%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP218-1 : 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 : n009.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 01:31:50 PM UTC 2026
% Result : Unsatisfiable 26.43s 5.83s
% Output : CNFRefutation 26.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 54
% Syntax : Number of formulae : 577 ( 162 unt; 13 def)
% Number of atoms : 2028 (1146 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 958 ( 340 ~; 618 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 246 ( 0 sgn 246 !; 0 ?; 206 :)
% 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,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c10 = inverse(sk_c6)
| inverse(sk_c1) = sk_c10 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| inverse(sk_c1) = sk_c10 ),
inference(reorient_equations,[],[f7]) ).
fof(f13,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c10 = inverse(sk_c7)
| inverse(sk_c1) = sk_c10 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c10 = inverse(sk_c6)
| sk_c10 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c10 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f17]) ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = inverse(sk_c7)
| sk_c10 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c10 = inverse(sk_c6)
| sk_c9 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c9 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c9 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c10 = inverse(sk_c7)
| sk_c9 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c10 = inverse(sk_c6)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c10 = inverse(sk_c7)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c10 = inverse(sk_c6)
| sk_c9 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c9 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f47]) ).
fof(f55,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c10 = inverse(sk_c6)
| sk_c9 = multiply(sk_c10,sk_c5) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c9 = multiply(sk_c10,sk_c5) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c9 = multiply(sk_c10,sk_c5) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c9 = multiply(sk_c10,sk_c5) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = inverse(sk_c7)
| sk_c9 = multiply(sk_c10,sk_c5) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c10 = inverse(sk_c6)
| sk_c5 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c5 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c5 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c5 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c10 = inverse(sk_c7)
| sk_c5 = multiply(sk_c4,sk_c10) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c6)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c7)
| sk_c10 = inverse(sk_c4) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( inverse(X7) != sk_c10
| multiply(X7,sk_c10) != X6
| multiply(sk_c10,X6) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != X3
| multiply(sk_c10,X3) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != inverse(X7)
| multiply(X7,sk_c10) != X6
| sk_c9 != multiply(sk_c10,X6)
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != inverse(X5)
| sk_c10 != inverse(X4)
| multiply(X4,sk_c10) != X3
| sk_c9 != multiply(sk_c10,X3)
| sk_c9 != multiply(X2,sk_c10)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c10 ),
inference(reorient_equations,[],[f85]) ).
fof(f87,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( sk_c10 != inverse(X7)
| multiply(X7,sk_c10) != X6
| sk_c9 != multiply(sk_c10,X6)
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != inverse(X5)
| sk_c10 != inverse(X4)
| multiply(X4,sk_c10) != X3
| sk_c9 != multiply(sk_c10,X3)
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c10 ),
inference(equality_resolution,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X6,X7,X4,X5] :
( sk_c10 != inverse(X7)
| multiply(X7,sk_c10) != X6
| sk_c9 != multiply(sk_c10,X6)
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != inverse(X5)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,multiply(X4,sk_c10))
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c10 ),
inference(equality_resolution,[],[f87]) ).
fof(f89,plain,
! [X0,X1,X7,X4,X5] :
( sk_c10 != inverse(X7)
| sk_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != inverse(X5)
| sk_c10 != inverse(X4)
| sk_c9 != multiply(sk_c10,multiply(X4,sk_c10))
| sk_c9 != multiply(inverse(X1),sk_c10)
| sk_c9 != multiply(X1,inverse(X1))
| sk_c10 != multiply(X0,sk_c9)
| inverse(X0) != sk_c10 ),
inference(equality_resolution,[],[f88]) ).
tcf(c_93,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_94,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c6) = sk_c10 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c10 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( inverse(sk_c1) = sk_c10 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c6) = sk_c10 )
| ( multiply(sk_c1,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c10 )
| ( multiply(sk_c1,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c1,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c6) = sk_c10 )
| ( multiply(sk_c2,sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_107,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c9 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_109,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c9 )
| ( multiply(sk_c7,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c2,sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c6) = sk_c10 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c7) = sk_c10 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c6) = sk_c10 )
| ( multiply(sk_c3,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_117,negated_conjecture,
( ( multiply(sk_c3,sk_c10) = sk_c9 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c6) = sk_c10 )
| ( multiply(sk_c10,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_122,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c10 )
| ( multiply(sk_c10,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_123,negated_conjecture,
( ( multiply(sk_c10,sk_c5) = sk_c9 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_124,negated_conjecture,
( ( multiply(sk_c7,sk_c10) = sk_c8 )
| ( multiply(sk_c10,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c10,sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c6) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c5 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_127,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c5 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_128,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c5 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_129,negated_conjecture,
( ( multiply(sk_c4,sk_c10) = sk_c5 )
| ( multiply(sk_c7,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_130,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c5 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c6) = sk_c10 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_132,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_133,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c7,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_135,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c7) = sk_c10 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_136,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X3) != sk_c10 )
| ( inverse(X2) != sk_c10 )
| ( inverse(X1) != sk_c10 )
| ( inverse(X0) != sk_c10 )
| ( multiply(X1,sk_c9) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 )
| ( multiply(inverse(X4),sk_c10) != sk_c9 )
| ( multiply(X4,inverse(X4)) != sk_c9 )
| ( multiply(sk_c10,multiply(X3,sk_c10)) != sk_c9 )
| ( multiply(sk_c10,multiply(X2,sk_c10)) != sk_c9 ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_138,plain,
multiply(inverse(sk_c10),sk_c10) = identity,
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_509,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_136]) ).
tcf(c_510,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c10) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_136]) ).
tcf(c_511,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_136]) ).
tcf(c_512,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_136]) ).
tcf(c_513,definition,
iPr_def_13 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_514,definition,
iPr_def_14 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_515,definition,
iPr_def_15 = multiply(sk_c7,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_516,definition,
iPr_def_16 = multiply(sk_c10,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_517,definition,
iPr_def_17 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_518,definition,
iPr_def_18 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_519,definition,
iPr_def_19 = multiply(sk_c4,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_520,definition,
iPr_def_20 = multiply(sk_c10,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_521,definition,
iPr_def_21 = multiply(sk_c3,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_522,definition,
iPr_def_22 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_523,definition,
iPr_def_23 = multiply(sk_c2,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_524,definition,
iPr_def_24 = multiply(sk_c1,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_525,definition,
iPr_def_25 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_526,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_512]) ).
tcf(c_528,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_511]) ).
tcf(c_529,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c10) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_510]) ).
tcf(c_531,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_509]) ).
tcf(c_532,negated_conjecture,
( ( iPr_def_14 = sk_c10 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_135,c_514,c_513]) ).
tcf(c_533,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_134,c_515]) ).
tcf(c_534,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_14 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_133,c_516]) ).
tcf(c_535,negated_conjecture,
( ( iPr_def_17 = sk_c10 )
| ( iPr_def_14 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_132,c_517]) ).
tcf(c_536,negated_conjecture,
( ( iPr_def_18 = sk_c10 )
| ( iPr_def_14 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_131,c_518]) ).
tcf(c_537,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_130,c_519]) ).
tcf(c_538,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_539,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_128]) ).
tcf(c_540,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_17 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_541,negated_conjecture,
( ( iPr_def_19 = sk_c5 )
| ( iPr_def_18 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_126]) ).
tcf(c_542,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_125,c_520]) ).
tcf(c_543,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_544,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_123]) ).
tcf(c_545,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_17 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_546,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_18 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_121]) ).
tcf(c_550,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_17 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_551,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_18 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_552,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_115,c_522]) ).
tcf(c_553,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_554,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_555,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_17 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_556,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_18 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_557,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_110,c_523]) ).
tcf(c_558,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_559,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_560,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_17 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_561,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_18 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_562,negated_conjecture,
( ( iPr_def_24 = sk_c10 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_105,c_524]) ).
tcf(c_565,negated_conjecture,
( ( iPr_def_24 = sk_c10 )
| ( iPr_def_17 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_566,negated_conjecture,
( ( iPr_def_24 = sk_c10 )
| ( iPr_def_18 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_567,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_13 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_100,c_525]) ).
