%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP284-1 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:43 PM UTC 2026
% Result : Unsatisfiable 8.53s 1.70s
% Output : CNFRefutation 8.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 39
% Syntax : Number of formulae : 369 ( 97 unt; 10 def)
% Number of atoms : 1366 ( 675 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 549 ( 164 ~; 385 |; 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 : 74 ( 0 sgn 74 !; 0 ?; 60 :)
% 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_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = inverse(sk_c4)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,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_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,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_10) ).
fof(f24,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,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_c7
| multiply(X1,sk_c7) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,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)
| sk_c5 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X1)
| sk_c5 != multiply(X1,sk_c7)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(reorient_equations,[],[f55]) ).
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_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_82,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_84,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c5 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c7 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(sk_c7,sk_c6) != sk_c5 )
| ( multiply(X3,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c5 )
| ( multiply(X1,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_359,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c5 ) ),
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_c7 )
| ( multiply(X0,sk_c6) != 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_c6) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_364,definition,
iPr_def_14 = multiply(sk_c7,sk_c6),
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_c7),
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_c5 ) ),
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_c7 )
| ( multiply(X0,sk_c6) != 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_c7) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_359]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( 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_c7 ) ),
inference(demodulation,[status(thm)],[c_104,c_368]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103,c_369]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102,c_370]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_384,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_371]) ).
tcf(c_385,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_21 = sk_c5 )
| ( iPr_def_15 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_389,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_372]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_392,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90,c_373]) ).
tcf(c_395,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_396,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_397,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_399,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_400,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_401,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_402,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_403,negated_conjecture,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_14 = 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_613,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_381,c_382]) ).
tcf(c_672,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_386,c_366]) ).
tcf(c_673,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_385,c_366]) ).
tcf(c_674,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_384,c_366]) ).
tcf(c_684,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_380,c_369]) ).
tcf(c_685,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_379,c_369]) ).
tcf(c_695,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_387,c_366]) ).
tcf(c_707,plain,
( ( sk_c5 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_388,c_366]) ).
tcf(c_719,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_389,c_369]) ).
tcf(c_738,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_390,c_389]) ).
tcf(c_739,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_390,c_369]) ).
tcf(c_758,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_391,c_364]) ).
tcf(c_778,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_22,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_392,c_364]) ).
tcf(c_791,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_14 != X0 )
| ( sk_c5 != X0 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_841,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_394,c_369]) ).
tcf(c_842,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_394,c_365]) ).
tcf(c_869,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c5 )
| ( sk_c5 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_405]) ).
tcf(c_875,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_392,c_371]) ).
tcf(c_876,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_391,c_371]) ).
tcf(c_877,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_382,c_371]) ).
tcf(c_892,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_392,c_373]) ).
tcf(c_893,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_391,c_373]) ).
tcf(c_910,plain,
( ( iPr_def_14 = sk_c5 )
| ( iPr_def_14 != iPr_def_21 )
| ( sk_c5 != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_791]) ).
tcf(c_915,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_370,c_79]) ).
tcf(c_916,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_368,c_79]) ).
tcf(c_917,plain,
multiply(iPr_def_22,sk_c1) = identity,
inference(superposition,[status(thm)],[c_372,c_79]) ).
tcf(c_918,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_367,c_79]) ).
tcf(c_934,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_395,c_369]) ).
tcf(c_936,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_395,c_364]) ).
tcf(c_980,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c7,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_396,c_364]) ).
tcf(c_1014,plain,
! [X0: $i] :
( ( X0 = sk_c5 )
| ( sk_c5 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_869]) ).
tcf(c_1032,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_397,c_369]) ).
tcf(c_1126,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_399,c_384]) ).
tcf(c_1180,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_400,c_385]) ).
tcf(c_1205,plain,
( ( iPr_def_15 = sk_c5 )
| ( iPr_def_15 != iPr_def_15 )
| ( sk_c5 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_1014]) ).
