%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP210-1 : 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 : n004.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 01:31:49 PM UTC 2026
% Result : Unsatisfiable 28.86s 10.04s
% Output : CNFRefutation 28.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 41
% Syntax : Number of formulae : 415 ( 58 unt; 0 def)
% Number of atoms : 1019 ( 972 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1068 ( 464 ~; 604 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 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 : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 278 ( 0 sgn 278 !; 0 ?; 238 :)
% 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(f9,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c9 = multiply(sk_c5,sk_c6)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c9 = multiply(sk_c6,sk_c10)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c10 = inverse(sk_c7)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = inverse(sk_c4)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = multiply(sk_c5,sk_c6)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c5)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c9 = multiply(sk_c6,sk_c10)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c10 = inverse(sk_c7)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c9 = multiply(sk_c5,sk_c6)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = inverse(sk_c5)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = multiply(sk_c6,sk_c10)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f45]) ).
fof(f49,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c10 = inverse(sk_c7)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c9 = multiply(sk_c5,sk_c6)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c5)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f59]) ).
fof(f63,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c10 = inverse(sk_c7)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c10 = multiply(sk_c4,sk_c9)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f74,plain,
( sk_c9 = multiply(sk_c5,sk_c6)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f73]) ).
fof(f75,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c6 = inverse(sk_c5)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c9 = multiply(sk_c6,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c9 = multiply(sk_c10,sk_c8)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c8 = multiply(sk_c7,sk_c10)
| sk_c10 = multiply(sk_c3,sk_c9) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c10 = inverse(sk_c7)
| sk_c10 = multiply(sk_c3,sk_c9) ),
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_c10) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != 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_c9 != multiply(X5,sk_c10)
| inverse(X4) != X5
| sk_c9 != multiply(X4,X5)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(X1,sk_c9)
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(reorient_equations,[],[f85]) ).
fof(f87,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( sk_c10 != inverse(X7)
| multiply(X7,sk_c10) != X6
| sk_c9 != multiply(sk_c10,X6)
| sk_c9 != multiply(X5,sk_c10)
| inverse(X4) != X5
| sk_c9 != multiply(X4,X5)
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f86]) ).
fof(f88,plain,
! [X2,X3,X0,X6,X7,X4] :
( sk_c10 != inverse(X7)
| multiply(X7,sk_c10) != X6
| sk_c9 != multiply(sk_c10,X6)
| sk_c9 != multiply(inverse(X4),sk_c10)
| sk_c9 != multiply(X4,inverse(X4))
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f87]) ).
fof(f89,plain,
! [X2,X3,X0,X7,X4] :
( sk_c10 != inverse(X7)
| sk_c9 != multiply(sk_c10,multiply(X7,sk_c10))
| sk_c9 != multiply(inverse(X4),sk_c10)
| sk_c9 != multiply(X4,inverse(X4))
| sk_c10 != multiply(X3,sk_c9)
| sk_c10 != inverse(X3)
| sk_c10 != multiply(X2,sk_c9)
| sk_c10 != inverse(X2)
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) ),
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_98,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c6,sk_c10) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c7,sk_c10) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c5,sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c6,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c7,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c6,sk_c10) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_118,negated_conjecture,
( ( multiply(sk_c7,sk_c10) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c4,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c5,sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_126,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c7,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c7) = sk_c10 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_128,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_129,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( multiply(sk_c4,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_130,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( multiply(sk_c5,sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_132,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( multiply(sk_c6,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_133,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_134,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( multiply(sk_c7,sk_c10) = sk_c8 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_135,negated_conjecture,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c3,sk_c9) = 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 )
| ( multiply(X2,sk_c9) != sk_c10 )
| ( multiply(X1,sk_c9) != sk_c10 )
| ( multiply(inverse(X4),sk_c10) != sk_c9 )
| ( multiply(inverse(X0),sk_c9) != sk_c10 )
| ( multiply(X4,inverse(X4)) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c10 )
| ( multiply(sk_c10,multiply(X3,sk_c10)) != sk_c9 ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_137,plain,
multiply(identity,sk_c10) = sk_c10,
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_138,plain,
multiply(inverse(sk_c10),sk_c10) = identity,
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_331,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),sk_c10) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_136]) ).
tcf(c_332,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_136]) ).
tcf(c_333,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c9) != sk_c10 )
| ( multiply(X0,inverse(X0)) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_136]) ).
tcf(c_334,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_136]) ).
tcf(c_335,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_136]) ).
tcf(c_336,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_337,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_342,plain,
sk_c10 = sk_c10,
inference(instantiation,[status(thm)],[c_336]) ).
tcf(c_563,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_337]) ).
tcf(c_564,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c9 )
| ( sk_c9 != sk_c10 )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_563]) ).
tcf(c_565,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_566,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = sk_c10 )
| ( sk_c10 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_569,plain,
( ~ iPr_def_11
| ( inverse(sk_c4) != sk_c10 )
| ( multiply(sk_c4,sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_332]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_593,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c10 )
| ( sk_c10 != inverse(X0) )
| ( inverse(X0) != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_565]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_597,plain,
( ( multiply(inverse(sk_c9),sk_c9) = sk_c10 )
| ( sk_c10 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_566]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_566]) ).
tcf(c_606,plain,
( ~ iPr_def_12
| ( multiply(sk_c9,inverse(sk_c9)) != sk_c10 )
| ( multiply(inverse(sk_c9),sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_333]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = inverse(X0) )
| ( sk_c10 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_611,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = multiply(inverse(X0),sk_c9) )
| ( sk_c10 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_614,plain,
! [X0: $i] :
( ( inverse(sk_c5) = X0 )
| ( X0 != sk_c6 )
| ( inverse(sk_c5) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_595]) ).
tcf(c_621,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c9),sk_c9) = X0 )
| ( X0 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(inverse(X0),sk_c9) = X3 )
| ( X3 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_600]) ).
tcf(c_625,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != sk_c9 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_589]) ).
tcf(c_628,plain,
! [X0: $i] :
( ( sk_c10 = identity )
| ( identity != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c10 = multiply(X0,X1) )
| ( sk_c10 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_631,plain,
( ( sk_c10 = multiply(sk_c10,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( multiply(sk_c10,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_634,plain,
! [X0: $i] :
( ( multiply(sk_c9,inverse(sk_c9)) = sk_c10 )
| ( sk_c10 != X0 )
| ( multiply(sk_c9,inverse(sk_c9)) != X0 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_640,plain,
( ( inverse(sk_c5) = multiply(identity,sk_c6) )
| ( inverse(sk_c5) != sk_c6 )
| ( multiply(identity,sk_c6) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_614]) ).
tcf(c_647,plain,
multiply(inverse(sk_c9),sk_c9) = identity,
inference(instantiation,[status(thm)],[c_94]) ).
tcf(c_657,plain,
( ( sk_c10 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c10 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_611]) ).
