%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP358-1 : 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 : n019.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 01:33:23 PM UTC 2026
% Result : Unsatisfiable 10.46s 2.17s
% Output : CNFRefutation 10.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 39
% Syntax : Number of formulae : 252 ( 108 unt; 11 def)
% Number of atoms : 708 ( 427 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 346 ( 131 ~; 215 |; 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_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c3)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c4)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = inverse(sk_c3)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c7 = inverse(sk_c4)
| sk_c6 = inverse(sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = inverse(sk_c3)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = inverse(sk_c4)
| sk_c7 = multiply(sk_c8,sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c3)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c7 = inverse(sk_c4)
| sk_c2 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f47]) ).
fof(f53,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = multiply(sk_c3,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c3)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c8) != sk_c6
| inverse(X4) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X1)
| multiply(X1,sk_c8) != X0
| sk_c7 != multiply(sk_c8,X0)
| sk_c6 != inverse(sk_c8)
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X1,X4] :
( sk_c6 != multiply(X4,sk_c8)
| sk_c6 != inverse(X4)
| sk_c7 != inverse(X3)
| sk_c6 != multiply(X3,sk_c7)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(X2,sk_c8)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(sk_c8,multiply(X1,sk_c8))
| sk_c6 != inverse(sk_c8)
| multiply(sk_c7,sk_c6) != sk_c8 ),
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_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c8,sk_c2) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c2 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c2 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(X3,sk_c8) != sk_c6 )
| ( multiply(X2,sk_c7) != sk_c6 )
| ( multiply(X1,sk_c8) != sk_c7 )
| ( multiply(sk_c8,multiply(X0,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_c7) != sk_c6 ) ),
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_c6 )
| ( multiply(X0,sk_c8) != 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
| ( inverse(sk_c8) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c8,sk_c2),
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_c8 ) ),
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_c6 )
| ( multiply(X0,sk_c8) != 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_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_417,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_418]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113,c_419]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112,c_420]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_421]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110,c_422]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_20 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_23 = sk_c2 )
| ( iPr_def_22 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_20 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_22 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_20 = sk_c6 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_14 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_740,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_435,c_420]) ).
tcf(c_741,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_432,c_420]) ).
tcf(c_794,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_444,c_420]) ).
tcf(c_837,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c8,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_438,c_424]) ).
tcf(c_854,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_421,c_84]) ).
tcf(c_855,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_419,c_84]) ).
tcf(c_856,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_418,c_84]) ).
tcf(c_857,plain,
multiply(iPr_def_15,sk_c8) = identity,
inference(superposition,[status(thm)],[c_415,c_84]) ).
tcf(c_858,plain,
multiply(iPr_def_17,sk_c1) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_1652,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_16 )
| ( inverse(sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_416,c_427]) ).
tcf(c_1672,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 )
| ( sk_c6 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1652,c_418]) ).
tcf(c_1759,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_22 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_422,c_428]) ).
tcf(c_1761,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_23 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_423,c_428]) ).
tcf(c_1776,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_17 )
| ( sk_c7 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_1761,c_417]) ).
tcf(c_1784,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_21 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_1759,c_421]) ).
tcf(c_1873,plain,
( ~ iPr_def_10
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_429]) ).
tcf(c_2303,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2304,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_422,c_85]) ).
tcf(c_2305,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_420,c_85]) ).
tcf(c_2306,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_416,c_85]) ).
tcf(c_2308,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c8,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_423,c_85]) ).
tcf(c_2310,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2313,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_854,c_85]) ).
tcf(c_2314,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_855,c_85]) ).
tcf(c_2315,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_856,c_85]) ).
tcf(c_2316,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_857,c_85]) ).
tcf(c_2317,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_858,c_85]) ).
tcf(c_2323,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2317,c_83]) ).
tcf(c_2324,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2316,c_83]) ).
tcf(c_2325,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2315,c_83]) ).
tcf(c_2326,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2314,c_83]) ).
tcf(c_2327,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2313,c_83]) ).
tcf(c_3563,plain,
multiply(iPr_def_17,iPr_def_23) = sk_c8,
inference(superposition,[status(thm)],[c_423,c_2323]) ).
tcf(c_3566,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_23,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3563,c_85]) ).
