%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP290-1 : 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 : n020.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 01:32:44 PM UTC 2026
% Result : Unsatisfiable 4.75s 2.22s
% Output : CNFRefutation 4.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 39
% Syntax : Number of formulae : 330 ( 93 unt; 11 def)
% Number of atoms : 1174 ( 607 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 546 ( 184 ~; 362 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 76 !; 0 ?; 56 :)
% 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_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c4 = multiply(sk_c3,sk_c8)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = inverse(sk_c3)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c5)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c6,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c8,sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c4 = multiply(sk_c3,sk_c8)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = multiply(sk_c5,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != inverse(X4)
| sk_c8 != multiply(X4,sk_c6)
| sk_c8 != inverse(X3)
| multiply(X3,sk_c8) != X2
| sk_c7 != multiply(sk_c8,X2)
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X3,X0,X1,X4] :
( sk_c6 != inverse(X4)
| sk_c8 != multiply(X4,sk_c6)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(sk_c8,multiply(X3,sk_c8))
| sk_c7 != multiply(sk_c6,sk_c8)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| multiply(sk_c8,sk_c7) != 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_c6,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c8 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c8,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c4 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c6,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c8,sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c4 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c6 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c6) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X2,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c8 ) ),
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_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
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_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
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_c6,sk_c8) != sk_c7 )
| ( multiply(sk_c8,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c8,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c6,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c8,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c2,sk_c7),
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_c8),
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_c7 )
| ( 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_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_417,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114,c_418]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_113,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c4 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_112,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111,c_421]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109,c_422]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_20 = sk_c4 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103,c_423]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97,c_424]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_18 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_18 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_740,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_437,c_415]) ).
tcf(c_749,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_437,c_418]) ).
tcf(c_750,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_436,c_418]) ).
tcf(c_763,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_438,c_418]) ).
tcf(c_764,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_438,c_415]) ).
tcf(c_782,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_440,c_418]) ).
tcf(c_797,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_441,c_418]) ).
tcf(c_819,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_442,c_418]) ).
tcf(c_846,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_443,c_420]) ).
tcf(c_848,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_443,c_414]) ).
tcf(c_860,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c6,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_444,c_415]) ).
tcf(c_861,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_444,c_414]) ).
tcf(c_875,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c8,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_439,c_421]) ).
tcf(c_889,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_432,c_422]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_903,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_444,c_424]) ).
tcf(c_904,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_443,c_424]) ).
tcf(c_913,plain,
multiply(iPr_def_19,sk_c3) = identity,
inference(superposition,[status(thm)],[c_419,c_84]) ).
tcf(c_914,plain,
multiply(iPr_def_16,sk_c5) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_915,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_916,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_1017,plain,
( ( sk_c7 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_448,c_418]) ).
tcf(c_1066,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_449,c_422]) ).
tcf(c_1067,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c8,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_449,c_414]) ).
tcf(c_1121,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_450,c_422]) ).
tcf(c_1263,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_454,c_418]) ).
tcf(c_1320,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_14) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_455,c_418]) ).
tcf(c_1369,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != iPr_def_22 )
| ( X0 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_902]) ).
tcf(c_1391,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_14) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_456,c_418]) ).
tcf(c_1392,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_456,c_415]) ).
tcf(c_1518,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_459,c_441]) ).
tcf(c_1521,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_14) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_459,c_418]) ).
tcf(c_1835,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( sk_c7 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_456,c_425]) ).
tcf(c_1836,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_18 )
| ( sk_c7 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_455,c_425]) ).
tcf(c_1958,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_22 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_422,c_427]) ).
tcf(c_1959,plain,
( ~ iPr_def_12
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_427]) ).
tcf(c_1975,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_22 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1958,c_417]) ).
tcf(c_2074,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_420,c_428]) ).
tcf(c_2075,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_424,c_428]) ).
tcf(c_2077,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_84,c_428]) ).
tcf(c_2086,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2075,c_423]) ).
tcf(c_2090,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2074,c_419]) ).
tcf(c_2160,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_18 )
| ( inverse(sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_418,c_429]) ).
tcf(c_2161,plain,
( ~ iPr_def_10
| ( sk_c8 != sk_c6 )
| ( inverse(identity) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_83,c_429]) ).
tcf(c_2162,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_84,c_429]) ).
tcf(c_2179,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_16 )
| ( sk_c8 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_2160,c_416]) ).
tcf(c_2329,plain,
( ~ iPr_def_13
| ( inverse(sk_c6) != sk_c8 )
| ( multiply(sk_c8,iPr_def_15) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_415,c_426]) ).