tcf(c_660,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c10 = multiply(inverse(X0),sk_c9) )
| ( sk_c10 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_611]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_677,plain,
( ( sk_c10 = multiply(sk_c6,sk_c10) )
| ( sk_c10 != sk_c9 )
| ( multiply(sk_c6,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_680,plain,
! [X0: $i] :
( ( sk_c10 = multiply(identity,X0) )
| ( sk_c10 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_681,plain,
( ( sk_c10 = multiply(identity,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = X3 )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk_c10 = multiply(X0,X1) )
| ( sk_c10 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(inverse(X0),sk_c9) )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c9) != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_706,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(X0,X1) )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_708,plain,
( ( sk_c10 = multiply(sk_c1,sk_c2) )
| ( sk_c10 != sk_c10 )
| ( multiply(sk_c1,sk_c2) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_726,plain,
sk_c9 = sk_c9,
inference(instantiation,[status(thm)],[c_336]) ).
tcf(c_734,plain,
( ( sk_c10 = multiply(sk_c2,sk_c9) )
| ( sk_c10 != sk_c10 )
| ( multiply(sk_c2,sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_736,plain,
( ( sk_c10 = inverse(sk_c3) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c3) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_608]) ).
tcf(c_754,plain,
multiply(identity,sk_c6) = sk_c6,
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_812,plain,
! [X0: $i] :
( ( sk_c10 = sk_c9 )
| ( sk_c9 != X0 )
| ( sk_c10 != X0 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_828,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c9,inverse(sk_c9)) = sk_c10 )
| ( sk_c10 != multiply(X0,X1) )
| ( multiply(sk_c9,inverse(sk_c9)) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_634]) ).
tcf(c_850,plain,
! [X0: $i] :
( ( multiply(inverse(X0),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(sk_c2,sk_c9) )
| ( multiply(inverse(X0),sk_c9) != multiply(sk_c2,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_601]) ).
tcf(c_853,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( sk_c10 != inverse(sk_c3) )
| ( inverse(sk_c3) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_593]) ).
tcf(c_876,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_674]) ).
tcf(c_877,plain,
( ( identity = sk_c10 )
| ( identity != identity )
| ( sk_c10 != identity ) ),
inference(instantiation,[status(thm)],[c_876]) ).
tcf(c_889,plain,
( ( multiply(inverse(sk_c9),sk_c9) = multiply(identity,identity) )
| ( multiply(identity,identity) != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_621]) ).
tcf(c_893,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_932,plain,
! [X0: $i] :
( ( multiply(sk_c5,sk_c6) = X0 )
| ( X0 != sk_c9 )
| ( multiply(sk_c5,sk_c6) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_933,plain,
( ( multiply(sk_c5,sk_c6) = sk_c10 )
| ( sk_c10 != sk_c9 )
| ( multiply(sk_c5,sk_c6) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_932]) ).
tcf(c_941,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c9) = X0 )
| ( X0 != sk_c10 )
| ( multiply(sk_c3,sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_943,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X0) = X1 )
| ( X1 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_951,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_687]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(identity,X1) )
| ( multiply(inverse(X0),sk_c9) != multiply(identity,X1) ) ),
inference(instantiation,[status(thm)],[c_601]) ).
tcf(c_965,plain,
( ( multiply(inverse(sk_c10),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( multiply(inverse(sk_c10),sk_c9) != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_964]) ).
tcf(c_971,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(X1,X2) )
| ( sk_c9 != X2 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_1013,plain,
! [X0: $i] :
( ( X0 = multiply(inverse(sk_c9),sk_c9) )
| ( X0 != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_698]) ).
tcf(c_1039,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c10 = multiply(X0,X1) )
| ( sk_c10 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_688]) ).
tcf(c_1040,plain,
( ( sk_c10 = multiply(sk_c10,sk_c10) )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( multiply(sk_c10,sk_c10) != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_1039]) ).
tcf(c_1143,plain,
( ( sk_c9 = multiply(sk_c10,sk_c8) )
| ( sk_c9 != sk_c9 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_1148,plain,
( ( sk_c9 = multiply(identity,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_1150,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_1217,plain,
inverse(sk_c3) = inverse(sk_c3),
inference(instantiation,[status(thm)],[c_336]) ).
tcf(c_1274,plain,
multiply(identity,identity) = identity,
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1307,plain,
multiply(identity,sk_c9) = sk_c9,
inference(instantiation,[status(thm)],[c_93]) ).
tcf(c_1337,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(sk_c1,sk_c2) )
| ( X1 != X0 )
| ( multiply(sk_c1,sk_c2) != X0 ) ),
inference(instantiation,[status(thm)],[c_706]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c1,sk_c2) = X1 )
| ( X1 != X0 )
| ( multiply(sk_c1,sk_c2) != X0 ) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_1498,plain,
( ( identity = multiply(inverse(sk_c9),sk_c9) )
| ( identity != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_1605,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c3,sk_c9) = multiply(X0,X1) )
| ( multiply(sk_c3,sk_c9) != sk_c10 )
| ( multiply(X0,X1) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_941]) ).
tcf(c_1609,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c3,sk_c9) = X1 )
| ( X1 != X0 )
| ( multiply(sk_c3,sk_c9) != X0 ) ),
inference(instantiation,[status(thm)],[c_687]) ).
tcf(c_1872,plain,
( ( inverse(sk_c3) = sk_c10 )
| ~ iPr_def_11
| ( inverse(sk_c4) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_332,c_121]) ).
tcf(c_1878,plain,
( ( inverse(sk_c4) = sk_c10 )
| ~ iPr_def_11
| ( inverse(sk_c3) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_332,c_128]) ).
tcf(c_1881,plain,
( ( multiply(sk_c4,sk_c9) = sk_c10 )
| ~ iPr_def_11
| ( inverse(sk_c3) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_332,c_129]) ).
tcf(c_2242,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != multiply(sk_c1,sk_c2) )
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_2243,plain,
( ( sk_c10 = identity )
| ( identity != multiply(sk_c1,sk_c2) )
| ( sk_c10 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_2242]) ).
tcf(c_2246,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c9) = multiply(X1,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_971]) ).
tcf(c_2327,plain,
! [X0: $i] :
( ( multiply(identity,X0) = sk_c10 )
| ( sk_c10 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_943]) ).
tcf(c_2339,plain,
! [X0: $i] :
( ( multiply(identity,X0) = sk_c9 )
| ( sk_c9 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_943]) ).
tcf(c_2340,plain,
( ( multiply(identity,sk_c10) = sk_c9 )
| ( sk_c9 != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_2339]) ).
tcf(c_2341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(identity,X0) )
| ( X2 != X1 )
| ( multiply(identity,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_706]) ).
tcf(c_2343,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = multiply(identity,X0) )
| ( sk_c10 != X1 )
| ( multiply(identity,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_2380,plain,
( ( inverse(sk_c3) = sk_c10 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_1872,c_120,c_569,c_1872,c_1881,c_1878]) ).
tcf(c_2382,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_2380,c_569,c_1881,c_1878,c_2380]) ).
tcf(c_2399,plain,
! [X0: $i] :
( ( inverse(sk_c4) = X0 )
| ( inverse(sk_c1) = sk_c2 )
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_337,c_104]) ).
