%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP332-1 : 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 : n008.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 01:33:02 PM UTC 2026
% Result : Unsatisfiable 21.10s 4.79s
% Output : CNFRefutation 21.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 38
% Syntax : Number of formulae : 289 ( 128 unt; 11 def)
% Number of atoms : 827 ( 484 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 348 ( 119 ~; 229 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f43,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c6 = multiply(sk_c8,sk_c7)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c8,sk_c5)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c5 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c6) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != inverse(X4)
| multiply(X4,sk_c8) != X3
| sk_c7 != multiply(sk_c8,X3)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1)
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( sk_c8 != inverse(X4)
| sk_c7 != multiply(sk_c8,multiply(X4,sk_c8))
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c6 != multiply(sk_c8,sk_c7)
| sk_c7 != multiply(X1,sk_c6)
| sk_c7 != inverse(X1)
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(equality_resolution,[],[f66]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c8,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c8,sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c5 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c2,sk_c6) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c5 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c8) != sk_c7 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_413,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = multiply(sk_c2,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = multiply(sk_c8,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c6 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_413,c_415,c_414]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_417,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114,c_418]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111,c_421]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_16 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109,c_422]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_15 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_862,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_444,c_414]) ).
tcf(c_906,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_17,sk_c5) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_436,c_419]) ).
tcf(c_945,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_445,c_421]) ).
tcf(c_947,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_439,c_421]) ).
tcf(c_993,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_994,plain,
multiply(iPr_def_17,sk_c4) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_995,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_996,plain,
multiply(iPr_def_22,sk_c2) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_1022,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_446,c_440]) ).
tcf(c_1025,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_446,c_414]) ).
tcf(c_1215,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c7,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_451,c_414]) ).
tcf(c_1963,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_84,c_427]) ).
tcf(c_2077,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_15 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_415,c_428]) ).
tcf(c_2080,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_428]) ).
tcf(c_2229,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_429]) ).
tcf(c_2230,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_429]) ).
tcf(c_2358,plain,
( ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c8,iPr_def_21) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_421,c_426]) ).
tcf(c_2361,plain,
( ~ iPr_def_13
| ( inverse(inverse(sk_c8)) != sk_c8 )
| ( multiply(sk_c8,identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_426]) ).
tcf(c_2379,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_20 )
| ( multiply(sk_c8,iPr_def_21) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2358,c_420]) ).
tcf(c_2573,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(iPr_def_21,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1022,c_414]) ).
tcf(c_2709,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2710,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2712,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c5,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_2714,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_424,c_85]) ).
tcf(c_2717,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2720,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_993,c_85]) ).
tcf(c_2721,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_994,c_85]) ).
tcf(c_2722,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_995,c_85]) ).
tcf(c_2723,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_996,c_85]) ).
tcf(c_2729,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2723,c_83]) ).
tcf(c_2730,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2722,c_83]) ).
tcf(c_2731,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2721,c_83]) ).
tcf(c_2732,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2720,c_83]) ).
tcf(c_2823,plain,
multiply(iPr_def_22,iPr_def_16) = sk_c6,
inference(superposition,[status(thm)],[c_416,c_2729]) ).
tcf(c_2826,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_16,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2823,c_85]) ).
tcf(c_2828,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_424,c_2730]) ).
tcf(c_2838,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_24,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2828,c_85]) ).
tcf(c_3410,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c8,
inference(superposition,[status(thm)],[c_418,c_2731]) ).
tcf(c_3424,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_18,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3410,c_85]) ).
tcf(c_3426,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_421,c_2732]) ).
tcf(c_3429,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3426,c_85]) ).
tcf(c_4196,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_450,c_862]) ).
tcf(c_4207,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4196,c_2828]) ).
tcf(c_4515,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4207,c_414]) ).
tcf(c_5231,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_17,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_437,c_906]) ).
tcf(c_5234,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_5231,c_3410]) ).
tcf(c_6448,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_452,c_1025]) ).
tcf(c_6461,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6448,c_2828]) ).
tcf(c_7056,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6461,c_4207]) ).
tcf(c_8801,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_7056,c_440]) ).