tcf(c_570,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_17 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_571,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_18 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_572,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_573,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_574,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_575,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_578,plain,
sk_c10 = sk_c10,
inference(instantiation,[status(thm)],[c_572]) ).
tcf(c_846,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_536,c_535]) ).
tcf(c_882,plain,
( ( sk_c10 = iPr_def_14 )
| ( multiply(sk_c6,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_534,c_517]) ).
tcf(c_913,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c10,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_543,c_516]) ).
tcf(c_921,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c6,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_544,c_517]) ).
tcf(c_963,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,sk_c5) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_532,c_520]) ).
tcf(c_964,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(sk_c10,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_541,c_520]) ).
tcf(c_1009,plain,
multiply(iPr_def_25,sk_c1) = identity,
inference(superposition,[status(thm)],[c_525,c_94]) ).
tcf(c_1010,plain,
multiply(iPr_def_18,sk_c6) = identity,
inference(superposition,[status(thm)],[c_518,c_94]) ).
tcf(c_1011,plain,
multiply(iPr_def_13,sk_c7) = identity,
inference(superposition,[status(thm)],[c_513,c_94]) ).
tcf(c_1012,plain,
multiply(iPr_def_22,sk_c2) = identity,
inference(superposition,[status(thm)],[c_522,c_94]) ).
tcf(c_1013,plain,
multiply(iPr_def_14,sk_c4) = identity,
inference(superposition,[status(thm)],[c_514,c_94]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_1082,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_572]) ).
tcf(c_1085,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_1086,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1055]) ).
tcf(c_1096,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_550,c_524]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = inverse(X0) )
| ( sk_c10 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_1122,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1085]) ).
tcf(c_1133,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_551,c_524]) ).
tcf(c_1158,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_1162,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_14 )
| ( iPr_def_14 != inverse(sk_c4) )
| ( inverse(X0) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_1122]) ).
tcf(c_1164,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_18 )
| ( iPr_def_18 != inverse(sk_c6) )
| ( inverse(X0) != inverse(sk_c6) ) ),
inference(instantiation,[status(thm)],[c_1122]) ).
tcf(c_1166,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_22 )
| ( iPr_def_22 != inverse(sk_c2) )
| ( inverse(X0) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_1122]) ).
tcf(c_1168,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1122]) ).
tcf(c_1175,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_552,c_523]) ).
tcf(c_1185,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_553,c_523]) ).
tcf(c_1195,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_554,c_523]) ).
tcf(c_1205,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_555,c_523]) ).
tcf(c_1215,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_556,c_523]) ).
tcf(c_1242,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_557,c_542]) ).
tcf(c_1277,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != iPr_def_13 )
| ( inverse(X0) != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_1055]) ).
tcf(c_1280,plain,
! [X0: $i] :
( ( sk_c10 = inverse(X0) )
| ( sk_c10 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1116]) ).
tcf(c_1351,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_560,c_550]) ).
tcf(c_1356,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_560,c_545]) ).
tcf(c_1379,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != iPr_def_25 )
| ( inverse(X0) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_1085]) ).
tcf(c_1396,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_561,c_551]) ).
tcf(c_1433,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_562,c_519]) ).
tcf(c_1438,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_562,c_532]) ).
tcf(c_1463,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_14 )
| ( inverse(X0) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1158]) ).
tcf(c_1466,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(X0) )
| ( X1 != iPr_def_25 )
| ( inverse(X0) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_1158]) ).
tcf(c_1552,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_22 )
| ( iPr_def_22 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_1580,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_565,c_519]) ).
tcf(c_1625,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_566,c_519]) ).
tcf(c_1664,plain,
( ( inverse(sk_c4) = iPr_def_14 )
| ( iPr_def_14 != inverse(sk_c4) )
| ( inverse(sk_c4) != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_1162]) ).
tcf(c_1665,plain,
inverse(sk_c4) = inverse(sk_c4),
inference(instantiation,[status(thm)],[c_1082]) ).
tcf(c_1683,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_567,c_519]) ).
tcf(c_1688,plain,
( ( iPr_def_14 = iPr_def_25 )
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_567,c_532]) ).
tcf(c_1720,plain,
( ( inverse(sk_c6) = iPr_def_18 )
| ( iPr_def_18 != inverse(sk_c6) )
| ( inverse(sk_c6) != inverse(sk_c6) ) ),
inference(instantiation,[status(thm)],[c_1164]) ).
tcf(c_1721,plain,
inverse(sk_c6) = inverse(sk_c6),
inference(instantiation,[status(thm)],[c_1082]) ).
tcf(c_1734,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c2) )
| ( X0 != sk_c2 ) ),
inference(instantiation,[status(thm)],[c_574]) ).
tcf(c_1735,plain,
( ( inverse(sk_c10) = inverse(sk_c2) )
| ( sk_c10 != sk_c2 ) ),
inference(instantiation,[status(thm)],[c_1734]) ).
tcf(c_1736,plain,
( ( inverse(sk_c2) = iPr_def_22 )
| ( iPr_def_22 != inverse(sk_c2) )
| ( inverse(sk_c2) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_1166]) ).
tcf(c_1737,plain,
inverse(sk_c2) = inverse(sk_c2),
inference(instantiation,[status(thm)],[c_1082]) ).
tcf(c_1813,plain,
! [X0: $i] :
( ( inverse(X0) = inverse(sk_c1) )
| ( X0 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_574]) ).
tcf(c_1814,plain,
( ( inverse(sk_c10) = inverse(sk_c1) )
| ( sk_c10 != sk_c1 ) ),
inference(instantiation,[status(thm)],[c_1813]) ).
tcf(c_1815,plain,
( ( inverse(sk_c1) = iPr_def_25 )
| ( iPr_def_25 != inverse(sk_c1) )
| ( inverse(sk_c1) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1168]) ).
tcf(c_1816,plain,
inverse(sk_c1) = inverse(sk_c1),
inference(instantiation,[status(thm)],[c_1082]) ).
tcf(c_1849,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_570,c_519]) ).
tcf(c_1919,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_571,c_519]) ).
tcf(c_1992,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c9,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_517,c_95]) ).
tcf(c_1993,plain,
! [X0: $i] : multiply(sk_c10,multiply(sk_c8,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_516,c_95]) ).
tcf(c_1994,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c10,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_515,c_95]) ).
tcf(c_1995,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c9,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_524,c_95]) ).
tcf(c_1996,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c3,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_523,c_95]) ).
tcf(c_1997,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c10,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_521,c_95]) ).
tcf(c_1998,plain,
! [X0: $i] : multiply(sk_c10,multiply(sk_c5,X0)) = multiply(iPr_def_20,X0),
inference(superposition,[status(thm)],[c_520,c_95]) ).
tcf(c_1999,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c10,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_519,c_95]) ).
tcf(c_2001,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_94,c_95]) ).
tcf(c_2003,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1009,c_95]) ).
tcf(c_2004,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1010,c_95]) ).
tcf(c_2005,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1011,c_95]) ).
tcf(c_2006,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1012,c_95]) ).
tcf(c_2007,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1013,c_95]) ).
tcf(c_2009,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2007,c_93]) ).
tcf(c_2010,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2006,c_93]) ).
tcf(c_2011,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2005,c_93]) ).
tcf(c_2012,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2004,c_93]) ).
tcf(c_2013,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2003,c_93]) ).
tcf(c_2048,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c4) )
| ( X0 != iPr_def_14 )
| ( inverse(sk_c4) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1463]) ).
tcf(c_2049,plain,
( ( sk_c10 = inverse(sk_c4) )
| ( sk_c10 != iPr_def_14 )
| ( inverse(sk_c4) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1280]) ).
tcf(c_2096,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_25 )
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_846,c_571]) ).
tcf(c_2097,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_25 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_846,c_570]) ).
tcf(c_2104,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_846,c_519]) ).
tcf(c_2524,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_572]) ).
