%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 01:32:47 PM UTC 2026
% Result : Unsatisfiable 7.09s 1.79s
% Output : CNFRefutation 7.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 35
% Syntax : Number of formulae : 243 ( 115 unt; 10 def)
% Number of atoms : 706 ( 401 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 270 ( 87 ~; 183 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 62 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f7,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c6 = inverse(sk_c2)
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(reorient_equations,[],[f9]) ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c4 = multiply(sk_c5,sk_c6)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c2) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = inverse(sk_c3)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c5,sk_c4) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| sk_c6 = multiply(sk_c5,sk_c4) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c4 = multiply(sk_c5,sk_c6)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c2)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c5 = inverse(sk_c3)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| sk_c4 = inverse(sk_c6) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c4 = multiply(sk_c5,sk_c6)
| sk_c4 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( inverse(sk_c3) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c5 = inverse(sk_c3)
| sk_c4 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| sk_c4 = multiply(sk_c1,sk_c6) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c4
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c4 = multiply(sk_c5,sk_c6)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c2) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c2)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c2,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c2,sk_c5)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c3) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c5 = inverse(sk_c3)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c4) = sk_c5
| inverse(sk_c1) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c5 = multiply(sk_c3,sk_c4)
| sk_c6 = inverse(sk_c1) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
! [X2,X0,X1] :
( multiply(X2,sk_c4) != sk_c5
| inverse(X2) != sk_c5
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c4
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c4
| inverse(sk_c6) != sk_c4
| multiply(sk_c5,sk_c4) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
! [X2,X0,X1] :
( sk_c5 != multiply(X2,sk_c4)
| sk_c5 != inverse(X2)
| sk_c6 != multiply(X1,sk_c5)
| sk_c6 != inverse(X1)
| sk_c4 != multiply(sk_c5,sk_c6)
| inverse(X0) != sk_c6
| sk_c4 != multiply(X0,sk_c6)
| sk_c4 != inverse(sk_c6)
| sk_c6 != multiply(sk_c5,sk_c4)
| multiply(sk_c6,sk_c5) != sk_c4 ),
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_82,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c4 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_83,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c6,sk_c5) = sk_c4 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_85,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c5 )
| ( multiply(sk_c6,sk_c5) = sk_c4 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c5,sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c3) = sk_c5 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c3,sk_c4) = sk_c5 )
| ( multiply(sk_c5,sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c6) = sk_c4 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c2) = sk_c6 )
| ( inverse(sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c6) = sk_c4 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c5 )
| ( inverse(sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c6) = sk_c4 )
| ( multiply(sk_c3,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c4 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c3) = sk_c5 )
| ( multiply(sk_c1,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c1,sk_c6) = sk_c4 )
| ( multiply(sk_c3,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c4 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c2) = sk_c6 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( inverse(sk_c3) = sk_c5 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c6 )
| ( multiply(sk_c3,sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_106,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(sk_c6) != sk_c4 )
| ( inverse(X2) != sk_c5 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c6 )
| ( multiply(sk_c5,sk_c4) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 )
| ( multiply(sk_c6,sk_c5) != sk_c4 )
| ( multiply(X2,sk_c4) != sk_c5 )
| ( multiply(X1,sk_c5) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c4 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_359,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
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_c4) != sk_c5 ) ),
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_c6) != sk_c4 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_106]) ).
tcf(c_362,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c6) != sk_c4 )
| ( multiply(sk_c5,sk_c4) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c4 )
| ( multiply(sk_c6,sk_c5) != sk_c4 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_106]) ).
tcf(c_363,definition,
iPr_def_13 = multiply(sk_c6,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_364,definition,
iPr_def_14 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_365,definition,
iPr_def_15 = multiply(sk_c5,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_366,definition,
iPr_def_16 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_367,definition,
iPr_def_17 = multiply(sk_c3,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_368,definition,
iPr_def_18 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_369,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_370,definition,
iPr_def_20 = multiply(sk_c2,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_371,definition,
iPr_def_21 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_372,definition,
iPr_def_22 = multiply(sk_c1,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_373,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c4 )
| ( iPr_def_15 != sk_c6 )
| ( iPr_def_14 != sk_c4 )
| ( iPr_def_13 != sk_c4 ) ),
inference(demodulation,[status(thm)],[c_362,c_366,c_365,c_364,c_363]) ).
