%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:27 PM UTC 2026
% Result : Unsatisfiable 17.97s 3.21s
% Output : CNFRefutation 17.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 43
% Syntax : Number of formulae : 355 ( 125 unt; 12 def)
% Number of atoms : 1131 ( 617 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 488 ( 159 ~; 329 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 97 !; 0 ?; 74 :)
% 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_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c9 = inverse(sk_c4)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f12]) ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( inverse(sk_c8) = sk_c7
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f24,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = inverse(sk_c5)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f24]) ).
fof(f28,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( inverse(sk_c8) = sk_c7
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c9 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f36]) ).
fof(f40,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c9 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f48]) ).
fof(f54,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = inverse(sk_c3) ),
inference(reorient_equations,[],[f56]) ).
fof(f64,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
( inverse(sk_c8) = sk_c7
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f64]) ).
fof(f66,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f67,plain,
( sk_c9 = inverse(sk_c4)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f66]) ).
fof(f68,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f69,plain,
( sk_c9 = multiply(sk_c4,sk_c8)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f68]) ).
fof(f70,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f71,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f70]) ).
fof(f72,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f73,plain,
( sk_c6 = inverse(sk_c5)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f72]) ).
fof(f74,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f75,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c9 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f74]) ).
fof(f76,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( multiply(X5,sk_c7) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c9
| inverse(X2) != sk_c9
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != multiply(X5,sk_c7)
| inverse(X4) != X5
| sk_c8 != multiply(X4,X5)
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3)
| inverse(sk_c8) != sk_c7
| sk_c9 != multiply(X2,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X1,sk_c8)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9) ),
inference(reorient_equations,[],[f76]) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != multiply(inverse(X4),sk_c7)
| sk_c8 != multiply(X4,inverse(X4))
| sk_c9 != multiply(X3,sk_c8)
| sk_c9 != inverse(X3)
| inverse(sk_c8) != sk_c7
| sk_c9 != multiply(X2,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X1,sk_c8)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9) ),
inference(equality_resolution,[],[f77]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_90,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_94,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c8 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c4) = sk_c9 )
| ( multiply(sk_c3,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_124,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c9 )
| ( multiply(sk_c4,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_125,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c9 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_127,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c9 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X4) != sk_c8 )
| ( inverse(X2) != sk_c9 )
| ( inverse(X1) != sk_c9 )
| ( inverse(X0) != sk_c9 )
| ( multiply(X4,sk_c8) != sk_c7 )
| ( multiply(X2,sk_c7) != sk_c9 )
| ( multiply(X1,sk_c8) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 )
| ( multiply(inverse(X3),sk_c7) != sk_c8 )
| ( multiply(X3,inverse(X3)) != sk_c8 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_474,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c7) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_476,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_477,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_128]) ).
tcf(c_478,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_479,definition,
iPr_def_15 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,definition,
iPr_def_16 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_481,definition,
iPr_def_17 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_482,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_483,definition,
iPr_def_19 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_484,definition,
iPr_def_20 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_485,definition,
iPr_def_21 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_486,definition,
iPr_def_22 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_487,definition,
iPr_def_23 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_488,definition,
iPr_def_24 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_489,definition,
iPr_def_25 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_490,definition,
iPr_def_26 = multiply(sk_c1,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_491,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_478,c_479]) ).
tcf(c_492,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_477]) ).
tcf(c_493,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_476]) ).
tcf(c_494,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_475]) ).
tcf(c_495,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c7) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_474]) ).
tcf(c_496,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c8) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_473]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_127,c_481,c_480]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_126,c_482]) ).
tcf(c_499,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_125,c_483]) ).
tcf(c_500,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_124,c_484]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_123,c_485]) ).
tcf(c_502,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_22 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_516,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_517,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_518,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_519,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_520,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_522,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_524,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_526,negated_conjecture,
( ( iPr_def_25 = sk_c9 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_528,negated_conjecture,
( ( iPr_def_26 = sk_c8 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_529,negated_conjecture,
( ( iPr_def_26 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_530,negated_conjecture,
( ( iPr_def_26 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_531,negated_conjecture,
( ( iPr_def_26 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_532,negated_conjecture,
( ( iPr_def_26 = sk_c8 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_990,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_510,c_483]) ).
