%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP349-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 01:33:18 PM UTC 2026
% Result : Unsatisfiable 57.61s 9.05s
% Output : CNFRefutation 57.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 52
% Syntax : Number of formulae : 500 ( 120 unt; 0 def)
% Number of atoms : 1120 (1028 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 1002 ( 382 ~; 620 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 297 ( 0 sgn 297 !; 0 ?; 266 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c10 = inverse(sk_c4)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c10 = inverse(sk_c5)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f13]) ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c6)
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(reorient_equations,[],[f17]) ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = inverse(sk_c5)
| sk_c10 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c10 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f29]) ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c7 = inverse(sk_c6)
| sk_c10 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c10 = multiply(sk_c9,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c8 = inverse(sk_c10) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = inverse(sk_c10) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c8 = inverse(sk_c10) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c10 = inverse(sk_c5)
| sk_c8 = inverse(sk_c10) ),
inference(reorient_equations,[],[f43]) ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = inverse(sk_c6)
| sk_c8 = inverse(sk_c10) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c10 = inverse(sk_c4)
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c10 = inverse(sk_c5)
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f71,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c10 = inverse(sk_c4)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c5)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f75]) ).
fof(f79,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c6,sk_c7)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c7 = inverse(sk_c6)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f81]) ).
fof(f85,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c9 = multiply(sk_c4,sk_c10)
| sk_c9 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f85]) ).
fof(f89,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f92,plain,
( sk_c10 = inverse(sk_c5)
| sk_c9 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f94,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c9 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f93]) ).
fof(f97,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f98,plain,
( sk_c7 = inverse(sk_c6)
| sk_c9 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f97]) ).
fof(f99,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_48) ).
fof(f100,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c9 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f99]) ).
fof(f103,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_50) ).
fof(f104,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f106,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f105]) ).
fof(f107,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_52) ).
fof(f108,plain,
( sk_c10 = inverse(sk_c5)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f107]) ).
fof(f109,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_53) ).
fof(f110,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f109]) ).
fof(f113,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_55) ).
fof(f114,plain,
( sk_c7 = inverse(sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f113]) ).
fof(f115,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_56) ).
fof(f116,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f115]) ).
fof(f119,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_58) ).
fof(f120,plain,
( sk_c10 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f119]) ).
fof(f121,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_59) ).
fof(f122,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f121]) ).
fof(f123,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_60) ).
fof(f124,plain,
( sk_c10 = inverse(sk_c5)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f123]) ).
fof(f125,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_61) ).
fof(f126,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f125]) ).
fof(f129,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_63) ).
fof(f130,plain,
( sk_c7 = inverse(sk_c6)
| sk_c8 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f129]) ).
fof(f133,negated_conjecture,
! [X2,X3,X0,X1,X6,X4,X5] :
( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9
| inverse(sk_c10) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_65) ).
fof(f134,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sk_c9 != multiply(X6,sk_c8)
| inverse(X5) != X6
| sk_c9 != multiply(X5,X6)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2)
| sk_c9 != multiply(X1,sk_c8)
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9
| sk_c8 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c8)
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(reorient_equations,[],[f133]) ).
fof(f135,plain,
! [X2,X3,X0,X6,X4,X5] :
( sk_c9 != multiply(X6,sk_c8)
| inverse(X5) != X6
| sk_c9 != multiply(X5,X6)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2)
| sk_c9 != multiply(inverse(X0),sk_c8)
| sk_c9 != multiply(X0,inverse(X0))
| sk_c8 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c8)
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(equality_resolution,[],[f134]) ).
fof(f136,plain,
! [X2,X3,X0,X4,X5] :
( sk_c9 != multiply(inverse(X5),sk_c8)
| sk_c9 != multiply(X5,inverse(X5))
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,sk_c8)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X2)
| sk_c9 != multiply(inverse(X0),sk_c8)
| sk_c9 != multiply(X0,inverse(X0))
| sk_c8 != inverse(sk_c10)
| sk_c10 != multiply(sk_c9,sk_c8)
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(equality_resolution,[],[f135]) ).
tcf(c_117,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_118,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_120,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c9 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_124,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_132,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( multiply(sk_c9,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_135,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c9,sk_c8) = sk_c10 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( inverse(sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_142,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( inverse(sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_144,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c9 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_145,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,sk_c2) = sk_c9 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_146,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c9 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_147,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c1,sk_c2) = sk_c9 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_148,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c9 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_149,negated_conjecture,
( ( multiply(sk_c1,sk_c2) = sk_c9 )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_150,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = sk_c9 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_153,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_154,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_155,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_157,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_158,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_160,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_162,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_163,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_164,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_166,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_167,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c9 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_169,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_170,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_171,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_172,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_174,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_175,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f116]) ).
tcf(c_177,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_178,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_179,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_180,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_182,negated_conjecture,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_184,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(sk_c10) != sk_c8 )
| ( inverse(X4) != sk_c8 )
| ( inverse(X3) != sk_c10 )
| ( inverse(X2) != sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 )
| ( multiply(X4,sk_c9) != sk_c8 )
| ( multiply(X3,sk_c9) != sk_c10 )
| ( multiply(X2,sk_c10) != sk_c9 )
| ( multiply(inverse(X1),sk_c8) != sk_c9 )
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X1,inverse(X1)) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(cnf_transformation,[],[f136]) ).
tcf(c_186,plain,
multiply(inverse(sk_c9),sk_c9) = identity,
inference(instantiation,[status(thm)],[c_118]) ).
tcf(c_765,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_184]) ).
tcf(c_766,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_184]) ).
tcf(c_767,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c8) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_184]) ).
tcf(c_768,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_184]) ).
tcf(c_769,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_184]) ).
tcf(c_770,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_771,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_773,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_776,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_770]) ).
tcf(c_1104,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_1105,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != sk_c8 )
| ( X0 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_1106,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_770]) ).
tcf(c_1111,plain,
( ( sk_c8 = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1105]) ).
tcf(c_1112,plain,
multiply(identity,sk_c8) = sk_c8,
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_1114,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_1119,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( X0 != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_1133,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(X0,X1) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1119]) ).
tcf(c_1134,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(identity,sk_c8) )
| ( X1 != sk_c8 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_772]) ).
tcf(c_1177,plain,
! [X0: $i,X1: $i] :
( ( multiply(multiply(inverse(X0),X0),X1) = multiply(identity,sk_c8) )
| ( X1 != sk_c8 )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_1134]) ).
tcf(c_1180,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_770]) ).
tcf(c_1182,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = X0 )
| ( sk_c10 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_1265,plain,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = identity ) ),
inference(superposition,[status(thm)],[c_174,c_118]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_1341,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,multiply(sk_c10,X0)) = multiply(sk_c8,X0) ) ),
inference(superposition,[status(thm)],[c_121,c_119]) ).
tcf(c_1344,plain,
! [X0: $i] :
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(sk_c4,multiply(sk_c10,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_136,c_119]) ).
tcf(c_1346,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c10,multiply(sk_c8,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_154,c_119]) ).
tcf(c_1357,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,multiply(sk_c8,X0)) = multiply(sk_c10,X0) ) ),
inference(superposition,[status(thm)],[c_134,c_119]) ).
