%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP274-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:32:41 PM UTC 2026
% Result : Unsatisfiable 1.40s 1.77s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 41
% Syntax : Number of formulae : 339 ( 92 unt; 10 def)
% Number of atoms : 1190 ( 618 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 524 ( 168 ~; 356 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = inverse(sk_c4)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c7,sk_c5) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c5
| multiply(X1,sk_c5) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != inverse(X1)
| sk_c7 != multiply(X1,sk_c5)
| sk_c6 != multiply(sk_c7,sk_c5)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7) ),
inference(reorient_equations,[],[f54]) ).
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,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c1) = sk_c7 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c5 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c5 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 )
| ( multiply(X3,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_359,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_106]) ).
tcf(c_360,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c5) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_106]) ).
tcf(c_361,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_106]) ).
tcf(c_362,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_106]) ).
tcf(c_363,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c5) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_364,definition,
iPr_def_14 = multiply(sk_c7,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_365,definition,
iPr_def_15 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_366,definition,
iPr_def_16 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_367,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_368,definition,
iPr_def_18 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_369,definition,
iPr_def_19 = multiply(sk_c3,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_370,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_371,definition,
iPr_def_21 = multiply(sk_c2,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_372,definition,
iPr_def_22 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_373,definition,
iPr_def_23 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_374,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c5 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_363,c_365,c_364]) ).
tcf(c_375,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_362]) ).
tcf(c_376,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_361]) ).
tcf(c_377,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c5) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_360]) ).
tcf(c_378,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_359]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_105,c_367,c_366]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_104,c_368]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_103,c_369]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_102,c_370]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_371]) ).
tcf(c_385,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_389,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_392,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_393,negated_conjecture,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90,c_372]) ).
tcf(c_395,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_396,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_397,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_398,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_399,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_85,c_373]) ).
tcf(c_400,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_401,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_402,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_403,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_404,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_621,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_384,c_385]) ).
tcf(c_631,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_382,c_364]) ).
tcf(c_647,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_18,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_385,c_365]) ).
tcf(c_657,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_382,c_366]) ).
tcf(c_658,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_381,c_366]) ).
tcf(c_659,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_380,c_366]) ).
tcf(c_660,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_379,c_366]) ).
tcf(c_671,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_385,c_369]) ).
tcf(c_672,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_384,c_369]) ).
tcf(c_681,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c6,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_387,c_365]) ).
tcf(c_696,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_388,c_366]) ).
tcf(c_743,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_390,c_389]) ).
tcf(c_744,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_390,c_369]) ).
tcf(c_763,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_391,c_369]) ).
tcf(c_830,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_393,c_366]) ).
tcf(c_861,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_899,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_861]) ).
tcf(c_924,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_861]) ).
tcf(c_934,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_386,c_373]) ).
tcf(c_939,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_370,c_79]) ).
tcf(c_940,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_368,c_79]) ).
tcf(c_941,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_372,c_79]) ).
tcf(c_942,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_367,c_79]) ).
tcf(c_958,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_395,c_394]) ).
tcf(c_962,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_395,c_369]) ).
tcf(c_980,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_989,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_396,c_373]) ).
tcf(c_993,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_396,c_386]) ).
tcf(c_1007,plain,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_16 != iPr_def_16 )
| ( sk_c6 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_899]) ).
tcf(c_1008,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_404]) ).
tcf(c_1013,plain,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_18 != iPr_def_18 )
| ( sk_c6 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_924]) ).
tcf(c_1014,plain,
iPr_def_18 = iPr_def_18,
inference(instantiation,[status(thm)],[c_404]) ).
tcf(c_1024,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_397,c_373]) ).
tcf(c_1025,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_397,c_387]) ).
tcf(c_1027,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_22,sk_c5) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_397,c_364]) ).
tcf(c_1046,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_15) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_398,c_371]) ).
tcf(c_1108,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_399,c_369]) ).
tcf(c_1178,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_400,c_369]) ).
tcf(c_1226,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_1229,plain,
! [X0: $i] :
( ( X0 = iPr_def_16 )
| ( iPr_def_16 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_980]) ).
tcf(c_1247,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_401,c_391]) ).