tcf(c_1011,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_512,c_490]) ).
tcf(c_1012,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_507,c_490]) ).
tcf(c_1013,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_506,c_490]) ).
tcf(c_1016,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_501,c_490]) ).
tcf(c_1017,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_500,c_490]) ).
tcf(c_1038,plain,
multiply(iPr_def_15,sk_c8) = identity,
inference(superposition,[status(thm)],[c_479,c_90]) ).
tcf(c_1039,plain,
multiply(iPr_def_21,sk_c4) = identity,
inference(superposition,[status(thm)],[c_485,c_90]) ).
tcf(c_1040,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_482,c_90]) ).
tcf(c_1041,plain,
multiply(iPr_def_25,sk_c1) = identity,
inference(superposition,[status(thm)],[c_489,c_90]) ).
tcf(c_1042,plain,
multiply(iPr_def_23,sk_c2) = identity,
inference(superposition,[status(thm)],[c_487,c_90]) ).
tcf(c_1043,plain,
multiply(iPr_def_22,sk_c3) = identity,
inference(superposition,[status(thm)],[c_486,c_90]) ).
tcf(c_1052,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_15,iPr_def_23) = identity ) ),
inference(superposition,[status(thm)],[c_511,c_1038]) ).
tcf(c_1073,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_513,c_490]) ).
tcf(c_1140,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c3,iPr_def_15) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_514,c_481]) ).
tcf(c_1175,plain,
( ( sk_c7 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_516,c_483]) ).
tcf(c_1191,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c6,iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_517,c_480]) ).
tcf(c_1215,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_518,c_481]) ).
tcf(c_1216,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c6,iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_518,c_480]) ).
tcf(c_1251,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_24) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_519,c_481]) ).
tcf(c_1252,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c6,iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_519,c_480]) ).
tcf(c_1281,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c6,iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_520,c_480]) ).
tcf(c_1388,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_522,c_483]) ).
tcf(c_1566,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(sk_c3,iPr_def_15) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_526,c_481]) ).
tcf(c_1629,plain,
( ( sk_c8 = iPr_def_26 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_528,c_483]) ).
tcf(c_1654,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_26) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_529,c_488]) ).
tcf(c_1690,plain,
( ( sk_c8 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_530,c_490]) ).
tcf(c_1776,plain,
( ( sk_c8 = iPr_def_26 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_531,c_490]) ).
tcf(c_1851,plain,
( ( sk_c8 = iPr_def_26 )
| ( multiply(sk_c3,iPr_def_15) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_532,c_481]) ).
tcf(c_1920,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_21 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_519,c_491]) ).
tcf(c_1921,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_20 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_518,c_491]) ).
tcf(c_2031,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c2) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_488,c_493]) ).
tcf(c_2032,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_89,c_493]) ).
tcf(c_2034,plain,
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( inverse(iPr_def_15) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_1038,c_493]) ).
tcf(c_2045,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2031,c_487]) ).
tcf(c_2119,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_26 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_490,c_494]) ).
tcf(c_2121,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_90,c_494]) ).
tcf(c_2141,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_26 )
| ( sk_c9 != iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_2119,c_489]) ).
tcf(c_2317,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_484,c_91]) ).
tcf(c_2318,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_483,c_91]) ).
tcf(c_2320,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_488,c_91]) ).
tcf(c_2323,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2325,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1038,c_91]) ).
tcf(c_2326,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1039,c_91]) ).
tcf(c_2327,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1040,c_91]) ).
tcf(c_2328,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1041,c_91]) ).
tcf(c_2329,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1042,c_91]) ).
tcf(c_2330,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1043,c_91]) ).
tcf(c_2334,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2330,c_89]) ).
tcf(c_2335,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2329,c_89]) ).
tcf(c_2336,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2328,c_89]) ).
tcf(c_2337,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2327,c_89]) ).
tcf(c_2338,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2326,c_89]) ).
tcf(c_2339,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2325,c_89]) ).
tcf(c_3017,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_17 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_481,c_495]) ).
tcf(c_3034,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_22 )
| ( sk_c9 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3017,c_486]) ).
tcf(c_3130,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_20 )
| ( inverse(sk_c4) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_484,c_496]) ).
