%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP280-1 : 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 : n010.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 01:32:42 PM UTC 2026
% Result : Unsatisfiable 21.38s 4.97s
% Output : CNFRefutation 21.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 44
% Syntax : Number of formulae : 368 ( 129 unt; 12 def)
% Number of atoms : 1189 ( 656 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 545 ( 193 ~; 352 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 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 : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 96 !; 0 ?; 69 :)
% 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_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c5 = inverse(sk_c4)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c9 = inverse(sk_c6)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f15]) ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c5 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = inverse(sk_c6)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c5 = inverse(sk_c4)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c5 = inverse(sk_c4)
| sk_c8 = multiply(sk_c9,sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f55,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f61,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = inverse(sk_c6)
| sk_c3 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = multiply(sk_c9,sk_c7)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = multiply(sk_c4,sk_c5)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c5 = inverse(sk_c4)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c9 = multiply(sk_c5,sk_c8)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c7 = multiply(sk_c6,sk_c9)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = inverse(sk_c2) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X3) != X4
| sk_c9 != multiply(X3,X4)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X2)
| multiply(X2,sk_c9) != X1
| sk_c8 != multiply(sk_c9,X1)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X2,X3,X0,X4,X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != multiply(X4,sk_c8)
| inverse(X3) != X4
| sk_c9 != multiply(X3,X4)
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f78]) ).
fof(f80,plain,
! [X2,X3,X0,X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(X5,sk_c9)
| sk_c9 != multiply(inverse(X3),sk_c8)
| sk_c9 != multiply(X3,inverse(X3))
| sk_c8 != multiply(sk_c9,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(sk_c9,multiply(X2,sk_c9))
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f79]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_90,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c9,sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c9 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c9 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c4) = sk_c5 )
| ( multiply(sk_c9,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_120,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c3 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c3 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c9,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c4,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c4) = sk_c5 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c7 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c2) = sk_c9 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c9 )
| ( inverse(X2) != sk_c9 )
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( multiply(sk_c9,sk_c8) != sk_c7 )
| ( multiply(X2,sk_c9) != sk_c7 )
| ( multiply(X0,sk_c9) != sk_c8 )
| ( multiply(inverse(X1),sk_c8) != sk_c9 )
| ( multiply(X1,inverse(X1)) != sk_c9 )
| ( multiply(sk_c9,multiply(X3,sk_c9)) != sk_c8 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_469,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_470,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_471,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_472,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_473,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c9,sk_c7) != sk_c8 )
| ( multiply(sk_c9,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_474,definition,
iPr_def_14 = multiply(sk_c9,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_475,definition,
iPr_def_15 = multiply(sk_c9,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_476,definition,
iPr_def_16 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_477,definition,
iPr_def_17 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_478,definition,
iPr_def_18 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_479,definition,
iPr_def_19 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_480,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_481,definition,
iPr_def_21 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_482,definition,
iPr_def_22 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_483,definition,
iPr_def_23 = multiply(sk_c9,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_484,definition,
iPr_def_24 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_485,definition,
iPr_def_25 = multiply(sk_c1,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_486,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c8 )
| ( iPr_def_14 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_473,c_475,c_474]) ).
tcf(c_487,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_472]) ).
tcf(c_488,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_471]) ).
tcf(c_489,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_470]) ).
tcf(c_490,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_469]) ).
tcf(c_491,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_127,c_477,c_476]) ).
tcf(c_492,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_126,c_478]) ).
tcf(c_493,negated_conjecture,
( ( iPr_def_19 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_125,c_479]) ).
tcf(c_494,negated_conjecture,
( ( iPr_def_20 = sk_c5 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_124,c_480]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_17 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_123,c_481]) ).
tcf(c_496,negated_conjecture,
( ( iPr_def_17 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_121,c_482]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_509,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109,c_484]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_20 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_514,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_515,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_103,c_485]) ).
tcf(c_516,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_517,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_518,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_20 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_519,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_521,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_524,negated_conjecture,
( ( iPr_def_20 = sk_c5 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_526,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_527,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_528,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_533,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_527]) ).