tcf(c_3568,plain,
multiply(iPr_def_15,iPr_def_24) = sk_c2,
inference(superposition,[status(thm)],[c_424,c_2324]) ).
tcf(c_3715,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_416,c_2325]) ).
tcf(c_3721,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3715,c_85]) ).
tcf(c_3723,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c7,
inference(superposition,[status(thm)],[c_420,c_2326]) ).
tcf(c_3724,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_740,c_2326]) ).
tcf(c_3729,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3723,c_85]) ).
tcf(c_3839,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_794,c_2326]) ).
tcf(c_3840,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3839,c_3723]) ).
tcf(c_4023,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_422,c_2327]) ).
tcf(c_4029,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4023,c_85]) ).
tcf(c_7900,plain,
multiply(sk_c3,iPr_def_24) = multiply(iPr_def_22,sk_c2),
inference(superposition,[status(thm)],[c_424,c_2304]) ).
tcf(c_8225,plain,
multiply(sk_c4,iPr_def_14) = multiply(iPr_def_20,sk_c6),
inference(superposition,[status(thm)],[c_414,c_2305]) ).
tcf(c_9095,plain,
multiply(sk_c1,iPr_def_24) = multiply(iPr_def_23,sk_c2),
inference(superposition,[status(thm)],[c_424,c_2308]) ).
tcf(c_9623,plain,
( ( sk_c8 = iPr_def_17 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_3724,c_3723]) ).
tcf(c_10696,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2310,c_83]) ).
tcf(c_10716,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c6,
inference(superposition,[status(thm)],[c_414,c_10696]) ).
tcf(c_10722,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_10696]) ).
tcf(c_10723,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_10696]) ).
tcf(c_10834,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2327,c_10696]) ).
tcf(c_10835,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2326,c_10696]) ).
tcf(c_10836,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2325,c_10696]) ).
tcf(c_10837,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2324,c_10696]) ).
tcf(c_10838,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2323,c_10696]) ).
tcf(c_10906,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_10696,c_10696]) ).
tcf(c_11757,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_10723,c_10906]) ).
tcf(c_11772,plain,
multiply(sk_c8,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_11757,c_4029]) ).
tcf(c_11773,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_11757,c_2303]) ).
tcf(c_11774,plain,
multiply(sk_c7,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_11757,c_3729]) ).
tcf(c_11775,plain,
multiply(sk_c8,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_11757,c_3721]) ).
tcf(c_11778,plain,
multiply(sk_c8,identity) = multiply(iPr_def_17,iPr_def_23),
inference(superposition,[status(thm)],[c_11757,c_3566]) ).
tcf(c_11785,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_11757,c_10722]) ).
tcf(c_11790,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_11774,c_3723]) ).
tcf(c_11791,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_11773,c_414]) ).
tcf(c_11951,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_11785,c_84]) ).
tcf(c_13907,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c7 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_434,c_1784]) ).
tcf(c_14537,plain,
( ( sk_c8 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(forward_subsumption_resolution,[status(thm)],[c_13907,c_9623]) ).
tcf(c_14544,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_23 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1776,c_14537]) ).
tcf(c_14754,plain,
( ( sk_c7 = iPr_def_22 )
| ~ iPr_def_11
| ( iPr_def_23 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_447,c_14544]) ).
tcf(c_14755,plain,
( ( sk_c8 = iPr_def_21 )
| ~ iPr_def_11
| ( iPr_def_23 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_446,c_14544]) ).
tcf(c_14866,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_21)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c3,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_10834,c_426]) ).
tcf(c_14867,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_21)) != sk_c8 )
| ( multiply(sk_c3,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_10834,c_428]) ).
tcf(c_14869,plain,
multiply(sk_c3,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_10834,c_84]) ).
tcf(c_14873,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_10834,c_10696]) ).
tcf(c_14874,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_10834,c_11757]) ).
tcf(c_14882,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_22 )
| ( inverse(inverse(iPr_def_21)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_14867,c_422]) ).
tcf(c_14886,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_21)) != sk_c8 )
| ( multiply(sk_c8,iPr_def_22) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_14866,c_422]) ).
tcf(c_14895,plain,
( ( iPr_def_23 != iPr_def_24 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_14754,c_1784,c_14755,c_14754]) ).