tcf(c_2417,plain,
! [X0: $i] :
( ( multiply(sk_c6,sk_c10) = X0 )
| ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( X0 != sk_c9 ) ),
inference(resolution,[status(thm)],[c_337,c_116]) ).
tcf(c_2453,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X1) = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_337,c_93]) ).
tcf(c_2454,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X1),X1) = X0 )
| ( X0 != identity ) ),
inference(resolution,[status(thm)],[c_337,c_94]) ).
tcf(c_2458,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_337,c_336]) ).
tcf(c_2468,plain,
( ( sk_c10 = multiply(inverse(sk_c9),sk_c9) )
| ( sk_c10 != multiply(identity,identity) )
| ( multiply(inverse(sk_c9),sk_c9) != multiply(identity,identity) ) ),
inference(instantiation,[status(thm)],[c_660]) ).
tcf(c_2477,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( X0 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_589]) ).
tcf(c_2480,plain,
( ( sk_c9 = sk_c10 )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( sk_c10 != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_2477]) ).
tcf(c_2520,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = multiply(identity,X2) )
| ( X1 != X2 )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_2521,plain,
( ( multiply(sk_c10,sk_c10) = multiply(identity,sk_c10) )
| ( sk_c10 != identity )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_2520]) ).
tcf(c_2623,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_336]) ).
tcf(c_2636,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != multiply(sk_c1,sk_c2) )
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_1150]) ).
tcf(c_2780,plain,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ~ iPr_def_13
| ( inverse(sk_c7) != sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_134,c_334]) ).
tcf(c_2781,plain,
( ( multiply(sk_c2,sk_c9) = sk_c10 )
| ~ iPr_def_13
| ( inverse(sk_c7) != sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_118,c_334]) ).
tcf(c_2782,plain,
( ( multiply(sk_c1,sk_c2) = sk_c10 )
| ~ iPr_def_13
| ( inverse(sk_c7) != sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_102,c_334]) ).
tcf(c_2783,plain,
( ( inverse(sk_c3) = sk_c10 )
| ~ iPr_def_13
| ( inverse(sk_c7) != sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_126,c_334]) ).
tcf(c_2784,plain,
( ( inverse(sk_c1) = sk_c2 )
| ~ iPr_def_13
| ( inverse(sk_c7) != sk_c10 )
| ( multiply(sk_c10,sk_c8) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_110,c_334]) ).
tcf(c_3496,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_335,c_335,c_2382]) ).
tcf(c_3530,plain,
! [X0: $i,X1: $i] : multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_93,c_95]) ).
tcf(c_3531,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_94,c_95]) ).
tcf(c_3592,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(identity,sk_c10) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_121,c_3530]) ).
tcf(c_3620,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(identity,multiply(X0,multiply(X1,X2))) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_95,c_3530]) ).
tcf(c_3711,plain,
multiply(identity,sk_c10) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_3592,c_137]) ).
tcf(c_3713,plain,
multiply(inverse(identity),sk_c10) = sk_c10,
inference(superposition,[status(thm)],[c_3711,c_3531]) ).
tcf(c_3885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(X0,X2) = X4 )
| ( X4 != multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_338,c_337]) ).
tcf(c_3892,plain,
( ( sk_c10 = multiply(sk_c1,sk_c2) )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(resolution,[status(thm)],[c_2458,c_99]) ).
tcf(c_3893,plain,
( ( sk_c10 = multiply(sk_c1,sk_c2) )
| ( inverse(sk_c7) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2458,c_103]) ).
tcf(c_3910,plain,
( ( sk_c9 = multiply(sk_c10,sk_c8) )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2458,c_101]) ).
tcf(c_3918,plain,
( ( sk_c10 = multiply(sk_c2,sk_c9) )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(resolution,[status(thm)],[c_2458,c_115]) ).
tcf(c_3919,plain,
( ( sk_c10 = multiply(sk_c2,sk_c9) )
| ( inverse(sk_c7) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2458,c_119]) ).
tcf(c_3920,plain,
( ( sk_c10 = inverse(sk_c3) )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2458,c_120]) ).
tcf(c_3922,plain,
( ( sk_c10 = inverse(sk_c3) )
| ( inverse(sk_c7) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2458,c_127]) ).
tcf(c_3931,plain,
! [X0: $i] : X0 = multiply(identity,X0),
inference(resolution,[status(thm)],[c_2458,c_93]) ).
tcf(c_3933,plain,
! [X0: $i] : identity = multiply(inverse(X0),X0),
inference(resolution,[status(thm)],[c_2458,c_94]) ).
tcf(c_3983,plain,
( ( sk_c10 = sk_c9 )
| ( sk_c9 != multiply(sk_c10,sk_c8) )
| ( sk_c10 != multiply(sk_c10,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_812]) ).
tcf(c_3985,plain,
! [X0: $i] :
( ( sk_c9 = X0 )
| ( sk_c9 != multiply(sk_c10,sk_c8) )
| ( X0 != multiply(sk_c10,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_589]) ).
tcf(c_3988,plain,
( ( sk_c9 = sk_c10 )
| ( sk_c9 != multiply(sk_c10,sk_c8) )
| ( sk_c10 != multiply(sk_c10,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_3985]) ).
tcf(c_4310,plain,
! [X0: $i] :
( ( identity = multiply(sk_c1,sk_c2) )
| ( identity != X0 )
| ( multiply(sk_c1,sk_c2) != X0 ) ),
inference(instantiation,[status(thm)],[c_1337]) ).
tcf(c_4720,plain,
( ( sk_c10 = identity )
| ( identity != multiply(inverse(sk_c9),sk_c9) )
| ( sk_c10 != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_628]) ).
tcf(c_4853,plain,
! [X0: $i] : multiply(identity,multiply(X0,sk_c10)) = multiply(X0,sk_c10),
inference(superposition,[status(thm)],[c_3711,c_3620]) ).
tcf(c_5419,plain,
( ( sk_c9 = multiply(sk_c1,sk_c2) )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( multiply(sk_c1,sk_c2) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_2477]) ).
tcf(c_5434,plain,
! [X0: $i,X1: $i] :
( ( sk_c9 = multiply(X0,X1) )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( multiply(X0,X1) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_2477]) ).
tcf(c_5435,plain,
( ( sk_c9 = multiply(sk_c10,sk_c10) )
| ( sk_c9 != multiply(identity,sk_c9) )
| ( multiply(sk_c10,sk_c10) != multiply(identity,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_5434]) ).
tcf(c_6182,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(identity,X1) = X2 )
| ( X2 != X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_2453,c_337]) ).
tcf(c_6345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X2),X2) = X0 )
| ( X1 != identity )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_2454,c_337]) ).
tcf(c_6896,plain,
! [X0: $i] :
( ( sk_c10 = inverse(sk_c3) )
| ( inverse(sk_c4) = X0 )
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_3920,c_337]) ).
tcf(c_7175,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c3,sk_c9) = X1 )
| ( X1 != multiply(identity,X0) )
| ( multiply(sk_c3,sk_c9) != multiply(identity,X0) ) ),
inference(instantiation,[status(thm)],[c_1609]) ).
tcf(c_7176,plain,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( multiply(sk_c3,sk_c9) != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_7175]) ).