tcf(c_909,plain,
( ( sk_c8 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_506,c_481]) ).
tcf(c_910,plain,
( ( sk_c9 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_494,c_481]) ).
tcf(c_926,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_17,sk_c3) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_491,c_483]) ).
tcf(c_931,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c9,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_498,c_483]) ).
tcf(c_960,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_480,c_90]) ).
tcf(c_961,plain,
multiply(iPr_def_16,sk_c6) = identity,
inference(superposition,[status(thm)],[c_476,c_90]) ).
tcf(c_962,plain,
multiply(iPr_def_24,sk_c1) = identity,
inference(superposition,[status(thm)],[c_484,c_90]) ).
tcf(c_963,plain,
multiply(iPr_def_17,sk_c2) = identity,
inference(superposition,[status(thm)],[c_477,c_90]) ).
tcf(c_997,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_528]) ).
tcf(c_1005,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_509,c_485]) ).
tcf(c_1010,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_24,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_509,c_474]) ).
tcf(c_1013,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_509,c_491]) ).
tcf(c_1034,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_997]) ).
tcf(c_1035,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_527]) ).
tcf(c_1045,plain,
( ( sk_c7 = iPr_def_18 )
| ( iPr_def_18 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_1034]) ).
tcf(c_1051,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c9,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_510,c_475]) ).
tcf(c_1063,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_511,c_485]) ).
tcf(c_1068,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(iPr_def_24,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_511,c_474]) ).
tcf(c_1112,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_512,c_481]) ).
tcf(c_1125,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_513,c_485]) ).
tcf(c_1130,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_24,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_513,c_474]) ).
tcf(c_1277,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(sk_c9,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_516,c_475]) ).
tcf(c_1332,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_518,c_481]) ).
tcf(c_1519,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_524,c_481]) ).
tcf(c_1625,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_16 )
| ( sk_c8 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_521,c_486]) ).
tcf(c_1695,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_18 )
| ( inverse(sk_c6) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_478,c_488]) ).
tcf(c_1696,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_485,c_488]) ).
tcf(c_1699,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_90,c_488]) ).
tcf(c_1713,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_25 )
| ( sk_c9 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_1696,c_484]) ).
tcf(c_1717,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_18 )
| ( sk_c9 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1695,c_476]) ).
tcf(c_1790,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_18 )
| ( inverse(sk_c6) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_478,c_490]) ).
tcf(c_1791,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_485,c_490]) ).
tcf(c_1794,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_90,c_490]) ).
tcf(c_1808,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_25 )
| ( sk_c9 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_1791,c_484]) ).
tcf(c_1812,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_18 )
| ( sk_c9 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1790,c_476]) ).
tcf(c_1913,plain,
( ~ iPr_def_13
| ( inverse(sk_c1) != sk_c9 )
| ( multiply(sk_c9,iPr_def_25) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_485,c_487]) ).
tcf(c_1930,plain,
( ~ iPr_def_13
| ( sk_c9 != iPr_def_24 )
| ( multiply(sk_c9,iPr_def_25) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1913,c_484]) ).
tcf(c_2026,plain,
( ~ iPr_def_11
| ( multiply(sk_c4,iPr_def_20) != sk_c9 )
| ( multiply(inverse(sk_c4),sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_480,c_489]) ).
tcf(c_2028,plain,
( ~ iPr_def_11
| ( multiply(sk_c1,iPr_def_24) != sk_c9 )
| ( multiply(inverse(sk_c1),sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_484,c_489]) ).
tcf(c_2037,plain,
( ~ iPr_def_11
| ( multiply(iPr_def_24,sk_c8) != sk_c9 )
| ( multiply(sk_c1,iPr_def_24) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_2028,c_484]) ).
tcf(c_2045,plain,
( ~ iPr_def_11
| ( multiply(iPr_def_20,sk_c8) != sk_c9 )
| ( multiply(sk_c4,iPr_def_20) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_2026,c_480]) ).
tcf(c_2110,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_475,c_91]) ).
tcf(c_2111,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_481,c_91]) ).
tcf(c_2112,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_479,c_91]) ).