tcf(c_3156,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_21 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3130,c_485]) ).
tcf(c_3252,plain,
( ~ iPr_def_14
| ( inverse(identity) != sk_c8 )
| ( multiply(inverse(identity),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_89,c_492]) ).
tcf(c_4052,plain,
multiply(iPr_def_22,iPr_def_17) = sk_c7,
inference(superposition,[status(thm)],[c_481,c_2334]) ).
tcf(c_4057,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_488,c_2335]) ).
tcf(c_4062,plain,
multiply(iPr_def_25,iPr_def_26) = sk_c9,
inference(superposition,[status(thm)],[c_490,c_2336]) ).
tcf(c_4075,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_483,c_2337]) ).
tcf(c_4238,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_484,c_2338]) ).
tcf(c_5003,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1011,c_2336]) ).
tcf(c_5004,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5003,c_4062]) ).
tcf(c_5161,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1012,c_2336]) ).
tcf(c_5162,plain,
( ( sk_c9 = iPr_def_22 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_5161,c_4062]) ).
tcf(c_5177,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1013,c_2336]) ).
tcf(c_5178,plain,
( ( sk_c9 = iPr_def_22 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5177,c_4062]) ).
tcf(c_5220,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1016,c_2336]) ).
tcf(c_5221,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5220,c_4062]) ).
tcf(c_5232,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1017,c_2336]) ).
tcf(c_5233,plain,
( ( sk_c9 = iPr_def_20 )
| ( sk_c9 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_5232,c_4062]) ).
tcf(c_5450,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1073,c_2336]) ).
tcf(c_5451,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_5450,c_4062]) ).
tcf(c_5462,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(iPr_def_22,iPr_def_17) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1140,c_2334]) ).
tcf(c_5463,plain,
( ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_5462,c_4052]) ).
tcf(c_5663,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_17) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1215,c_2334]) ).
tcf(c_5664,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5663,c_4052]) ).
tcf(c_5698,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_22,iPr_def_17) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1251,c_2334]) ).
tcf(c_5699,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_5698,c_4052]) ).
tcf(c_6075,plain,
( ( sk_c9 = iPr_def_25 )
| ( multiply(iPr_def_22,iPr_def_17) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1566,c_2334]) ).
tcf(c_6076,plain,
( ( sk_c7 = iPr_def_15 )
| ( sk_c9 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_6075,c_4052]) ).
tcf(c_6391,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_1654,c_2335]) ).
tcf(c_6392,plain,
( ( sk_c8 = iPr_def_26 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_6391,c_4057]) ).
tcf(c_6415,plain,
( ( sk_c8 = iPr_def_26 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1690,c_2336]) ).
tcf(c_6416,plain,
( ( sk_c8 = iPr_def_26 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6415,c_4062]) ).
tcf(c_6427,plain,
( ( sk_c8 = iPr_def_26 )
| ( multiply(iPr_def_25,iPr_def_26) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1776,c_2336]) ).
tcf(c_6428,plain,
( ( sk_c8 = iPr_def_26 )
| ( sk_c9 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_6427,c_4062]) ).
tcf(c_6439,plain,
( ( sk_c8 = iPr_def_26 )
| ( multiply(iPr_def_22,iPr_def_17) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1851,c_2334]) ).
tcf(c_6440,plain,
( ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_26 ) ),
inference(light_normalisation,[status(thm)],[c_6439,c_4052]) ).
tcf(c_6699,plain,
multiply(sk_c5,iPr_def_16) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_480,c_2318]) ).
tcf(c_7851,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2323,c_89]) ).
tcf(c_7875,plain,
multiply(inverse(sk_c6),iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_480,c_7851]) ).
tcf(c_7878,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_7851]) ).
tcf(c_7879,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_7851]) ).
tcf(c_7880,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_91,c_7851]) ).
tcf(c_7924,plain,
multiply(inverse(iPr_def_15),identity) = sk_c8,
inference(superposition,[status(thm)],[c_1038,c_7851]) ).
tcf(c_7963,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2339,c_7851]) ).
tcf(c_7964,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2338,c_7851]) ).
tcf(c_7965,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2337,c_7851]) ).
tcf(c_7966,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2336,c_7851]) ).