tcf(c_1250,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_401,c_369]) ).
tcf(c_1304,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_402,c_392]) ).
tcf(c_1308,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_402,c_369]) ).
tcf(c_1356,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(sk_c2,iPr_def_15) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_403,c_371]) ).
tcf(c_1465,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_20 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_392,c_374]) ).
tcf(c_1466,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_391,c_374]) ).
tcf(c_1607,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_373,c_80]) ).
tcf(c_1608,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_365,c_80]) ).
tcf(c_1609,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_369,c_80]) ).
tcf(c_1611,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c5,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_364,c_80]) ).
tcf(c_1614,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1616,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_939,c_80]) ).
tcf(c_1617,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_940,c_80]) ).
tcf(c_1618,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_941,c_80]) ).
tcf(c_1619,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_942,c_80]) ).
tcf(c_1621,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1619,c_78]) ).
tcf(c_1622,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1618,c_78]) ).
tcf(c_1623,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1617,c_78]) ).
tcf(c_1624,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1616,c_78]) ).
tcf(c_1645,plain,
( ( iPr_def_18 = iPr_def_16 )
| ( iPr_def_18 != sk_c6 )
| ( iPr_def_16 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1229]) ).
tcf(c_1678,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_18 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_743,c_374]) ).
tcf(c_1853,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_19 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1025,c_993]) ).
tcf(c_1858,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1025,c_373]) ).
tcf(c_1977,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1304,c_1247]) ).
tcf(c_1983,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1304,c_373]) ).
tcf(c_2037,plain,
multiply(iPr_def_17,iPr_def_21) = sk_c5,
inference(superposition,[status(thm)],[c_371,c_1621]) ).
tcf(c_2057,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_373,c_375]) ).
tcf(c_2060,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_79,c_375]) ).
tcf(c_2078,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_2057,c_372]) ).
tcf(c_2153,plain,
! [X0: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1226]) ).
tcf(c_2170,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_366,c_376]) ).
tcf(c_2171,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_14 )
| ( inverse(sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_364,c_376]) ).
tcf(c_2195,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 )
| ( sk_c6 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2170,c_368]) ).
tcf(c_2297,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c7) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_364,c_377]) ).
tcf(c_2298,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_371,c_377]) ).
tcf(c_2300,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c5)) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_79,c_377]) ).
tcf(c_2314,plain,
( ~ iPr_def_11
| ( sk_c5 != iPr_def_17 )
| ( sk_c7 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2298,c_367]) ).
tcf(c_2423,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_78,c_378]) ).
tcf(c_2734,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_21,iPr_def_17) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_387,c_631]) ).
tcf(c_2820,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_21,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2037,c_80]) ).
tcf(c_2822,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_373,c_1622]) ).
tcf(c_2875,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_366,c_1623]) ).
tcf(c_2878,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2875,c_80]) ).
tcf(c_2880,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_369,c_1624]) ).
tcf(c_2883,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2880,c_80]) ).
tcf(c_3236,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_657,c_1623]) ).
tcf(c_3237,plain,
( ( sk_c5 = iPr_def_17 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3236,c_2875]) ).
tcf(c_3276,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_658,c_1623]) ).
tcf(c_3277,plain,
( ( sk_c5 = iPr_def_17 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3276,c_2875]) ).
tcf(c_3311,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_659,c_1623]) ).
tcf(c_3312,plain,
( ( sk_c5 = iPr_def_17 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_3311,c_2875]) ).
tcf(c_3323,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_660,c_1623]) ).
tcf(c_3324,plain,
( ( sk_c5 = iPr_def_17 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3323,c_2875]) ).
tcf(c_3335,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_671,c_1624]) ).
tcf(c_3336,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3335,c_2880]) ).
tcf(c_3365,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_14,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_392,c_681]) ).
tcf(c_3442,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_21,iPr_def_23) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1853,c_2822]) ).
tcf(c_3509,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_696,c_1623]) ).
tcf(c_3510,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_3509,c_2875]) ).
tcf(c_3650,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_744,c_1624]) ).
tcf(c_3651,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3650,c_2880]) ).
tcf(c_3712,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_763,c_1624]) ).