tcf(c_2330,plain,
( ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c8,iPr_def_20) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_420,c_426]) ).
tcf(c_2331,plain,
( ~ iPr_def_13
| ( inverse(sk_c1) != sk_c8 )
| ( multiply(sk_c8,iPr_def_24) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_424,c_426]) ).
tcf(c_2332,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_426]) ).
tcf(c_2342,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_23 )
| ( multiply(sk_c8,iPr_def_24) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2331,c_423]) ).
tcf(c_2346,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_19 )
| ( multiply(sk_c8,iPr_def_20) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2330,c_419]) ).
tcf(c_2654,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2655,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2656,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c4,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_421,c_85]) ).
tcf(c_2657,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_420,c_85]) ).
tcf(c_2658,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2662,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2664,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_913,c_85]) ).
tcf(c_2665,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_914,c_85]) ).
tcf(c_2666,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_915,c_85]) ).
tcf(c_2667,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_916,c_85]) ).
tcf(c_2673,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2667,c_83]) ).
tcf(c_2674,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2666,c_83]) ).
tcf(c_2675,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2665,c_83]) ).
tcf(c_2676,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2664,c_83]) ).
tcf(c_2767,plain,
( ( iPr_def_14 = iPr_def_22 )
| ( multiply(sk_c8,iPr_def_15) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1518,c_414]) ).
tcf(c_2783,plain,
multiply(iPr_def_17,iPr_def_22) = sk_c7,
inference(superposition,[status(thm)],[c_422,c_2673]) ).
tcf(c_2786,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_22,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2783,c_85]) ).
tcf(c_2812,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_424,c_2674]) ).
tcf(c_2823,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_24,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2812,c_85]) ).
tcf(c_3021,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_443,c_740]) ).
tcf(c_3255,plain,
multiply(iPr_def_16,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_418,c_2675]) ).
tcf(c_3256,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_16,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_749,c_2675]) ).
tcf(c_3261,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_18,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3255,c_85]) ).
tcf(c_3269,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_420,c_2676]) ).
tcf(c_3272,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3269,c_85]) ).
tcf(c_3372,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_16,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_763,c_2675]) ).
tcf(c_3373,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3372,c_3255]) ).
tcf(c_3466,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_444,c_764]) ).
tcf(c_3741,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_846,c_2676]) ).
tcf(c_3742,plain,
( ( sk_c8 = iPr_def_23 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_3741,c_3269]) ).
tcf(c_3791,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_449,c_848]) ).
tcf(c_3800,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3791,c_2812]) ).
tcf(c_4100,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_23) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_456,c_860]) ).
tcf(c_4135,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_450,c_861]) ).
tcf(c_4145,plain,
( ( sk_c8 = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4135,c_2812]) ).
tcf(c_5126,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1066,c_2673]) ).
tcf(c_5127,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5126,c_2783]) ).
tcf(c_5171,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1121,c_2673]) ).
tcf(c_5172,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_5171,c_2783]) ).
tcf(c_7430,plain,
multiply(sk_c6,iPr_def_14) = multiply(iPr_def_15,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2655]) ).
tcf(c_7602,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_14) = multiply(iPr_def_15,sk_c7) ) ),
inference(superposition,[status(thm)],[c_456,c_7430]) ).
tcf(c_7603,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_14) = multiply(iPr_def_15,sk_c7) ) ),
inference(superposition,[status(thm)],[c_455,c_7430]) ).
tcf(c_7875,plain,
multiply(sk_c3,iPr_def_14) = multiply(iPr_def_20,sk_c7),
inference(superposition,[status(thm)],[c_414,c_2657]) ).
tcf(c_7876,plain,
multiply(sk_c3,iPr_def_21) = multiply(iPr_def_20,sk_c4),
inference(superposition,[status(thm)],[c_421,c_2657]) ).
tcf(c_7886,plain,
( ( sk_c6 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_21) = multiply(iPr_def_20,iPr_def_20) ) ),
inference(superposition,[status(thm)],[c_875,c_2657]) ).
tcf(c_8083,plain,
multiply(iPr_def_19,multiply(iPr_def_20,sk_c4)) = iPr_def_21,
inference(superposition,[status(thm)],[c_7876,c_2676]) ).
tcf(c_8085,plain,
multiply(sk_c5,iPr_def_15) = multiply(iPr_def_18,sk_c8),
inference(superposition,[status(thm)],[c_415,c_2658]) ).
tcf(c_8789,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c7,iPr_def_23) = multiply(iPr_def_17,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_3466,c_2786]) ).
tcf(c_8790,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_23) = multiply(iPr_def_17,iPr_def_15) ) ),
inference(superposition,[status(thm)],[c_3021,c_2786]) ).