tcf(c_8802,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_7056,c_438]) ).
tcf(c_11192,plain,
multiply(sk_c7,iPr_def_19) = multiply(iPr_def_14,sk_c5),
inference(superposition,[status(thm)],[c_419,c_2709]) ).
tcf(c_11837,plain,
multiply(sk_c8,iPr_def_14) = multiply(iPr_def_15,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2710]) ).
tcf(c_12550,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_24,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2714]) ).
tcf(c_12558,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_14) = multiply(iPr_def_24,iPr_def_24) ) ),
inference(superposition,[status(thm)],[c_1215,c_2714]) ).
tcf(c_13048,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_19,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_5234,c_4515]) ).
tcf(c_16483,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_8802,c_8801]) ).
tcf(c_18047,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2717,c_83]) ).
tcf(c_18052,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_18047]) ).
tcf(c_18054,plain,
multiply(inverse(sk_c3),iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_421,c_18047]) ).
tcf(c_18055,plain,
multiply(inverse(sk_c8),iPr_def_19) = sk_c5,
inference(superposition,[status(thm)],[c_419,c_18047]) ).
tcf(c_18056,plain,
multiply(inverse(sk_c4),iPr_def_18) = sk_c8,
inference(superposition,[status(thm)],[c_418,c_18047]) ).
tcf(c_18057,plain,
multiply(inverse(sk_c1),iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_424,c_18047]) ).
tcf(c_18058,plain,
multiply(inverse(sk_c2),iPr_def_16) = sk_c6,
inference(superposition,[status(thm)],[c_416,c_18047]) ).
tcf(c_18059,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_18047]) ).
tcf(c_18060,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_18047]) ).
tcf(c_18203,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2732,c_18047]) ).
tcf(c_18204,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2731,c_18047]) ).
tcf(c_18205,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2730,c_18047]) ).
tcf(c_18206,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2729,c_18047]) ).
tcf(c_18280,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_18047,c_18047]) ).
tcf(c_22235,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_18060,c_18280]) ).
tcf(c_22250,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_22235,c_2709]) ).
tcf(c_22251,plain,
multiply(sk_c1,sk_c7) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_22235,c_2714]) ).
tcf(c_22252,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_22235,c_2710]) ).
tcf(c_22254,plain,
multiply(sk_c8,sk_c5) = multiply(iPr_def_19,identity),
inference(superposition,[status(thm)],[c_22235,c_2712]) ).
tcf(c_22255,plain,
multiply(sk_c8,identity) = multiply(iPr_def_17,iPr_def_18),
inference(superposition,[status(thm)],[c_22235,c_3424]) ).
tcf(c_22256,plain,
multiply(sk_c7,identity) = multiply(iPr_def_23,iPr_def_24),
inference(superposition,[status(thm)],[c_22235,c_2838]) ).
tcf(c_22263,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_22235,c_18059]) ).
tcf(c_22266,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_22256,c_2828]) ).
tcf(c_22267,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_22255,c_3410]) ).
tcf(c_22268,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(light_normalisation,[status(thm)],[c_22254,c_419]) ).
tcf(c_22270,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_22252,c_415]) ).
tcf(c_22271,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_22251,c_424]) ).
tcf(c_22272,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_22250,c_414]) ).
tcf(c_22484,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_22263,c_84]) ).
tcf(c_24046,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_18203,c_84]) ).
tcf(c_24051,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_20)) != sk_c8 )
| ( multiply(sk_c3,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_18203,c_427]) ).
tcf(c_24052,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_18203,c_18047]) ).
tcf(c_24053,plain,
multiply(sk_c3,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_18203,c_22235]) ).
tcf(c_24054,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_21 )
| ( inverse(inverse(iPr_def_20)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_24051,c_421]) ).
tcf(c_24069,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_947,c_24046]) ).
tcf(c_24070,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_945,c_24046]) ).
tcf(c_24141,plain,
inverse(iPr_def_20) = sk_c3,
inference(demodulation,[status(thm)],[c_24053,c_22235]) ).
tcf(c_28868,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_24070,c_24069]) ).
tcf(c_28939,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_24070,c_424]) ).