tcf(c_2113,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c9,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_478,c_91]) ).
tcf(c_2114,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c9,X0)) = multiply(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_485,c_91]) ).
tcf(c_2115,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c3,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_483,c_91]) ).
tcf(c_2116,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c9,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_482,c_91]) ).
tcf(c_2118,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2120,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_960,c_91]) ).
tcf(c_2121,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_961,c_91]) ).
tcf(c_2122,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_962,c_91]) ).
tcf(c_2123,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_963,c_91]) ).
tcf(c_2129,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2123,c_89]) ).
tcf(c_2130,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2122,c_89]) ).
tcf(c_2131,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2121,c_89]) ).
tcf(c_2132,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2120,c_89]) ).
tcf(c_2917,plain,
multiply(iPr_def_17,iPr_def_22) = sk_c9,
inference(superposition,[status(thm)],[c_482,c_2129]) ).
tcf(c_3412,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_22,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_2917,c_91]) ).
tcf(c_3427,plain,
multiply(iPr_def_24,iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_485,c_2130]) ).
tcf(c_3430,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(iPr_def_25,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_3427,c_91]) ).
tcf(c_3432,plain,
multiply(iPr_def_16,iPr_def_18) = sk_c9,
inference(superposition,[status(thm)],[c_478,c_2131]) ).
tcf(c_3435,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_18,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_3432,c_91]) ).
tcf(c_3437,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c5,
inference(superposition,[status(thm)],[c_481,c_2132]) ).
tcf(c_3444,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_21,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_3437,c_91]) ).
tcf(c_4082,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_497,c_926]) ).
tcf(c_4084,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c9 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_4082,c_2917]) ).
tcf(c_4177,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( sk_c9 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_4084,c_509]) ).
tcf(c_4319,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( multiply(sk_c6,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_4177,c_478]) ).
tcf(c_5224,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1005,c_2130]) ).
tcf(c_5225,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_5224,c_3427]) ).
tcf(c_5379,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_515,c_1010]) ).
tcf(c_5387,plain,
( ( sk_c9 = iPr_def_16 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5379,c_3427]) ).
tcf(c_5446,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_24 )
| ( multiply(iPr_def_16,iPr_def_18) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1013,c_1051]) ).
tcf(c_5466,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( sk_c9 = iPr_def_24 )
| ( sk_c9 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5446,c_3432]) ).
tcf(c_5590,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_517,c_1068]) ).
tcf(c_5599,plain,
( ( sk_c9 = iPr_def_19 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5590,c_3427]) ).
tcf(c_5722,plain,
( ( sk_c9 = iPr_def_14 )
| ( multiply(sk_c6,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_5387,c_478]) ).
tcf(c_6571,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_519,c_1130]) ).
tcf(c_6581,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6571,c_3427]) ).
tcf(c_6758,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6581,c_5599]) ).
tcf(c_6759,plain,
( ( iPr_def_16 = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6581,c_5387]) ).
tcf(c_7250,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_6758,c_485]) ).
tcf(c_7569,plain,
( ( iPr_def_16 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_6759,c_485]) ).
tcf(c_8255,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_24 )
| ( iPr_def_24 != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_528]) ).
tcf(c_8256,plain,
( ( sk_c9 = iPr_def_24 )
| ( iPr_def_24 != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_8255]) ).
tcf(c_9056,plain,
( ~ iPr_def_13
| ( inverse(sk_c7) != sk_c9 )
| ( multiply(iPr_def_15,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_2110,c_487]) ).
tcf(c_9658,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_25,sk_c8),
inference(superposition,[status(thm)],[c_474,c_2114]) ).
tcf(c_10108,plain,
multiply(sk_c2,iPr_def_14) = multiply(iPr_def_22,sk_c8),
inference(superposition,[status(thm)],[c_474,c_2116]) ).
tcf(c_10109,plain,
multiply(sk_c2,iPr_def_15) = multiply(iPr_def_22,sk_c7),
inference(superposition,[status(thm)],[c_475,c_2116]) ).