tcf(c_9158,plain,
( ( sk_c6 = iPr_def_22 )
| ( sk_c8 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_3256,c_3255]) ).
tcf(c_10412,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_14) = multiply(iPr_def_15,iPr_def_24) ) ),
inference(superposition,[status(thm)],[c_450,c_7602]) ).
tcf(c_10418,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_14) = multiply(iPr_def_15,iPr_def_17) ) ),
inference(superposition,[status(thm)],[c_432,c_7602]) ).
tcf(c_10461,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_14) = multiply(iPr_def_15,iPr_def_24) ) ),
inference(superposition,[status(thm)],[c_449,c_7603]) ).
tcf(c_10467,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_14) = multiply(iPr_def_15,iPr_def_17) ) ),
inference(superposition,[status(thm)],[c_431,c_7603]) ).
tcf(c_11231,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2662,c_83]) ).
tcf(c_11236,plain,
multiply(inverse(sk_c8),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_414,c_11231]) ).
tcf(c_11237,plain,
multiply(inverse(sk_c6),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_415,c_11231]) ).
tcf(c_11238,plain,
multiply(inverse(sk_c8),iPr_def_21) = sk_c4,
inference(superposition,[status(thm)],[c_421,c_11231]) ).
tcf(c_11240,plain,
multiply(inverse(sk_c5),iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_418,c_11231]) ).
tcf(c_11243,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_11231]) ).
tcf(c_11244,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_11231]) ).
tcf(c_11262,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_797,c_11231]) ).
tcf(c_11263,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_782,c_11231]) ).
tcf(c_11264,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_763,c_11231]) ).
tcf(c_11265,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_750,c_11231]) ).
tcf(c_11266,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_749,c_11231]) ).
tcf(c_11316,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1521,c_11231]) ).
tcf(c_11318,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1391,c_11231]) ).
tcf(c_11319,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1320,c_11231]) ).
tcf(c_11322,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(iPr_def_14),iPr_def_15) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_1392,c_11231]) ).
tcf(c_11362,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2676,c_11231]) ).
tcf(c_11363,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2675,c_11231]) ).
tcf(c_11364,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2674,c_11231]) ).
tcf(c_11365,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2673,c_11231]) ).
tcf(c_11377,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(iPr_def_22),iPr_def_15) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_3466,c_11231]) ).
tcf(c_11383,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(iPr_def_14),iPr_def_15) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_4100,c_11231]) ).
tcf(c_11412,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11231,c_11231]) ).
tcf(c_12224,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11244,c_11412]) ).
tcf(c_12233,plain,
multiply(sk_c8,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_12224,c_2654]) ).
tcf(c_12236,plain,
multiply(sk_c6,sk_c8) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_12224,c_2655]) ).
tcf(c_12237,plain,
multiply(sk_c8,sk_c4) = multiply(iPr_def_21,identity),
inference(superposition,[status(thm)],[c_12224,c_2656]) ).
tcf(c_12238,plain,
multiply(sk_c8,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_12224,c_3272]) ).
tcf(c_12239,plain,
multiply(sk_c6,identity) = multiply(iPr_def_16,iPr_def_18),
inference(superposition,[status(thm)],[c_12224,c_3261]) ).
tcf(c_12241,plain,
multiply(sk_c8,identity) = multiply(iPr_def_23,iPr_def_24),
inference(superposition,[status(thm)],[c_12224,c_2823]) ).
tcf(c_12247,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12224,c_11243]) ).
tcf(c_12249,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_12241,c_2812]) ).
tcf(c_12251,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_12239,c_3255]) ).
tcf(c_12253,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_12237,c_421]) ).
tcf(c_12254,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_12236,c_415]) ).
tcf(c_12257,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_12233,c_414]) ).
tcf(c_12291,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_432,c_1975]) ).
tcf(c_12292,plain,
( ( sk_c8 = iPr_def_18 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_431,c_1975]) ).
tcf(c_12429,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_12247,c_84]) ).
tcf(c_12446,plain,
( ( sk_c8 = iPr_def_18 )
| ~ iPr_def_12 ),
inference(forward_subsumption_resolution,[status(thm)],[c_12292,c_9158]) ).
tcf(c_12646,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_444,c_2086]) ).
tcf(c_12647,plain,
( ( sk_c8 = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_443,c_2086]) ).
tcf(c_13257,plain,
multiply(sk_c3,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_11362,c_84]) ).
tcf(c_13261,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_19)) != sk_c7 )
| ( multiply(sk_c3,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_11362,c_427]) ).
tcf(c_13262,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_11362,c_11231]) ).