tcf(c_2729,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c2 )
| ( sk_c2 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_2734,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_2742,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_17 )
| ( inverse(sk_c6) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_517,c_531]) ).
tcf(c_2743,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_524,c_531]) ).
tcf(c_2766,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_25 )
| ( sk_c10 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2743,c_525]) ).
tcf(c_2770,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_18 )
| ( sk_c10 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2742,c_518]) ).
tcf(c_3178,plain,
( ~ iPr_def_11
| ( multiply(sk_c6,iPr_def_18) != sk_c9 )
| ( multiply(inverse(sk_c6),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_518,c_529]) ).
tcf(c_3211,plain,
( ( sk_c10 = inverse(sk_c6) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c6) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1116]) ).
tcf(c_3316,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_18 )
| ( iPr_def_18 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_3441,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_13 )
| ( iPr_def_13 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_3677,plain,
( ( iPr_def_20 = iPr_def_23 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1356,c_1242]) ).
tcf(c_3833,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1396,c_1351]) ).
tcf(c_4075,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( iPr_def_13 = iPr_def_18 )
| ( sk_c10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1438,c_536]) ).
tcf(c_4178,plain,
! [X0: $i] :
( ( inverse(sk_c1) = X0 )
| ( X0 != iPr_def_25 )
| ( inverse(sk_c1) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_1379]) ).
tcf(c_4391,plain,
( ( iPr_def_14 = iPr_def_25 )
| ( iPr_def_13 = iPr_def_17 )
| ( sk_c10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1688,c_535]) ).
tcf(c_4737,plain,
multiply(iPr_def_14,iPr_def_19) = sk_c10,
inference(superposition,[status(thm)],[c_519,c_2009]) ).
tcf(c_4885,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c1) )
| ( X0 != iPr_def_25 )
| ( inverse(sk_c1) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_1466]) ).
tcf(c_5037,plain,
! [X0: $i] :
( ( sk_c10 = iPr_def_14 )
| ( multiply(sk_c6,multiply(iPr_def_16,X0)) = multiply(iPr_def_17,X0) ) ),
inference(superposition,[status(thm)],[c_882,c_95]) ).
tcf(c_5041,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_19,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_4737,c_95]) ).
tcf(c_5043,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c3,
inference(superposition,[status(thm)],[c_523,c_2010]) ).
tcf(c_5046,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_23,X0)) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_5043,c_95]) ).
tcf(c_5048,plain,
multiply(iPr_def_13,iPr_def_15) = sk_c10,
inference(superposition,[status(thm)],[c_515,c_2011]) ).
tcf(c_5060,plain,
! [X0: $i] : multiply(iPr_def_13,multiply(iPr_def_15,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_5048,c_95]) ).
tcf(c_5062,plain,
multiply(iPr_def_18,iPr_def_17) = sk_c9,
inference(superposition,[status(thm)],[c_517,c_2012]) ).
tcf(c_5068,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_17,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_5062,c_95]) ).
tcf(c_5070,plain,
multiply(iPr_def_25,iPr_def_24) = sk_c9,
inference(superposition,[status(thm)],[c_524,c_2013]) ).
tcf(c_5155,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c10,multiply(iPr_def_15,X0)) = multiply(iPr_def_16,X0) ) ),
inference(superposition,[status(thm)],[c_913,c_95]) ).
tcf(c_5261,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_16 )
| ( multiply(sk_c6,multiply(iPr_def_20,X0)) = multiply(iPr_def_17,X0) ) ),
inference(superposition,[status(thm)],[c_921,c_95]) ).
tcf(c_5382,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(iPr_def_24,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_5070,c_95]) ).
tcf(c_5427,plain,
( ( sk_c10 = iPr_def_17 )
| ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_540,c_963]) ).
tcf(c_5430,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_537,c_963]) ).
tcf(c_5432,plain,
( ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5430,c_4737]) ).
tcf(c_5439,plain,
( ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_17 )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_5427,c_4737]) ).
tcf(c_5492,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(iPr_def_24,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_566,c_964]) ).
tcf(c_6098,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_5432,c_567]) ).
tcf(c_7292,plain,
( ( sk_c2 = inverse(sk_c4) )
| ( sk_c2 != iPr_def_14 )
| ( inverse(sk_c4) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2048]) ).
tcf(c_7329,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1096,c_2013]) ).
tcf(c_7330,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c10 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7329,c_5070]) ).
tcf(c_7497,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(iPr_def_25,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1133,c_2013]) ).
tcf(c_7498,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c10 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_7497,c_5070]) ).
tcf(c_7851,plain,
( ( inverse(sk_c1) = iPr_def_14 )
| ( iPr_def_14 != iPr_def_25 )
| ( inverse(sk_c1) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_4178]) ).
tcf(c_7853,plain,
( ( sk_c10 = inverse(sk_c1) )
| ( sk_c10 != iPr_def_14 )
| ( inverse(sk_c1) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1280]) ).
tcf(c_7997,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_1205,c_2010]) ).
tcf(c_7998,plain,
( ( sk_c3 = iPr_def_22 )
| ( sk_c10 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7997,c_5043]) ).
tcf(c_8500,plain,
( ( inverse(sk_c6) = sk_c10 )
| ( sk_c10 != iPr_def_13 )
| ( inverse(sk_c6) != iPr_def_13 ) ),
inference(instantiation,[status(thm)],[c_1277]) ).
tcf(c_8700,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1433,c_2009]) ).
tcf(c_8701,plain,
( ( sk_c10 = iPr_def_24 )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_8700,c_4737]) ).
tcf(c_9173,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1580,c_2009]) ).
tcf(c_9174,plain,
( ( sk_c10 = iPr_def_24 )
| ( sk_c10 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_9173,c_4737]) ).
tcf(c_9387,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1625,c_2009]) ).
tcf(c_9388,plain,
( ( sk_c10 = iPr_def_24 )
| ( sk_c10 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_9387,c_4737]) ).
tcf(c_9462,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1683,c_2009]) ).
tcf(c_9463,plain,
( ( sk_c10 = iPr_def_25 )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_9462,c_4737]) ).
tcf(c_9750,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1849,c_2009]) ).
tcf(c_9751,plain,
( ( sk_c10 = iPr_def_25 )
| ( sk_c10 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_9750,c_4737]) ).
tcf(c_9832,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1919,c_2009]) ).
tcf(c_9833,plain,
( ( sk_c10 = iPr_def_25 )
| ( sk_c10 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_9832,c_4737]) ).
tcf(c_10008,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c10) = sk_c9 )
| ( sk_c9 != X1 )
| ( multiply(inverse(X0),sk_c10) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_12170,plain,
multiply(sk_c4,iPr_def_16) = multiply(iPr_def_19,sk_c8),
inference(superposition,[status(thm)],[c_516,c_1999]) ).
tcf(c_12440,plain,
multiply(iPr_def_14,multiply(iPr_def_19,sk_c8)) = iPr_def_16,
inference(superposition,[status(thm)],[c_12170,c_2009]) ).
tcf(c_13237,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_2097,c_2096]) ).
tcf(c_13666,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2001,c_93]) ).
tcf(c_13673,plain,
multiply(inverse(sk_c10),iPr_def_16) = sk_c8,
inference(superposition,[status(thm)],[c_516,c_13666]) ).
tcf(c_13677,plain,
multiply(inverse(sk_c3),iPr_def_21) = sk_c10,
inference(superposition,[status(thm)],[c_521,c_13666]) ).
tcf(c_13678,plain,
multiply(inverse(sk_c10),iPr_def_20) = sk_c5,
inference(superposition,[status(thm)],[c_520,c_13666]) ).
tcf(c_13680,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_93,c_13666]) ).
tcf(c_13681,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_94,c_13666]) ).
tcf(c_13817,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2013,c_13666]) ).
tcf(c_13818,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2012,c_13666]) ).
tcf(c_13819,plain,
! [X0: $i] : multiply(inverse(iPr_def_13),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2011,c_13666]) ).
tcf(c_13820,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2010,c_13666]) ).