tcf(c_374,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c4 ) ),
inference(demodulation,[status(thm)],[c_361]) ).
tcf(c_375,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c4) != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_360]) ).
tcf(c_376,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_359]) ).
tcf(c_377,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_105,c_368,c_367]) ).
tcf(c_378,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104,c_369]) ).
tcf(c_379,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103,c_370]) ).
tcf(c_380,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_102,c_371]) ).
tcf(c_381,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_382,negated_conjecture,
( ( iPr_def_22 = sk_c4 )
| ( iPr_def_17 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_100,c_372]) ).
tcf(c_383,negated_conjecture,
( ( iPr_def_22 = sk_c4 )
| ( iPr_def_19 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_386,negated_conjecture,
( ( iPr_def_22 = sk_c4 )
| ( iPr_def_14 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_387,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_16 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_388,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_16 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_389,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_16 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_390,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_16 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_391,negated_conjecture,
( ( iPr_def_16 = sk_c4 )
| ( iPr_def_14 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_392,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_393,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_394,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_395,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_396,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_397,negated_conjecture,
( ( iPr_def_17 = sk_c5 )
| ( iPr_def_13 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_399,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_13 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_400,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_13 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_721,plain,
( ( sk_c4 = iPr_def_14 )
| ( multiply(sk_c3,iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_386,c_367]) ).
tcf(c_722,plain,
( ( sk_c4 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_386,c_365]) ).
tcf(c_891,plain,
( ( sk_c4 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_391,c_365]) ).
tcf(c_915,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_17,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_392,c_364]) ).
tcf(c_955,plain,
multiply(iPr_def_21,sk_c2) = identity,
inference(superposition,[status(thm)],[c_371,c_79]) ).
tcf(c_956,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_369,c_79]) ).
tcf(c_957,plain,
multiply(iPr_def_16,sk_c6) = identity,
inference(superposition,[status(thm)],[c_366,c_79]) ).
tcf(c_958,plain,
multiply(iPr_def_18,sk_c1) = identity,
inference(superposition,[status(thm)],[c_368,c_79]) ).
tcf(c_972,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_19,sk_c4) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_393,c_365]) ).
tcf(c_973,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_19,sk_c6) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_393,c_364]) ).
tcf(c_1005,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,sk_c5) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_394,c_363]) ).
tcf(c_1047,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_21) = identity ) ),
inference(superposition,[status(thm)],[c_395,c_957]) ).
tcf(c_1104,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_14) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_396,c_367]) ).
tcf(c_1622,plain,
( ~ iPr_def_12
| ( sk_c4 != iPr_def_14 )
| ( inverse(sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_364,c_374]) ).
tcf(c_1725,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c5,X0)) = multiply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_363,c_80]) ).
tcf(c_1726,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_364,c_80]) ).
tcf(c_1727,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c5,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_370,c_80]) ).
tcf(c_1729,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c4,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_365,c_80]) ).
tcf(c_1730,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c6,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_372,c_80]) ).
tcf(c_1732,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_79,c_80]) ).
tcf(c_1734,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_955,c_80]) ).
tcf(c_1735,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_956,c_80]) ).
tcf(c_1736,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_957,c_80]) ).
tcf(c_1737,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_958,c_80]) ).
tcf(c_1740,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1737,c_78]) ).
tcf(c_1741,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1736,c_78]) ).
tcf(c_1742,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1735,c_78]) ).
tcf(c_1743,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1734,c_78]) ).
tcf(c_2312,plain,
( ~ iPr_def_11
| ( sk_c5 != iPr_def_17 )
| ( inverse(sk_c3) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_367,c_375]) ).
tcf(c_2315,plain,
( ~ iPr_def_11
| ( sk_c5 != identity )
| ( inverse(inverse(sk_c4)) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_79,c_375]) ).