tcf(c_10110,plain,
multiply(sk_c2,iPr_def_23) = multiply(iPr_def_22,sk_c3),
inference(superposition,[status(thm)],[c_483,c_2116]) ).
tcf(c_13944,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2118,c_89]) ).
tcf(c_13949,plain,
multiply(inverse(sk_c9),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_474,c_13944]) ).
tcf(c_13950,plain,
multiply(inverse(sk_c9),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_475,c_13944]) ).
tcf(c_13952,plain,
multiply(inverse(sk_c5),iPr_def_19) = sk_c8,
inference(superposition,[status(thm)],[c_479,c_13944]) ).
tcf(c_13955,plain,
multiply(inverse(sk_c9),iPr_def_23) = sk_c3,
inference(superposition,[status(thm)],[c_483,c_13944]) ).
tcf(c_13957,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_13944]) ).
tcf(c_13958,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_13944]) ).
tcf(c_13976,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(inverse(sk_c9),iPr_def_15) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1277,c_13944]) ).
tcf(c_13977,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(inverse(sk_c9),iPr_def_15) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1051,c_13944]) ).
tcf(c_14078,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2132,c_13944]) ).
tcf(c_14079,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2131,c_13944]) ).
tcf(c_14080,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2130,c_13944]) ).
tcf(c_14081,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2129,c_13944]) ).
tcf(c_14113,plain,
multiply(inverse(sk_c2),multiply(iPr_def_22,sk_c3)) = iPr_def_23,
inference(superposition,[status(thm)],[c_10110,c_13944]) ).
tcf(c_14125,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_13944,c_13944]) ).
tcf(c_15203,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_13958,c_14125]) ).
tcf(c_15216,plain,
multiply(sk_c9,sk_c7) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_15203,c_2110]) ).
tcf(c_15229,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_15203,c_13957]) ).
tcf(c_15238,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_15216,c_475]) ).
tcf(c_15252,plain,
multiply(sk_c5,identity) = multiply(iPr_def_20,iPr_def_21),
inference(superposition,[status(thm)],[c_15203,c_3444]) ).
tcf(c_16099,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_14078,c_90]) ).
tcf(c_16100,plain,
( ~ iPr_def_11
| ( multiply(sk_c4,inverse(inverse(iPr_def_20))) != sk_c9 )
| ( multiply(inverse(inverse(iPr_def_20)),sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_14078,c_489]) ).
tcf(c_16101,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_14078,c_13944]) ).
tcf(c_16102,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_14078,c_15203]) ).
tcf(c_16115,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_1519,c_16099]) ).
tcf(c_16116,plain,
( ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1332,c_16099]) ).
tcf(c_16117,plain,
( ( identity = iPr_def_21 )
| ( sk_c9 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1112,c_16099]) ).
tcf(c_16118,plain,
( ( identity = iPr_def_21 )
| ( sk_c9 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_910,c_16099]) ).
tcf(c_16119,plain,
( ( identity = iPr_def_21 )
| ( sk_c8 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_909,c_16099]) ).
tcf(c_18315,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c9,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_16115,c_475]) ).
tcf(c_18400,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c9,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_16116,c_474]) ).
tcf(c_18613,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_16117,c_485]) ).
tcf(c_18943,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_16102,c_15203]) ).
tcf(c_18958,plain,
multiply(sk_c4,sk_c5) = iPr_def_21,
inference(superposition,[status(thm)],[c_3437,c_16101]) ).
tcf(c_19036,plain,
( ( iPr_def_17 = iPr_def_24 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_16118,c_16117]) ).
tcf(c_19077,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_17,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_16118,c_931]) ).
tcf(c_19104,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_17) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_16118,c_482]) ).
tcf(c_19185,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_18 )
| ( sk_c9 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_19077,c_2917]) ).
tcf(c_20671,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_16119,c_16116]) ).
tcf(c_21022,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_16)) != sk_c9 )
| ( multiply(sk_c9,multiply(sk_c6,sk_c9)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14079,c_487]) ).
tcf(c_21023,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_16)) != sk_c9 )
| ( multiply(sk_c6,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14079,c_490]) ).