tcf(c_1358,plain,
! [X0: $i] :
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,multiply(sk_c8,X0)) = multiply(sk_c10,X0) ) ),
inference(superposition,[status(thm)],[c_131,c_119]) ).
tcf(c_1359,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,multiply(sk_c8,X0)) = multiply(sk_c10,X0) ) ),
inference(superposition,[status(thm)],[c_129,c_119]) ).
tcf(c_1360,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_150,c_119]) ).
tcf(c_1361,plain,
! [X0: $i] :
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_147,c_119]) ).
tcf(c_1362,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_145,c_119]) ).
tcf(c_1363,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c2,multiply(sk_c8,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_166,c_119]) ).
tcf(c_1366,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c3,multiply(sk_c9,X0)) = multiply(sk_c8,X0) ) ),
inference(superposition,[status(thm)],[c_182,c_119]) ).
tcf(c_1368,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c3,multiply(sk_c9,X0)) = multiply(sk_c8,X0) ) ),
inference(superposition,[status(thm)],[c_177,c_119]) ).
tcf(c_1370,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_118,c_119]) ).
tcf(c_1417,plain,
! [X0: $i] :
( ( multiply(multiply(inverse(X0),X0),sk_c8) = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_1177]) ).
tcf(c_1418,plain,
( ( multiply(multiply(inverse(sk_c9),sk_c9),sk_c8) = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_1417]) ).
tcf(c_1480,plain,
! [X0: $i] :
( ( sk_c8 = multiply(multiply(inverse(X0),X0),sk_c8) )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(multiply(inverse(X0),X0),sk_c8) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1133]) ).
tcf(c_1481,plain,
( ( sk_c8 = multiply(multiply(inverse(sk_c9),sk_c9),sk_c8) )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(multiply(inverse(sk_c9),sk_c9),sk_c8) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1480]) ).
tcf(c_1514,plain,
! [X0: $i] :
( ( sk_c10 = X0 )
| ( sk_c10 != sk_c10 )
| ( X0 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1223]) ).
tcf(c_1515,plain,
sk_c10 = sk_c10,
inference(instantiation,[status(thm)],[c_770]) ).
tcf(c_1548,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_1267]) ).
tcf(c_1549,plain,
( ( identity = sk_c9 )
| ( identity != identity )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_1548]) ).
tcf(c_1559,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c10) = sk_c8 )
| ( multiply(sk_c4,multiply(sk_c10,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_120,c_119]) ).
tcf(c_1670,plain,
! [X0: $i] :
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_146,c_119]) ).
tcf(c_2251,plain,
( ( inverse(sk_c3) = sk_c8 )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_766,c_172]) ).
tcf(c_2253,plain,
( ( multiply(sk_c9,sk_c8) = sk_c10 )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_766,c_132]) ).
tcf(c_2265,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != multiply(multiply(inverse(X1),X1),sk_c8) )
| ( X0 != multiply(multiply(inverse(X1),X1),sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_2320,plain,
( ( inverse(sk_c4) = sk_c10 )
| ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_768,c_177]) ).
tcf(c_2321,plain,
( ( inverse(sk_c5) = sk_c10 )
| ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_768,c_179]) ).
tcf(c_2322,plain,
( ( inverse(sk_c6) = sk_c7 )
| ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_768,c_182]) ).
tcf(c_2325,plain,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ~ iPr_def_13
| ( inverse(sk_c3) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_768,c_180]) ).
tcf(c_2449,plain,
multiply(identity,sk_c10) = sk_c10,
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_2490,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c9,sk_c8) != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_769,c_170]) ).
tcf(c_2497,plain,
( ( sk_c10 = inverse(sk_c5) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c5) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1514]) ).
tcf(c_2524,plain,
! [X0: $i] :
( ( identity = multiply(inverse(X0),X0) )
| ( identity != identity )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_1548]) ).
tcf(c_2525,plain,
( ( identity = multiply(inverse(sk_c9),sk_c9) )
| ( identity != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_2524]) ).
tcf(c_2613,plain,
! [X0: $i] :
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = X0 )
| ( X0 != sk_c8 ) ),
inference(resolution,[status(thm)],[c_771,c_179]) ).
tcf(c_2617,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c9) = X0 )
| ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( X0 != sk_c8 ) ),
inference(resolution,[status(thm)],[c_771,c_180]) ).
tcf(c_2629,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X1),X1) = X0 )
| ( X0 != identity ) ),
inference(resolution,[status(thm)],[c_771,c_118]) ).
tcf(c_2633,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_771,c_770]) ).
tcf(c_2742,plain,
! [X0: $i] :
( ( sk_c10 = X0 )
| ( sk_c10 != inverse(sk_c5) )
| ( X0 != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_1223]) ).
tcf(c_2779,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(multiply(inverse(X2),X2),sk_c8) )
| ( multiply(X0,X1) != multiply(multiply(inverse(X2),X2),sk_c8) ) ),
inference(instantiation,[status(thm)],[c_2265]) ).
tcf(c_2780,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X2) = multiply(multiply(inverse(X1),X1),sk_c8) )
| ( X2 != sk_c8 )
| ( X0 != multiply(inverse(X1),X1) ) ),
inference(instantiation,[status(thm)],[c_772]) ).
tcf(c_3765,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c6) = sk_c7 )
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_126,c_769]) ).
tcf(c_3781,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1370,c_117]) ).
tcf(c_3863,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_3781,c_3781]) ).
tcf(c_4053,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_3863,c_118]) ).
tcf(c_4120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(X0,X2) = X4 )
| ( X4 != multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_772,c_771]) ).
tcf(c_4161,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2633,c_147]) ).
tcf(c_4163,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(resolution,[status(thm)],[c_2633,c_144]) ).
tcf(c_4165,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2633,c_148]) ).
tcf(c_4172,plain,
( ( sk_c9 = multiply(sk_c2,sk_c8) )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2633,c_163]) ).
tcf(c_4174,plain,
( ( sk_c9 = multiply(sk_c2,sk_c8) )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(resolution,[status(thm)],[c_2633,c_160]) ).
tcf(c_4176,plain,
( ( sk_c9 = multiply(sk_c2,sk_c8) )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2633,c_164]) ).
tcf(c_4190,plain,
! [X0: $i] : X0 = multiply(identity,X0),
inference(resolution,[status(thm)],[c_2633,c_117]) ).
tcf(c_4432,plain,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = identity ) ),
inference(superposition,[status(thm)],[c_158,c_4053]) ).
tcf(c_4433,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c1,sk_c2) = identity ) ),
inference(superposition,[status(thm)],[c_155,c_4053]) ).
tcf(c_4434,plain,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,sk_c2) = identity ) ),
inference(superposition,[status(thm)],[c_153,c_4053]) ).
tcf(c_4442,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_4053,c_119]) ).
tcf(c_4521,plain,
( ( sk_c10 = multiply(identity,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1514]) ).
tcf(c_4678,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_4432,c_150]) ).
tcf(c_4726,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_4433,c_147]) ).
tcf(c_4789,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_4434,c_145]) ).
tcf(c_5337,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = multiply(inverse(X1),identity),
inference(superposition,[status(thm)],[c_4442,c_3781]) ).