tcf(c_13821,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2009,c_13666]) ).
tcf(c_13864,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_13666,c_13666]) ).
tcf(c_15119,plain,
( ~ iPr_def_10
| ( sk_c10 != sk_c9 )
| ( inverse(inverse(identity)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_13680,c_531]) ).
tcf(c_15175,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_13681,c_13864]) ).
tcf(c_15189,plain,
multiply(sk_c10,sk_c8) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_15175,c_1993]) ).
tcf(c_15194,plain,
multiply(sk_c10,sk_c5) = multiply(iPr_def_20,identity),
inference(superposition,[status(thm)],[c_15175,c_1998]) ).
tcf(c_15200,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_15175,c_13680]) ).
tcf(c_15201,plain,
multiply(iPr_def_20,identity) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_15194,c_520]) ).
tcf(c_15206,plain,
multiply(iPr_def_16,identity) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_15189,c_516]) ).
tcf(c_15256,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_15200,c_94]) ).
tcf(c_15570,plain,
multiply(sk_c1,iPr_def_25) = identity,
inference(superposition,[status(thm)],[c_13817,c_94]) ).
tcf(c_15571,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_25)) != sk_c10 )
| ( multiply(sk_c10,multiply(sk_c1,sk_c10)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_13817,c_528]) ).
tcf(c_15574,plain,
multiply(sk_c1,identity) = inverse(iPr_def_25),
inference(superposition,[status(thm)],[c_13817,c_15175]) ).
tcf(c_15701,plain,
inverse(iPr_def_25) = sk_c1,
inference(demodulation,[status(thm)],[c_15574,c_15175]) ).
tcf(c_15703,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_13237,c_15701]) ).
tcf(c_15708,plain,
( ~ iPr_def_11
| ( multiply(iPr_def_25,sk_c1) != sk_c9 )
| ( multiply(inverse(iPr_def_25),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_15701,c_529]) ).
tcf(c_15718,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( multiply(sk_c1,sk_c10) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_15708,c_1009,c_15701]) ).
tcf(c_16121,plain,
multiply(sk_c6,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_13818,c_94]) ).
tcf(c_16124,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_13818,c_13666]) ).
tcf(c_16125,plain,
multiply(sk_c6,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_13818,c_15175]) ).
tcf(c_16228,plain,
inverse(iPr_def_18) = sk_c6,
inference(demodulation,[status(thm)],[c_16125,c_15175]) ).
tcf(c_16247,plain,
multiply(sk_c6,sk_c9) = iPr_def_17,
inference(superposition,[status(thm)],[c_5062,c_16124]) ).
tcf(c_16327,plain,
multiply(sk_c7,iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_13819,c_94]) ).
tcf(c_16330,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_13,X0)) = X0,
inference(superposition,[status(thm)],[c_13819,c_13666]) ).
tcf(c_16565,plain,
multiply(sk_c7,sk_c10) = iPr_def_15,
inference(superposition,[status(thm)],[c_5048,c_16330]) ).
tcf(c_16816,plain,
multiply(sk_c2,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_13820,c_94]) ).
tcf(c_16819,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_13820,c_13666]) ).
tcf(c_16820,plain,
multiply(sk_c2,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_13820,c_15175]) ).
tcf(c_16830,plain,
( ( identity = iPr_def_23 )
| ( sk_c10 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1215,c_16816]) ).
tcf(c_16831,plain,
( ( identity = iPr_def_23 )
| ( sk_c10 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_1205,c_16816]) ).
tcf(c_16832,plain,
( ( identity = iPr_def_23 )
| ( sk_c9 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_1195,c_16816]) ).
tcf(c_16833,plain,
( ( identity = iPr_def_23 )
| ( sk_c8 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_1185,c_16816]) ).
tcf(c_16834,plain,
( ( identity = iPr_def_23 )
| ( sk_c10 = iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_1175,c_16816]) ).
tcf(c_16864,plain,
inverse(iPr_def_22) = sk_c2,
inference(demodulation,[status(thm)],[c_16820,c_15175]) ).
tcf(c_16880,plain,
multiply(sk_c2,sk_c3) = iPr_def_23,
inference(superposition,[status(thm)],[c_5043,c_16819]) ).
tcf(c_17313,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_16831,c_16830]) ).
tcf(c_17598,plain,
( ( identity = iPr_def_23 )
| ( multiply(sk_c6,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_16832,c_517]) ).
tcf(c_17718,plain,
( ( identity = iPr_def_23 )
| ( multiply(sk_c10,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_16833,c_516]) ).
tcf(c_17809,plain,
( ( iPr_def_13 = iPr_def_17 )
| ( identity = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_16834,c_16831]) ).
tcf(c_18037,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = iPr_def_13 )
| ( iPr_def_13 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_3441]) ).
tcf(c_18118,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_23,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_17313,c_93]) ).
tcf(c_18144,plain,
( ( iPr_def_13 = iPr_def_17 )
| ( inverse(iPr_def_23) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_17809,c_15200]) ).
tcf(c_18391,plain,
multiply(sk_c4,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_13821,c_94]) ).
tcf(c_18394,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_13821,c_13666]) ).
tcf(c_18395,plain,
multiply(sk_c4,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_13821,c_15175]) ).
tcf(c_18406,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( identity = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_2104,c_18391]) ).
tcf(c_18420,plain,
inverse(iPr_def_14) = sk_c4,
inference(demodulation,[status(thm)],[c_18395,c_15175]) ).
tcf(c_18463,plain,
( ( iPr_def_19 = iPr_def_23 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_18406,c_17313]) ).
tcf(c_18908,plain,
multiply(sk_c4,sk_c10) = iPr_def_19,
inference(superposition,[status(thm)],[c_4737,c_18394]) ).
tcf(c_19025,plain,
( ( iPr_def_19 = iPr_def_21 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_18463,c_3833]) ).
tcf(c_20862,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( iPr_def_13 = iPr_def_18 )
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_4075,c_566]) ).
tcf(c_22033,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c1 = sk_c4 ) ),
inference(light_normalisation,[status(thm)],[c_15703,c_18420]) ).
tcf(c_22844,plain,
multiply(sk_c10,identity) = multiply(iPr_def_14,iPr_def_19),
inference(superposition,[status(thm)],[c_15175,c_5041]) ).
tcf(c_24113,plain,
( ( iPr_def_14 = iPr_def_25 )
| ( iPr_def_13 = iPr_def_17 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_4391,c_570]) ).
tcf(c_24572,plain,
multiply(sk_c10,identity) = multiply(iPr_def_13,iPr_def_15),
inference(superposition,[status(thm)],[c_15175,c_5060]) ).
tcf(c_24969,plain,
( ( iPr_def_13 = iPr_def_17 )
| ( inverse(iPr_def_20) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_3677,c_18144]) ).
tcf(c_25119,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1086]) ).
tcf(c_25120,plain,
( ( inverse(sk_c10) = sk_c10 )
| ( sk_c10 != inverse(sk_c1) )
| ( inverse(sk_c10) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_25119]) ).
tcf(c_25745,plain,
( ( iPr_def_13 = iPr_def_17 )
| ( multiply(iPr_def_20,iPr_def_20) = identity ) ),
inference(superposition,[status(thm)],[c_24969,c_94]) ).
tcf(c_26091,plain,
( ( iPr_def_22 = inverse(sk_c1) )
| ( iPr_def_22 != iPr_def_25 )
| ( inverse(sk_c1) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_4885]) ).
tcf(c_26094,plain,
( ( sk_c10 = iPr_def_22 )
| ( iPr_def_22 != inverse(sk_c1) )
| ( sk_c10 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1552]) ).
tcf(c_26132,plain,
( ( sk_c1 = inverse(sk_c1) )
| ( sk_c1 != iPr_def_25 )
| ( inverse(sk_c1) != iPr_def_25 ) ),
inference(instantiation,[status(thm)],[c_4885]) ).