tcf(c_21027,plain,
multiply(sk_c6,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_14079,c_90]) ).
tcf(c_21029,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_14079,c_13944]) ).
tcf(c_21030,plain,
multiply(sk_c6,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_14079,c_15203]) ).
tcf(c_21046,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_4319,c_21027]) ).
tcf(c_23774,plain,
inverse(iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_21030,c_15203]) ).
tcf(c_23794,plain,
multiply(sk_c6,sk_c9) = iPr_def_18,
inference(superposition,[status(thm)],[c_3432,c_21029]) ).
tcf(c_27862,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_5722,c_21027]) ).
tcf(c_27991,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_27862,c_485]) ).
tcf(c_28012,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_25,sk_c8) = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_27991,c_9658]) ).
tcf(c_28426,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_24)) != sk_c9 )
| ( multiply(sk_c9,multiply(sk_c1,sk_c9)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14080,c_487]) ).
tcf(c_28427,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_24)) != sk_c9 )
| ( multiply(sk_c1,sk_c9) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14080,c_490]) ).
tcf(c_28428,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_24)) != sk_c9 )
| ( multiply(sk_c1,sk_c9) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14080,c_488]) ).
tcf(c_28431,plain,
multiply(sk_c1,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_14080,c_90]) ).
tcf(c_28433,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_14080,c_13944]) ).
tcf(c_28434,plain,
multiply(sk_c1,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_14080,c_15203]) ).
tcf(c_28454,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_25 )
| ( inverse(inverse(iPr_def_24)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_28427,c_485]) ).
tcf(c_28458,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_24)) != sk_c9 )
| ( multiply(sk_c9,iPr_def_25) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_28426,c_485]) ).
tcf(c_28465,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1125,c_28431]) ).
tcf(c_28466,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1063,c_28431]) ).
tcf(c_28467,plain,
( ( identity = iPr_def_25 )
| ( sk_c9 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1005,c_28431]) ).
tcf(c_33151,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( identity = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_28466,c_28465]) ).
tcf(c_33552,plain,
( ( iPr_def_16 = iPr_def_21 )
| ( identity = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_28467,c_28465]) ).
tcf(c_33632,plain,
( ( identity = iPr_def_25 )
| ( multiply(sk_c6,iPr_def_16) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_28467,c_478]) ).
tcf(c_33646,plain,
( ( identity = iPr_def_25 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_33632,c_21027]) ).
tcf(c_33831,plain,
inverse(iPr_def_24) = sk_c1,
inference(demodulation,[status(thm)],[c_28434,c_15203]) ).
tcf(c_33978,plain,
multiply(sk_c1,sk_c9) = iPr_def_25,
inference(superposition,[status(thm)],[c_3427,c_28433]) ).
tcf(c_36426,plain,
! [X0: $i] :
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_25,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_33646,c_89]) ).
tcf(c_36568,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(iPr_def_25,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_33151,c_89]) ).
tcf(c_36704,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_21 )
| ( multiply(iPr_def_25,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_33552,c_89]) ).
tcf(c_36733,plain,
multiply(sk_c2,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_14081,c_90]) ).
tcf(c_36735,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_14081,c_13944]) ).
tcf(c_36736,plain,
multiply(sk_c2,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_14081,c_15203]) ).
tcf(c_37358,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c9 = iPr_def_16 )
| ( iPr_def_15 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_515,c_1625]) ).
tcf(c_38797,plain,
inverse(iPr_def_17) = sk_c2,
inference(demodulation,[status(thm)],[c_36736,c_15203]) ).
tcf(c_38813,plain,
multiply(sk_c2,sk_c9) = iPr_def_22,
inference(superposition,[status(thm)],[c_2917,c_36735]) ).
tcf(c_44126,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( multiply(iPr_def_25,sk_c8) = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_7250,c_9658]) ).
tcf(c_45572,plain,
( ( iPr_def_16 = iPr_def_21 )
| ( multiply(iPr_def_25,sk_c8) = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_7569,c_9658]) ).
tcf(c_47122,plain,
( ( identity = iPr_def_21 )
| ( multiply(inverse(sk_c9),iPr_def_15) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_18315,c_13944]) ).