tcf(c_5453,plain,
! [X0: $i] :
( ( multiply(X0,sk_c8) = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_1134]) ).
tcf(c_5454,plain,
( ( multiply(sk_c9,sk_c8) = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_5453]) ).
tcf(c_6126,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = multiply(inverse(identity),identity),
inference(superposition,[status(thm)],[c_117,c_5337]) ).
tcf(c_6389,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(demodulation,[status(thm)],[c_6126,c_118]) ).
tcf(c_6392,plain,
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_137,c_6389]) ).
tcf(c_6401,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_6389,c_119]) ).
tcf(c_6408,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_6401,c_117]) ).
tcf(c_6411,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_118,c_6408]) ).
tcf(c_6412,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_6389,c_6408]) ).
tcf(c_6430,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_6412,c_6411]) ).
tcf(c_6475,plain,
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c10)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_118,c_765]) ).
tcf(c_6477,plain,
( ~ iPr_def_10
| ( sk_c9 != identity ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6475,c_6430]) ).
tcf(c_6518,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c9 != identity )
| ( multiply(inverse(X0),sk_c8) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_767,c_6389]) ).
tcf(c_6525,plain,
( ~ iPr_def_12
| ( sk_c9 != identity ) ),
inference(superposition,[status(thm)],[c_118,c_6518]) ).
tcf(c_6592,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c10) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_6392,c_136]) ).
tcf(c_6599,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c10,sk_c8) = identity ) ),
inference(superposition,[status(thm)],[c_6592,c_6389]) ).
tcf(c_6788,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_6599,c_154]) ).
tcf(c_6842,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c1,sk_c2) = identity ) ),
inference(superposition,[status(thm)],[c_6788,c_6389]) ).
tcf(c_7297,plain,
! [X0: $i] :
( ( sk_c8 = multiply(X0,sk_c8) )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(X0,sk_c8) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1133]) ).
tcf(c_7298,plain,
( ( sk_c8 = multiply(sk_c9,sk_c8) )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(sk_c9,sk_c8) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_7297]) ).
tcf(c_7444,plain,
( ( sk_c10 = multiply(identity,inverse(sk_c5)) )
| ( sk_c10 != inverse(sk_c5) )
| ( multiply(identity,inverse(sk_c5)) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_2742]) ).
tcf(c_7445,plain,
multiply(identity,inverse(sk_c5)) = inverse(sk_c5),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_7450,plain,
! [X0: $i] :
( ( sk_c10 = inverse(X0) )
| ( sk_c10 != inverse(sk_c5) )
| ( inverse(X0) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_2742]) ).
tcf(c_7451,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c5) )
| ( X0 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_773]) ).
tcf(c_7963,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,sk_c8) = multiply(multiply(inverse(X1),X1),sk_c8) )
| ( sk_c8 != sk_c8 )
| ( X0 != multiply(inverse(X1),X1) ) ),
inference(instantiation,[status(thm)],[c_2780]) ).
tcf(c_7964,plain,
( ( multiply(sk_c9,sk_c8) = multiply(multiply(inverse(sk_c9),sk_c9),sk_c8) )
| ( sk_c8 != sk_c8 )
| ( sk_c9 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_7963]) ).
tcf(c_8031,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_4163,c_765]) ).
tcf(c_8190,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_4165,c_766]) ).
tcf(c_8230,plain,
( ( sk_c9 = multiply(sk_c2,sk_c8) )
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_4174,c_765]) ).
tcf(c_8315,plain,
( ( sk_c9 = multiply(sk_c2,sk_c8) )
| ~ iPr_def_11
| ( inverse(sk_c5) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_4176,c_766]) ).
tcf(c_9181,plain,
( ( inverse(sk_c3) = sk_c8 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_2251,c_171,c_2251]) ).
tcf(c_9214,plain,
! [X0: $i] :
( ( inverse(sk_c3) = X0 )
| ~ iPr_def_11
| ( X0 != sk_c8 ) ),
inference(resolution,[status(thm)],[c_9181,c_771]) ).
tcf(c_9462,plain,
( ( inverse(sk_c5) = sk_c10 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_2321,c_171,c_2321]) ).
tcf(c_9473,plain,
! [X0: $i] :
( ( inverse(sk_c5) = X0 )
| ~ iPr_def_13
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_9462,c_771]) ).
tcf(c_9666,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != multiply(inverse(X1),X1) )
| ( X0 != multiply(inverse(X1),X1) ) ),
inference(instantiation,[status(thm)],[c_1182]) ).
tcf(c_9667,plain,
( ( sk_c9 = identity )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c9 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_9666]) ).
tcf(c_9816,plain,
( ( multiply(sk_c9,sk_c8) = sk_c10 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_2253,c_131,c_2253]) ).
tcf(c_9852,plain,
( ( sk_c10 = multiply(sk_c9,sk_c8) )
| ~ iPr_def_11 ),
inference(resolution,[status(thm)],[c_9816,c_2633]) ).
tcf(c_9956,plain,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_2325,c_172,c_2325]) ).
tcf(c_9977,plain,
! [X0: $i] :
( ( multiply(sk_c5,sk_c9) = X0 )
| ~ iPr_def_13
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_9956,c_771]) ).
tcf(c_10567,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_8031,c_4789,c_6477,c_8031]) ).
tcf(c_10573,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_8190,c_4161,c_8190]) ).
tcf(c_10579,plain,
( ( sk_c9 = multiply(sk_c2,sk_c8) )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_8230,c_4789,c_6477,c_8230]) ).
tcf(c_10585,plain,
( ( sk_c9 = multiply(sk_c2,sk_c8) )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_8315,c_4172,c_8315]) ).
tcf(c_10701,plain,
( ( inverse(sk_c5) = sk_c10 )
| ~ iPr_def_11
| ( sk_c10 != sk_c8 )
| ( inverse(sk_c3) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_2613,c_766]) ).
tcf(c_12889,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c6) = sk_c7 )
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_126,c_769]) ).
tcf(c_12890,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c5) = sk_c10 )
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_123,c_769]) ).
tcf(c_12891,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_121,c_769]) ).
tcf(c_12892,plain,
( iPr_def_11
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_12889,c_174,c_142,c_134,c_2322,c_3765,c_4678,c_6477,c_6525]) ).
tcf(c_12893,plain,
( iPr_def_11
| ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(renaming,[status(thm)],[c_12892]) ).
tcf(c_12924,plain,
( iPr_def_11
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_12890,c_171,c_139,c_131,c_123,c_769,c_2321,c_4726,c_6477,c_6525]) ).
tcf(c_12925,plain,
( iPr_def_11
| ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(renaming,[status(thm)],[c_12924]) ).
tcf(c_12932,plain,
( iPr_def_11
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_12891,c_169,c_137,c_129,c_121,c_769,c_2320,c_4789,c_6477,c_6525]) ).
tcf(c_12933,plain,
( iPr_def_11
| ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(renaming,[status(thm)],[c_12932]) ).
tcf(c_13164,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1370,c_117]) ).
tcf(c_13231,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_119,c_13164]) ).
tcf(c_13239,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_13164,c_13164]) ).
tcf(c_13279,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_13239,c_118]) ).