tcf(c_27650,plain,
( ( sk_c10 = iPr_def_18 )
| ( iPr_def_18 != inverse(sk_c6) )
| ( sk_c10 != inverse(sk_c6) ) ),
inference(instantiation,[status(thm)],[c_3316]) ).
tcf(c_28090,plain,
! [X0: $i] :
( ( X0 = sk_c1 )
| ( sk_c1 != inverse(sk_c1) )
| ( X0 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_2734]) ).
tcf(c_28091,plain,
( ( sk_c10 = sk_c1 )
| ( sk_c10 != inverse(sk_c1) )
| ( sk_c1 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_28090]) ).
tcf(c_28900,plain,
! [X0: $i] :
( ( sk_c10 = sk_c3 )
| ( sk_c3 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_35132,plain,
! [X0: $i] :
( ( X0 = sk_c2 )
| ( sk_c2 != inverse(sk_c4) )
| ( X0 != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_2729]) ).
tcf(c_35133,plain,
( ( sk_c10 = sk_c2 )
| ( sk_c2 != inverse(sk_c4) )
| ( sk_c10 != inverse(sk_c4) ) ),
inference(instantiation,[status(thm)],[c_35132]) ).
tcf(c_35533,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_536,c_535]) ).
tcf(c_35842,plain,
( ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,sk_c5) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_532,c_520]) ).
tcf(c_35844,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(sk_c10,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_540,c_520]) ).
tcf(c_36186,plain,
multiply(iPr_def_14,sk_c4) = identity,
inference(superposition,[status(thm)],[c_514,c_94]) ).
tcf(c_36670,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_524,c_531]) ).
tcf(c_36692,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_25 )
| ( sk_c10 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_36670,c_525]) ).
tcf(c_37595,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_36186,c_95]) ).
tcf(c_37596,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_37595,c_93]) ).
tcf(c_39926,plain,
multiply(iPr_def_14,iPr_def_19) = sk_c10,
inference(superposition,[status(thm)],[c_519,c_37596]) ).
tcf(c_40372,plain,
( ( sk_c10 = iPr_def_18 )
| ( sk_c10 = iPr_def_13 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_541,c_35842]) ).
tcf(c_40389,plain,
( ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_18 )
| ( sk_c10 = iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_40372,c_39926]) ).
tcf(c_41949,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_17 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_35533,c_35844]) ).
tcf(c_41975,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_41949,c_39926]) ).
tcf(c_43336,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( iPr_def_13 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_20862,c_1438]) ).
tcf(c_44101,plain,
( ( iPr_def_13 = iPr_def_18 )
| ( sk_c10 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_43336,c_5492]) ).
tcf(c_44154,plain,
( ( iPr_def_13 = iPr_def_18 )
| ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_44101,c_4737]) ).
tcf(c_44642,plain,
( ( iPr_def_14 = iPr_def_25 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_24113,c_1688]) ).
tcf(c_45957,plain,
( ( identity = iPr_def_23 )
| ( multiply(iPr_def_13,iPr_def_15) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_16834,c_17718]) ).
tcf(c_46002,plain,
( ( identity = iPr_def_23 )
| ( sk_c10 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_45957,c_5048]) ).
tcf(c_46244,plain,
( ( identity = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_46002,c_519]) ).
tcf(c_46261,plain,
( ( identity = iPr_def_23 )
| ( multiply(iPr_def_19,sk_c8) = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_46244,c_12170]) ).
tcf(c_47840,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(sk_c3,X0) = multiply(iPr_def_22,X0) ) ),
inference(superposition,[status(thm)],[c_18118,c_5046]) ).
tcf(c_47879,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(sk_c3,sk_c10) = multiply(iPr_def_22,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_47840]) ).
tcf(c_55474,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_13864,c_94]) ).
tcf(c_55477,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_13864,c_13666]) ).
tcf(c_55478,plain,
! [X0: $i] : inverse(inverse(X0)) = multiply(X0,identity),
inference(superposition,[status(thm)],[c_13864,c_15175]) ).
tcf(c_55479,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_55478,c_15175]) ).
tcf(c_55498,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( multiply(inverse(X0),sk_c10) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_529,c_55474]) ).
tcf(c_55512,plain,
( ~ iPr_def_11
| ( sk_c9 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_55498]) ).
tcf(c_57240,plain,
( ( sk_c10 = sk_c3 )
| ( sk_c3 != iPr_def_22 )
| ( sk_c10 != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_28900]) ).
tcf(c_59892,plain,
multiply(sk_c9,inverse(iPr_def_17)) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_55474,c_5068]) ).
tcf(c_59898,plain,
multiply(iPr_def_16,inverse(sk_c8)) = multiply(sk_c10,identity),
inference(superposition,[status(thm)],[c_55474,c_1993]) ).
tcf(c_59904,plain,
multiply(sk_c10,inverse(iPr_def_15)) = multiply(iPr_def_13,identity),
inference(superposition,[status(thm)],[c_55474,c_5060]) ).
tcf(c_59905,plain,
multiply(iPr_def_19,inverse(sk_c10)) = multiply(sk_c4,identity),
inference(superposition,[status(thm)],[c_55474,c_1999]) ).
tcf(c_59906,plain,
multiply(iPr_def_21,inverse(sk_c10)) = multiply(sk_c3,identity),
inference(superposition,[status(thm)],[c_55474,c_1997]) ).
tcf(c_59908,plain,
multiply(sk_c9,inverse(iPr_def_24)) = multiply(iPr_def_25,identity),
inference(superposition,[status(thm)],[c_55474,c_5382]) ).
tcf(c_59913,plain,
multiply(sk_c3,inverse(iPr_def_23)) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_55474,c_5046]) ).
tcf(c_59915,plain,
multiply(iPr_def_20,inverse(sk_c5)) = multiply(sk_c10,identity),
inference(superposition,[status(thm)],[c_55474,c_1998]) ).
tcf(c_59918,plain,
multiply(sk_c10,inverse(iPr_def_19)) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_55474,c_5041]) ).
tcf(c_59919,plain,
multiply(iPr_def_25,identity) = inverse(sk_c1),
inference(superposition,[status(thm)],[c_55474,c_2013]) ).
tcf(c_60690,plain,
inverse(sk_c1) = iPr_def_25,
inference(superposition,[status(thm)],[c_15701,c_55479]) ).
tcf(c_61092,plain,
( ( inverse(sk_c6) = iPr_def_13 )
| ( iPr_def_13 != iPr_def_18 )
| ( inverse(sk_c6) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_18037]) ).
tcf(c_62601,plain,
multiply(sk_c10,sk_c8) = iPr_def_16,
inference(superposition,[status(thm)],[c_13673,c_55477]) ).
tcf(c_62602,plain,
multiply(sk_c3,sk_c10) = iPr_def_21,
inference(superposition,[status(thm)],[c_13677,c_55477]) ).
tcf(c_62603,plain,
multiply(sk_c10,sk_c5) = iPr_def_20,
inference(superposition,[status(thm)],[c_13678,c_55477]) ).
tcf(c_62656,plain,
( ~ iPr_def_12
| ( sk_c10 != sk_c9 )
| ( inverse(inverse(sk_c10)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_55477,c_528]) ).
tcf(c_62700,plain,
( ~ iPr_def_12
| ( sk_c10 != sk_c9 ) ),
inference(ground_joinability,[status(thm)],[c_62656,c_55479]) ).
tcf(c_65479,plain,
( ( sk_c10 = iPr_def_18 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_561,c_62700]) ).
tcf(c_65482,plain,
( ( sk_c10 = iPr_def_13 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_557,c_62700]) ).
tcf(c_65487,plain,
( ( sk_c10 = iPr_def_18 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_546,c_62700]) ).
tcf(c_65488,plain,
( ( sk_c10 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_545,c_62700]) ).
tcf(c_65490,plain,
( ( sk_c10 = iPr_def_13 )
| ~ iPr_def_12
| ( sk_c10 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_542,c_62700]) ).
tcf(c_65728,plain,
multiply(sk_c9,inverse(iPr_def_17)) = iPr_def_18,
inference(demodulation,[status(thm)],[c_59892,c_15175]) ).