tcf(c_2341,plain,
( ~ iPr_def_11
| ( sk_c5 != iPr_def_19 )
| ( sk_c5 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2312,c_369]) ).
tcf(c_2675,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c6 = iPr_def_18 )
| ( iPr_def_13 != iPr_def_14 )
| ( sk_c4 != iPr_def_16 )
| ( sk_c4 != iPr_def_14 )
| ( sk_c6 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_381,c_373]) ).
tcf(c_3509,plain,
multiply(iPr_def_18,iPr_def_22) = sk_c6,
inference(superposition,[status(thm)],[c_372,c_1740]) ).
tcf(c_3522,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_22,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3509,c_80]) ).
tcf(c_3524,plain,
multiply(iPr_def_16,iPr_def_13) = sk_c5,
inference(superposition,[status(thm)],[c_363,c_1741]) ).
tcf(c_3620,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_13,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3524,c_80]) ).
tcf(c_3804,plain,
multiply(iPr_def_19,iPr_def_17) = sk_c4,
inference(superposition,[status(thm)],[c_367,c_1742]) ).
tcf(c_3807,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_17,X0)) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3804,c_80]) ).
tcf(c_3809,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c5,
inference(superposition,[status(thm)],[c_370,c_1743]) ).
tcf(c_3812,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_20,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3809,c_80]) ).
tcf(c_5668,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_396,c_972]) ).
tcf(c_5914,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_394,c_973]) ).
tcf(c_6923,plain,
multiply(sk_c6,iPr_def_14) = multiply(iPr_def_13,sk_c6),
inference(superposition,[status(thm)],[c_364,c_1725]) ).
tcf(c_6924,plain,
multiply(sk_c6,iPr_def_15) = multiply(iPr_def_13,sk_c4),
inference(superposition,[status(thm)],[c_365,c_1725]) ).
tcf(c_7534,plain,
multiply(iPr_def_16,multiply(iPr_def_13,sk_c6)) = iPr_def_14,
inference(superposition,[status(thm)],[c_6923,c_1741]) ).
tcf(c_7714,plain,
multiply(sk_c5,iPr_def_13) = multiply(iPr_def_14,sk_c5),
inference(superposition,[status(thm)],[c_363,c_1726]) ).
tcf(c_7721,plain,
multiply(sk_c5,multiply(iPr_def_13,sk_c4)) = multiply(iPr_def_14,iPr_def_15),
inference(superposition,[status(thm)],[c_6924,c_1726]) ).
tcf(c_8116,plain,
multiply(sk_c2,iPr_def_14) = multiply(iPr_def_20,sk_c6),
inference(superposition,[status(thm)],[c_364,c_1727]) ).
tcf(c_8117,plain,
multiply(sk_c2,iPr_def_15) = multiply(iPr_def_20,sk_c4),
inference(superposition,[status(thm)],[c_365,c_1727]) ).
tcf(c_8268,plain,
multiply(iPr_def_21,multiply(iPr_def_20,sk_c6)) = iPr_def_14,
inference(superposition,[status(thm)],[c_8116,c_1743]) ).
tcf(c_8442,plain,
multiply(sk_c1,iPr_def_13) = multiply(iPr_def_22,sk_c5),
inference(superposition,[status(thm)],[c_363,c_1730]) ).
tcf(c_9707,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1732,c_78]) ).
tcf(c_9727,plain,
multiply(inverse(sk_c5),iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_364,c_9707]) ).
tcf(c_9729,plain,
multiply(inverse(sk_c3),iPr_def_17) = sk_c4,
inference(superposition,[status(thm)],[c_367,c_9707]) ).
tcf(c_9730,plain,
multiply(inverse(sk_c5),iPr_def_15) = sk_c4,
inference(superposition,[status(thm)],[c_365,c_9707]) ).
tcf(c_9732,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_78,c_9707]) ).
tcf(c_9733,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_79,c_9707]) ).
tcf(c_9780,plain,
( ( sk_c4 = iPr_def_14 )
| ( multiply(inverse(sk_c3),iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_721,c_9707]) ).