tcf(c_13394,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_13279,c_119]) ).
tcf(c_14966,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,identity)) = inverse(X1),
inference(superposition,[status(thm)],[c_13279,c_13231]) ).
tcf(c_15068,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,identity)) = multiply(X2,inverse(multiply(X1,X2))),
inference(superposition,[status(thm)],[c_13394,c_13231]) ).
tcf(c_15089,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(light_normalisation,[status(thm)],[c_15068,c_14966]) ).
tcf(c_15735,plain,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ~ iPr_def_11
| ( sk_c10 != sk_c8 )
| ( inverse(sk_c3) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_2617,c_766]) ).
tcf(c_16013,plain,
( ( inverse(sk_c5) = sk_c10 )
| ~ iPr_def_11
| ( sk_c10 != sk_c8 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10701,c_9214]) ).
tcf(c_16293,plain,
! [X0: $i] : multiply(X0,inverse(identity)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_118,c_15089]) ).
tcf(c_16405,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(X1,X0)),X2)) = multiply(inverse(X1),X2),
inference(superposition,[status(thm)],[c_15089,c_119]) ).
tcf(c_16748,plain,
( ( sk_c8 = inverse(sk_c10) )
| ( sk_c8 != sk_c8 )
| ( inverse(sk_c10) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1105]) ).
tcf(c_17676,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(identity),X1)) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[c_118,c_16405]) ).
tcf(c_18772,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(X0,sk_c8) )
| ( sk_c8 != multiply(multiply(inverse(X1),X1),sk_c8) )
| ( multiply(X0,sk_c8) != multiply(multiply(inverse(X1),X1),sk_c8) ) ),
inference(instantiation,[status(thm)],[c_2779]) ).
tcf(c_18773,plain,
( ( sk_c8 = multiply(sk_c9,sk_c8) )
| ( sk_c8 != multiply(multiply(inverse(sk_c9),sk_c9),sk_c8) )
| ( multiply(sk_c9,sk_c8) != multiply(multiply(inverse(sk_c9),sk_c9),sk_c8) ) ),
inference(instantiation,[status(thm)],[c_18772]) ).
tcf(c_18859,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X2,X0) = X1 )
| ( X2 != identity )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_4190,c_4120]) ).
tcf(c_18860,plain,
( ( multiply(sk_c9,sk_c9) = sk_c9 )
| ( sk_c9 != identity )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_18859]) ).
tcf(c_18975,plain,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ~ iPr_def_11
| ( sk_c10 != sk_c8 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15735,c_9214]) ).
tcf(c_19269,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ~ iPr_def_10
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(resolution,[status(thm)],[c_10567,c_771]) ).
tcf(c_19298,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ~ iPr_def_11
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(resolution,[status(thm)],[c_10573,c_771]) ).
tcf(c_19349,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ~ iPr_def_10
| ( X0 != multiply(sk_c2,sk_c8) ) ),
inference(resolution,[status(thm)],[c_10579,c_771]) ).
tcf(c_19487,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ~ iPr_def_11
| ( X0 != multiply(sk_c2,sk_c8) ) ),
inference(resolution,[status(thm)],[c_10585,c_771]) ).
tcf(c_21765,plain,
! [X0: $i] :
( ( sk_c10 = sk_c8 )
| ( sk_c8 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_1114]) ).
tcf(c_23042,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c10 )
| ( inverse(sk_c5) != sk_c8 ) ),
inference(resolution,[status(thm)],[c_9977,c_768]) ).
tcf(c_23203,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23042,c_9473]) ).
tcf(c_23818,plain,
! [X0: $i] :
( ( sk_c8 = sk_c10 )
| ( sk_c8 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_24113,plain,
( ( sk_c8 = multiply(sk_c9,sk_c10) )
| ( sk_c8 != sk_c8 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_1105]) ).
tcf(c_26061,plain,
( ( sk_c10 = sk_c8 )
| ( sk_c8 != multiply(identity,inverse(sk_c5)) )
| ( sk_c10 != multiply(identity,inverse(sk_c5)) ) ),
inference(instantiation,[status(thm)],[c_21765]) ).
tcf(c_27292,plain,
inverse(inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[c_16293,c_117]) ).
tcf(c_27293,plain,
inverse(inverse(inverse(inverse(identity)))) = identity,
inference(superposition,[status(thm)],[c_16293,c_118]) ).
tcf(c_27294,plain,
inverse(identity) = identity,
inference(light_normalisation,[status(thm)],[c_27293,c_27292]) ).
tcf(c_27296,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,multiply(identity,X1)),
inference(light_normalisation,[status(thm)],[c_17676,c_27294]) ).
tcf(c_27297,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_27296,c_117]) ).
tcf(c_27309,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_27297,c_118]) ).
tcf(c_27312,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[c_16293,c_27294]) ).
tcf(c_27497,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c8,multiply(sk_c3,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_1265,c_119]) ).
tcf(c_27534,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c8,multiply(sk_c3,X0)) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_27497,c_117]) ).
tcf(c_27543,plain,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c8,sk_c8) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_182,c_27534]) ).
tcf(c_27633,plain,
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_137,c_27309]) ).
tcf(c_27643,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_27309,c_119]) ).
tcf(c_27666,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_27643,c_117]) ).
tcf(c_27670,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_118,c_27666]) ).
tcf(c_27677,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_158,c_27666]) ).
tcf(c_27678,plain,
! [X0: $i] :
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_155,c_27666]) ).
tcf(c_27679,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_153,c_27666]) ).
tcf(c_27694,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_27312,c_27670]) ).
tcf(c_27740,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c10) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_27633,c_136]) ).
tcf(c_27746,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c10,sk_c8) = identity ) ),
inference(superposition,[status(thm)],[c_27740,c_27309]) ).
tcf(c_27782,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_27746,c_154]) ).
tcf(c_27796,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c2) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_27782,c_27694]) ).
tcf(c_30924,plain,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,sk_c9) = multiply(sk_c10,sk_c8) ) ),
inference(superposition,[status(thm)],[c_27543,c_1357]) ).
tcf(c_31099,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_1360,c_27677]) ).
tcf(c_31106,plain,
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,sk_c9) = sk_c9 ) ),
inference(instantiation,[status(thm)],[c_31099]) ).
tcf(c_31164,plain,
! [X0: $i] :
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_1361,c_27678]) ).
tcf(c_31172,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,sk_c9) = sk_c9 ) ),
inference(instantiation,[status(thm)],[c_31164]) ).
tcf(c_31229,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_1362,c_27679]) ).
tcf(c_31238,plain,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,sk_c9) = sk_c9 ) ),
inference(instantiation,[status(thm)],[c_31229]) ).
tcf(c_33543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(X0,X1) )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_33544,plain,
( ( sk_c9 = multiply(sk_c9,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( multiply(sk_c9,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_33543]) ).
tcf(c_37011,plain,
( ( sk_c10 = sk_c8 )
| ( sk_c8 != multiply(sk_c9,sk_c8) )
| ( sk_c10 != multiply(sk_c9,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_21765]) ).
tcf(c_37113,plain,
! [X0: $i] :
( ( sk_c8 = X0 )
| ( sk_c8 != multiply(sk_c9,sk_c10) )
| ( X0 != multiply(sk_c9,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_1104]) ).