tcf(c_65766,plain,
multiply(iPr_def_17,inverse(iPr_def_17)) = multiply(sk_c6,iPr_def_18),
inference(superposition,[status(thm)],[c_65728,c_1992]) ).
tcf(c_65767,plain,
multiply(iPr_def_17,inverse(iPr_def_17)) = identity,
inference(light_normalisation,[status(thm)],[c_65766,c_16121]) ).
tcf(c_67642,plain,
( ( sk_c10 = iPr_def_18 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_65479,c_578,c_518,c_1720,c_1721,c_3211,c_5432,c_8500,c_27650,c_44154,c_61092,c_65487]) ).
tcf(c_67648,plain,
( iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_526,c_67642]) ).
tcf(c_67652,plain,
( iPr_def_11
| ( sk_c10 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_67648,c_526,c_2766,c_9388,c_9833,c_67642]) ).
tcf(c_68516,plain,
( ( sk_c10 = iPr_def_13 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_65482,c_5432,c_65490]) ).
tcf(c_68522,plain,
( iPr_def_11
| iPr_def_10
| ( sk_c10 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_526,c_68516]) ).
tcf(c_68526,plain,
( iPr_def_11
| ( sk_c10 = iPr_def_13 ) ),
inference(global_subsumption_just,[status(thm)],[c_68522,c_526,c_2766,c_8701,c_9463,c_68516]) ).
tcf(c_70744,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_17 )
| ~ iPr_def_12
| ( iPr_def_14 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_846,c_65488]) ).
tcf(c_71661,plain,
multiply(iPr_def_16,inverse(sk_c8)) = sk_c10,
inference(demodulation,[status(thm)],[c_59898,c_15175]) ).
tcf(c_71668,plain,
( ( sk_c10 = iPr_def_14 )
| ( multiply(iPr_def_16,inverse(iPr_def_15)) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_533,c_71661]) ).
tcf(c_73797,plain,
multiply(sk_c10,inverse(iPr_def_15)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_59904,c_15175]) ).
tcf(c_73909,plain,
multiply(inverse(sk_c10),iPr_def_13) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_73797,c_13666]) ).
tcf(c_73913,plain,
multiply(iPr_def_15,inverse(iPr_def_15)) = multiply(sk_c7,iPr_def_13),
inference(superposition,[status(thm)],[c_73797,c_1994]) ).
tcf(c_73914,plain,
multiply(iPr_def_15,inverse(iPr_def_15)) = identity,
inference(light_normalisation,[status(thm)],[c_73913,c_16327]) ).
tcf(c_75592,plain,
multiply(iPr_def_19,inverse(sk_c10)) = sk_c4,
inference(demodulation,[status(thm)],[c_59905,c_15175]) ).
tcf(c_79789,plain,
multiply(iPr_def_21,inverse(sk_c10)) = sk_c3,
inference(demodulation,[status(thm)],[c_59906,c_15175]) ).
tcf(c_79792,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( multiply(iPr_def_19,inverse(sk_c10)) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_19025,c_79789]) ).
tcf(c_79886,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(iPr_def_21,inverse(iPr_def_24)) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_566,c_79789]) ).
tcf(c_79887,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(iPr_def_21,inverse(iPr_def_24)) = sk_c3 ) ),
inference(superposition,[status(thm)],[c_565,c_79789]) ).
tcf(c_79988,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c3 = sk_c4 ) ),
inference(light_normalisation,[status(thm)],[c_79792,c_75592]) ).
tcf(c_81479,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c1 = sk_c3 ) ),
inference(superposition,[status(thm)],[c_79988,c_22033]) ).
tcf(c_81504,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(sk_c3) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_79988,c_514]) ).
tcf(c_83561,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_18 )
| ( inverse(iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_556,c_81504]) ).
tcf(c_83591,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c2 = iPr_def_14 )
| ( sk_c10 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_83561,c_16864]) ).
tcf(c_84120,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( inverse(sk_c3) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_81479,c_525]) ).
tcf(c_86515,plain,
( ~ iPr_def_10
| ( sk_c10 != iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_36692,c_2770,c_2766,c_9174,c_9388]) ).
tcf(c_86517,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_86515,c_2770,c_9751,c_9833,c_86515]) ).
tcf(c_86519,plain,
( iPr_def_12
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_526,c_86517]) ).
tcf(c_88879,plain,
multiply(sk_c9,inverse(iPr_def_24)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_59908,c_15175]) ).
tcf(c_88905,plain,
( ( sk_c10 = iPr_def_18 )
| ( multiply(iPr_def_21,inverse(iPr_def_24)) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_551,c_88879]) ).
tcf(c_88906,plain,
( ( sk_c10 = iPr_def_17 )
| ( multiply(iPr_def_21,inverse(iPr_def_24)) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_550,c_88879]) ).
tcf(c_88922,plain,
multiply(iPr_def_24,inverse(iPr_def_24)) = multiply(sk_c1,iPr_def_25),
inference(superposition,[status(thm)],[c_88879,c_1995]) ).
tcf(c_88924,plain,
multiply(iPr_def_24,inverse(iPr_def_24)) = identity,
inference(light_normalisation,[status(thm)],[c_88922,c_15570]) ).
tcf(c_90955,plain,
( ( identity = iPr_def_23 )
| ( multiply(inverse(iPr_def_19),iPr_def_19) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_46261,c_13666]) ).
tcf(c_95533,plain,
multiply(sk_c3,inverse(iPr_def_23)) = iPr_def_22,
inference(demodulation,[status(thm)],[c_59913,c_15175]) ).
tcf(c_95566,plain,
multiply(iPr_def_23,inverse(iPr_def_23)) = multiply(sk_c2,iPr_def_22),
inference(superposition,[status(thm)],[c_95533,c_1996]) ).
tcf(c_95567,plain,
multiply(iPr_def_23,inverse(iPr_def_23)) = identity,
inference(light_normalisation,[status(thm)],[c_95566,c_16816]) ).
tcf(c_96341,plain,
( ( sk_c10 = iPr_def_14 )
| ( multiply(iPr_def_17,inverse(iPr_def_15)) = multiply(sk_c6,sk_c10) ) ),
inference(superposition,[status(thm)],[c_71668,c_5037]) ).
tcf(c_98380,plain,
multiply(iPr_def_20,inverse(sk_c5)) = sk_c10,
inference(demodulation,[status(thm)],[c_59915,c_15175]) ).
tcf(c_98386,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_20,inverse(iPr_def_19)) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_539,c_98380]) ).
tcf(c_98387,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_20,inverse(iPr_def_19)) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_538,c_98380]) ).
tcf(c_102220,plain,
multiply(sk_c10,inverse(iPr_def_19)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_59918,c_15175]) ).
tcf(c_102245,plain,
( ( identity = iPr_def_23 )
| ( multiply(iPr_def_16,inverse(iPr_def_19)) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_46002,c_102220]) ).
tcf(c_102323,plain,
multiply(inverse(sk_c10),iPr_def_14) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_102220,c_13666]) ).
tcf(c_102325,plain,
multiply(iPr_def_19,inverse(iPr_def_19)) = multiply(sk_c4,iPr_def_14),
inference(superposition,[status(thm)],[c_102220,c_1999]) ).
tcf(c_102328,plain,
multiply(iPr_def_19,inverse(iPr_def_19)) = identity,
inference(light_normalisation,[status(thm)],[c_102325,c_18391]) ).
tcf(c_105379,plain,
( ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_40389,c_578,c_518,c_1720,c_1721,c_3211,c_5432,c_8500,c_27650,c_44154,c_61092]) ).
tcf(c_105469,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_105379,c_571]) ).
tcf(c_107507,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_20 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_41975,c_35533]) ).
tcf(c_107510,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_41975,c_570]) ).
tcf(c_110298,plain,
( ( sk_c3 = iPr_def_25 )
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_88905,c_79886]) ).
tcf(c_110406,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_110298,c_556]) ).