tcf(c_9794,plain,
( ( sk_c4 = iPr_def_14 )
| ( multiply(inverse(sk_c5),iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_891,c_9707]) ).
tcf(c_9843,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1743,c_9707]) ).
tcf(c_9844,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1742,c_9707]) ).
tcf(c_9845,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_1741,c_9707]) ).
tcf(c_9846,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1740,c_9707]) ).
tcf(c_9884,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_9707,c_9707]) ).
tcf(c_10461,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_9733,c_9884]) ).
tcf(c_10469,plain,
multiply(sk_c2,sk_c5) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_10461,c_1727]) ).
tcf(c_10472,plain,
multiply(sk_c5,sk_c6) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_10461,c_1726]) ).
tcf(c_10474,plain,
multiply(sk_c5,sk_c4) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_10461,c_1729]) ).
tcf(c_10479,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_10461,c_9732]) ).
tcf(c_10481,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_10474,c_365]) ).
tcf(c_10482,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_10472,c_364]) ).
tcf(c_10485,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_10469,c_370]) ).
tcf(c_10900,plain,
multiply(sk_c2,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_9843,c_79]) ).
tcf(c_10904,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_21)) != sk_c6 )
| ( multiply(sk_c2,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_9843,c_376]) ).
tcf(c_10905,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_9843,c_9707]) ).
tcf(c_10906,plain,
multiply(sk_c2,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_9843,c_10461]) ).
tcf(c_10970,plain,
inverse(iPr_def_21) = sk_c2,
inference(demodulation,[status(thm)],[c_10906,c_10461]) ).
tcf(c_11301,plain,
multiply(sk_c2,sk_c5) = iPr_def_20,
inference(superposition,[status(thm)],[c_3809,c_10905]) ).
tcf(c_11985,plain,
multiply(sk_c3,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_9844,c_79]) ).
tcf(c_11988,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_19)) != sk_c5 )
| ( multiply(sk_c3,sk_c4) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_9844,c_375]) ).
tcf(c_11990,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_9844,c_9707]) ).
tcf(c_11991,plain,
multiply(sk_c3,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_9844,c_10461]) ).
tcf(c_12303,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(superposition,[status(thm)],[c_11985,c_1742]) ).
tcf(c_12328,plain,
inverse(iPr_def_19) = sk_c3,
inference(demodulation,[status(thm)],[c_11991,c_10461]) ).
tcf(c_12350,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_15) = sk_c4 ) ),
inference(superposition,[status(thm)],[c_972,c_11990]) ).
tcf(c_12353,plain,
multiply(sk_c3,sk_c4) = iPr_def_17,
inference(superposition,[status(thm)],[c_3804,c_11990]) ).
tcf(c_12356,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_14) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_5914,c_11990]) ).
tcf(c_12358,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c3,iPr_def_15) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5668,c_11990]) ).
tcf(c_12635,plain,
multiply(sk_c6,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_9845,c_79]) ).
tcf(c_12640,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_9845,c_9707]) ).
tcf(c_12641,plain,
multiply(sk_c6,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_9845,c_10461]) ).
tcf(c_13235,plain,
multiply(sk_c1,identity) = multiply(iPr_def_22,iPr_def_16),
inference(superposition,[status(thm)],[c_12635,c_1730]) ).
tcf(c_13236,plain,
multiply(sk_c5,identity) = multiply(iPr_def_14,iPr_def_16),
inference(superposition,[status(thm)],[c_12635,c_1726]) ).
tcf(c_13386,plain,
multiply(sk_c6,identity) = multiply(iPr_def_18,iPr_def_22),
inference(superposition,[status(thm)],[c_10461,c_3522]) ).
tcf(c_13393,plain,
inverse(iPr_def_16) = sk_c6,
inference(light_normalisation,[status(thm)],[c_13386,c_3509,c_12641]) ).
tcf(c_13425,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_12641,c_13393]) ).
tcf(c_13544,plain,
! [X0: $i] :
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,multiply(iPr_def_16,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_394,c_12640]) ).
tcf(c_13560,plain,
multiply(sk_c6,sk_c5) = iPr_def_13,
inference(superposition,[status(thm)],[c_3524,c_12640]) ).
