thm)],[c_68852,c_65189]) ).
tcf(c_68898,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),multiply(sk_c4,X0)) = multiply(inverse(iPr_def_13),X0),
inference(superposition,[status(thm)],[c_68859,c_80]) ).
tcf(c_69020,plain,
multiply(sk_c7,inverse(iPr_def_13)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_35554,c_9786]) ).
tcf(c_70234,plain,
( ( iPr_def_13 = iPr_def_19 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_65174,c_65232,c_65229,c_67803]) ).
tcf(c_70240,plain,
( iPr_def_11
| ( iPr_def_13 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_54317,c_70234]) ).
tcf(c_70745,plain,
multiply(inverse(iPr_def_15),multiply(iPr_def_15,sk_c6)) = multiply(inverse(iPr_def_13),iPr_def_16),
inference(superposition,[status(thm)],[c_61872,c_68898]) ).
tcf(c_70762,plain,
multiply(inverse(iPr_def_15),multiply(iPr_def_15,sk_c6)) = sk_c6,
inference(light_normalisation,[status(thm)],[c_70745,c_65190]) ).
tcf(c_73020,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_70762,c_70745,c_70240,c_69020,c_68863,c_66159,c_66158,c_66150,c_65131,c_64642,c_64631,c_63516,c_63496,c_63060,c_62351,c_62346,c_62290,c_62201,c_62174,c_62172,c_62043,c_61947,c_61859,c_61808,c_61752,c_61366,c_54392,c_51726,c_51603,c_54317,c_49195,c_49194,c_47843,c_47842,c_35554,c_16677,c_14971,c_14955,c_14949,c_13602,c_13546,c_12817,c_12140,c_9319,c_6457,c_394,c_392,c_391,c_386,c_379,c_377,c_376]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP211-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n007.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 14:07:43 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 17.97/8.77 % SZS status Started for theBenchmark.p
% 17.97/8.77 % SZS status Unsatisfiable for theBenchmark.p
% 17.97/8.77
% 17.97/8.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.97/8.77
% 17.97/8.77 % ------ iProver source info
% 17.97/8.77
% 17.97/8.77 % git: date: 2026-07-19 20:42:38 +0200
% 17.97/8.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.97/8.77 % git: non_committed_changes: false
% 17.97/8.77
% 17.97/8.77 % ------ Parsing...% successful
% 17.97/8.77
% 17.97/8.77
% 17.97/8.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.97/8.77
% 17.97/8.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 17.97/8.77
% 17.97/8.77 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.97/8.77
% 17.97/8.77 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 17.97/8.77 % ------ Proving...
% 17.97/8.77 % ------ Problem Properties
% 17.97/8.77
% 17.97/8.77 %
% 17.97/8.77 % clauses 42
% 17.97/8.77 % conjectures 29
% 17.97/8.77 % EPR 26
% 17.97/8.77 % Horn 16
% 17.97/8.77 % unary 13
% 17.97/8.77 % binary 25
% 17.97/8.77 % lits 75
% 17.97/8.77 % lits eq 69
% 17.97/8.77 % fd_pure 0
% 17.97/8.77 % fd_pseudo 0
% 17.97/8.77 % fd_cond 0
% 17.97/8.77 % fd_pseudo_cond 0
% 17.97/8.77 % AC symbols 0
% 17.97/8.77
% 17.97/8.77 % ------ Schedule dynamic 5 is on
% 17.97/8.77
% 17.97/8.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.97/8.77
% 17.97/8.77
% 17.97/8.77 % ------
% 17.97/8.77 % Current options:
% 17.97/8.77 % ------
% 17.97/8.77
% 17.97/8.77
% 17.97/8.77 %
% 17.97/8.77
% 17.97/8.77 % ------ Proving...
% 17.97/8.77 %
% 17.97/8.77
% 17.97/8.77 % SZS status Unsatisfiable for theBenchmark.p
% 17.97/8.77
% 17.97/8.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.97/8.78
% 17.97/8.78
%------------------------------------------------------------------------------