tcf(c_1206,plain,
iPr_def_15 = iPr_def_15,
inference(instantiation,[status(thm)],[c_404]) ).
tcf(c_1226,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_401,c_366]) ).
tcf(c_1227,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_401,c_386]) ).
tcf(c_1282,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_402,c_387]) ).
tcf(c_1323,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_403,c_366]) ).
tcf(c_1383,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_402,c_374]) ).
tcf(c_1385,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_18 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_400,c_374]) ).
tcf(c_1386,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_16 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_399,c_374]) ).
tcf(c_1394,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_17 )
| ( iPr_def_14 != iPr_def_15 )
| ( sk_c5 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_383,c_374]) ).
tcf(c_1603,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_364,c_80]) ).
tcf(c_1604,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_1605,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_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_c2,multiply(sk_c7,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_371,c_80]) ).
tcf(c_1610,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1612,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_915,c_80]) ).
tcf(c_1613,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_916,c_80]) ).
tcf(c_1614,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_917,c_80]) ).
tcf(c_1615,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_918,c_80]) ).
tcf(c_1617,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1615,c_78]) ).
tcf(c_1618,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1614,c_78]) ).
tcf(c_1619,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1613,c_78]) ).
tcf(c_1620,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1612,c_78]) ).
tcf(c_1676,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_613,c_371]) ).
tcf(c_1677,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_613,c_392]) ).
tcf(c_1678,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_613,c_391]) ).
tcf(c_1680,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_17,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_613,c_364]) ).
tcf(c_1907,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1282,c_1227]) ).
tcf(c_1962,plain,
multiply(iPr_def_17,iPr_def_21) = sk_c7,
inference(superposition,[status(thm)],[c_371,c_1617]) ).
tcf(c_1972,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_373,c_375]) ).
tcf(c_1973,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_371,c_375]) ).
tcf(c_1975,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_79,c_375]) ).
tcf(c_1989,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_21 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1973,c_367]) ).
tcf(c_1993,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_23 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_1972,c_372]) ).
tcf(c_2098,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c4) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_366,c_376]) ).
tcf(c_2100,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c5)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_79,c_376]) ).
tcf(c_2118,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 )
| ( sk_c6 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2098,c_368]) ).
tcf(c_2258,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c7) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_364,c_377]) ).
tcf(c_2259,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c3) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_369,c_377]) ).
tcf(c_2276,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( sk_c7 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2259,c_370]) ).
tcf(c_2389,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_373,c_378]) ).
tcf(c_2390,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_21 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_371,c_378]) ).
tcf(c_2406,plain,
( ~ iPr_def_10
| ( sk_c5 != iPr_def_21 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2390,c_367]) ).
tcf(c_2776,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_373,c_1618]) ).
tcf(c_2779,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_23,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2776,c_80]) ).
tcf(c_2781,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_366,c_1619]) ).
tcf(c_2821,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2781,c_80]) ).
tcf(c_2823,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_369,c_1620]) ).
tcf(c_2833,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2823,c_80]) ).
tcf(c_3071,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_672,c_1619]) ).
tcf(c_3072,plain,
( ( sk_c5 = iPr_def_21 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3071,c_2781]) ).
tcf(c_3087,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_673,c_1619]) ).
tcf(c_3088,plain,
( ( sk_c5 = iPr_def_21 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_3087,c_2781]) ).
tcf(c_3099,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_674,c_1619]) ).
tcf(c_3100,plain,
( ( sk_c5 = iPr_def_21 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_3099,c_2781]) ).
tcf(c_3157,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_684,c_1620]) ).
tcf(c_3158,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3157,c_2823]) ).
tcf(c_3169,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_685,c_1620]) ).
tcf(c_3170,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_3169,c_2823]) ).
tcf(c_3181,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_695,c_1619]) ).
tcf(c_3182,plain,
( ( sk_c5 = iPr_def_21 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3181,c_2781]) ).
tcf(c_3285,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_719,c_1620]) ).