tcf(c_110940,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c10) = sk_c9 )
| ( sk_c9 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c10) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_10008]) ).
tcf(c_110941,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c10) = multiply(X1,X2) )
| ( sk_c10 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_575]) ).
tcf(c_110942,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c9 )
| ( sk_c9 != multiply(sk_c10,sk_c10) )
| ( multiply(inverse(sk_c10),sk_c10) != multiply(sk_c10,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_110940]) ).
tcf(c_110943,plain,
( ( multiply(inverse(sk_c10),sk_c10) = multiply(sk_c10,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_110941]) ).
tcf(c_111394,plain,
( ( sk_c3 = iPr_def_25 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_88906,c_79887]) ).
tcf(c_112075,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_17 )
| ( inverse(iPr_def_25) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_111394,c_84120]) ).
tcf(c_112111,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_111394,c_555]) ).
tcf(c_112160,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_17 )
| ( sk_c1 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_112075,c_15701]) ).
tcf(c_112403,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_112111,c_110406]) ).
tcf(c_121761,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c10) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c10) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_121763,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c10) = multiply(X1,X2) )
| ( sk_c10 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_575]) ).
tcf(c_121764,plain,
! [X0: $i] :
( ( sk_c9 = identity )
| ( identity != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_121767,plain,
! [X0: $i,X1: $i] :
( ( sk_c9 = multiply(inverse(X0),sk_c10) )
| ( sk_c9 != X1 )
| ( multiply(inverse(X0),sk_c10) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_121780,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c9 = multiply(X0,X1) )
| ( sk_c9 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_121785,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c10) = multiply(inverse(X1),X2) )
| ( sk_c10 != X2 )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_121763]) ).
tcf(c_121808,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(inverse(X0),sk_c10) )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c10) != X1 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_121821,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = X3 )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_573]) ).
tcf(c_121822,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk_c9 = multiply(X0,X1) )
| ( sk_c9 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_121780]) ).
tcf(c_121835,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c9 = multiply(inverse(X0),sk_c10) )
| ( sk_c9 != multiply(inverse(X1),X2) )
| ( multiply(inverse(X0),sk_c10) != multiply(inverse(X1),X2) ) ),
inference(instantiation,[status(thm)],[c_121767]) ).
tcf(c_121900,plain,
! [X0: $i] :
( ( X0 = multiply(inverse(sk_c10),sk_c10) )
| ( X0 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_121808]) ).
tcf(c_121942,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c10) = multiply(inverse(X1),sk_c10) )
| ( sk_c10 != sk_c10 )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_121785]) ).
tcf(c_121972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(X0,X1) = X4 )
| ( X4 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_121821]) ).
tcf(c_122009,plain,
( ( identity = multiply(inverse(sk_c10),sk_c10) )
| ( identity != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_121900]) ).
tcf(c_122498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( multiply(X0,X1) = multiply(X4,X5) )
| ( multiply(X4,X5) != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_121972]) ).
tcf(c_122509,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = iPr_def_21 )
| ( iPr_def_21 != multiply(sk_c3,sk_c10) )
| ( multiply(X0,X1) != multiply(sk_c3,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_121972]) ).
tcf(c_122657,plain,
( ( sk_c9 = identity )
| ( identity != multiply(inverse(sk_c10),sk_c10) )
| ( sk_c9 != multiply(inverse(sk_c10),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_121764]) ).
tcf(c_122705,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c2),sk_c10) = multiply(iPr_def_22,X0) )
| ( sk_c10 != X0 )
| ( inverse(sk_c2) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_121763]) ).
tcf(c_122706,plain,
( ( multiply(inverse(sk_c2),sk_c10) = multiply(iPr_def_22,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c2) != iPr_def_22 ) ),
inference(instantiation,[status(thm)],[c_122705]) ).
tcf(c_123424,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c10) = multiply(inverse(sk_c2),sk_c10) )
| ( sk_c10 != sk_c10 )
| ( inverse(X0) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_121942]) ).
tcf(c_123425,plain,
( ( multiply(inverse(sk_c10),sk_c10) = multiply(inverse(sk_c2),sk_c10) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c10) != inverse(sk_c2) ) ),
inference(instantiation,[status(thm)],[c_123424]) ).
tcf(c_124165,plain,
( ( sk_c9 = multiply(sk_c3,sk_c10) )
| ( sk_c9 != iPr_def_21 )
| ( multiply(sk_c3,sk_c10) != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_121780]) ).
tcf(c_124322,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(sk_c3,sk_c10) )
| ( X1 != sk_c10 )
| ( X0 != sk_c3 ) ),
inference(instantiation,[status(thm)],[c_575]) ).
tcf(c_124323,plain,
( ( multiply(sk_c10,sk_c10) = multiply(sk_c3,sk_c10) )
| ( sk_c10 != sk_c3 )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_124322]) ).
tcf(c_124791,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(inverse(X0),sk_c10) = multiply(X3,X4) )
| ( multiply(X3,X4) != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c10) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_122498]) ).
tcf(c_124794,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c9 = multiply(inverse(X0),sk_c10) )
| ( sk_c9 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c10) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_121767]) ).
tcf(c_124795,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(inverse(X0),sk_c10) = X3 )
| ( X3 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c10) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_121761]) ).
tcf(c_124798,plain,
( ( sk_c9 = multiply(inverse(sk_c10),sk_c10) )
| ( sk_c9 != multiply(sk_c10,sk_c10) )
| ( multiply(inverse(sk_c10),sk_c10) != multiply(sk_c10,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_124794]) ).
tcf(c_125089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(sk_c2),sk_c10) = multiply(X1,X2) )
| ( multiply(X1,X2) != multiply(iPr_def_22,X0) )
| ( multiply(inverse(sk_c2),sk_c10) != multiply(iPr_def_22,X0) ) ),
inference(instantiation,[status(thm)],[c_124791]) ).
tcf(c_125619,plain,
! [X0: $i,X1: $i] :
( ( sk_c9 = multiply(X0,X1) )
| ( sk_c9 != multiply(sk_c3,sk_c10) )
| ( multiply(X0,X1) != multiply(sk_c3,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_121822]) ).
tcf(c_125620,plain,
( ( sk_c9 = multiply(sk_c10,sk_c10) )
| ( sk_c9 != multiply(sk_c3,sk_c10) )
| ( multiply(sk_c10,sk_c10) != multiply(sk_c3,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_125619]) ).
tcf(c_157325,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c2),sk_c10) = multiply(sk_c3,sk_c10) )
| ( multiply(sk_c3,sk_c10) != multiply(iPr_def_22,X0) )
| ( multiply(inverse(sk_c2),sk_c10) != multiply(iPr_def_22,X0) ) ),
inference(instantiation,[status(thm)],[c_125089]) ).
tcf(c_157326,plain,
( ( multiply(inverse(sk_c2),sk_c10) = iPr_def_21 )
| ( iPr_def_21 != multiply(sk_c3,sk_c10) )
| ( multiply(inverse(sk_c2),sk_c10) != multiply(sk_c3,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_122509]) ).
tcf(c_157327,plain,
( ( multiply(inverse(sk_c2),sk_c10) = multiply(sk_c3,sk_c10) )
| ( multiply(sk_c3,sk_c10) != multiply(iPr_def_22,sk_c10) )
| ( multiply(inverse(sk_c2),sk_c10) != multiply(iPr_def_22,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_157325]) ).
tcf(c_159074,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_16,inverse(iPr_def_15)) = multiply(sk_c10,identity) ) ),
inference(superposition,[status(thm)],[c_55474,c_5155]) ).
tcf(c_176286,plain,
( ( sk_c9 = iPr_def_16 )
| ( multiply(iPr_def_17,inverse(iPr_def_19)) = multiply(sk_c6,sk_c10) ) ),
inference(superposition,[status(thm)],[c_98386,c_5261]) ).