tcf(c_3713,plain,
( ( sk_c6 = iPr_def_14 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3712,c_2880]) ).
tcf(c_3786,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_830,c_1623]) ).
tcf(c_3787,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3786,c_2875]) ).
tcf(c_4156,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_934,c_1622]) ).
tcf(c_4157,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4156,c_2822]) ).
tcf(c_4168,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_962,c_1624]) ).
tcf(c_4169,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_4168,c_2880]) ).
tcf(c_4538,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1046,c_1621]) ).
tcf(c_4539,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_4538,c_2037]) ).
tcf(c_4595,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1108,c_1624]) ).
tcf(c_4596,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_4595,c_2880]) ).
tcf(c_4851,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1178,c_1624]) ).
tcf(c_4852,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4851,c_2880]) ).
tcf(c_4966,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_18 != iPr_def_16 )
| ( iPr_def_16 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_2153]) ).
tcf(c_4979,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1250,c_1624]) ).
tcf(c_4980,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4979,c_2880]) ).
tcf(c_5016,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1308,c_1624]) ).
tcf(c_5017,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5016,c_2880]) ).
tcf(c_5097,plain,
( ( sk_c6 = iPr_def_23 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1356,c_1621]) ).
tcf(c_5098,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c6 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_5097,c_2037]) ).
tcf(c_5502,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_23,sk_c5),
inference(superposition,[status(thm)],[c_364,c_1607]) ).
tcf(c_5665,plain,
multiply(sk_c6,iPr_def_14) = multiply(iPr_def_15,sk_c5),
inference(superposition,[status(thm)],[c_364,c_1608]) ).
tcf(c_6143,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_365,c_1609]) ).
tcf(c_6150,plain,
multiply(sk_c3,multiply(iPr_def_15,sk_c5)) = multiply(iPr_def_19,iPr_def_14),
inference(superposition,[status(thm)],[c_5665,c_1609]) ).
tcf(c_7618,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_21,iPr_def_14) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1977,c_3442]) ).
tcf(c_7636,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1614,c_78]) ).
tcf(c_7641,plain,
multiply(inverse(sk_c1),iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_373,c_7636]) ).
tcf(c_7642,plain,
multiply(inverse(sk_c6),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_365,c_7636]) ).
tcf(c_7645,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c5,
inference(superposition,[status(thm)],[c_364,c_7636]) ).
tcf(c_7647,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_78,c_7636]) ).
tcf(c_7648,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_7636]) ).
tcf(c_7736,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1624,c_7636]) ).
tcf(c_7737,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1623,c_7636]) ).
tcf(c_7738,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1622,c_7636]) ).
tcf(c_7739,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1621,c_7636]) ).
tcf(c_7746,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( multiply(inverse(sk_c1),iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1983,c_7636]) ).
tcf(c_7747,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( multiply(inverse(sk_c1),iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1858,c_7636]) ).
tcf(c_7777,plain,
multiply(inverse(sk_c6),multiply(iPr_def_15,sk_c5)) = iPr_def_14,
inference(superposition,[status(thm)],[c_5665,c_7636]) ).
tcf(c_7779,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7636,c_7636]) ).
tcf(c_8331,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7648,c_7779]) ).
tcf(c_8344,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_8331,c_1608]) ).
tcf(c_8346,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_8331,c_2883]) ).
tcf(c_8348,plain,
multiply(sk_c5,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_8331,c_2878]) ).
tcf(c_8350,plain,
multiply(sk_c7,sk_c5) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_8331,c_1611]) ).
tcf(c_8352,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_21),
inference(superposition,[status(thm)],[c_8331,c_2820]) ).
tcf(c_8357,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_8331,c_7647]) ).
tcf(c_8358,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_8352,c_2037]) ).
tcf(c_8360,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_8350,c_364]) ).
tcf(c_8364,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_8346,c_2880]) ).
tcf(c_8366,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_8344,c_365]) ).
tcf(c_8374,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_8357,c_79]) ).
tcf(c_8459,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_397,c_2078]) ).
tcf(c_8460,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_396,c_2078]) ).
tcf(c_8727,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_7736,c_79]) ).