tcf(c_47737,plain,
( ( identity = iPr_def_21 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_16117,c_18400]) ).
tcf(c_47785,plain,
( ( identity = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_47737,c_3427]) ).
tcf(c_47897,plain,
( ( identity = iPr_def_25 )
| ( identity = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_18613,c_28431]) ).
tcf(c_51950,plain,
( ( identity = iPr_def_22 )
| ( identity = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_19104,c_36733]) ).
tcf(c_51987,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_21 = iPr_def_22 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_51950,c_20671]) ).
tcf(c_59888,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_14125,c_90]) ).
tcf(c_59890,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_14125,c_13944]) ).
tcf(c_59891,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_14125,c_15203]) ).
tcf(c_59892,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_59891,c_15203]) ).
tcf(c_59921,plain,
( ~ iPr_def_10
| ( sk_c8 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1794,c_59892]) ).
tcf(c_59922,plain,
( ~ iPr_def_12
| ( sk_c7 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1699,c_59892]) ).
tcf(c_59946,plain,
inverse(sk_c2) = iPr_def_17,
inference(superposition,[status(thm)],[c_38797,c_59892]) ).
tcf(c_60573,plain,
multiply(iPr_def_19,inverse(sk_c8)) = multiply(sk_c5,identity),
inference(superposition,[status(thm)],[c_59888,c_2112]) ).
tcf(c_60582,plain,
multiply(sk_c5,inverse(iPr_def_21)) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_59888,c_3444]) ).
tcf(c_60589,plain,
multiply(sk_c9,inverse(iPr_def_18)) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_59888,c_3435]) ).
tcf(c_60590,plain,
multiply(iPr_def_22,inverse(sk_c9)) = multiply(sk_c2,identity),
inference(superposition,[status(thm)],[c_59888,c_2116]) ).
tcf(c_60591,plain,
multiply(iPr_def_25,inverse(sk_c9)) = multiply(sk_c1,identity),
inference(superposition,[status(thm)],[c_59888,c_2114]) ).
tcf(c_60592,plain,
multiply(iPr_def_18,inverse(sk_c9)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_59888,c_2113]) ).
tcf(c_60593,plain,
multiply(sk_c9,inverse(iPr_def_25)) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_59888,c_3430]) ).
tcf(c_60594,plain,
multiply(iPr_def_23,inverse(sk_c3)) = multiply(sk_c9,identity),
inference(superposition,[status(thm)],[c_59888,c_2115]) ).
tcf(c_60596,plain,
multiply(iPr_def_20,identity) = inverse(sk_c4),
inference(superposition,[status(thm)],[c_59888,c_2132]) ).
tcf(c_60597,plain,
multiply(iPr_def_16,identity) = inverse(sk_c6),
inference(superposition,[status(thm)],[c_59888,c_2131]) ).
tcf(c_60598,plain,
multiply(iPr_def_24,identity) = inverse(sk_c1),
inference(superposition,[status(thm)],[c_59888,c_2130]) ).
tcf(c_60599,plain,
multiply(iPr_def_17,identity) = inverse(sk_c2),
inference(superposition,[status(thm)],[c_59888,c_2129]) ).
tcf(c_60741,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_10
| ( identity != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_515,c_59921]) ).
tcf(c_60992,plain,
( ( sk_c9 = iPr_def_16 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_60741,c_28467,c_60741]) ).
tcf(c_60998,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c9 = iPr_def_16 )
| ( iPr_def_15 != iPr_def_25 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_37358,c_60992]) ).
tcf(c_61451,plain,
( ( sk_c8 = iPr_def_25 )
| ~ iPr_def_12
| ( identity != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_516,c_59922]) ).
tcf(c_61452,plain,
( ( sk_c9 = iPr_def_24 )
| ~ iPr_def_12
| ( identity != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_510,c_59922]) ).
tcf(c_61502,plain,
multiply(sk_c9,sk_c8) = iPr_def_14,
inference(superposition,[status(thm)],[c_13949,c_59890]) ).