tcf(c_3286,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_3285,c_2823]) ).
tcf(c_3419,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_739,c_1620]) ).
tcf(c_3420,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_3419,c_2823]) ).
tcf(c_3610,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_396,c_758]) ).
tcf(c_3619,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3610,c_2776]) ).
tcf(c_3717,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_19,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3619,c_364]) ).
tcf(c_3835,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_397,c_778]) ).
tcf(c_3845,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3835,c_2776]) ).
tcf(c_3906,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3845,c_3619]) ).
tcf(c_4151,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_841,c_1620]) ).
tcf(c_4152,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_4151,c_2823]) ).
tcf(c_4289,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_875,c_1617]) ).
tcf(c_4290,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4289,c_1962]) ).
tcf(c_4305,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_876,c_1617]) ).
tcf(c_4306,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4305,c_1962]) ).
tcf(c_4320,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_17,iPr_def_21) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_877,c_1617]) ).
tcf(c_4321,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_4320,c_1962]) ).
tcf(c_4508,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_934,c_1620]) ).
tcf(c_4509,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_4508,c_2823]) ).
tcf(c_4578,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_738,c_936]) ).
tcf(c_4594,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4578,c_2776]) ).
tcf(c_4695,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1032,c_1620]) ).
tcf(c_4696,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4695,c_2823]) ).
tcf(c_4890,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_3906,c_373]) ).
tcf(c_4891,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_14) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_3906,c_371]) ).
tcf(c_4892,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_3906,c_392]) ).
tcf(c_4893,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_3906,c_391]) ).
tcf(c_5193,plain,
( ( sk_c5 = iPr_def_14 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1323,c_1619]) ).
tcf(c_5194,plain,
( ( sk_c5 = iPr_def_15 )
| ( sk_c5 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5193,c_2781]) ).
tcf(c_5584,plain,
multiply(sk_c7,iPr_def_15) = multiply(iPr_def_14,sk_c7),
inference(superposition,[status(thm)],[c_365,c_1603]) ).
tcf(c_6196,plain,
multiply(sk_c3,iPr_def_15) = multiply(iPr_def_19,sk_c7),
inference(superposition,[status(thm)],[c_365,c_1605]) ).
tcf(c_6248,plain,
multiply(iPr_def_20,multiply(iPr_def_19,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_6196,c_1620]) ).
tcf(c_6289,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_23,sk_c6),
inference(superposition,[status(thm)],[c_364,c_1607]) ).
tcf(c_6566,plain,
multiply(sk_c2,iPr_def_14) = multiply(iPr_def_21,sk_c6),
inference(superposition,[status(thm)],[c_364,c_1608]) ).
tcf(c_7452,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c7,sk_c7) = multiply(iPr_def_22,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_842,c_2779]) ).
tcf(c_7872,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_17 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1678,c_1677]) ).
tcf(c_7930,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1610,c_78]) ).
tcf(c_7935,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_364,c_7930]) ).
tcf(c_7936,plain,
multiply(inverse(sk_c6),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_365,c_7930]) ).
tcf(c_7938,plain,
multiply(inverse(sk_c4),iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_366,c_7930]) ).
tcf(c_7939,plain,
multiply(inverse(sk_c1),iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_373,c_7930]) ).
tcf(c_7941,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_78,c_7930]) ).
tcf(c_7942,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_7930]) ).
tcf(c_7965,plain,
( ( sk_c5 = iPr_def_15 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_707,c_7930]) ).
tcf(c_7967,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_674,c_7930]) ).
tcf(c_7969,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_672,c_7930]) ).
tcf(c_7995,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(inverse(sk_c7),iPr_def_14) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_980,c_7930]) ).
tcf(c_8007,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(inverse(sk_c1),iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_893,c_7930]) ).
tcf(c_8019,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(inverse(sk_c4),iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1226,c_7930]) ).
tcf(c_8037,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1620,c_7930]) ).
tcf(c_8038,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1619,c_7930]) ).