tcf(c_28943,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_24070,c_414]) ).
tcf(c_29172,plain,
multiply(sk_c3,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_3426,c_24052]) ).
tcf(c_29327,plain,
! [X0: $i] :
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_28868,c_83]) ).
tcf(c_31447,plain,
multiply(sk_c4,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_18204,c_84]) ).
tcf(c_31453,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_18204,c_18047]) ).
tcf(c_31454,plain,
multiply(sk_c4,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_18204,c_22235]) ).
tcf(c_31502,plain,
inverse(iPr_def_17) = sk_c4,
inference(demodulation,[status(thm)],[c_31454,c_22235]) ).
tcf(c_32580,plain,
multiply(sk_c4,sk_c8) = iPr_def_18,
inference(superposition,[status(thm)],[c_3410,c_31453]) ).
tcf(c_34348,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2229,c_22263]) ).
tcf(c_34797,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_23)) != sk_c7 )
| ( multiply(sk_c1,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_18205,c_428]) ).
tcf(c_34798,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_18205,c_84]) ).
tcf(c_34801,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_23)) != sk_c7 )
| ( multiply(sk_c1,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_18205,c_429]) ).
tcf(c_34804,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_18205,c_18047]) ).
tcf(c_34805,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_18205,c_22235]) ).
tcf(c_34834,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( inverse(inverse(iPr_def_23)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_34797,c_424]) ).
tcf(c_35058,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_34805,c_22235]) ).
tcf(c_35192,plain,
multiply(sk_c1,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_2828,c_34804]) ).
tcf(c_37524,plain,
multiply(sk_c2,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_18206,c_84]) ).
tcf(c_37528,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_22)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c2,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_18206,c_426]) ).
tcf(c_37530,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_18206,c_18047]) ).
tcf(c_37531,plain,
multiply(sk_c2,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_18206,c_22235]) ).
tcf(c_37910,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_16483,c_37524]) ).
tcf(c_37915,plain,
multiply(inverse(sk_c2),identity) = iPr_def_22,
inference(superposition,[status(thm)],[c_37524,c_18047]) ).
tcf(c_38064,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_28939,c_34798]) ).
tcf(c_38083,plain,
( ( identity = iPr_def_21 )
| ( inverse(iPr_def_24) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_38064,c_22263]) ).
tcf(c_38156,plain,
inverse(iPr_def_22) = sk_c2,
inference(demodulation,[status(thm)],[c_37531,c_22235]) ).
tcf(c_38185,plain,
multiply(sk_c2,sk_c6) = iPr_def_16,
inference(superposition,[status(thm)],[c_2823,c_37530]) ).
tcf(c_38480,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_14) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_28943,c_34804]) ).
tcf(c_38481,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_24,sk_c8) = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_38480,c_12550]) ).
tcf(c_38719,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_29327,c_2573]) ).
tcf(c_39240,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(sk_c7,iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_38719,c_414]) ).
tcf(c_45847,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_24,iPr_def_24) = identity ) ),
inference(superposition,[status(thm)],[c_38083,c_84]) ).
tcf(c_58338,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_18280,c_84]) ).
tcf(c_58345,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_18280,c_22235]) ).
tcf(c_58346,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_58345,c_22235]) ).
tcf(c_58392,plain,
( ~ iPr_def_11
| ( sk_c8 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2080,c_58346]) ).
tcf(c_58393,plain,
( ~ iPr_def_12
| ( sk_c7 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1963,c_58346]) ).
tcf(c_58426,plain,
inverse(sk_c4) = iPr_def_17,
inference(superposition,[status(thm)],[c_31502,c_58346]) ).
tcf(c_58427,plain,
inverse(sk_c3) = iPr_def_20,
inference(superposition,[status(thm)],[c_24141,c_58346]) ).
tcf(c_58428,plain,
inverse(sk_c2) = iPr_def_22,
inference(superposition,[status(thm)],[c_38156,c_58346]) ).
tcf(c_58429,plain,
inverse(sk_c1) = iPr_def_23,
inference(superposition,[status(thm)],[c_35058,c_58346]) ).