tcf(c_61503,plain,
multiply(sk_c9,sk_c7) = iPr_def_15,
inference(superposition,[status(thm)],[c_13950,c_59890]) ).
tcf(c_61504,plain,
multiply(sk_c5,sk_c8) = iPr_def_19,
inference(superposition,[status(thm)],[c_13952,c_59890]) ).
tcf(c_61555,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_59890,c_487]) ).
tcf(c_61591,plain,
( ~ iPr_def_13
| ( sk_c9 != sk_c8 ) ),
inference(ground_joinability,[status(thm)],[c_61555,c_59892]) ).
tcf(c_63342,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_36426,c_28012]) ).
tcf(c_63709,plain,
( ( sk_c9 = iPr_def_24 )
| ~ iPr_def_13
| ( sk_c9 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_514,c_61591]) ).
tcf(c_63761,plain,
( ( sk_c8 = iPr_def_25 )
| ~ iPr_def_12 ),
inference(backward_subsumption_resolution,[status(thm)],[c_61451,c_63342]) ).
tcf(c_63964,plain,
( ( sk_c9 = iPr_def_24 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_61452,c_533,c_510,c_1035,c_1045,c_1717,c_5225,c_8256]) ).
tcf(c_65731,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( sk_c8 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_36568,c_44126]) ).
tcf(c_65959,plain,
( ( iPr_def_16 = iPr_def_21 )
| ( sk_c8 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_36704,c_45572]) ).
tcf(c_68743,plain,
multiply(iPr_def_19,inverse(sk_c8)) = sk_c5,
inference(demodulation,[status(thm)],[c_60573,c_15203]) ).
tcf(c_72914,plain,
multiply(sk_c5,inverse(iPr_def_21)) = iPr_def_20,
inference(demodulation,[status(thm)],[c_60582,c_15203]) ).
tcf(c_72938,plain,
multiply(iPr_def_21,inverse(iPr_def_21)) = multiply(sk_c4,iPr_def_20),
inference(superposition,[status(thm)],[c_72914,c_2111]) ).
tcf(c_72939,plain,
multiply(iPr_def_21,inverse(iPr_def_21)) = identity,
inference(light_normalisation,[status(thm)],[c_72938,c_16099]) ).
tcf(c_76647,plain,
multiply(sk_c9,inverse(iPr_def_18)) = iPr_def_16,
inference(demodulation,[status(thm)],[c_60589,c_15203]) ).
tcf(c_77862,plain,
multiply(iPr_def_22,inverse(sk_c9)) = sk_c2,
inference(demodulation,[status(thm)],[c_60590,c_15203]) ).
tcf(c_77929,plain,
multiply(sk_c9,inverse(sk_c9)) = multiply(iPr_def_17,sk_c2),
inference(superposition,[status(thm)],[c_77862,c_3412]) ).
tcf(c_77930,plain,
multiply(sk_c9,inverse(sk_c9)) = identity,
inference(light_normalisation,[status(thm)],[c_77929,c_963]) ).
tcf(c_79684,plain,
multiply(iPr_def_25,inverse(sk_c9)) = sk_c1,
inference(demodulation,[status(thm)],[c_60591,c_15203]) ).
tcf(c_79761,plain,
multiply(sk_c9,inverse(sk_c9)) = multiply(iPr_def_24,sk_c1),
inference(superposition,[status(thm)],[c_79684,c_3430]) ).
tcf(c_80080,plain,
multiply(iPr_def_18,inverse(sk_c9)) = sk_c6,
inference(demodulation,[status(thm)],[c_60592,c_15203]) ).
tcf(c_80155,plain,
multiply(sk_c9,inverse(sk_c9)) = multiply(iPr_def_16,sk_c6),
inference(superposition,[status(thm)],[c_80080,c_3435]) ).
tcf(c_82552,plain,
multiply(sk_c9,inverse(iPr_def_25)) = iPr_def_24,
inference(demodulation,[status(thm)],[c_60593,c_15203]) ).
tcf(c_82627,plain,
multiply(iPr_def_25,inverse(iPr_def_25)) = multiply(sk_c1,iPr_def_24),
inference(superposition,[status(thm)],[c_82552,c_2114]) ).