tcf(c_7301,plain,
! [X0: $i] :
( ( sk_c10 = X0 )
| ( inverse(sk_c5) = sk_c6 )
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(resolution,[status(thm)],[c_3892,c_337]) ).
tcf(c_7325,plain,
! [X0: $i] :
( ( sk_c10 = X0 )
| ( inverse(sk_c7) = sk_c10 )
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(resolution,[status(thm)],[c_3893,c_337]) ).
tcf(c_7757,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c4) )
| ( inverse(sk_c1) = sk_c2 )
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_2399,c_2458]) ).
tcf(c_8155,plain,
( ( multiply(inverse(sk_c1),sk_c9) = multiply(sk_c2,sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c1) != sk_c2 ) ),
inference(instantiation,[status(thm)],[c_2246]) ).
tcf(c_8162,plain,
( ( multiply(inverse(sk_c5),sk_c9) = multiply(multiply(identity,sk_c6),sk_c9) )
| ( sk_c9 != sk_c9 )
| ( inverse(sk_c5) != multiply(identity,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_2246]) ).
tcf(c_8349,plain,
multiply(identity,sk_c10) = sk_c10,
inference(superposition,[status(thm)],[c_3713,c_4853]) ).
tcf(c_8385,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_94,c_95]) ).
tcf(c_8550,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(inverse(sk_c4),sk_c10) = multiply(identity,sk_c9) ) ),
inference(superposition,[status(thm)],[c_121,c_8385]) ).
tcf(c_8551,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(inverse(sk_c4),sk_c10) = multiply(identity,sk_c9) ) ),
inference(superposition,[status(thm)],[c_105,c_8385]) ).
tcf(c_8567,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(inverse(sk_c7),sk_c8) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_126,c_8385]) ).
tcf(c_8568,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(inverse(sk_c7),sk_c8) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_110,c_8385]) ).
tcf(c_8913,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c10,sk_c8) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_111,c_8568]) ).
tcf(c_8927,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c10,sk_c8) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_8913,c_93]) ).
tcf(c_8943,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c10,sk_c10) = multiply(identity,sk_c9) ) ),
inference(superposition,[status(thm)],[c_120,c_8550]) ).
tcf(c_8962,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c10,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_8943,c_93]) ).
tcf(c_9010,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c10,sk_c10) = multiply(identity,sk_c9) ) ),
inference(superposition,[status(thm)],[c_104,c_8551]) ).
tcf(c_9144,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c10,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_9010,c_93]) ).
tcf(c_9203,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,sk_c9) )
| ( X1 != X0 )
| ( multiply(identity,sk_c9) != X0 ) ),
inference(instantiation,[status(thm)],[c_2341]) ).
tcf(c_9932,plain,
! [X0: $i] :
( ( sk_c10 = multiply(identity,identity) )
| ( sk_c10 != X0 )
| ( multiply(identity,identity) != X0 ) ),
inference(instantiation,[status(thm)],[c_2343]) ).
tcf(c_10112,plain,
( ( sk_c10 = sk_c9 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_8927,c_109]) ).
tcf(c_10692,plain,
( ( identity = sk_c9 )
| ( identity != multiply(sk_c1,sk_c2) )
| ( sk_c9 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_2636]) ).
tcf(c_10730,plain,
! [X0: $i] :
( ( sk_c9 = identity )
| ( identity != X0 )
| ( sk_c9 != X0 ) ),
inference(instantiation,[status(thm)],[c_589]) ).
tcf(c_10731,plain,
( ( sk_c9 = identity )
| ( identity != sk_c10 )
| ( sk_c9 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_10730]) ).
tcf(c_10764,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(inverse(sk_c10),sk_c9) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_8962,c_8385]) ).
tcf(c_10847,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c9 )
| ( sk_c9 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != identity ) ),
inference(instantiation,[status(thm)],[c_563]) ).
tcf(c_10854,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(inverse(sk_c10),sk_c9) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_9144,c_8385]) ).
tcf(c_10903,plain,
( ( sk_c9 = multiply(sk_c10,sk_c8) )
| ( sk_c10 = multiply(sk_c1,sk_c2) ) ),
inference(resolution,[status(thm)],[c_3910,c_2458]) ).
tcf(c_11626,plain,
( ( sk_c9 = identity )
| ( identity != sk_c9 )
| ( sk_c9 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_11838,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c2) = X0 )
| ( X0 != sk_c9 )
| ( multiply(sk_c1,sk_c2) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1338]) ).
tcf(c_12610,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c10,sk_c8) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_127,c_8567]) ).
tcf(c_12661,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c10,sk_c8) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_12610,c_93]) ).
tcf(c_12698,plain,
( ( identity = multiply(sk_c1,sk_c2) )
| ( identity != identity )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_4310]) ).
tcf(c_13210,plain,
( ( sk_c10 = sk_c9 )
| ( inverse(sk_c3) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_12661,c_125]) ).
tcf(c_18906,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c6,sk_c10) )
| ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( X0 != sk_c9 ) ),
inference(resolution,[status(thm)],[c_2417,c_2458]) ).
tcf(c_18907,plain,
( ( sk_c10 = multiply(sk_c6,sk_c10) )
| ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( sk_c10 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_18906]) ).
tcf(c_19629,plain,
( ( multiply(inverse(sk_c1),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(sk_c2,sk_c9) )
| ( multiply(inverse(sk_c1),sk_c9) != multiply(sk_c2,sk_c9) ) ),
inference(instantiation,[status(thm)],[c_850]) ).
tcf(c_20089,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c9) = multiply(identity,X0) )
| ( multiply(sk_c3,sk_c9) != sk_c10 )
| ( multiply(identity,X0) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_1605]) ).
tcf(c_20846,plain,
! [X0: $i] :
( ( multiply(identity,sk_c9) = X0 )
| ( X0 != sk_c9 )
| ( multiply(identity,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_943]) ).
tcf(c_20873,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(identity,sk_c9) )
| ( X2 != multiply(X0,X1) )
| ( multiply(identity,sk_c9) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_9203]) ).
tcf(c_20874,plain,
( ( sk_c10 = multiply(identity,sk_c9) )
| ( sk_c10 != multiply(sk_c10,sk_c10) )
| ( multiply(identity,sk_c9) != multiply(sk_c10,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_20873]) ).
tcf(c_26537,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(identity,sk_c9) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_108,c_4853]) ).
tcf(c_26540,plain,
multiply(identity,sk_c9) = sk_c9,
inference(global_subsumption_just,[status(thm)],[c_26537,c_1307]) ).
tcf(c_26571,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_94,c_95]) ).
tcf(c_26752,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_94,c_26571]) ).
tcf(c_26802,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(identity,X1)) = multiply(multiply(identity,X0),X1),
inference(superposition,[status(thm)],[c_26752,c_95]) ).
tcf(c_27859,plain,
! [X0: $i,X1: $i] : multiply(multiply(identity,X0),X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[c_93,c_26802]) ).
tcf(c_27925,plain,
! [X0: $i] : multiply(multiply(identity,X0),inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_27859,c_94]) ).
tcf(c_27964,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_93,c_27925]) ).