tcf(c_58655,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_58338,c_85]) ).
tcf(c_58660,plain,
multiply(iPr_def_14,inverse(sk_c8)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_58338,c_2709]) ).
tcf(c_58666,plain,
multiply(iPr_def_15,inverse(sk_c7)) = multiply(sk_c8,identity),
inference(superposition,[status(thm)],[c_58338,c_2710]) ).
tcf(c_58671,plain,
multiply(sk_c8,inverse(iPr_def_21)) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_58338,c_3429]) ).
tcf(c_58686,plain,
multiply(sk_c6,inverse(iPr_def_16)) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_58338,c_2826]) ).
tcf(c_58688,plain,
multiply(iPr_def_20,identity) = inverse(sk_c3),
inference(superposition,[status(thm)],[c_58338,c_2732]) ).
tcf(c_58689,plain,
multiply(iPr_def_17,identity) = inverse(sk_c4),
inference(superposition,[status(thm)],[c_58338,c_2731]) ).
tcf(c_58693,plain,
multiply(iPr_def_23,identity) = inverse(sk_c1),
inference(superposition,[status(thm)],[c_58338,c_2730]) ).
tcf(c_58695,plain,
multiply(iPr_def_22,identity) = inverse(sk_c2),
inference(superposition,[status(thm)],[c_58338,c_2729]) ).
tcf(c_59389,plain,
multiply(sk_c4,multiply(iPr_def_17,inverse(identity))) = identity,
inference(superposition,[status(thm)],[c_31447,c_58655]) ).
tcf(c_59435,plain,
multiply(sk_c3,multiply(iPr_def_20,inverse(identity))) = identity,
inference(superposition,[status(thm)],[c_24046,c_58655]) ).
tcf(c_59439,plain,
multiply(sk_c1,multiply(iPr_def_23,inverse(identity))) = identity,
inference(superposition,[status(thm)],[c_34798,c_58655]) ).
tcf(c_59521,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(sk_c7,multiply(iPr_def_14,inverse(iPr_def_14))) = identity ) ),
inference(superposition,[status(thm)],[c_39240,c_58655]) ).
tcf(c_59524,plain,
multiply(sk_c8,multiply(iPr_def_14,inverse(multiply(iPr_def_15,sk_c8)))) = identity,
inference(superposition,[status(thm)],[c_11837,c_58655]) ).
tcf(c_59722,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_24,multiply(iPr_def_24,inverse(identity))) = identity ) ),
inference(superposition,[status(thm)],[c_45847,c_58655]) ).
tcf(c_59756,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(X0,inverse(multiply(sk_c8,X0)))) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_58655,c_2709]) ).
tcf(c_59757,plain,
multiply(iPr_def_14,inverse(multiply(sk_c7,sk_c8))) = identity,
inference(superposition,[status(thm)],[c_58655,c_2709]) ).
tcf(c_59772,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(X0,inverse(multiply(sk_c5,X0)))) = multiply(sk_c8,identity),
inference(superposition,[status(thm)],[c_58655,c_2712]) ).
tcf(c_59806,plain,
multiply(sk_c7,inverse(multiply(iPr_def_23,iPr_def_24))) = identity,
inference(superposition,[status(thm)],[c_58655,c_2838]) ).
tcf(c_59845,plain,
multiply(sk_c7,inverse(sk_c7)) = identity,
inference(light_normalisation,[status(thm)],[c_59806,c_2828]) ).
tcf(c_59853,plain,
multiply(iPr_def_14,inverse(iPr_def_14)) = identity,
inference(light_normalisation,[status(thm)],[c_59757,c_414]) ).
tcf(c_59860,plain,
multiply(sk_c1,multiply(iPr_def_23,identity)) = identity,
inference(light_normalisation,[status(thm)],[c_59439,c_22263]) ).
tcf(c_59861,plain,
multiply(sk_c3,multiply(iPr_def_20,identity)) = identity,
inference(light_normalisation,[status(thm)],[c_59435,c_22263]) ).
tcf(c_59862,plain,
multiply(sk_c4,multiply(iPr_def_17,identity)) = identity,
inference(light_normalisation,[status(thm)],[c_59389,c_22263]) ).