tcf(c_7967,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2335,c_7851]) ).
tcf(c_7968,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2334,c_7851]) ).
tcf(c_8009,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7851,c_7851]) ).
tcf(c_8480,plain,
multiply(sk_c8,identity) = sk_c8,
inference(demodulation,[status(thm)],[c_7924,c_7963]) ).
tcf(c_8501,plain,
multiply(sk_c2,sk_c8) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_8480,c_2320]) ).
tcf(c_8502,plain,
multiply(sk_c4,sk_c8) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_8480,c_2317]) ).
tcf(c_8505,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_8502,c_484]) ).
tcf(c_8506,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_8501,c_488]) ).
tcf(c_8640,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7879,c_8009]) ).
tcf(c_8671,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_8640,c_7878]) ).
tcf(c_8685,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_8671,c_90]) ).
tcf(c_8962,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_525,c_2141]) ).
tcf(c_8963,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_524,c_2141]) ).
tcf(c_9260,plain,
multiply(sk_c8,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_7963,c_90]) ).
tcf(c_9265,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_7963,c_7851]) ).
tcf(c_9266,plain,
multiply(sk_c8,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_7963,c_8640]) ).
tcf(c_9323,plain,
multiply(sk_c2,identity) = multiply(iPr_def_24,iPr_def_15),
inference(superposition,[status(thm)],[c_9260,c_2320]) ).
tcf(c_9324,plain,
multiply(sk_c4,identity) = multiply(iPr_def_20,iPr_def_15),
inference(superposition,[status(thm)],[c_9260,c_2317]) ).
tcf(c_9463,plain,
inverse(iPr_def_15) = sk_c8,
inference(demodulation,[status(thm)],[c_9266,c_8640]) ).
tcf(c_9699,plain,
multiply(iPr_def_24,iPr_def_15) = sk_c2,
inference(demodulation,[status(thm)],[c_9323,c_8640]) ).
tcf(c_9700,plain,
multiply(inverse(iPr_def_24),sk_c2) = iPr_def_15,
inference(superposition,[status(thm)],[c_9699,c_7851]) ).
tcf(c_9705,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),multiply(sk_c2,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_9700,c_91]) ).
tcf(c_10018,plain,
multiply(iPr_def_20,iPr_def_15) = sk_c4,
inference(demodulation,[status(thm)],[c_9324,c_8640]) ).
tcf(c_10019,plain,
multiply(inverse(iPr_def_20),sk_c4) = iPr_def_15,
inference(superposition,[status(thm)],[c_10018,c_7851]) ).
tcf(c_10060,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),multiply(sk_c4,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_10019,c_91]) ).
tcf(c_10566,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_21)) != sk_c9 )
| ( multiply(sk_c4,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_7964,c_494]) ).
tcf(c_10569,plain,
multiply(sk_c4,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_7964,c_90]) ).
tcf(c_10574,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_7964,c_7851]) ).
tcf(c_10575,plain,
multiply(sk_c4,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_7964,c_8640]) ).
tcf(c_10699,plain,
multiply(inverse(iPr_def_20),identity) = multiply(iPr_def_15,iPr_def_21),
inference(superposition,[status(thm)],[c_10569,c_10060]) ).
tcf(c_10703,plain,
inverse(iPr_def_21) = sk_c4,
inference(demodulation,[status(thm)],[c_10575,c_8640]) ).
tcf(c_10782,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm)],[c_1039,c_10574]) ).
tcf(c_10783,plain,
multiply(sk_c4,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_4238,c_10574]) ).
tcf(c_10823,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_7965,c_90]) ).
tcf(c_10828,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_7965,c_7851]) ).
tcf(c_10829,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_7965,c_8640]) ).
tcf(c_10845,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1629,c_10823]) ).
tcf(c_10846,plain,
( ( identity = iPr_def_19 )
| ( sk_c9 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1388,c_10823]) ).
tcf(c_10847,plain,
( ( identity = iPr_def_19 )
| ( sk_c7 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1175,c_10823]) ).
tcf(c_10850,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_990,c_10823]) ).
tcf(c_10974,plain,
( ( identity = iPr_def_19 )
| ( inverse(iPr_def_26) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_10845,c_479]) ).
tcf(c_11193,plain,
( ( identity = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_25) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_10846,c_490]) ).