tcf(c_27967,plain,
multiply(sk_c10,inverse(sk_c10)) = identity,
inference(superposition,[status(thm)],[c_8349,c_27925]) ).
tcf(c_27976,plain,
multiply(sk_c9,inverse(sk_c9)) = identity,
inference(superposition,[status(thm)],[c_26540,c_27925]) ).
tcf(c_28004,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(multiply(identity,sk_c7),sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_111,c_27925]) ).
tcf(c_28034,plain,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c5,sk_c6) = identity ) ),
inference(superposition,[status(thm)],[c_123,c_27964]) ).
tcf(c_28035,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c5,sk_c6) = identity ) ),
inference(superposition,[status(thm)],[c_107,c_27964]) ).
tcf(c_28051,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c10 != identity )
| ( multiply(inverse(X0),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_27964,c_333]) ).
tcf(c_28052,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( multiply(inverse(X0),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_27964,c_331]) ).
tcf(c_28085,plain,
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_28052]) ).
tcf(c_28086,plain,
( ~ iPr_def_12
| ( sk_c10 != identity )
| ( multiply(inverse(sk_c10),sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_28051]) ).
tcf(c_28195,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c3) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_28034,c_122]) ).
tcf(c_28232,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_28035,c_106]) ).
tcf(c_32178,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c9) = multiply(X0,X1) )
| ( multiply(identity,sk_c9) != sk_c9 )
| ( multiply(X0,X1) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_20846]) ).
tcf(c_32179,plain,
( ( multiply(identity,sk_c9) = multiply(sk_c10,sk_c10) )
| ( multiply(identity,sk_c9) != sk_c9 )
| ( multiply(sk_c10,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_32178]) ).
tcf(c_35610,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X2,X0) = X1 )
| ( X2 != identity )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3931,c_3885]) ).
tcf(c_35611,plain,
( ( multiply(sk_c10,sk_c10) = sk_c10 )
| ( sk_c10 != identity )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_35610]) ).
tcf(c_35728,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( X0 != multiply(inverse(X1),X1) ) ),
inference(resolution,[status(thm)],[c_3933,c_337]) ).
tcf(c_35729,plain,
( ( identity = sk_c10 )
| ( sk_c10 != multiply(inverse(sk_c10),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_35728]) ).
tcf(c_35968,plain,
( ( sk_c10 = multiply(sk_c1,sk_c2) )
| ( multiply(sk_c10,sk_c8) = sk_c9 ) ),
inference(resolution,[status(thm)],[c_10903,c_2458]) ).
tcf(c_35973,plain,
( ( sk_c10 = multiply(identity,identity) )
| ( sk_c10 != sk_c9 )
| ( multiply(identity,identity) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_9932]) ).
tcf(c_37132,plain,
( ( multiply(identity,identity) = sk_c9 )
| ( sk_c9 != identity )
| ( multiply(identity,identity) != identity ) ),
inference(instantiation,[status(thm)],[c_2339]) ).
tcf(c_37134,plain,
sk_c10 = inverse(sk_c3),
inference(global_subsumption_just,[status(thm)],[c_6896,c_137,c_138,c_120,c_125,c_342,c_335,c_569,c_647,c_681,c_736,c_889,c_965,c_1274,c_1498,c_1872,c_1881,c_1878,c_2468,c_2623,c_2783,c_3922,c_4720,c_10764,c_10847,c_13210,c_28085,c_28086,c_28195,c_35973,c_37132]) ).
tcf(c_37160,plain,
inverse(sk_c1) = sk_c2,
inference(global_subsumption_just,[status(thm)],[c_7757,c_137,c_138,c_111,c_109,c_342,c_647,c_681,c_889,c_965,c_1274,c_1498,c_2468,c_2623,c_2784,c_3496,c_4720,c_10112,c_10847,c_10854,c_28085,c_28086,c_28232,c_35973,c_37132]) ).
tcf(c_37319,plain,
! [X0: $i] :
( ( sk_c10 = multiply(inverse(X0),X0) )
| ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(resolution,[status(thm)],[c_7301,c_2454]) ).
tcf(c_37320,plain,
( ( sk_c10 = multiply(inverse(sk_c10),sk_c10) )
| ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_37319]) ).
tcf(c_37371,plain,
! [X0: $i] :
( ( sk_c10 = multiply(inverse(X0),X0) )
| ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(resolution,[status(thm)],[c_7325,c_2454]) ).
tcf(c_37372,plain,
( ( sk_c10 = multiply(inverse(sk_c10),sk_c10) )
| ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_37371]) ).
tcf(c_37438,plain,
! [X0: $i] :
( ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( multiply(identity,X0) = multiply(sk_c6,sk_c10) )
| ( sk_c9 != X0 ) ),
inference(resolution,[status(thm)],[c_6182,c_116]) ).
tcf(c_37444,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c2) = sk_c10 )
| ( multiply(identity,X0) = multiply(sk_c10,sk_c8) )
| ( sk_c9 != X0 ) ),
inference(resolution,[status(thm)],[c_6182,c_101]) ).
tcf(c_37485,plain,
! [X0: $i] :
( ( multiply(sk_c4,sk_c9) = sk_c10 )
| ( multiply(identity,X0) = multiply(sk_c3,sk_c9) )
| ( sk_c10 != X0 ) ),
inference(resolution,[status(thm)],[c_6182,c_129]) ).
tcf(c_37486,plain,
! [X0: $i] :
( ( multiply(sk_c5,sk_c6) = sk_c9 )
| ( multiply(identity,X0) = multiply(sk_c3,sk_c9) )
| ( sk_c10 != X0 ) ),
inference(resolution,[status(thm)],[c_6182,c_130]) ).
tcf(c_37487,plain,
! [X0: $i] :
( ( multiply(sk_c6,sk_c10) = sk_c9 )
| ( multiply(identity,X0) = multiply(sk_c3,sk_c9) )
| ( sk_c10 != X0 ) ),
inference(resolution,[status(thm)],[c_6182,c_132]) ).
tcf(c_38012,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c2) = multiply(X0,sk_c9) )
| ( multiply(sk_c1,sk_c2) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_11838]) ).
tcf(c_38605,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c5),sk_c9) = X0 )
| ( X0 != multiply(multiply(identity,sk_c6),sk_c9) )
| ( multiply(inverse(sk_c5),sk_c9) != multiply(multiply(identity,sk_c6),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_624]) ).
tcf(c_38606,plain,
( ( multiply(inverse(sk_c5),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(multiply(identity,sk_c6),sk_c9) )
| ( multiply(inverse(sk_c5),sk_c9) != multiply(multiply(identity,sk_c6),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_38605]) ).
tcf(c_39103,plain,
! [X0: $i] :
( ( sk_c10 = multiply(multiply(identity,sk_c6),sk_c9) )
| ( sk_c10 != X0 )
| ( multiply(multiply(identity,sk_c6),sk_c9) != X0 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_39104,plain,
( ( sk_c10 = multiply(multiply(identity,sk_c6),sk_c9) )
| ( sk_c10 != sk_c10 )
| ( multiply(multiply(identity,sk_c6),sk_c9) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_39103]) ).