tcf(c_59926,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(X0,inverse(multiply(sk_c5,X0)))) = multiply(iPr_def_15,inverse(sk_c7)),
inference(light_normalisation,[status(thm)],[c_59772,c_58666]) ).
tcf(c_59935,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(X0,inverse(multiply(sk_c8,X0)))) = multiply(iPr_def_14,inverse(sk_c8)),
inference(light_normalisation,[status(thm)],[c_59756,c_58660]) ).
tcf(c_59982,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_24,multiply(iPr_def_24,identity)) = identity ) ),
inference(light_normalisation,[status(thm)],[c_59722,c_22263]) ).
tcf(c_63130,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_59982,c_59935,c_59926,c_59862,c_59861,c_59860,c_59853,c_59772,c_59756,c_59524,c_59521,c_58695,c_58693,c_58689,c_58688,c_58686,c_58671,c_58429,c_58428,c_58427,c_58426,c_59845,c_58393,c_58392,c_38481,c_38185,c_38156,c_37915,c_37910,c_37528,c_37531,c_35192,c_35058,c_34834,c_34801,c_34805,c_34348,c_32580,c_29172,c_24141,c_24054,c_24053,c_22272,c_22271,c_22270,c_22268,c_22267,c_22266,c_22254,c_22252,c_22250,c_22263,c_18058,c_18057,c_18056,c_18055,c_18054,c_18052,c_13048,c_12558,c_12550,c_11837,c_11192,c_2379,c_2361,c_2230,c_2077,c_22484,c_459,c_458,c_457,c_456,c_455,c_454,c_450,c_444,c_438,c_435,c_434,c_433,c_432,c_431,c_430,c_425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP332-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:30:25 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.41 Running first-order theorem proving
% 0.03/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.42
% 0.03/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.42
% 0.03/0.42 % Detected problem language: tptp
% 0.03/0.43 % Proving...
% 21.10/4.79 % SZS status Started for theBenchmark.p
% 21.10/4.79 % SZS status Unsatisfiable for theBenchmark.p
% 21.10/4.79
% 21.10/4.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.10/4.79
% 21.10/4.79 % ------ iProver source info
% 21.10/4.79
% 21.10/4.79 % git: date: 2026-07-19 20:42:38 +0200
% 21.10/4.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.10/4.79 % git: non_committed_changes: false
% 21.10/4.79
% 21.10/4.79 % ------ Parsing...% successful
% 21.10/4.79
% 21.10/4.79
% 21.10/4.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.10/4.79
% 21.10/4.79 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 21.10/4.79
% 21.10/4.79 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.10/4.79
% 21.10/4.79 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 21.10/4.79 % ------ Proving...
% 21.10/4.79 % ------ Problem Properties
% 21.10/4.79
% 21.10/4.79 %
% 21.10/4.79 % clauses 49
% 21.10/4.79 % conjectures 35
% 21.10/4.79 % EPR 31
% 21.10/4.79 % Horn 18
% 21.10/4.79 % unary 14
% 21.10/4.79 % binary 30
% 21.10/4.79 % lits 92
% 21.10/4.79 % lits eq 84
% 21.10/4.79 % fd_pure 0
% 21.10/4.79 % fd_pseudo 0
% 21.10/4.79 % fd_cond 0
% 21.10/4.79 % fd_pseudo_cond 0
% 21.10/4.79 % AC symbols 0
% 21.10/4.79
% 21.10/4.79 % ------ Schedule dynamic 5 is on
% 21.10/4.79
% 21.10/4.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.10/4.79
% 21.10/4.79
% 21.10/4.79 % ------
% 21.10/4.79 % Current options:
% 21.10/4.79 % ------
% 21.10/4.79
% 21.10/4.79
% 21.10/4.79 %
% 21.10/4.79
% 21.10/4.79 % ------ Proving...
% 21.10/4.79 %
% 21.10/4.79
% 21.10/4.79 % SZS status Unsatisfiable for theBenchmark.p
% 21.10/4.79
% 21.10/4.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.10/4.79
% 21.10/4.79
%------------------------------------------------------------------------------