tcf(c_8732,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7736,c_378]) ).
tcf(c_8733,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_7736,c_7636]) ).
tcf(c_8734,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_7736,c_8331]) ).
tcf(c_8735,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_19 )
| ( inverse(inverse(iPr_def_20)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_8732,c_369]) ).
tcf(c_8763,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_8734,c_8331]) ).
tcf(c_8770,plain,
multiply(sk_c3,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_2880,c_8733]) ).
tcf(c_9025,plain,
( ( sk_c7 = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_394,c_2195]) ).
tcf(c_9029,plain,
( ( sk_c6 = iPr_def_14 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_389,c_2195]) ).
tcf(c_9031,plain,
( ( sk_c7 = iPr_def_21 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_384,c_2195]) ).
tcf(c_9145,plain,
( ( sk_c7 = iPr_def_22 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_9025,c_4169,c_9025]) ).
tcf(c_9158,plain,
( ( sk_c6 = iPr_def_14 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_9029,c_3651,c_9029]) ).
tcf(c_9164,plain,
( ( sk_c7 = iPr_def_21 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_9031,c_3336,c_9031]) ).
tcf(c_9205,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_7737,c_79]) ).
tcf(c_9209,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_7737,c_376]) ).
tcf(c_9211,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_7737,c_7636]) ).
tcf(c_9212,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_7737,c_8331]) ).
tcf(c_9247,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_9212,c_8331]) ).
tcf(c_9306,plain,
( ( iPr_def_16 = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c5 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_621,c_2314]) ).
tcf(c_9309,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c5 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_387,c_2314]) ).
tcf(c_9310,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c5 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_386,c_2314]) ).
tcf(c_9446,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_647,c_9211]) ).
tcf(c_9448,plain,
multiply(sk_c4,sk_c5) = iPr_def_16,
inference(superposition,[status(thm)],[c_2875,c_9211]) ).
tcf(c_9537,plain,
multiply(sk_c1,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_7738,c_79]) ).
tcf(c_9543,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_7738,c_7636]) ).
tcf(c_9544,plain,
multiply(sk_c1,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_7738,c_8331]) ).
tcf(c_9563,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1024,c_9537]) ).
tcf(c_9564,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_989,c_9537]) ).
tcf(c_9681,plain,
( iPr_def_10
| ( sk_c7 = iPr_def_20 )
| ( sk_c5 != iPr_def_15 )
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_1465,c_1465,c_3237,c_5017,c_8459,c_9309]) ).
tcf(c_9682,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_20 )
| ( sk_c5 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_9681]) ).
tcf(c_9746,plain,
( iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( sk_c5 != iPr_def_15 )
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_1466,c_1466,c_3277,c_4980,c_8460,c_9310]) ).
tcf(c_9747,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_19 )
| ( sk_c5 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_9746]) ).
tcf(c_9881,plain,
( ( identity = iPr_def_23 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_9563,c_373]) ).
tcf(c_10551,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_14) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_1027,c_9543]) ).
tcf(c_10555,plain,
multiply(sk_c1,sk_c7) = iPr_def_23,
inference(superposition,[status(thm)],[c_2822,c_9543]) ).
tcf(c_10572,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c5) = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_10551,c_5502]) ).
tcf(c_10627,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c5 != iPr_def_15 )
| ( iPr_def_16 = iPr_def_18 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1678,c_958,c_1007,c_1008,c_1013,c_1014,c_1645,c_1678,c_2078,c_3312,c_3324,c_4596,c_4852,c_4966,c_9306]) ).
tcf(c_10628,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( iPr_def_16 = iPr_def_18 )
| ( sk_c5 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_10627]) ).
tcf(c_10629,plain,
( ( sk_c5 != iPr_def_15 )
| ( iPr_def_16 = iPr_def_18 )
| iPr_def_10
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_10628,c_958,c_1007,c_1008,c_1013,c_1014,c_1645,c_2078,c_4596,c_4852,c_4966,c_10628]) ).
tcf(c_10630,plain,
( iPr_def_12
| iPr_def_10
| ( iPr_def_16 = iPr_def_18 )
| ( sk_c5 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_10629]) ).