tcf(c_42747,plain,
inverse(sk_c1) = sk_c2,
inference(global_subsumption_just,[status(thm)],[c_28004,c_137,c_138,c_111,c_109,c_342,c_647,c_681,c_889,c_965,c_1274,c_1498,c_2468,c_2623,c_2784,c_3496,c_4720,c_10112,c_10847,c_10854,c_28085,c_28086,c_28232,c_35973,c_37132]) ).
tcf(c_42758,plain,
multiply(sk_c1,sk_c2) = identity,
inference(superposition,[status(thm)],[c_42747,c_27964]) ).
tcf(c_42764,plain,
( ~ iPr_def_12
| ( multiply(sk_c1,sk_c2) != sk_c10 )
| ( multiply(inverse(sk_c1),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_42747,c_333]) ).
tcf(c_43919,plain,
( ( multiply(sk_c9,inverse(sk_c9)) = multiply(inverse(sk_c9),sk_c9) )
| ( multiply(sk_c9,inverse(sk_c9)) != identity )
| ( multiply(inverse(sk_c9),sk_c9) != identity ) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_44458,plain,
! [X0: $i] :
( ( sk_c10 = multiply(sk_c10,sk_c8) )
| ( sk_c10 != multiply(identity,X0) )
| ( multiply(sk_c10,sk_c8) != multiply(identity,X0) ) ),
inference(instantiation,[status(thm)],[c_1039]) ).
tcf(c_44459,plain,
( ( sk_c10 = multiply(sk_c10,sk_c8) )
| ( sk_c10 != multiply(identity,sk_c10) )
| ( multiply(sk_c10,sk_c8) != multiply(identity,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_44458]) ).
tcf(c_49526,plain,
! [X0: $i] :
( ( multiply(sk_c6,sk_c10) = multiply(identity,X0) )
| ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( sk_c9 != X0 ) ),
inference(resolution,[status(thm)],[c_37438,c_2458]) ).
tcf(c_49642,plain,
! [X0: $i] :
( ( multiply(sk_c10,sk_c8) = multiply(identity,X0) )
| ( multiply(sk_c1,sk_c2) = sk_c10 )
| ( sk_c9 != X0 ) ),
inference(resolution,[status(thm)],[c_37444,c_2458]) ).
tcf(c_50708,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c9) = multiply(identity,X0) )
| ( multiply(sk_c4,sk_c9) = sk_c10 )
| ( sk_c10 != X0 ) ),
inference(resolution,[status(thm)],[c_37485,c_2458]) ).
tcf(c_50907,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c9) = multiply(identity,X0) )
| ( multiply(sk_c5,sk_c6) = sk_c9 )
| ( sk_c10 != X0 ) ),
inference(resolution,[status(thm)],[c_37486,c_2458]) ).
tcf(c_51232,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c9) = multiply(identity,X0) )
| ( multiply(sk_c6,sk_c10) = sk_c9 )
| ( sk_c10 != X0 ) ),
inference(resolution,[status(thm)],[c_37487,c_2458]) ).
tcf(c_56876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,sk_c9) = X3 )
| ( X3 != multiply(X1,X2) )
| ( multiply(X0,sk_c9) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_951]) ).
tcf(c_58560,plain,
( ( multiply(sk_c1,sk_c2) = multiply(identity,sk_c9) )
| ( multiply(identity,sk_c9) != sk_c9 )
| ( multiply(sk_c1,sk_c2) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_38012]) ).
tcf(c_58794,plain,
( ( multiply(sk_c9,inverse(sk_c9)) = sk_c10 )
| ( sk_c10 != multiply(inverse(sk_c9),sk_c9) )
| ( multiply(sk_c9,inverse(sk_c9)) != multiply(inverse(sk_c9),sk_c9) ) ),
inference(instantiation,[status(thm)],[c_828]) ).
tcf(c_63938,plain,
! [X0: $i,X1: $i] :
( ( multiply(multiply(identity,sk_c6),sk_c9) = multiply(X0,X1) )
| ( sk_c9 != X1 )
| ( multiply(identity,sk_c6) != X0 ) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_68292,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X2),X2) = X0 )
| ( X0 != multiply(inverse(X1),X1) ) ),
inference(resolution,[status(thm)],[c_6345,c_94]) ).
tcf(c_68293,plain,
( ( multiply(inverse(sk_c10),sk_c10) = sk_c10 )
| ( sk_c10 != multiply(inverse(sk_c10),sk_c10) ) ),
inference(instantiation,[status(thm)],[c_68292]) ).
tcf(c_68377,negated_conjecture,
inverse(sk_c1) = sk_c2,
inference(global_subsumption_just,[status(thm)],[c_104,c_137,c_138,c_111,c_109,c_342,c_647,c_681,c_889,c_965,c_1274,c_1498,c_2468,c_2623,c_2784,c_3496,c_4720,c_10112,c_10847,c_10854,c_28085,c_28086,c_28232,c_35973,c_37132]) ).
tcf(c_68379,negated_conjecture,
inverse(sk_c3) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_120,c_137,c_138,c_120,c_125,c_342,c_335,c_569,c_647,c_681,c_736,c_853,c_889,c_965,c_1217,c_1274,c_1498,c_1872,c_1881,c_1878,c_2468,c_2623,c_2783,c_3922,c_4720,c_10764,c_10847,c_13210,c_28085,c_28086,c_28195,c_35973,c_37132]) ).
tcf(c_68386,plain,
multiply(sk_c10,sk_c3) = identity,
inference(superposition,[status(thm)],[c_68379,c_94]) ).
tcf(c_68428,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_94,c_95]) ).
tcf(c_68471,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c10 )
| ( multiply(sk_c10,sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_8349,c_334]) ).
tcf(c_68475,plain,
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( multiply(inverse(sk_c10),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_27967,c_331]) ).
tcf(c_68476,plain,
( ~ iPr_def_10
| ( multiply(sk_c1,sk_c2) != sk_c9 )
| ( multiply(inverse(sk_c1),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_68377,c_331]) ).
tcf(c_68480,plain,
! [X0: $i] : multiply(sk_c10,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_68386,c_95]) ).
tcf(c_68526,plain,
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c10,sk_c10) = multiply(identity,sk_c9) ) ),
inference(superposition,[status(thm)],[c_133,c_68480]) ).
tcf(c_68527,plain,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c10,sk_c10) = multiply(identity,sk_c9) ) ),
inference(superposition,[status(thm)],[c_135,c_68480]) ).
tcf(c_68528,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c10,sk_c10) = multiply(identity,sk_c9) ) ),
inference(superposition,[status(thm)],[c_131,c_68480]) ).
tcf(c_68532,plain,
( ~ iPr_def_13
| ( inverse(sk_c3) != sk_c10 )
| ( multiply(identity,sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_68480,c_334]) ).
tcf(c_68555,plain,
( ~ iPr_def_12
| ( sk_c10 != identity )
| ( multiply(inverse(sk_c10),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_27967,c_333]) ).
tcf(c_68556,plain,
( ~ iPr_def_12
| ( multiply(sk_c1,sk_c2) != sk_c10 )
| ( multiply(inverse(sk_c1),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_68377,c_333]) ).