tcf(c_11393,plain,
( ( identity = iPr_def_19 )
| ( multiply(sk_c6,iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_10847,c_480]) ).
tcf(c_11535,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_10829,c_8640]) ).
tcf(c_11551,plain,
multiply(sk_c5,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_4075,c_10828]) ).
tcf(c_11978,plain,
( ( identity = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_10850,c_488]) ).
tcf(c_12739,plain,
multiply(sk_c1,iPr_def_25) = identity,
inference(superposition,[status(thm)],[c_7966,c_90]) ).
tcf(c_12744,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_7966,c_7851]) ).
tcf(c_12772,plain,
( ( identity = iPr_def_26 )
| ( identity = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_11193,c_12739]) ).
tcf(c_12838,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2032,c_8671]) ).
tcf(c_12943,plain,
( ~ iPr_def_13
| ( sk_c7 != identity ) ),
inference(ground_joinability,[status(thm)],[c_2034,c_9463]) ).
tcf(c_12964,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_519,c_12943]) ).
tcf(c_12965,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13
| ( identity != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_518,c_12943]) ).
tcf(c_13116,plain,
( ( identity = iPr_def_19 )
| ( inverse(iPr_def_26) = iPr_def_26 ) ),
inference(superposition,[status(thm)],[c_12772,c_8671]) ).
tcf(c_13511,plain,
multiply(sk_c1,sk_c9) = iPr_def_26,
inference(superposition,[status(thm)],[c_4062,c_12744]) ).
tcf(c_13722,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_12964,c_2045,c_5451,c_5699]) ).
tcf(c_13728,plain,
( ( sk_c9 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_12965,c_2045,c_5004,c_5664]) ).
tcf(c_14970,plain,
multiply(sk_c2,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_7967,c_90]) ).
tcf(c_14975,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_7967,c_7851]) ).
tcf(c_14976,plain,
multiply(sk_c2,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_7967,c_8640]) ).
tcf(c_14998,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_11978,c_14970]) ).
tcf(c_15013,plain,
multiply(inverse(iPr_def_24),identity) = multiply(iPr_def_15,iPr_def_23),
inference(superposition,[status(thm)],[c_14970,c_9705]) ).
tcf(c_15017,plain,
inverse(iPr_def_23) = sk_c2,
inference(demodulation,[status(thm)],[c_14976,c_8640]) ).
tcf(c_15039,plain,
multiply(sk_c2,sk_c8) = iPr_def_24,
inference(superposition,[status(thm)],[c_4057,c_14975]) ).
tcf(c_15063,plain,
( iPr_def_14
| ( iPr_def_15 != iPr_def_24 )
| ( sk_c9 = iPr_def_21 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1920,c_1920,c_3034,c_5162,c_5221,c_6428,c_8962,c_13722]) ).
tcf(c_15064,plain,
( iPr_def_14
| iPr_def_10
| ( sk_c9 = iPr_def_21 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_15063]) ).
tcf(c_15079,plain,
( iPr_def_14
| ( iPr_def_15 != iPr_def_24 )
| ( sk_c9 = iPr_def_20 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1921,c_1921,c_3034,c_5178,c_5233,c_6416,c_8963,c_13728]) ).
tcf(c_15080,plain,
( iPr_def_14
| iPr_def_10
| ( sk_c9 = iPr_def_20 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_15079]) ).
tcf(c_15431,plain,
! [X0: $i] :
( ( identity = iPr_def_19 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_14998,c_89]) ).
tcf(c_17111,plain,
multiply(sk_c3,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_7968,c_90]) ).
tcf(c_17116,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_7968,c_7851]) ).
tcf(c_17117,plain,
multiply(sk_c3,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_7968,c_8640]) ).
tcf(c_17511,plain,
inverse(iPr_def_22) = sk_c3,
inference(demodulation,[status(thm)],[c_17117,c_8640]) ).
tcf(c_17534,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm)],[c_1043,c_17116]) ).
tcf(c_17535,plain,
multiply(sk_c3,sk_c7) = iPr_def_17,
inference(superposition,[status(thm)],[c_4052,c_17116]) ).