tcf(c_178401,plain,
( ( sk_c10 = iPr_def_17 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_107510,c_138,c_578,c_525,c_846,c_1814,c_1815,c_1816,c_2524,c_7330,c_7851,c_7853,c_7998,c_13237,c_25120,c_26091,c_26094,c_26132,c_28091,c_55512,c_57240,c_62602,c_70744,c_86519,c_107507,c_110942,c_110943,c_112160,c_112403,c_122009,c_122657,c_124165,c_124323,c_124798,c_125620]) ).
tcf(c_178402,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_17 ) ),
inference(renaming,[status(thm)],[c_178401]) ).
tcf(c_178487,plain,
( ( iPr_def_17 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_178402,c_571]) ).
tcf(c_179896,plain,
( ( sk_c9 = multiply(inverse(sk_c2),sk_c10) )
| ( sk_c9 != iPr_def_21 )
| ( multiply(inverse(sk_c2),sk_c10) != iPr_def_21 ) ),
inference(instantiation,[status(thm)],[c_121780]) ).
tcf(c_179924,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c10) = sk_c9 )
| ( sk_c9 != multiply(inverse(sk_c2),sk_c10) )
| ( multiply(inverse(X0),sk_c10) != multiply(inverse(sk_c2),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_124795]) ).
tcf(c_179925,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c9 )
| ( sk_c9 != multiply(inverse(sk_c2),sk_c10) )
| ( multiply(inverse(sk_c10),sk_c10) != multiply(inverse(sk_c2),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_179924]) ).
tcf(c_179945,plain,
! [X0: $i] :
( ( sk_c9 = multiply(inverse(X0),sk_c10) )
| ( sk_c9 != multiply(inverse(sk_c2),sk_c10) )
| ( multiply(inverse(X0),sk_c10) != multiply(inverse(sk_c2),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_121835]) ).
tcf(c_179946,plain,
( ( sk_c9 = multiply(inverse(sk_c10),sk_c10) )
| ( sk_c9 != multiply(inverse(sk_c2),sk_c10) )
| ( multiply(inverse(sk_c10),sk_c10) != multiply(inverse(sk_c2),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_179945]) ).
tcf(c_198587,plain,
( ( sk_c10 = iPr_def_18 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_178487,c_138,c_578,c_514,c_521,c_522,c_846,c_1664,c_1665,c_1735,c_1736,c_1737,c_2049,c_2524,c_7292,c_7498,c_35133,c_47879,c_55512,c_67652,c_83591,c_122009,c_122657,c_122706,c_123425,c_157327,c_157326,c_179896,c_179925,c_179946]) ).
tcf(c_198588,plain,
( ( iPr_def_17 = iPr_def_18 )
| ( sk_c10 = iPr_def_18 ) ),
inference(renaming,[status(thm)],[c_198587]) ).
tcf(c_198646,plain,
iPr_def_17 = iPr_def_18,
inference(superposition,[status(thm)],[c_198588,c_178402]) ).
tcf(c_198759,plain,
( ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_105379,c_198646]) ).
tcf(c_201019,plain,
( ( sk_c10 = iPr_def_20 )
| ( sk_c10 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_5439,c_198759]) ).
tcf(c_201289,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c10 = iPr_def_18 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_201019,c_571]) ).
tcf(c_201290,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c10 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_201019,c_570]) ).
tcf(c_201833,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_201290,c_6098]) ).
tcf(c_203081,plain,
( ( iPr_def_14 = iPr_def_20 )
| ( iPr_def_13 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_201833,c_44642]) ).
tcf(c_203833,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( sk_c10 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_201289,c_105469]) ).
tcf(c_203913,plain,
( ( iPr_def_20 = iPr_def_25 )
| ( iPr_def_17 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_203833,c_201290]) ).
tcf(c_207533,plain,
( ( iPr_def_13 = iPr_def_17 )
| ( multiply(iPr_def_14,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_203081,c_25745]) ).
tcf(c_208163,plain,
iPr_def_17 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_203913,c_198646]) ).
tcf(c_208392,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_17,X0)) = X0,
inference(demodulation,[status(thm)],[c_16124,c_208163]) ).
tcf(c_208393,plain,
inverse(iPr_def_17) = sk_c6,
inference(demodulation,[status(thm)],[c_16228,c_208163]) ).
tcf(c_208451,plain,
multiply(iPr_def_17,iPr_def_17) = sk_c9,
inference(demodulation,[status(thm)],[c_5062,c_208163]) ).
tcf(c_208452,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c6,X0)) = X0,
inference(demodulation,[status(thm)],[c_2012,c_208163]) ).
tcf(c_208468,plain,
inverse(sk_c6) = iPr_def_17,
inference(demodulation,[status(thm)],[c_518,c_208163]) ).
tcf(c_210679,plain,
multiply(sk_c6,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_55474,c_208392]) ).
tcf(c_210747,plain,
multiply(iPr_def_17,identity) = inverse(sk_c6),
inference(superposition,[status(thm)],[c_55474,c_208452]) ).
tcf(c_211161,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_15119,c_2770,c_9751,c_9833,c_86515]) ).
tcf(c_211163,plain,
( iPr_def_12
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_526,c_211161]) ).
tcf(c_212271,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_210747,c_210679,c_208393,c_207533,c_208468,c_208451,c_208163,c_176286,c_159074,c_102328,c_102325,c_102323,c_102245,c_102220,c_98387,c_98380,c_96341,c_95567,c_95566,c_90955,c_88924,c_88922,c_211163,c_73914,c_73913,c_73909,c_73797,c_68526,c_65767,c_65766,c_62700,c_62603,c_62601,c_60690,c_59919,c_59915,c_24572,c_22844,c_18908,c_18420,c_17598,c_16880,c_16832,c_16565,c_16247,c_15718,c_15701,c_15571,c_15206,c_15201,c_13673,c_12440,c_12170,c_3178,c_15256,c_571,c_561,c_559,c_558,c_556,c_546,c_541,c_536,c_534,c_533,c_532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP218-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 14:10:43 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 26.43/5.83 % SZS status Started for theBenchmark.p
% 26.43/5.83 % SZS status Unsatisfiable for theBenchmark.p
% 26.43/5.83
% 26.43/5.83 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.43/5.83
% 26.43/5.83 % ------ iProver source info
% 26.43/5.83
% 26.43/5.83 % git: date: 2026-07-19 20:42:38 +0200
% 26.43/5.83 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.43/5.83 % git: non_committed_changes: false
% 26.43/5.83
% 26.43/5.83 % ------ Parsing...% successful
% 26.43/5.83
% 26.43/5.83
% 26.43/5.83 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.43/5.83
% 26.43/5.83 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 26.43/5.83
% 26.43/5.83 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.43/5.83
% 26.43/5.83 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 26.43/5.83 % ------ Proving...
% 26.43/5.83 % ------ Problem Properties
% 26.43/5.83
% 26.43/5.83 %
% 26.43/5.83 % clauses 60
% 26.43/5.83 % conjectures 44
% 26.43/5.83 % EPR 41
% 26.43/5.83 % Horn 19
% 26.43/5.83 % unary 16
% 26.43/5.83 % binary 40
% 26.43/5.83 % lits 108
% 26.43/5.83 % lits eq 102
% 26.43/5.83 % fd_pure 0
% 26.43/5.83 % fd_pseudo 0
% 26.43/5.83 % fd_cond 0
% 26.43/5.83 % fd_pseudo_cond 0
% 26.43/5.83 % AC symbols 0
% 26.43/5.83
% 26.43/5.83 % ------ Schedule dynamic 5 is on
% 26.43/5.83
% 26.43/5.83 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 26.43/5.83
% 26.43/5.83
% 26.43/5.83 % ------
% 26.43/5.83 % Current options:
% 26.43/5.83 % ------
% 26.43/5.83
% 26.43/5.83
% 26.43/5.83 %
% 26.43/5.83
% 26.43/5.83 % ------ Proving...
% 26.43/5.83 %
% 26.43/5.83
% 26.43/5.83 % SZS status Unsatisfiable for theBenchmark.p
% 26.43/5.83
% 26.43/5.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.43/5.84
% 26.43/5.84
%------------------------------------------------------------------------------