tcf(c_68573,plain,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(sk_c10,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_68527,c_93]) ).
tcf(c_68579,plain,
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(inverse(sk_c1),sk_c10) = multiply(identity,sk_c2) ) ),
inference(superposition,[status(thm)],[c_101,c_68428]) ).
tcf(c_68580,plain,
( ( inverse(sk_c7) = sk_c10 )
| ( multiply(inverse(sk_c1),sk_c10) = multiply(identity,sk_c2) ) ),
inference(superposition,[status(thm)],[c_103,c_68428]) ).
tcf(c_68581,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(inverse(sk_c1),sk_c10) = multiply(identity,sk_c2) ) ),
inference(superposition,[status(thm)],[c_99,c_68428]) ).
tcf(c_68593,plain,
( ( multiply(sk_c2,sk_c9) = sk_c10 )
| ( multiply(inverse(sk_c7),sk_c8) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_118,c_68428]) ).
tcf(c_68594,plain,
( ( multiply(sk_c1,sk_c2) = sk_c10 )
| ( multiply(inverse(sk_c7),sk_c8) = multiply(identity,sk_c10) ) ),
inference(superposition,[status(thm)],[c_102,c_68428]) ).
tcf(c_68605,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = multiply(identity,X2),
inference(superposition,[status(thm)],[c_95,c_68428]) ).
tcf(c_68666,plain,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c10,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_68528,c_93]) ).
tcf(c_68698,plain,
( ( multiply(sk_c10,sk_c8) = sk_c9 )
| ( multiply(sk_c10,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_68526,c_93]) ).
tcf(c_68701,plain,
inverse(sk_c7) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_68580,c_137,c_138,c_111,c_109,c_103,c_342,c_564,c_647,c_681,c_726,c_853,c_889,c_965,c_1040,c_1148,c_1217,c_1274,c_1307,c_1498,c_2243,c_2340,c_2468,c_2480,c_2521,c_2623,c_2784,c_3496,c_3893,c_3919,c_4720,c_8155,c_10112,c_10731,c_10847,c_10854,c_12698,c_19629,c_20874,c_28085,c_28086,c_28232,c_32179,c_35729,c_35973,c_37132,c_37134,c_37372,c_42758,c_42764,c_68293,c_68532,c_68573]) ).
tcf(c_68709,plain,
inverse(sk_c5) = sk_c6,
inference(global_subsumption_just,[status(thm)],[c_68581,c_137,c_138,c_120,c_111,c_125,c_109,c_103,c_99,c_342,c_335,c_564,c_569,c_631,c_647,c_681,c_708,c_726,c_736,c_853,c_889,c_965,c_1040,c_1148,c_1217,c_1274,c_1307,c_1498,c_1872,c_1881,c_1878,c_2243,c_2340,c_2468,c_2480,c_2521,c_2623,c_2784,c_2783,c_2782,c_3496,c_3893,c_3892,c_3919,c_3918,c_3922,c_4720,c_8155,c_10112,c_10731,c_10764,c_10847,c_10854,c_12698,c_13210,c_19629,c_20874,c_28085,c_28086,c_28195,c_28232,c_32179,c_35611,c_35729,c_35968,c_35973,c_37132,c_37320,c_37372,c_42758,c_42764,c_68293,c_68532,c_68573,c_68666]) ).
tcf(c_68713,plain,
( ~ iPr_def_12
| ( multiply(sk_c5,sk_c6) != sk_c10 )
| ( multiply(inverse(sk_c5),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_68709,c_333]) ).
tcf(c_68714,plain,
( ~ iPr_def_10
| ( multiply(sk_c5,sk_c6) != sk_c9 )
| ( multiply(inverse(sk_c5),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_68709,c_331]) ).
tcf(c_68860,plain,
( ~ iPr_def_13
| ( multiply(sk_c10,sk_c10) != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_68471,c_137,c_138,c_120,c_111,c_125,c_109,c_103,c_342,c_335,c_564,c_569,c_631,c_647,c_681,c_708,c_726,c_736,c_853,c_889,c_965,c_1040,c_1148,c_1217,c_1274,c_1307,c_1498,c_1872,c_1881,c_1878,c_2243,c_2340,c_2468,c_2480,c_2521,c_2623,c_2784,c_2783,c_2782,c_3496,c_3893,c_3919,c_3922,c_4720,c_8155,c_10112,c_10731,c_10764,c_10847,c_10854,c_12698,c_13210,c_19629,c_20874,c_28085,c_28086,c_28195,c_28232,c_32179,c_35611,c_35729,c_35968,c_35973,c_37132,c_37372,c_42758,c_42764,c_68293,c_68532,c_68573]) ).
tcf(c_68941,plain,
( ~ iPr_def_10
| ( sk_c9 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_68475,c_138,c_10847,c_28085]) ).
tcf(c_68943,plain,
( ~ iPr_def_13
| ( multiply(identity,sk_c10) != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_68532,c_137,c_138,c_120,c_125,c_342,c_335,c_569,c_647,c_681,c_736,c_853,c_889,c_965,c_1217,c_1274,c_1498,c_1872,c_1881,c_1878,c_2468,c_2623,c_2783,c_3922,c_4720,c_10764,c_10847,c_13210,c_28085,c_28086,c_28195,c_35973,c_37132,c_68532]) ).
tcf(c_68947,plain,
( ~ iPr_def_13
| ( sk_c10 != sk_c9 ) ),
inference(superposition,[status(thm)],[c_8349,c_68943]) ).
tcf(c_68948,plain,
( ~ iPr_def_12
| ( sk_c10 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_68555,c_597,c_606,c_647,c_657,c_27976,c_43919,c_58794]) ).
tcf(c_68950,plain,
multiply(sk_c10,sk_c8) = sk_c9,
inference(global_subsumption_just,[status(thm)],[c_68579,c_137,c_342,c_681,c_726,c_877,c_1040,c_1148,c_1307,c_2243,c_2480,c_2521,c_2623,c_3496,c_10731,c_12698,c_20874,c_32179,c_35968,c_42758,c_68698,c_68860,c_68941,c_68948]) ).
tcf(c_69175,plain,
( ( multiply(sk_c10,sk_c8) = multiply(identity,sk_c10) )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_68701,c_68593]) ).
tcf(c_69180,plain,
( ( multiply(sk_c10,sk_c8) = multiply(identity,sk_c10) )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_68701,c_68594]) ).
tcf(c_70061,plain,
( ~ iPr_def_10
| ( multiply(sk_c1,sk_c2) != sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_68476,c_726,c_1148,c_1307,c_2623,c_5419,c_10692,c_11626,c_12698,c_42758,c_58560,c_68941]) ).
tcf(c_70069,plain,
( ~ iPr_def_12
| ( multiply(sk_c1,sk_c2) != sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_68556,c_342,c_708,c_2243,c_2623,c_12698,c_42758,c_68948]) ).