tcf(c_13263,plain,
multiply(sk_c3,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_11362,c_12224]) ).
tcf(c_13355,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(iPr_def_15),multiply(iPr_def_14,iPr_def_14)) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_10412,c_11231]) ).
tcf(c_13366,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(iPr_def_15),multiply(iPr_def_14,iPr_def_14)) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_10418,c_11231]) ).
tcf(c_13379,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(inverse(iPr_def_15),multiply(iPr_def_14,iPr_def_14)) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_10461,c_11231]) ).
tcf(c_13390,plain,
( ( sk_c8 = iPr_def_18 )
| ( multiply(inverse(iPr_def_15),multiply(iPr_def_14,iPr_def_14)) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_10467,c_11231]) ).
tcf(c_13979,plain,
( ( sk_c6 = identity )
| ( identity != iPr_def_22 )
| ( sk_c6 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_1369]) ).
tcf(c_14306,plain,
inverse(iPr_def_19) = sk_c3,
inference(demodulation,[status(thm)],[c_13263,c_12224]) ).
tcf(c_14317,plain,
multiply(sk_c3,sk_c8) = iPr_def_20,
inference(superposition,[status(thm)],[c_3269,c_13262]) ).
tcf(c_14446,plain,
multiply(sk_c5,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_11363,c_84]) ).
tcf(c_14449,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_11363,c_429]) ).
tcf(c_14451,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_11363,c_11231]) ).
tcf(c_14452,plain,
multiply(sk_c5,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_11363,c_12224]) ).
tcf(c_14456,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_18 )
| ( inverse(inverse(iPr_def_16)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_14449,c_418]) ).
tcf(c_14467,plain,
( ( identity = iPr_def_18 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_1263,c_14446]) ).
tcf(c_14468,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1017,c_14446]) ).
tcf(c_14469,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_819,c_14446]) ).
tcf(c_14623,plain,
( iPr_def_13
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( sk_c7 != iPr_def_15 ) ),
inference(global_subsumption_just,[status(thm)],[c_1835,c_1835,c_3373,c_5172,c_12291,c_12646]) ).
tcf(c_14647,plain,
( iPr_def_13
| iPr_def_10
| ( sk_c7 = iPr_def_15 )
| ( sk_c8 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_453,c_14623]) ).
tcf(c_14649,plain,
( iPr_def_13
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_450,c_14623]) ).
tcf(c_14842,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c7 != iPr_def_15 )
| ( sk_c8 = iPr_def_18 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1836,c_1836,c_5127,c_12647]) ).
tcf(c_14843,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c8 = iPr_def_18 )
| ( sk_c7 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_14842]) ).
tcf(c_14849,plain,
( iPr_def_13
| iPr_def_10
| ( sk_c8 = iPr_def_18 )
| ( sk_c7 != iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14843,c_12446]) ).
tcf(c_14879,plain,
( iPr_def_13
| iPr_def_10
| ( sk_c8 = iPr_def_18 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_449,c_14849]) ).
tcf(c_15039,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( identity = iPr_def_18 )
| ( sk_c7 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_14467,c_425]) ).
tcf(c_15046,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_14) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_14467,c_418]) ).
tcf(c_15047,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_14467,c_415]) ).
tcf(c_15214,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c8,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_14468,c_414]) ).
tcf(c_15440,plain,
inverse(iPr_def_16) = sk_c5,
inference(demodulation,[status(thm)],[c_14452,c_12224]) ).
tcf(c_15449,plain,
multiply(sk_c5,identity) = sk_c5,
inference(superposition,[status(thm)],[c_914,c_14451]) ).
tcf(c_15450,plain,
multiply(sk_c5,sk_c6) = iPr_def_18,
inference(superposition,[status(thm)],[c_3255,c_14451]) ).
tcf(c_16023,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_1959,c_12247]) ).
tcf(c_17222,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_11364,c_84]) ).
tcf(c_17246,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_904,c_17222]) ).
tcf(c_17247,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_903,c_17222]) ).
tcf(c_17300,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( sk_c8 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2161,c_12247]) ).
tcf(c_17328,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c6 != identity )
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_456,c_17300]) ).
tcf(c_17329,plain,
( ( sk_c8 = iPr_def_18 )
| ~ iPr_def_10
| ( sk_c6 != identity )
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_455,c_17300]) ).
tcf(c_17513,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c7 != iPr_def_15 )
| ( identity = iPr_def_18 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_15039,c_2086,c_14469,c_14468,c_15039]) ).
tcf(c_17514,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( identity = iPr_def_18 )
| ( sk_c7 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_17513]) ).
tcf(c_19751,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_11365,c_84]) ).