tcf(c_38023,plain,
( ( sk_c8 = sk_c10 )
| ( sk_c8 != multiply(identity,inverse(sk_c5)) )
| ( sk_c10 != multiply(identity,inverse(sk_c5)) ) ),
inference(instantiation,[status(thm)],[c_23818]) ).
tcf(c_43117,plain,
( ~ iPr_def_11
| ( sk_c10 != sk_c8 )
| ( inverse(sk_c5) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_18975,c_766]) ).
tcf(c_43118,plain,
( ~ iPr_def_11
| ( sk_c10 != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_43117,c_16013,c_43117]) ).
tcf(c_43284,plain,
! [X0: $i] :
( ( sk_c9 = multiply(inverse(X0),X0) )
| ~ iPr_def_10
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(resolution,[status(thm)],[c_19269,c_2629]) ).
tcf(c_43285,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ~ iPr_def_10
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_43284]) ).
tcf(c_43892,plain,
! [X0: $i] :
( ( sk_c9 = multiply(inverse(X0),X0) )
| ~ iPr_def_11
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(resolution,[status(thm)],[c_19298,c_2629]) ).
tcf(c_43893,plain,
( ( sk_c9 = multiply(inverse(sk_c9),sk_c9) )
| ~ iPr_def_11
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_43892]) ).
tcf(c_44575,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(sk_c9,sk_c10) )
| ( X1 != sk_c10 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_772]) ).
tcf(c_44593,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_19349,c_186,c_1180,c_2525,c_6477,c_6842,c_9667,c_43285]) ).
tcf(c_44597,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_19487,c_186,c_1106,c_1111,c_1112,c_1418,c_1481,c_5454,c_6842,c_7298,c_7964,c_9852,c_18773,c_37011,c_43118,c_43893]) ).
tcf(c_47114,plain,
( ( sk_c8 = multiply(identity,inverse(sk_c5)) )
| ( sk_c8 != multiply(sk_c9,sk_c10) )
| ( multiply(identity,inverse(sk_c5)) != multiply(sk_c9,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_37113]) ).
tcf(c_47595,plain,
( ( inverse(sk_c10) = inverse(sk_c5) )
| ( sk_c10 != sk_c5 ) ),
inference(instantiation,[status(thm)],[c_7451]) ).
tcf(c_49450,plain,
( ( sk_c10 = inverse(sk_c10) )
| ( sk_c10 != inverse(sk_c5) )
| ( inverse(sk_c10) != inverse(sk_c5) ) ),
inference(instantiation,[status(thm)],[c_7450]) ).
tcf(c_61932,plain,
( ( multiply(identity,inverse(sk_c5)) = multiply(sk_c9,sk_c10) )
| ( identity != sk_c9 )
| ( inverse(sk_c5) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_44575]) ).
tcf(c_62480,negated_conjecture,
( iPr_def_13
| iPr_def_12
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_769,c_769,c_44593,c_44597]) ).
tcf(c_62493,plain,
inverse(inverse(identity)) = inverse(identity),
inference(superposition,[status(thm)],[c_16293,c_117]) ).
tcf(c_62494,plain,
inverse(inverse(inverse(inverse(identity)))) = identity,
inference(superposition,[status(thm)],[c_16293,c_118]) ).
tcf(c_62495,plain,
inverse(identity) = identity,
inference(light_normalisation,[status(thm)],[c_62494,c_62493]) ).
tcf(c_62497,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[c_16293,c_62495]) ).
tcf(c_62593,plain,
! [X0: $i] : multiply(multiply(X0,identity),inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_62497,c_118]) ).
tcf(c_62603,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(demodulation,[status(thm)],[c_62593,c_117,c_119]) ).
tcf(c_62618,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_62603,c_119]) ).
tcf(c_62620,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_62603,c_119]) ).
tcf(c_62678,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_62618,c_117]) ).
tcf(c_62681,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(superposition,[status(thm)],[c_118,c_62678]) ).
tcf(c_62684,plain,
! [X0: $i] :
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(sk_c4,multiply(sk_c10,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_137,c_62678]) ).
tcf(c_62688,plain,
! [X0: $i] :
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_155,c_62678]) ).
tcf(c_62694,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(multiply(X0,identity),X1)) = X1,
inference(superposition,[status(thm)],[c_62497,c_62678]) ).
tcf(c_62698,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(inverse(multiply(X0,X1)),X2))) = X2,
inference(superposition,[status(thm)],[c_62678,c_119]) ).
tcf(c_62701,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(light_normalisation,[status(thm)],[c_62694,c_62681]) ).
tcf(c_62710,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c8,multiply(sk_c3,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_174,c_62701]) ).
tcf(c_62768,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(inverse(sk_c3),sk_c8) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_179,c_62701]) ).
tcf(c_62769,plain,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(inverse(sk_c3),sk_c8) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_177,c_62701]) ).
tcf(c_62772,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_119,c_62701]) ).
tcf(c_62804,negated_conjecture,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_765,c_186,c_1180,c_2525,c_6477,c_6842,c_9667,c_43285]) ).
tcf(c_62806,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( inverse(sk_c10) != sk_c8 )
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_769,c_62804]) ).
tcf(c_62841,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_62497,c_62681]) ).
tcf(c_62855,plain,
( ( inverse(sk_c2) = sk_c1 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_158,c_62841]) ).
tcf(c_62870,plain,
! [X0: $i] :
( ( inverse(sk_c2) = sk_c1 )
| ( multiply(sk_c6,multiply(sk_c7,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_62855,c_62678]) ).
tcf(c_62871,plain,
( ( inverse(sk_c2) = sk_c1 )
| ( multiply(sk_c6,sk_c7) = identity ) ),
inference(superposition,[status(thm)],[c_62855,c_62603]) ).
tcf(c_62970,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c2) = sk_c1 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_62871,c_157]) ).
tcf(c_63244,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))) = identity,
inference(superposition,[status(thm)],[c_119,c_62620]) ).
tcf(c_64068,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c8,sk_c8) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_171,c_62768]) ).
tcf(c_64085,plain,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c8,sk_c8) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_169,c_62769]) ).
tcf(c_64365,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_163,c_62688]) ).
tcf(c_64754,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(inverse(multiply(inverse(X1),X0)),X2)) = multiply(X1,X2),
inference(superposition,[status(thm)],[c_62698,c_62678]) ).
tcf(c_65471,plain,
! [X0: $i] :
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( multiply(inverse(sk_c9),multiply(sk_c1,multiply(sk_c2,X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_148,c_62772]) ).
tcf(c_65472,plain,
! [X0: $i] :
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(inverse(sk_c9),multiply(sk_c1,multiply(sk_c2,X0))) = X0 ) ),
inference(superposition,[status(thm)],[c_146,c_62772]) ).
tcf(c_65626,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(multiply(X0,X1)),X0)),identity) = X1,
inference(superposition,[status(thm)],[c_118,c_62772]) ).
tcf(c_66313,plain,
( ( inverse(sk_c2) = sk_c1 )
| ( multiply(sk_c6,sk_c9) = sk_c8 )
| ( multiply(sk_c9,sk_c8) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_135,c_62870]) ).