tcf(c_8039,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1618,c_7930]) ).
tcf(c_8040,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1617,c_7930]) ).
tcf(c_8041,plain,
multiply(inverse(sk_c7),multiply(iPr_def_14,sk_c7)) = iPr_def_15,
inference(superposition,[status(thm)],[c_5584,c_7930]) ).
tcf(c_8068,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7930,c_7930]) ).
tcf(c_8449,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c5 )
| ( inverse(inverse(identity)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_7941,c_378]) ).
tcf(c_8469,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_7942,c_8068]) ).
tcf(c_8478,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_8469,c_1603]) ).
tcf(c_8481,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_8469,c_1604]) ).
tcf(c_8482,plain,
multiply(sk_c6,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_8469,c_2833]) ).
tcf(c_8483,plain,
multiply(sk_c5,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_8469,c_2821]) ).
tcf(c_8491,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_8469,c_7941]) ).
tcf(c_8495,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_8483,c_2781]) ).
tcf(c_8496,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_8482,c_2823]) ).
tcf(c_8497,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_8481,c_365]) ).
tcf(c_8500,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_8478,c_364]) ).
tcf(c_8907,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_4893,c_4892]) ).
tcf(c_9031,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c6,sk_c6) = multiply(iPr_def_20,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_3717,c_2833]) ).
tcf(c_9309,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_4890,c_6289]) ).
tcf(c_9388,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_21,sk_c6) = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_4891,c_6566]) ).
tcf(c_9793,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c5 != iPr_def_15 )
| iPr_def_11
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_1383,c_374,c_910,c_1205,c_1206,c_1282,c_1993,c_2406,c_3182,c_4290,c_4321,c_4696]) ).
tcf(c_9794,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c7 = iPr_def_20 )
| ( sk_c5 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_9793]) ).
tcf(c_9825,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_386,c_9794]) ).
tcf(c_9983,plain,
( ( iPr_def_19 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_613,c_1989]) ).
tcf(c_10239,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c3,sk_c7) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_8037,c_378]) ).
tcf(c_10241,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_8037,c_79]) ).
tcf(c_10245,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_20)) != sk_c7 )
| ( multiply(sk_c3,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_8037,c_377]) ).
tcf(c_10246,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_8037,c_7930]) ).
tcf(c_10247,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_8037,c_8469]) ).
tcf(c_10414,plain,
( ( sk_c6 = iPr_def_18 )
| ( sk_c5 != iPr_def_15 )
| iPr_def_11
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_1385,c_374,c_910,c_1180,c_1205,c_1206,c_1993,c_2406,c_3088,c_3158,c_3420,c_4509]) ).
tcf(c_10415,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c6 = iPr_def_18 )
| ( sk_c5 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_10414]) ).
tcf(c_10509,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c5 != iPr_def_15 )
| iPr_def_11
| iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_1386,c_374,c_910,c_1126,c_1205,c_1206,c_1993,c_2406,c_3100,c_3170,c_3286,c_4152]) ).
tcf(c_10510,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c6 = iPr_def_16 )
| ( sk_c5 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_10509]) ).
tcf(c_10536,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c6 = iPr_def_16 )
| ( iPr_def_14 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_399,c_10510]) ).
tcf(c_10800,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_10247,c_8469]) ).
tcf(c_10813,plain,
multiply(sk_c3,sk_c6) = iPr_def_19,
inference(superposition,[status(thm)],[c_2823,c_10246]) ).
tcf(c_10880,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_8038,c_79]) ).
tcf(c_10883,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c4,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_8038,c_376]) ).
tcf(c_10885,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_8038,c_7930]) ).
tcf(c_10886,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_8038,c_8469]) ).
tcf(c_11164,plain,
( ~ iPr_def_11
| ( inverse(sk_c7) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_2258,c_2276,c_2258,c_3619,c_3845]) ).
tcf(c_11182,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_11
| ( inverse(iPr_def_22) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_392,c_11164]) ).