tcf(c_11021,plain,
( ~ iPr_def_12
| ( inverse(sk_c7) != sk_c6 ) ),
inference(global_subsumption_just,[status(thm)],[c_2171,c_2171,c_9158]) ).
tcf(c_11192,plain,
( ( identity = iPr_def_23 )
| ( multiply(inverse(sk_c1),iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_9881,c_7636]) ).
tcf(c_11286,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_7739,c_79]) ).
tcf(c_11289,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_17)) != sk_c5 )
| ( multiply(sk_c2,sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7739,c_377]) ).
tcf(c_11292,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_7739,c_7636]) ).
tcf(c_11293,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_7739,c_8331]) ).
tcf(c_11301,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_21 )
| ( inverse(inverse(iPr_def_17)) != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_11289,c_371]) ).
tcf(c_11345,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_11293,c_8331]) ).
tcf(c_11350,plain,
multiply(sk_c2,sk_c5) = iPr_def_21,
inference(superposition,[status(thm)],[c_2037,c_11292]) ).
tcf(c_11550,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2423,c_8357]) ).
tcf(c_11582,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_14 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_392,c_11550]) ).
tcf(c_11677,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_11582,c_11350,c_11345,c_11301,c_11286,c_11192,c_11021,c_10630,c_10572,c_10555,c_9747,c_9682,c_9564,c_9544,c_9537,c_9448,c_9446,c_9247,c_9209,c_9212,c_9205,c_9164,c_9158,c_9145,c_8770,c_8763,c_8735,c_8732,c_8734,c_8727,c_8366,c_8364,c_8360,c_8358,c_8350,c_8348,c_8346,c_8344,c_8357,c_7777,c_7747,c_7746,c_7645,c_7642,c_7641,c_7618,c_6150,c_6143,c_5665,c_5098,c_4980,c_4539,c_4157,c_3787,c_3713,c_3510,c_3365,c_2734,c_2300,c_2297,c_2060,c_8374,c_763,c_672,c_621,c_397,c_383,c_382,c_381,c_380,c_379,c_374,c_370,c_368,c_367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP274-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:20:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/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...
% 1.40/1.77 % SZS status Started for theBenchmark.p
% 1.40/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.40/1.77
% 1.40/1.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.40/1.77
% 1.40/1.77 % ------ iProver source info
% 1.40/1.77
% 1.40/1.77 % git: date: 2026-07-19 20:42:38 +0200
% 1.40/1.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.40/1.77 % git: non_committed_changes: false
% 1.40/1.77
% 1.40/1.77 % ------ Parsing...% successful
% 1.40/1.77
% 1.40/1.77
% 1.40/1.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.40/1.77
% 1.40/1.77 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.40/1.77
% 1.40/1.77 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.40/1.77
% 1.40/1.77 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.40/1.77 % ------ Proving...
% 1.40/1.77 % ------ Problem Properties
% 1.40/1.77
% 1.40/1.77 %
% 1.40/1.77 % clauses 43
% 1.40/1.77 % conjectures 30
% 1.40/1.77 % EPR 26
% 1.40/1.77 % Horn 17
% 1.40/1.77 % unary 13
% 1.40/1.77 % binary 25
% 1.40/1.77 % lits 81
% 1.40/1.77 % lits eq 73
% 1.40/1.77 % fd_pure 0
% 1.40/1.77 % fd_pseudo 0
% 1.40/1.77 % fd_cond 0
% 1.40/1.77 % fd_pseudo_cond 0
% 1.40/1.77 % AC symbols 0
% 1.40/1.77
% 1.40/1.77 % ------ Schedule dynamic 5 is on
% 1.40/1.77
% 1.40/1.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.40/1.77
% 1.40/1.77
% 1.40/1.77 % ------
% 1.40/1.77 % Current options:
% 1.40/1.77 % ------
% 1.40/1.77
% 1.40/1.77
% 1.40/1.77 %
% 1.40/1.77
% 1.40/1.77 % ------ Proving...
% 1.40/1.77 %
% 1.40/1.77
% 1.40/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.40/1.77
% 1.40/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.40/1.77
% 1.40/1.77
%------------------------------------------------------------------------------