tcf(c_82629,plain,
multiply(iPr_def_25,inverse(iPr_def_25)) = identity,
inference(light_normalisation,[status(thm)],[c_82627,c_28431]) ).
tcf(c_84068,plain,
multiply(iPr_def_23,inverse(sk_c3)) = sk_c9,
inference(demodulation,[status(thm)],[c_60594,c_15203]) ).
tcf(c_85436,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_84068,c_82629,c_82627,c_82552,c_80155,c_80080,c_79761,c_79684,c_77862,c_76647,c_72939,c_72938,c_72914,c_68743,c_65959,c_65731,c_63964,c_63761,c_63709,c_61504,c_61503,c_61502,c_60998,c_60599,c_60598,c_60597,c_60596,c_60594,c_60593,c_60592,c_60591,c_60590,c_60589,c_60582,c_60573,c_59946,c_77930,c_51987,c_47897,c_47785,c_47122,c_38813,c_38797,c_36733,c_33978,c_33831,c_28458,c_28454,c_28428,c_23794,c_23774,c_21046,c_21023,c_21022,c_19185,c_19036,c_18958,c_18943,c_16100,c_15252,c_15238,c_15229,c_14113,c_13977,c_13976,c_13955,c_13950,c_13949,c_10110,c_10109,c_10108,c_9056,c_5466,c_2045,c_2037,c_1930,c_1812,c_1808,c_1717,c_1713,c_1277,c_526,c_525,c_519,c_513,c_507,c_501,c_496,c_495,c_494,c_493,c_492,c_491,c_486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP280-1 : 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 : n010.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 14:21:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.44 Running first-order theorem proving
% 0.14/0.44 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
% 0.14/0.46
% 0.14/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.46
% 0.14/0.46 % Detected problem language: tptp
% 0.14/0.48 % Proving...
% 21.38/4.97 % SZS status Started for theBenchmark.p
% 21.38/4.97 % SZS status Unsatisfiable for theBenchmark.p
% 21.38/4.97
% 21.38/4.97 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.38/4.97
% 21.38/4.97 % ------ iProver source info
% 21.38/4.97
% 21.38/4.97 % git: date: 2026-07-19 20:42:38 +0200
% 21.38/4.97 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.38/4.97 % git: non_committed_changes: false
% 21.38/4.97
% 21.38/4.97 % ------ Parsing...% successful
% 21.38/4.97
% 21.38/4.97
% 21.38/4.97 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.38/4.97
% 21.38/4.97 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 21.38/4.97
% 21.38/4.97 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.38/4.97
% 21.38/4.97 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 21.38/4.97 % ------ Proving...
% 21.38/4.97 % ------ Problem Properties
% 21.38/4.97
% 21.38/4.97 %
% 21.38/4.97 % clauses 56
% 21.38/4.97 % conjectures 41
% 21.38/4.97 % EPR 37
% 21.38/4.97 % Horn 19
% 21.38/4.97 % unary 15
% 21.38/4.97 % binary 36
% 21.38/4.97 % lits 105
% 21.38/4.97 % lits eq 97
% 21.38/4.97 % fd_pure 0
% 21.38/4.97 % fd_pseudo 0
% 21.38/4.97 % fd_cond 0
% 21.38/4.97 % fd_pseudo_cond 0
% 21.38/4.97 % AC symbols 0
% 21.38/4.97
% 21.38/4.97 % ------ Schedule dynamic 5 is on
% 21.38/4.97
% 21.38/4.97 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.38/4.97
% 21.38/4.97
% 21.38/4.97 % ------
% 21.38/4.97 % Current options:
% 21.38/4.97 % ------
% 21.38/4.97
% 21.38/4.97
% 21.38/4.97 %
% 21.38/4.97
% 21.38/4.97 % ------ Proving...
% 21.38/4.97 %
% 21.38/4.97
% 21.38/4.97 % SZS status Unsatisfiable for theBenchmark.p
% 21.38/4.97
% 21.38/4.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.38/4.97
% 21.38/4.97
%------------------------------------------------------------------------------