tcf(c_11183,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_11
| ( inverse(iPr_def_22) != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_391,c_11164]) ).
tcf(c_11245,plain,
( ( inverse(iPr_def_22) != iPr_def_22 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_11182,c_2276,c_11182,c_11183]) ).
tcf(c_11246,plain,
( ~ iPr_def_11
| ( inverse(iPr_def_22) != iPr_def_22 ) ),
inference(renaming,[status(thm)],[c_11245]) ).
tcf(c_11338,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(superposition,[status(thm)],[c_10880,c_1619]) ).
tcf(c_11504,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_10886,c_8469]) ).
tcf(c_11512,plain,
multiply(sk_c4,sk_c5) = iPr_def_16,
inference(superposition,[status(thm)],[c_2781,c_10885]) ).
tcf(c_11593,plain,
multiply(sk_c1,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_8039,c_79]) ).
tcf(c_11597,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c7 )
| ( multiply(sk_c1,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_8039,c_377]) ).
tcf(c_11598,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_8039,c_7930]) ).
tcf(c_11599,plain,
multiply(sk_c1,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_8039,c_8469]) ).
tcf(c_11623,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_893,c_11593]) ).
tcf(c_11624,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_892,c_11593]) ).
tcf(c_11855,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(superposition,[status(thm)],[c_11593,c_1618]) ).
tcf(c_12257,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_11624,c_11623]) ).
tcf(c_12450,plain,
inverse(iPr_def_22) = sk_c1,
inference(demodulation,[status(thm)],[c_11599,c_8469]) ).
tcf(c_12452,plain,
( ~ iPr_def_11
| ( sk_c1 != iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_11246,c_12450]) ).
tcf(c_12455,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_8907,c_12450]) ).
tcf(c_12456,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_17) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_7872,c_12450]) ).
tcf(c_12522,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_14) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_758,c_11598]) ).
tcf(c_12523,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_917,c_11598]) ).
tcf(c_12524,plain,
multiply(sk_c1,sk_c7) = iPr_def_23,
inference(superposition,[status(thm)],[c_2776,c_11598]) ).
tcf(c_12535,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c6) = sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_12522,c_6289]) ).
tcf(c_12705,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(iPr_def_14)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_401,c_2100]) ).
tcf(c_12713,plain,
( ( sk_c6 = iPr_def_18 )
| ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(iPr_def_21)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_385,c_2100]) ).
tcf(c_13239,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_23,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_12257,c_78]) ).
tcf(c_13253,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_8040,c_79]) ).
tcf(c_13256,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c6 )
| ( multiply(sk_c2,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_8040,c_376]) ).
tcf(c_13258,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_8040,c_7930]) ).
tcf(c_13259,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_8040,c_8469]) ).
tcf(c_13274,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1676,c_13253]) ).
tcf(c_13325,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_13259,c_8469]) ).
tcf(c_13443,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_13274,c_8491]) ).
tcf(c_13445,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_13274,c_78]) ).
tcf(c_13540,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_918,c_13258]) ).
tcf(c_13541,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_14) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1680,c_13258]) ).
tcf(c_13543,plain,
multiply(sk_c2,sk_c7) = iPr_def_21,
inference(superposition,[status(thm)],[c_1962,c_13258]) ).
tcf(c_13561,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_21,sk_c6) = sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_13541,c_6566]) ).
tcf(c_14187,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c6 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_13239,c_9309]) ).
tcf(c_14323,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_14187,c_365]) ).
tcf(c_15223,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c6 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_13445,c_9388]) ).
tcf(c_15489,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_14323,c_13239]) ).
tcf(c_15612,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c7,iPr_def_21) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_15223,c_364]) ).
tcf(c_15851,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_15489,c_3906]) ).
tcf(c_17043,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1907,c_15612]) ).
tcf(c_17045,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(inverse(sk_c7),iPr_def_14) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_15612,c_7930]) ).
tcf(c_17142,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_12456,c_13325]) ).