tcf(c_17600,plain,
multiply(iPr_def_15,iPr_def_21) = inverse(iPr_def_20),
inference(demodulation,[status(thm)],[c_10699,c_8640]) ).
tcf(c_17604,plain,
multiply(sk_c8,inverse(iPr_def_20)) = iPr_def_21,
inference(superposition,[status(thm)],[c_17600,c_9265]) ).
tcf(c_17965,plain,
multiply(iPr_def_20,inverse(iPr_def_20)) = multiply(sk_c4,iPr_def_21),
inference(superposition,[status(thm)],[c_17604,c_2317]) ).
tcf(c_17968,plain,
multiply(iPr_def_20,inverse(iPr_def_20)) = identity,
inference(light_normalisation,[status(thm)],[c_17965,c_10569]) ).
tcf(c_19147,plain,
( ~ iPr_def_14
| ( sk_c8 != identity )
| ( multiply(identity,sk_c7) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_3252,c_8671]) ).
tcf(c_19148,plain,
( ~ iPr_def_14
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_19147,c_89]) ).
tcf(c_23088,plain,
( ( iPr_def_15 = iPr_def_26 )
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_13116,c_10974]) ).
tcf(c_27649,plain,
multiply(iPr_def_15,iPr_def_23) = inverse(iPr_def_24),
inference(demodulation,[status(thm)],[c_15013,c_8640]) ).
tcf(c_27652,plain,
( ( sk_c8 = iPr_def_19 )
| ( inverse(iPr_def_24) = identity ) ),
inference(demodulation,[status(thm)],[c_1052,c_27649]) ).
tcf(c_27667,plain,
multiply(sk_c8,inverse(iPr_def_24)) = iPr_def_23,
inference(superposition,[status(thm)],[c_27649,c_9265]) ).
tcf(c_27715,plain,
multiply(iPr_def_24,inverse(iPr_def_24)) = multiply(sk_c2,iPr_def_23),
inference(superposition,[status(thm)],[c_27667,c_2320]) ).
tcf(c_27719,plain,
multiply(iPr_def_24,inverse(iPr_def_24)) = identity,
inference(light_normalisation,[status(thm)],[c_27715,c_14970]) ).
tcf(c_27820,plain,
( ( identity = iPr_def_19 )
| ( inverse(iPr_def_24) = identity ) ),
inference(superposition,[status(thm)],[c_27719,c_15431]) ).
tcf(c_30609,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_16)) = sk_c7,
inference(superposition,[status(thm)],[c_480,c_7880]) ).
tcf(c_30669,plain,
! [X0: $i] :
( ( identity = iPr_def_19 )
| ( multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_16)) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_11393,c_7880]) ).
tcf(c_30670,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_16)) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1281,c_7880]) ).
tcf(c_30671,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_21 )
| ( multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_16)) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1252,c_7880]) ).
tcf(c_30672,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_20 )
| ( multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_16)) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1216,c_7880]) ).
tcf(c_30673,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(multiply(X0,sk_c6)),multiply(X0,iPr_def_16)) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1191,c_7880]) ).
tcf(c_30744,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c8)),multiply(X0,identity)) = iPr_def_15,
inference(superposition,[status(thm)],[c_9260,c_7880]) ).
tcf(c_30745,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),multiply(X0,identity)) = iPr_def_21,
inference(superposition,[status(thm)],[c_10569,c_7880]) ).
tcf(c_30746,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c3)),multiply(X0,identity)) = iPr_def_22,
inference(superposition,[status(thm)],[c_17111,c_7880]) ).
tcf(c_30857,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c3)),X0) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_30746,c_8640]) ).
tcf(c_30858,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c4)),X0) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_30745,c_8640]) ).
tcf(c_30859,plain,
! [X0: $i] : multiply(inverse(multiply(X0,sk_c8)),X0) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_30744,c_8640]) ).
tcf(c_37316,plain,
( ~ iPr_def_12
| ( sk_c9 != iPr_def_21 )
| ( multiply(sk_c4,sk_c9) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_10566,c_485,c_10703]) ).
tcf(c_39689,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_24,identity) = identity ) ),
inference(superposition,[status(thm)],[c_27652,c_27719]) ).
tcf(c_40488,plain,
( ( identity = iPr_def_19 )
| ( multiply(iPr_def_24,identity) = identity ) ),
inference(superposition,[status(thm)],[c_27820,c_27719]) ).