tcf(c_14896,plain,
( ~ iPr_def_11
| ( iPr_def_23 != iPr_def_24 ) ),
inference(renaming,[status(thm)],[c_14895]) ).
tcf(c_15069,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(superposition,[status(thm)],[c_14869,c_2327]) ).
tcf(c_15110,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_14874,c_11757]) ).
tcf(c_15123,plain,
multiply(sk_c3,sk_c8) = iPr_def_22,
inference(superposition,[status(thm)],[c_4023,c_14873]) ).
tcf(c_15453,plain,
multiply(sk_c4,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_10835,c_84]) ).
tcf(c_15456,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c7 )
| ( multiply(sk_c4,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_10835,c_429]) ).
tcf(c_15457,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_10835,c_10696]) ).
tcf(c_15458,plain,
multiply(sk_c4,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_10835,c_11757]) ).
tcf(c_15461,plain,
( ~ iPr_def_10
| ( sk_c6 != iPr_def_20 )
| ( inverse(inverse(iPr_def_19)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_15456,c_420]) ).
tcf(c_15475,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_741,c_15453]) ).
tcf(c_15561,plain,
inverse(iPr_def_19) = sk_c4,
inference(demodulation,[status(thm)],[c_15458,c_11757]) ).
tcf(c_15761,plain,
( ( identity = iPr_def_20 )
| ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_17,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_15475,c_837]) ).
tcf(c_15810,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_24 )
| ( sk_c7 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_15761,c_3563]) ).
tcf(c_15914,plain,
multiply(sk_c4,sk_c7) = iPr_def_20,
inference(superposition,[status(thm)],[c_3723,c_15457]) ).
tcf(c_20046,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_18)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c5,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_10836,c_426]) ).
tcf(c_20049,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_10836,c_84]) ).
tcf(c_20053,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_10836,c_10696]) ).
tcf(c_20054,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_10836,c_11757]) ).
tcf(c_20096,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_20054,c_11757]) ).
tcf(c_20799,plain,
multiply(sk_c5,sk_c8) = iPr_def_16,
inference(superposition,[status(thm)],[c_3715,c_20053]) ).
tcf(c_21706,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_15)) != sk_c6 )
| ( multiply(sk_c8,sk_c8) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_10837,c_427]) ).
tcf(c_21707,plain,
multiply(sk_c8,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_10837,c_84]) ).
tcf(c_21711,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_10837,c_10696]) ).
tcf(c_21712,plain,
multiply(sk_c8,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_10837,c_11757]) ).
tcf(c_21877,plain,
multiply(sk_c5,identity) = multiply(iPr_def_16,iPr_def_15),
inference(superposition,[status(thm)],[c_21707,c_2306]) ).
tcf(c_21878,plain,
multiply(sk_c3,identity) = multiply(iPr_def_22,iPr_def_15),
inference(superposition,[status(thm)],[c_21707,c_2304]) ).
tcf(c_22512,plain,
inverse(iPr_def_15) = sk_c8,
inference(demodulation,[status(thm)],[c_21712,c_11757]) ).
tcf(c_22614,plain,
multiply(sk_c8,sk_c2) = iPr_def_24,
inference(superposition,[status(thm)],[c_3568,c_21711]) ).
tcf(c_24425,plain,
multiply(iPr_def_22,iPr_def_15) = sk_c3,
inference(demodulation,[status(thm)],[c_21878,c_11757]) ).
tcf(c_24431,plain,
multiply(inverse(iPr_def_22),sk_c3) = iPr_def_15,
inference(superposition,[status(thm)],[c_24425,c_10696]) ).
tcf(c_24456,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),multiply(sk_c3,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_24431,c_85]) ).
tcf(c_25144,plain,
multiply(inverse(iPr_def_22),iPr_def_22) = multiply(iPr_def_15,sk_c8),
inference(superposition,[status(thm)],[c_15123,c_24456]) ).
tcf(c_25166,plain,
multiply(inverse(iPr_def_22),multiply(iPr_def_22,sk_c2)) = multiply(iPr_def_15,iPr_def_24),
inference(superposition,[status(thm)],[c_7900,c_24456]) ).
tcf(c_25167,plain,
multiply(inverse(iPr_def_22),sk_c3) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_11757,c_24456]) ).