tcf(c_17168,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(sk_c1,sk_c7) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_17142,c_371]) ).
tcf(c_17169,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(sk_c1) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_17142,c_367]) ).
tcf(c_17719,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1907,c_13443]) ).
tcf(c_18131,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c1 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_17719,c_12455]) ).
tcf(c_18161,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_18131,c_373]) ).
tcf(c_18162,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_14) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_18131,c_372]) ).
tcf(c_18363,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c1 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_18162,c_12455]) ).
tcf(c_18618,plain,
( ( iPr_def_19 = iPr_def_20 )
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_18363,c_12452]) ).
tcf(c_18634,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_22) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_18363,c_372]) ).
tcf(c_18732,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_18634,c_18618,c_18161,c_18131,c_17169,c_17168,c_17045,c_17043,c_15851,c_15223,c_13561,c_13543,c_13540,c_13325,c_13256,c_13253,c_12713,c_12705,c_12535,c_12524,c_12523,c_12450,c_11855,c_11623,c_11597,c_11512,c_11504,c_11338,c_10883,c_10813,c_10800,c_10536,c_10415,c_10245,c_10239,c_10241,c_9983,c_9825,c_9031,c_8500,c_8497,c_8496,c_8495,c_8483,c_8482,c_8481,c_8478,c_8491,c_8449,c_8041,c_8019,c_8007,c_7995,c_7969,c_7967,c_7965,c_7939,c_7938,c_7936,c_7935,c_7452,c_6566,c_6289,c_6248,c_6196,c_5584,c_5194,c_4594,c_4306,c_3906,c_3619,c_3286,c_3072,c_2389,c_2276,c_2118,c_1975,c_1394,c_383,c_382,c_380,c_379,c_374,c_372,c_370,c_368,c_367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP284-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 14:26:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 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
% 0.11/0.40
% 0.11/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.40
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.41 % Proving...
% 8.53/1.70 % SZS status Started for theBenchmark.p
% 8.53/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 8.53/1.70
% 8.53/1.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.53/1.70
% 8.53/1.70 % ------ iProver source info
% 8.53/1.70
% 8.53/1.70 % git: date: 2026-07-19 20:42:38 +0200
% 8.53/1.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.53/1.70 % git: non_committed_changes: false
% 8.53/1.70
% 8.53/1.70 % ------ Parsing...% successful
% 8.53/1.70
% 8.53/1.70
% 8.53/1.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.53/1.70
% 8.53/1.70 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.53/1.70
% 8.53/1.70 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.53/1.70
% 8.53/1.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.53/1.70 % ------ Proving...
% 8.53/1.70 % ------ Problem Properties
% 8.53/1.70
% 8.53/1.70 %
% 8.53/1.70 % clauses 43
% 8.53/1.70 % conjectures 30
% 8.53/1.70 % EPR 26
% 8.53/1.70 % Horn 17
% 8.53/1.70 % unary 13
% 8.53/1.70 % binary 25
% 8.53/1.70 % lits 81
% 8.53/1.70 % lits eq 73
% 8.53/1.70 % fd_pure 0
% 8.53/1.70 % fd_pseudo 0
% 8.53/1.70 % fd_cond 0
% 8.53/1.70 % fd_pseudo_cond 0
% 8.53/1.70 % AC symbols 0
% 8.53/1.70
% 8.53/1.70 % ------ Schedule dynamic 5 is on
% 8.53/1.70
% 8.53/1.70 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.53/1.70
% 8.53/1.70
% 8.53/1.70 % ------
% 8.53/1.70 % Current options:
% 8.53/1.70 % ------
% 8.53/1.70
% 8.53/1.70
% 8.53/1.70 %
% 8.53/1.70
% 8.53/1.70 % ------ Proving...
% 8.53/1.70 %
% 8.53/1.70
% 8.53/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 8.53/1.70
% 8.53/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.53/1.71
% 8.53/1.71
%------------------------------------------------------------------------------