tcf(c_19755,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_17)) != sk_c7 )
| ( multiply(sk_c2,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_11365,c_427]) ).
tcf(c_19756,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_11365,c_11231]) ).
tcf(c_19757,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_11365,c_12224]) ).
tcf(c_19772,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_889,c_19751]) ).
tcf(c_19835,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_19757,c_12224]) ).
tcf(c_19840,plain,
multiply(sk_c2,sk_c7) = iPr_def_22,
inference(superposition,[status(thm)],[c_2783,c_19756]) ).
tcf(c_22095,plain,
( ( identity = iPr_def_18 )
| ( multiply(inverse(sk_c5),iPr_def_18) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_15046,c_11231]) ).
tcf(c_23110,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_14469,c_15214]) ).
tcf(c_23134,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_23110,c_2812]) ).
tcf(c_24912,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_23134,c_15047]) ).
tcf(c_39976,plain,
( ( iPr_def_14 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c6) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_2767,c_2329]) ).
tcf(c_40223,plain,
( ~ iPr_def_13
| ( sk_c8 != identity )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2332,c_12247]) ).
tcf(c_41432,plain,
( iPr_def_13
| ( sk_c8 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(global_subsumption_just,[status(thm)],[c_14647,c_3373,c_4145,c_13979,c_14649,c_17328,c_19772]) ).
tcf(c_47565,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_41432,c_40223,c_39976,c_24912,c_22095,c_19840,c_19835,c_19755,c_19751,c_17514,c_17329,c_17247,c_17246,c_16023,c_15450,c_15449,c_15440,c_14879,c_14456,c_14446,c_14317,c_14306,c_13390,c_13379,c_13366,c_13355,c_13261,c_13257,c_12257,c_12254,c_12253,c_12251,c_12249,c_12239,c_12238,c_12237,c_12236,c_12233,c_12247,c_11383,c_11377,c_11322,c_11319,c_11318,c_11316,c_11266,c_11265,c_11264,c_11263,c_11262,c_11240,c_11238,c_11237,c_11236,c_8790,c_8789,c_8085,c_8083,c_7886,c_7876,c_7875,c_7430,c_4145,c_3800,c_3742,c_3466,c_3021,c_2346,c_2342,c_2179,c_2162,c_2090,c_2077,c_12429,c_1067,c_875,c_435,c_434,c_433,c_432,c_431,c_430,c_425,c_419,c_417,c_416]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP290-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n020.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 14:23:48 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...
% 4.75/2.22 % SZS status Started for theBenchmark.p
% 4.75/2.22 % SZS status Unsatisfiable for theBenchmark.p
% 4.75/2.22
% 4.75/2.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.75/2.22
% 4.75/2.22 % ------ iProver source info
% 4.75/2.22
% 4.75/2.22 % git: date: 2026-07-19 20:42:38 +0200
% 4.75/2.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.75/2.22 % git: non_committed_changes: false
% 4.75/2.22
% 4.75/2.22 % ------ Parsing...% successful
% 4.75/2.22
% 4.75/2.22
% 4.75/2.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.75/2.22
% 4.75/2.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.75/2.22
% 4.75/2.22 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.75/2.22
% 4.75/2.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.75/2.22 % ------ Proving...
% 4.75/2.22 % ------ Problem Properties
% 4.75/2.22
% 4.75/2.22 %
% 4.75/2.22 % clauses 49
% 4.75/2.22 % conjectures 35
% 4.75/2.22 % EPR 31
% 4.75/2.22 % Horn 18
% 4.75/2.22 % unary 14
% 4.75/2.22 % binary 30
% 4.75/2.22 % lits 92
% 4.75/2.22 % lits eq 84
% 4.75/2.23 % fd_pure 0
% 4.75/2.23 % fd_pseudo 0
% 4.75/2.23 % fd_cond 0
% 4.75/2.23 % fd_pseudo_cond 0
% 4.75/2.23 % AC symbols 0
% 4.75/2.23
% 4.75/2.23 % ------ Schedule dynamic 5 is on
% 4.75/2.23
% 4.75/2.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.75/2.23
% 4.75/2.23
% 4.75/2.23 % ------
% 4.75/2.23 % Current options:
% 4.75/2.23 % ------
% 4.75/2.23
% 4.75/2.23
% 4.75/2.23 %
% 4.75/2.23
% 4.75/2.23 % ------ Proving...
% 4.75/2.23 %
% 4.75/2.23
% 4.75/2.23 % SZS status Unsatisfiable for theBenchmark.p
% 4.75/2.23
% 4.75/2.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.75/2.23
% 4.75/2.23
%------------------------------------------------------------------------------