tcf(c_66375,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(demodulation,[status(thm)],[c_65626,c_62681]) ).
tcf(c_66404,plain,
( ( inverse(sk_c10) = sk_c8 )
| ( inverse(multiply(inverse(sk_c9),sk_c10)) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_138,c_66375]) ).
tcf(c_67640,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c2) = sk_c1 ) ),
inference(global_subsumption_just,[status(thm)],[c_62970,c_27796]) ).
tcf(c_67648,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c1,sk_c2) = identity ) ),
inference(superposition,[status(thm)],[c_67640,c_118]) ).
tcf(c_67690,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c6,sk_c7) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_67648,c_149]) ).
tcf(c_67742,plain,
! [X0: $i] :
( ( sk_c9 = identity )
| ( multiply(sk_c6,multiply(sk_c7,X0)) = multiply(sk_c9,X0) ) ),
inference(superposition,[status(thm)],[c_67690,c_119]) ).
tcf(c_69921,plain,
! [X0: $i] :
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(sk_c9,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_1344,c_62684]) ).
tcf(c_71309,plain,
! [X0: $i] :
( ( inverse(sk_c10) = sk_c8 )
| ( multiply(inverse(sk_c9),X0) = X0 ) ),
inference(superposition,[status(thm)],[c_69921,c_62678]) ).
tcf(c_71442,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c9,identity) = multiply(sk_c10,sk_c8) ) ),
inference(superposition,[status(thm)],[c_62681,c_1346]) ).
tcf(c_71925,plain,
inverse(sk_c10) = sk_c8,
inference(superposition,[status(thm)],[c_71309,c_66404]) ).
tcf(c_71977,plain,
( iPr_def_13
| iPr_def_12
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_62480,c_71925]) ).
tcf(c_72251,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,sk_c9) = multiply(sk_c10,sk_c8) ) ),
inference(superposition,[status(thm)],[c_64068,c_1358]) ).
tcf(c_72566,plain,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,sk_c9) = multiply(sk_c10,sk_c8) ) ),
inference(superposition,[status(thm)],[c_64085,c_1359]) ).
tcf(c_72717,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,sk_c8) = multiply(sk_c1,sk_c9) ) ),
inference(superposition,[status(thm)],[c_163,c_1361]) ).
tcf(c_72789,plain,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c9,sk_c8) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_72717,c_64365]) ).
tcf(c_72899,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,multiply(sk_c3,X0)) = multiply(sk_c2,X0) ) ),
inference(superposition,[status(thm)],[c_62710,c_1363]) ).
tcf(c_74116,plain,
! [X0: $i] :
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c8,multiply(sk_c10,X0)) = multiply(sk_c3,multiply(sk_c8,X0)) ) ),
inference(superposition,[status(thm)],[c_1341,c_1368]) ).
tcf(c_74877,plain,
! [X0: $i] :
( ( inverse(sk_c6) = sk_c7 )
| ( multiply(sk_c9,multiply(sk_c8,X0)) = multiply(sk_c2,multiply(sk_c9,X0)) ) ),
inference(superposition,[status(thm)],[c_1366,c_72899]) ).
tcf(c_79606,plain,
! [X0: $i] :
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( sk_c9 != X0 )
| ( multiply(sk_c10,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_79608,plain,
multiply(sk_c10,sk_c8) = multiply(sk_c10,sk_c8),
inference(instantiation,[status(thm)],[c_770]) ).
tcf(c_79609,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c10,sk_c8) = X1 )
| ( X1 != X0 )
| ( multiply(sk_c10,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_79610,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( sk_c9 != multiply(X0,X1) )
| ( multiply(sk_c10,sk_c8) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_79606]) ).
tcf(c_79612,plain,
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( sk_c9 != multiply(sk_c9,sk_c9) )
| ( multiply(sk_c10,sk_c8) != multiply(sk_c9,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_79610]) ).
tcf(c_79622,plain,
! [X0: $i] :
( ( multiply(sk_c10,sk_c8) = X0 )
| ( X0 != multiply(sk_c10,sk_c8) )
| ( multiply(sk_c10,sk_c8) != multiply(sk_c10,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_79609]) ).
tcf(c_79641,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c10,sk_c8) = multiply(X0,X1) )
| ( multiply(sk_c10,sk_c8) != multiply(sk_c10,sk_c8) )
| ( multiply(X0,X1) != multiply(sk_c10,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_79622]) ).
tcf(c_79643,plain,
( ( multiply(sk_c10,sk_c8) = multiply(sk_c9,sk_c9) )
| ( multiply(sk_c10,sk_c8) != multiply(sk_c10,sk_c8) )
| ( multiply(sk_c9,sk_c9) != multiply(sk_c10,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_79641]) ).
tcf(c_79668,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_79693,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c10 )
| ( sk_c10 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_79764,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != inverse(sk_c10) )
| ( X0 != inverse(sk_c10) ) ),
inference(instantiation,[status(thm)],[c_79668]) ).
tcf(c_80034,plain,
! [X0: $i] :
( ( X0 = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( X0 != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_79693]) ).
tcf(c_80552,plain,
! [X0: $i,X1: $i] :
( ( inverse(sk_c3) = X1 )
| ( X1 != X0 )
| ( inverse(sk_c3) != X0 ) ),
inference(instantiation,[status(thm)],[c_771]) ).
tcf(c_80816,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(identity,sk_c10) )
| ( X1 != sk_c10 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_772]) ).
tcf(c_83435,plain,
! [X0: $i] :
( ( inverse(sk_c3) = X0 )
| ( X0 != sk_c8 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_80552]) ).
tcf(c_84409,plain,
( ( sk_c10 = sk_c8 )
| ( sk_c8 != inverse(sk_c10) )
| ( sk_c10 != inverse(sk_c10) ) ),
inference(instantiation,[status(thm)],[c_79764]) ).
tcf(c_92582,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( sk_c10 != sk_c8 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_83435]) ).
tcf(c_92633,plain,
! [X0: $i] :
( ( multiply(X0,sk_c8) = multiply(identity,sk_c10) )
| ( sk_c8 != sk_c10 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_80816]) ).
tcf(c_92636,plain,
( ( multiply(sk_c9,sk_c8) = multiply(identity,sk_c10) )
| ( sk_c8 != sk_c10 )
| ( sk_c9 != identity ) ),
inference(instantiation,[status(thm)],[c_92633]) ).
tcf(c_97496,plain,
inverse(sk_c4) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_74116,c_186,c_776,c_1106,c_1111,c_1112,c_1418,c_1481,c_5454,c_6842,c_7298,c_7964,c_9852,c_12933,c_18773,c_31238,c_33544,c_37011,c_43118,c_43893,c_72566,c_79608,c_79612,c_79643]) ).
tcf(c_97559,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c10,X0)) = X0,
inference(superposition,[status(thm)],[c_97496,c_62678]) ).
tcf(c_99139,plain,
inverse(sk_c6) = sk_c7,
inference(global_subsumption_just,[status(thm)],[c_74877,c_186,c_776,c_1106,c_1111,c_1112,c_1418,c_1481,c_5454,c_6842,c_7298,c_7964,c_9852,c_12893,c_18773,c_30924,c_31106,c_33544,c_37011,c_43118,c_43893,c_79608,c_79612,c_79643]) ).