tcf(c_13886,plain,
multiply(sk_c5,identity) = multiply(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_10461,c_3620]) ).
tcf(c_13890,plain,
multiply(iPr_def_14,iPr_def_16) = sk_c5,
inference(light_normalisation,[status(thm)],[c_13886,c_3524,c_13236]) ).
tcf(c_13898,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c4,sk_c6) = multiply(iPr_def_19,iPr_def_14) ) ),
inference(superposition,[status(thm)],[c_915,c_3807]) ).
tcf(c_13913,plain,
multiply(sk_c4,identity) = multiply(iPr_def_19,iPr_def_17),
inference(superposition,[status(thm)],[c_10461,c_3807]) ).
tcf(c_13917,plain,
multiply(sk_c4,identity) = sk_c4,
inference(light_normalisation,[status(thm)],[c_13913,c_3804]) ).
tcf(c_14010,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c5,sk_c5) = multiply(iPr_def_21,iPr_def_13) ) ),
inference(superposition,[status(thm)],[c_1005,c_3812]) ).
tcf(c_14022,plain,
multiply(sk_c5,identity) = multiply(iPr_def_21,iPr_def_20),
inference(superposition,[status(thm)],[c_10461,c_3812]) ).
tcf(c_14190,plain,
multiply(inverse(iPr_def_14),sk_c5) = iPr_def_16,
inference(superposition,[status(thm)],[c_13890,c_9707]) ).
tcf(c_14203,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(inverse(iPr_def_14),iPr_def_17) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_392,c_14190]) ).
tcf(c_14206,plain,
multiply(inverse(inverse(iPr_def_14)),iPr_def_16) = sk_c5,
inference(superposition,[status(thm)],[c_14190,c_9707]) ).
tcf(c_14287,plain,
multiply(iPr_def_22,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_13235,c_10461]) ).
tcf(c_14292,plain,
multiply(inverse(iPr_def_22),sk_c1) = iPr_def_16,
inference(superposition,[status(thm)],[c_14287,c_9707]) ).
tcf(c_14452,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),multiply(sk_c1,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_14292,c_80]) ).
tcf(c_14464,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_13236,c_13890]) ).
tcf(c_14492,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(inverse(inverse(iPr_def_14)),iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_14203,c_9707]) ).
tcf(c_14546,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,identity) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1047,c_13544]) ).
tcf(c_14752,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c1,sk_c6) != sk_c4 ) ),
inference(superposition,[status(thm)],[c_9846,c_374]) ).
tcf(c_14753,plain,
multiply(sk_c1,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_9846,c_79]) ).
tcf(c_14757,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_18)) != sk_c6 )
| ( multiply(sk_c1,sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_9846,c_376]) ).
tcf(c_14758,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_9846,c_9707]) ).
tcf(c_14759,plain,
multiply(sk_c1,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_9846,c_10461]) ).
tcf(c_14770,plain,
( ~ iPr_def_12
| ( sk_c4 != iPr_def_22 )
| ( inverse(inverse(iPr_def_18)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_14752,c_372]) ).
tcf(c_14790,plain,
inverse(iPr_def_18) = sk_c1,
inference(demodulation,[status(thm)],[c_14759,c_10461]) ).
tcf(c_14803,plain,
multiply(sk_c1,sk_c6) = iPr_def_22,
inference(superposition,[status(thm)],[c_3509,c_14758]) ).
tcf(c_15920,plain,
multiply(inverse(iPr_def_22),iPr_def_22) = multiply(iPr_def_16,sk_c6),
inference(superposition,[status(thm)],[c_14803,c_14452]) ).
tcf(c_15932,plain,
multiply(inverse(iPr_def_22),identity) = multiply(iPr_def_16,iPr_def_18),
inference(superposition,[status(thm)],[c_14753,c_14452]) ).
tcf(c_15937,plain,
multiply(inverse(iPr_def_22),multiply(iPr_def_22,sk_c5)) = multiply(iPr_def_16,iPr_def_13),
inference(superposition,[status(thm)],[c_8442,c_14452]) ).