tcf(c_25174,plain,
multiply(inverse(iPr_def_22),iPr_def_22) = identity,
inference(light_normalisation,[status(thm)],[c_25144,c_857]) ).
tcf(c_25175,plain,
multiply(inverse(iPr_def_22),multiply(iPr_def_22,sk_c2)) = sk_c2,
inference(light_normalisation,[status(thm)],[c_25166,c_3568]) ).
tcf(c_26039,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_17)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c1,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_10838,c_426]) ).
tcf(c_26042,plain,
multiply(sk_c1,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_10838,c_84]) ).
tcf(c_26046,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_10838,c_10696]) ).
tcf(c_26047,plain,
multiply(sk_c1,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_10838,c_11757]) ).
tcf(c_26246,plain,
inverse(iPr_def_17) = sk_c1,
inference(demodulation,[status(thm)],[c_26047,c_11757]) ).
tcf(c_26877,plain,
multiply(sk_c1,sk_c8) = iPr_def_23,
inference(superposition,[status(thm)],[c_3563,c_26046]) ).
tcf(c_29125,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_26877,c_26246,c_26039,c_26042,c_25175,c_25174,c_25167,c_25166,c_25144,c_24431,c_24425,c_22614,c_22512,c_21878,c_21877,c_21706,c_21712,c_21707,c_20799,c_20096,c_20046,c_20049,c_15914,c_15810,c_15561,c_15461,c_15458,c_15453,c_15123,c_15110,c_15069,c_14896,c_14886,c_14882,c_14867,c_14869,c_11791,c_11790,c_11778,c_11775,c_11774,c_11773,c_11772,c_11785,c_10716,c_9095,c_8225,c_3840,c_11951,c_1873,c_1672,c_459,c_458,c_457,c_456,c_455,c_454,c_453,c_452,c_451,c_450,c_447,c_446,c_445,c_441,c_440,c_439,c_435,c_434,c_433,c_432,c_431,c_430,c_425,c_421,c_419,c_418,c_417,c_415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP358-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % 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 14:34:04 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 10.46/2.17 % SZS status Started for theBenchmark.p
% 10.46/2.17 % SZS status Unsatisfiable for theBenchmark.p
% 10.46/2.17
% 10.46/2.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.46/2.17
% 10.46/2.17 % ------ iProver source info
% 10.46/2.17
% 10.46/2.17 % git: date: 2026-07-19 20:42:38 +0200
% 10.46/2.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.46/2.17 % git: non_committed_changes: false
% 10.46/2.17
% 10.46/2.17 % ------ Parsing...% successful
% 10.46/2.17
% 10.46/2.17
% 10.46/2.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.46/2.17
% 10.46/2.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.46/2.17
% 10.46/2.17 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.46/2.17
% 10.46/2.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.46/2.17 % ------ Proving...
% 10.46/2.17 % ------ Problem Properties
% 10.46/2.17
% 10.46/2.17 %
% 10.46/2.17 % clauses 49
% 10.46/2.17 % conjectures 35
% 10.46/2.17 % EPR 31
% 10.46/2.17 % Horn 18
% 10.46/2.17 % unary 14
% 10.46/2.17 % binary 30
% 10.46/2.17 % lits 92
% 10.46/2.17 % lits eq 84
% 10.46/2.17 % fd_pure 0
% 10.46/2.17 % fd_pseudo 0
% 10.46/2.17 % fd_cond 0
% 10.46/2.17 % fd_pseudo_cond 0
% 10.46/2.17 % AC symbols 0
% 10.46/2.17
% 10.46/2.17 % ------ Schedule dynamic 5 is on
% 10.46/2.17
% 10.46/2.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.46/2.17
% 10.46/2.17
% 10.46/2.17 % ------
% 10.46/2.17 % Current options:
% 10.46/2.17 % ------
% 10.46/2.17
% 10.46/2.17
% 10.46/2.17 %
% 10.46/2.17
% 10.46/2.17 % ------ Proving...
% 10.46/2.17 %
% 10.46/2.17
% 10.46/2.17 % SZS status Unsatisfiable for theBenchmark.p
% 10.46/2.17
% 10.46/2.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.46/2.17
% 10.46/2.17
%------------------------------------------------------------------------------