tcf(c_99214,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = X0,
inference(superposition,[status(thm)],[c_99139,c_62678]) ).
tcf(c_99325,plain,
inverse(sk_c5) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_72789,c_186,c_776,c_1106,c_1111,c_1112,c_1418,c_1481,c_5454,c_6842,c_7298,c_7964,c_9852,c_12925,c_18773,c_31172,c_33544,c_37011,c_43118,c_43893,c_72251,c_79608,c_79612,c_79643]) ).
tcf(c_99390,plain,
inverse(sk_c10) = sk_c5,
inference(superposition,[status(thm)],[c_99325,c_62841]) ).
tcf(c_99394,plain,
multiply(sk_c10,sk_c5) = identity,
inference(superposition,[status(thm)],[c_99325,c_118]) ).
tcf(c_99439,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c10) = sk_c8 )
| ( multiply(sk_c9,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_1559,c_97559]) ).
tcf(c_99506,plain,
( ( multiply(sk_c9,sk_c10) = sk_c8 )
| ( sk_c10 != sk_c8 ) ),
inference(equality_factoring,[status(thm)],[c_99439]) ).
tcf(c_99742,plain,
! [X0: $i] :
( ( sk_c9 = identity )
| ( multiply(sk_c9,X0) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_67742,c_99214]) ).
tcf(c_99779,plain,
sk_c9 = identity,
inference(superposition,[status(thm)],[c_99742,c_62681]) ).
tcf(c_99793,plain,
~ iPr_def_12,
inference(backward_subsumption_resolution,[status(thm)],[c_6525,c_99779]) ).
tcf(c_99794,plain,
( iPr_def_13
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c8 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_71977,c_99793]) ).
tcf(c_99796,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c9,sk_c9) = multiply(sk_c10,sk_c8) ) ),
inference(light_normalisation,[status(thm)],[c_71442,c_99779]) ).
tcf(c_99808,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c9,sk_c9) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_99796,c_154]) ).
tcf(c_99888,plain,
multiply(sk_c9,sk_c9) = sk_c9,
inference(global_subsumption_just,[status(thm)],[c_99808,c_776,c_18860,c_99779]) ).
tcf(c_99892,plain,
inverse(multiply(inverse(sk_c9),sk_c9)) = sk_c9,
inference(superposition,[status(thm)],[c_99888,c_66375]) ).
tcf(c_99894,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c9,multiply(inverse(sk_c9),X0))) = X0,
inference(superposition,[status(thm)],[c_99888,c_62698]) ).
tcf(c_99896,plain,
multiply(inverse(sk_c9),sk_c9) = sk_c9,
inference(superposition,[status(thm)],[c_99888,c_62701]) ).
tcf(c_99897,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c9,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_99888,c_119]) ).
tcf(c_99905,plain,
inverse(sk_c9) = sk_c9,
inference(light_normalisation,[status(thm)],[c_99892,c_99896]) ).
tcf(c_99907,plain,
! [X0: $i] : multiply(sk_c9,X0) = X0,
inference(light_normalisation,[status(thm)],[c_99894,c_99897,c_99905]) ).
tcf(c_100122,plain,
! [X0: $i] :
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = X0 ) ),
inference(light_normalisation,[status(thm)],[c_1670,c_99907]) ).
tcf(c_100135,plain,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_162,c_100122]) ).
tcf(c_101530,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))) = sk_c9,
inference(light_normalisation,[status(thm)],[c_63244,c_99779]) ).
tcf(c_101573,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,multiply(identity,X1))))) = sk_c9,
inference(superposition,[status(thm)],[c_117,c_101530]) ).
tcf(c_102647,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,multiply(sk_c9,X1))))) = sk_c9,
inference(light_normalisation,[status(thm)],[c_101573,c_99779]) ).
tcf(c_102680,plain,
! [X0: $i] : multiply(X0,inverse(multiply(X0,multiply(sk_c9,identity)))) = sk_c9,
inference(superposition,[status(thm)],[c_117,c_102647]) ).
tcf(c_102995,plain,
! [X0: $i] : multiply(X0,inverse(multiply(X0,multiply(sk_c9,sk_c9)))) = sk_c9,
inference(light_normalisation,[status(thm)],[c_102680,c_99779]) ).
tcf(c_103007,plain,
multiply(identity,inverse(multiply(sk_c9,sk_c9))) = sk_c9,
inference(superposition,[status(thm)],[c_117,c_102995]) ).
tcf(c_103029,plain,
inverse(multiply(identity,multiply(sk_c9,sk_c9))) = sk_c9,
inference(superposition,[status(thm)],[c_102995,c_117]) ).
tcf(c_103152,plain,
multiply(sk_c9,inverse(multiply(sk_c9,sk_c9))) = sk_c9,
inference(light_normalisation,[status(thm)],[c_103007,c_99779]) ).
tcf(c_103167,plain,
multiply(sk_c9,sk_c9) = identity,
inference(superposition,[status(thm)],[c_103152,c_62620]) ).
tcf(c_103189,plain,
inverse(sk_c9) = sk_c9,
inference(light_normalisation,[status(thm)],[c_103029,c_99779,c_103167]) ).
tcf(c_104582,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X1,identity),
inference(superposition,[status(thm)],[c_118,c_64754]) ).
tcf(c_105086,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(X1,sk_c9),
inference(light_normalisation,[status(thm)],[c_104582,c_99779]) ).
tcf(c_105087,plain,
! [X0: $i] : multiply(X0,sk_c9) = X0,
inference(demodulation,[status(thm)],[c_105086,c_62678]) ).
tcf(c_105114,plain,
( ( sk_c10 = sk_c5 )
| ( multiply(sk_c9,sk_c10) = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_124,c_105087]) ).
tcf(c_105124,plain,
( ( sk_c8 = sk_c1 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_100135,c_105087]) ).
tcf(c_105131,plain,
( ( sk_c8 = sk_c3 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_178,c_105087]) ).
tcf(c_105135,plain,
! [X0: $i] :
( ~ iPr_def_13
| ( X0 != sk_c8 )
| ( inverse(X0) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_768,c_105087]) ).
tcf(c_105504,plain,
multiply(sk_c9,sk_c10) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_105114,c_1106,c_1515,c_2497,c_16748,c_47595,c_49450,c_71925,c_84409,c_99325,c_99506,c_105114]) ).
tcf(c_105514,plain,
( iPr_def_13
| ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_99794,c_105504]) ).
tcf(c_105521,plain,
! [X0: $i] : multiply(sk_c9,multiply(sk_c10,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_105504,c_119]) ).
tcf(c_105646,plain,
~ iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_105135,c_186,c_776,c_1106,c_1111,c_1112,c_1180,c_1418,c_1481,c_1515,c_1549,c_2497,c_5454,c_6842,c_7298,c_7444,c_7445,c_7964,c_9852,c_12925,c_16748,c_18773,c_23203,c_24113,c_31172,c_33544,c_37011,c_38023,c_43118,c_43893,c_47114,c_47595,c_49450,c_61932,c_71925,c_72251,c_79608,c_79612,c_79643,c_84409,c_99506,c_99779,c_105114]) ).