tcf(c_42989,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_22 )
| ( inverse(inverse(multiply(sk_c8,sk_c3))) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_30857,c_496]) ).
tcf(c_42992,plain,
inverse(multiply(identity,sk_c3)) = iPr_def_22,
inference(superposition,[status(thm)],[c_30857,c_8640]) ).
tcf(c_44304,plain,
( ~ iPr_def_10
| ( sk_c9 != iPr_def_21 )
| ( inverse(inverse(multiply(sk_c8,sk_c4))) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_30858,c_496]) ).
tcf(c_44306,plain,
( ~ iPr_def_11
| ( sk_c9 != iPr_def_21 )
| ( inverse(inverse(multiply(sk_c7,sk_c4))) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_30858,c_495]) ).
tcf(c_44307,plain,
inverse(multiply(identity,sk_c4)) = iPr_def_21,
inference(superposition,[status(thm)],[c_30858,c_8640]) ).
tcf(c_44439,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_15 )
| ( inverse(inverse(multiply(sk_c8,sk_c8))) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_30859,c_493]) ).
tcf(c_45283,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_44439,c_44306,c_44304,c_44307,c_42989,c_42992,c_40488,c_39689,c_37316,c_30673,c_30672,c_30671,c_30670,c_30669,c_30609,c_27719,c_27715,c_23088,c_19148,c_17968,c_17965,c_17604,c_17535,c_17534,c_17511,c_15080,c_15064,c_15039,c_15017,c_13511,c_12838,c_12739,c_11551,c_11535,c_10845,c_10823,c_10783,c_10782,c_10703,c_10018,c_9699,c_9463,c_9260,c_8671,c_8506,c_8505,c_7875,c_6699,c_6440,c_6392,c_6076,c_5463,c_5178,c_5162,c_8685,c_3156,c_2121,c_502,c_501,c_500,c_499,c_498,c_497,c_491,c_486,c_479]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP249-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 14:15:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 17.97/3.21 % SZS status Started for theBenchmark.p
% 17.97/3.21 % SZS status Unsatisfiable for theBenchmark.p
% 17.97/3.21
% 17.97/3.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.97/3.21
% 17.97/3.21 % ------ iProver source info
% 17.97/3.21
% 17.97/3.21 % git: date: 2026-07-19 20:42:38 +0200
% 17.97/3.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.97/3.21 % git: non_committed_changes: false
% 17.97/3.21
% 17.97/3.21 % ------ Parsing...% successful
% 17.97/3.21
% 17.97/3.21
% 17.97/3.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.97/3.21
% 17.97/3.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 17.97/3.21
% 17.97/3.21 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.97/3.21
% 17.97/3.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 17.97/3.21 % ------ Proving...
% 17.97/3.21 % ------ Problem Properties
% 17.97/3.21
% 17.97/3.21 %
% 17.97/3.21 % clauses 57
% 17.97/3.21 % conjectures 42
% 17.97/3.21 % EPR 37
% 17.97/3.21 % Horn 20
% 17.97/3.21 % unary 15
% 17.97/3.21 % binary 36
% 17.97/3.21 % lits 108
% 17.97/3.21 % lits eq 98
% 17.97/3.21 % fd_pure 0
% 17.97/3.21 % fd_pseudo 0
% 17.97/3.21 % fd_cond 0
% 17.97/3.21 % fd_pseudo_cond 0
% 17.97/3.21 % AC symbols 0
% 17.97/3.21
% 17.97/3.21 % ------ Schedule dynamic 5 is on
% 17.97/3.21
% 17.97/3.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.97/3.21
% 17.97/3.21
% 17.97/3.21 % ------
% 17.97/3.21 % Current options:
% 17.97/3.21 % ------
% 17.97/3.21
% 17.97/3.21
% 17.97/3.21 %
% 17.97/3.21
% 17.97/3.21 % ------ Proving...
% 17.97/3.21 %
% 17.97/3.21
% 17.97/3.21 % SZS status Unsatisfiable for theBenchmark.p
% 17.97/3.21
% 17.97/3.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.97/3.22
% 17.97/3.22
%------------------------------------------------------------------------------