tcf(c_15938,plain,
multiply(inverse(iPr_def_22),sk_c1) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_10461,c_14452]) ).
tcf(c_15944,plain,
multiply(inverse(iPr_def_22),iPr_def_22) = identity,
inference(light_normalisation,[status(thm)],[c_15920,c_957]) ).
tcf(c_15945,plain,
multiply(inverse(iPr_def_22),multiply(iPr_def_22,sk_c5)) = sk_c5,
inference(light_normalisation,[status(thm)],[c_15937,c_3524]) ).
tcf(c_17560,plain,
multiply(iPr_def_16,iPr_def_18) = inverse(iPr_def_22),
inference(demodulation,[status(thm)],[c_15932,c_10461]) ).
tcf(c_17570,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_20,inverse(iPr_def_22)) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_17560,c_13544]) ).
tcf(c_17626,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_17570,c_17560,c_15945,c_15944,c_15938,c_15937,c_15920,c_14803,c_14790,c_14770,c_14757,c_14753,c_14546,c_14492,c_14464,c_14292,c_14206,c_14022,c_14010,c_13917,c_13913,c_13898,c_13890,c_13560,c_13425,c_13393,c_12358,c_12356,c_12353,c_12350,c_12328,c_12303,c_11988,c_11301,c_10970,c_10904,c_10900,c_10485,c_10482,c_10481,c_10474,c_10479,c_9794,c_9780,c_9730,c_9729,c_9727,c_8268,c_8117,c_7721,c_7714,c_7534,c_6924,c_6923,c_5668,c_2675,c_2341,c_2315,c_1622,c_1104,c_722,c_400,c_399,c_397,c_390,c_389,c_388,c_387,c_383,c_382,c_381,c_380,c_379,c_378,c_377,c_373,c_371,c_369,c_368,c_366]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP305-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n001.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Wed Sep 23 14:31:20 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.46 % Proving...
% 7.09/1.79 % SZS status Started for theBenchmark.p
% 7.09/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 7.09/1.79
% 7.09/1.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.09/1.79
% 7.09/1.79 % ------ iProver source info
% 7.09/1.79
% 7.09/1.79 % git: date: 2026-07-19 20:42:38 +0200
% 7.09/1.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.09/1.79 % git: non_committed_changes: false
% 7.09/1.79
% 7.09/1.79 % ------ Parsing...% successful
% 7.09/1.79
% 7.09/1.79
% 7.09/1.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.09/1.79
% 7.09/1.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.09/1.79
% 7.09/1.79 % ------ Preprocessing... gs_s sp: 3 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.09/1.79
% 7.09/1.79 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.09/1.79 % ------ Proving...
% 7.09/1.79 % ------ Problem Properties
% 7.09/1.79
% 7.09/1.79 %
% 7.09/1.79 % clauses 42
% 7.09/1.79 % conjectures 29
% 7.09/1.79 % EPR 26
% 7.09/1.79 % Horn 16
% 7.09/1.79 % unary 13
% 7.09/1.79 % binary 25
% 7.09/1.79 % lits 79
% 7.09/1.79 % lits eq 73
% 7.09/1.79 % fd_pure 0
% 7.09/1.79 % fd_pseudo 0
% 7.09/1.79 % fd_cond 0
% 7.09/1.79 % fd_pseudo_cond 0
% 7.09/1.79 % AC symbols 0
% 7.09/1.79
% 7.09/1.79 % ------ Schedule dynamic 5 is on
% 7.09/1.79
% 7.09/1.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.09/1.79
% 7.09/1.79
% 7.09/1.79 % ------
% 7.09/1.79 % Current options:
% 7.09/1.79 % ------
% 7.09/1.79
% 7.09/1.79
% 7.09/1.79 %
% 7.09/1.79
% 7.09/1.79 % ------ Proving...
% 7.09/1.79 %
% 7.09/1.79
% 7.09/1.79 % SZS status Unsatisfiable for theBenchmark.p
% 7.09/1.79
% 7.09/1.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.09/1.80
% 7.09/1.80
%------------------------------------------------------------------------------