tcf(c_105648,plain,
( ( multiply(sk_c10,sk_c8) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c10 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_105514,c_105646]) ).
tcf(c_105714,plain,
multiply(sk_c9,sk_c10) = multiply(sk_c8,sk_c9),
inference(superposition,[status(thm)],[c_105087,c_105521]) ).
tcf(c_110348,plain,
! [X0: $i] :
( ( sk_c10 = sk_c5 )
| ( multiply(sk_c9,multiply(sk_c1,multiply(sk_c2,X0))) = X0 ) ),
inference(demodulation,[status(thm)],[c_65471,c_103189,c_105087]) ).
tcf(c_110361,plain,
( ( sk_c10 = sk_c5 )
| ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c9,multiply(sk_c1,sk_c9)) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_167,c_110348]) ).
tcf(c_110723,plain,
! [X0: $i] :
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c9,multiply(sk_c1,multiply(sk_c2,X0))) = X0 ) ),
inference(demodulation,[status(thm)],[c_65472,c_103189]) ).
tcf(c_110737,plain,
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c9,multiply(sk_c1,sk_c9)) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_162,c_110723]) ).
tcf(c_112803,plain,
( ( multiply(sk_c9,sk_c8) = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( multiply(sk_c9,sk_c8) != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_80034]) ).
tcf(c_112939,plain,
multiply(sk_c9,sk_c8) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_66313,c_186,c_776,c_1106,c_1111,c_1112,c_1180,c_1418,c_1481,c_1515,c_1549,c_2449,c_2497,c_4521,c_5454,c_6842,c_7298,c_7444,c_7445,c_7964,c_9852,c_12925,c_16748,c_18773,c_24113,c_31172,c_33544,c_37011,c_38023,c_43118,c_43893,c_47114,c_47595,c_49450,c_61932,c_71925,c_72251,c_79608,c_79612,c_79643,c_84409,c_92636,c_99506,c_99779,c_105114,c_112803]) ).
tcf(c_112951,plain,
multiply(sk_c10,sk_c8) != sk_c9,
inference(backward_subsumption_resolution,[status(thm)],[c_105648,c_112939]) ).
tcf(c_113104,plain,
sk_c8 = sk_c3,
inference(backward_subsumption_resolution,[status(thm)],[c_105131,c_112951]) ).
tcf(c_113105,plain,
sk_c8 = sk_c1,
inference(backward_subsumption_resolution,[status(thm)],[c_105124,c_112951]) ).
tcf(c_114203,plain,
multiply(sk_c9,multiply(sk_c1,sk_c9)) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_110361,c_186,c_776,c_1106,c_1111,c_1112,c_1180,c_1418,c_1481,c_1515,c_1549,c_2449,c_2497,c_4521,c_5454,c_6842,c_7298,c_7444,c_7445,c_7964,c_9852,c_12925,c_16748,c_18773,c_23203,c_24113,c_31172,c_33544,c_37011,c_38023,c_43118,c_43893,c_47114,c_47595,c_49450,c_61932,c_62806,c_71925,c_72251,c_79608,c_79612,c_79643,c_84409,c_92636,c_99506,c_99793,c_99779,c_105114,c_110737,c_112803]) ).
tcf(c_114205,plain,
sk_c10 = sk_c8,
inference(light_normalisation,[status(thm)],[c_114203,c_105504,c_105714,c_112939,c_113105]) ).
tcf(c_114268,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c7,sk_c10) = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_175,c_114205]) ).
tcf(c_114299,plain,
inverse(sk_c3) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_114268,c_186,c_776,c_1106,c_1111,c_1112,c_1180,c_1418,c_1481,c_1515,c_1549,c_2449,c_2490,c_2497,c_2525,c_4521,c_5454,c_6477,c_6842,c_7298,c_7444,c_7445,c_7964,c_9667,c_9852,c_12925,c_16748,c_18773,c_23203,c_24113,c_26061,c_31172,c_33544,c_37011,c_38023,c_43118,c_43285,c_43893,c_47114,c_47595,c_49450,c_61932,c_71925,c_72251,c_79608,c_79612,c_79643,c_84409,c_92582,c_92636,c_99506,c_99793,c_99779,c_105114,c_112803]) ).
tcf(c_114301,plain,
sk_c10 = sk_c5,
inference(light_normalisation,[status(thm)],[c_114299,c_99390,c_113104,c_114205]) ).
tcf(c_114313,plain,
multiply(sk_c10,sk_c10) = identity,
inference(demodulation,[status(thm)],[c_99394,c_114301]) ).
tcf(c_114505,plain,
sk_c9 != sk_c9,
inference(light_normalisation,[status(thm)],[c_112951,c_99779,c_114205,c_114313]) ).
tcf(c_114506,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_114505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP349-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n026.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Wed Sep 23 14:35:10 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.63 Running first-order theorem proving
% 0.10/0.63 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.64
% 0.14/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.64
% 0.14/0.64 % Detected problem language: tptp
% 0.14/0.65 % Proving...
% 57.61/9.05 % SZS status Started for theBenchmark.p
% 57.61/9.05 % SZS status Unsatisfiable for theBenchmark.p
% 57.61/9.05
% 57.61/9.05 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 57.61/9.05
% 57.61/9.05 % ------ iProver source info
% 57.61/9.05
% 57.61/9.05 % git: date: 2026-07-19 20:42:38 +0200
% 57.61/9.05 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 57.61/9.05 % git: non_committed_changes: false
% 57.61/9.05
% 57.61/9.05 % ------ Parsing...% successful
% 57.61/9.05
% 57.61/9.05
% 57.61/9.05 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 57.61/9.05
% 57.61/9.05 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 57.61/9.05
% 57.61/9.05 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 57.61/9.05
% 57.61/9.05 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 57.61/9.05 % ------ Proving...
% 57.61/9.05 % ------ Problem Properties
% 57.61/9.05
% 57.61/9.05 %
% 57.61/9.05 % clauses 72
% 57.61/9.05 % conjectures 69
% 57.61/9.05 % EPR 0
% 57.61/9.05 % Horn 7
% 57.61/9.05 % unary 3
% 57.61/9.05 % binary 64
% 57.61/9.05 % lits 151
% 57.61/9.05 % lits eq 143
% 57.61/9.05 % fd_pure 0
% 57.61/9.05 % fd_pseudo 0
% 57.61/9.05 % fd_cond 0
% 57.61/9.05 % fd_pseudo_cond 0
% 57.61/9.05 % AC symbols 0
% 57.61/9.05
% 57.61/9.05 % ------ Input Options Time Limit: Unbounded
% 57.61/9.05
% 57.61/9.05
% 57.61/9.05 % ------
% 57.61/9.05 % Current options:
% 57.61/9.05 % ------
% 57.61/9.05
% 57.61/9.05
% 57.61/9.05 %
% 57.61/9.05
% 57.61/9.05 % ------ Proving...
% 57.61/9.05 %
% 57.61/9.05
% 57.61/9.05 % SZS status Unsatisfiable for theBenchmark.p
% 57.61/9.05
% 57.61/9.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 57.61/9.06
% 57.61/9.06
%------------------------------------------------------------------------------