tcf(c_70304,plain,
( ~ iPr_def_12
| ( multiply(inverse(sk_c5),sk_c9) != sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_68713,c_137,c_98,c_342,c_681,c_726,c_877,c_933,c_1040,c_1143,c_1148,c_1307,c_2243,c_2480,c_2521,c_2623,c_3496,c_3983,c_10731,c_12698,c_20874,c_32179,c_35968,c_42758,c_44459,c_68698,c_68713,c_68860,c_68941,c_68948,c_69180,c_70069]) ).
tcf(c_70310,plain,
( ~ iPr_def_10
| ( multiply(sk_c6,sk_c10) != sk_c9 )
| ( multiply(sk_c5,sk_c6) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_68709,c_68714]) ).
tcf(c_71099,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,identity)),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_93,c_68605]) ).
tcf(c_77117,plain,
( ( multiply(sk_c1,sk_c2) = sk_c10 )
| ( multiply(inverse(multiply(sk_c6,identity)),sk_c9) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_100,c_71099]) ).
tcf(c_77119,plain,
( ( multiply(sk_c3,sk_c9) = sk_c10 )
| ( multiply(inverse(multiply(sk_c7,identity)),sk_c8) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_134,c_71099]) ).
tcf(c_82027,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(multiply(identity,sk_c6),sk_c9) = X2 )
| ( X2 != multiply(X0,X1) )
| ( multiply(multiply(identity,sk_c6),sk_c9) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_56876]) ).
tcf(c_82037,plain,
! [X0: $i] :
( ( multiply(multiply(identity,sk_c6),sk_c9) = multiply(sk_c6,X0) )
| ( sk_c9 != X0 )
| ( multiply(identity,sk_c6) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_63938]) ).
tcf(c_82038,plain,
( ( multiply(multiply(identity,sk_c6),sk_c9) = multiply(sk_c6,sk_c10) )
| ( sk_c9 != sk_c10 )
| ( multiply(identity,sk_c6) != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_82037]) ).
tcf(c_95214,plain,
! [X0: $i] :
( ( multiply(multiply(identity,sk_c6),sk_c9) = X0 )
| ( X0 != multiply(sk_c6,sk_c10) )
| ( multiply(multiply(identity,sk_c6),sk_c9) != multiply(sk_c6,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_82027]) ).
tcf(c_95215,plain,
( ( multiply(multiply(identity,sk_c6),sk_c9) = sk_c10 )
| ( sk_c10 != multiply(sk_c6,sk_c10) )
| ( multiply(multiply(identity,sk_c6),sk_c9) != multiply(sk_c6,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_95214]) ).
tcf(c_96050,plain,
multiply(sk_c2,sk_c9) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_49526,c_137,c_138,c_120,c_111,c_125,c_109,c_103,c_99,c_116,c_114,c_342,c_335,c_564,c_569,c_631,c_640,c_647,c_681,c_708,c_726,c_736,c_754,c_853,c_877,c_889,c_965,c_1040,c_1143,c_1148,c_1217,c_1274,c_1307,c_1498,c_1872,c_1881,c_1878,c_2243,c_2340,c_2468,c_2480,c_2521,c_2623,c_2784,c_2783,c_2782,c_2781,c_3496,c_3893,c_3892,c_3919,c_3918,c_3922,c_3983,c_3988,c_4720,c_8155,c_8162,c_10112,c_10731,c_10764,c_10847,c_10854,c_12698,c_13210,c_18907,c_19629,c_20874,c_28085,c_28086,c_28195,c_28232,c_32179,c_35611,c_35729,c_35968,c_35973,c_37132,c_37320,c_37372,c_38606,c_39104,c_42758,c_42764,c_44459,c_68293,c_68532,c_68573,c_68666,c_68698,c_68860,c_68941,c_68948,c_69175,c_70304,c_70310,c_82038,c_95215]) ).
tcf(c_96062,plain,
multiply(sk_c1,sk_c2) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_49642,c_137,c_138,c_120,c_111,c_125,c_109,c_103,c_99,c_100,c_98,c_342,c_335,c_564,c_569,c_631,c_640,c_647,c_677,c_681,c_708,c_726,c_736,c_754,c_853,c_877,c_889,c_965,c_1040,c_1143,c_1148,c_1217,c_1274,c_1307,c_1498,c_1872,c_1881,c_1878,c_2243,c_2340,c_2468,c_2480,c_2521,c_2623,c_2784,c_2783,c_2782,c_3496,c_3893,c_3892,c_3919,c_3918,c_3922,c_3983,c_3988,c_4720,c_8155,c_8162,c_10112,c_10731,c_10764,c_10847,c_10854,c_12698,c_13210,c_19629,c_20874,c_28085,c_28086,c_28195,c_28232,c_32179,c_35611,c_35729,c_35968,c_35973,c_37132,c_37320,c_37372,c_38606,c_39104,c_42758,c_42764,c_44459,c_68293,c_68532,c_68573,c_68666,c_68698,c_68860,c_68941,c_68948,c_69180,c_70304,c_70310,c_82038,c_95215]) ).
tcf(c_96074,plain,
! [X0: $i] :
( ( multiply(sk_c3,sk_c9) = multiply(identity,X0) )
| ( sk_c10 != X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_50708,c_93,c_342,c_726,c_734,c_2327,c_2780,c_3496,c_8155,c_19629,c_20089,c_37160,c_42764,c_50907,c_51232,c_68701,c_68950,c_70310,c_96050,c_96062]) ).
tcf(c_96076,plain,
( ( multiply(sk_c3,sk_c9) = multiply(identity,sk_c10) )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_96074]) ).
tcf(c_97711,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = sk_c9 )
| ( sk_c9 != multiply(X0,X1) )
| ( sk_c10 != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_812]) ).
tcf(c_97712,plain,
( ( sk_c10 = sk_c9 )
| ( sk_c9 != multiply(sk_c10,sk_c10) )
| ( sk_c10 != multiply(sk_c10,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_97711]) ).
tcf(c_100420,plain,
multiply(sk_c1,sk_c2) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_77117,c_137,c_138,c_120,c_111,c_125,c_109,c_103,c_99,c_100,c_98,c_342,c_335,c_564,c_569,c_631,c_640,c_647,c_677,c_681,c_708,c_726,c_736,c_754,c_853,c_877,c_889,c_965,c_1040,c_1143,c_1148,c_1217,c_1274,c_1307,c_1498,c_1872,c_1881,c_1878,c_2243,c_2340,c_2468,c_2480,c_2521,c_2623,c_2784,c_2783,c_2782,c_3496,c_3893,c_3892,c_3919,c_3918,c_3922,c_3983,c_3988,c_4720,c_8155,c_8162,c_10112,c_10731,c_10764,c_10847,c_10854,c_12698,c_13210,c_19629,c_20874,c_28085,c_28086,c_28195,c_28232,c_32179,c_35611,c_35729,c_35968,c_35973,c_37132,c_37320,c_37372,c_38606,c_39104,c_42758,c_42764,c_44459,c_68293,c_68532,c_68573,c_68666,c_68698,c_68860,c_68941,c_68948,c_69180,c_70304,c_70310,c_82038,c_95215]) ).
tcf(c_100424,plain,
( ~ iPr_def_10
| ( sk_c10 != sk_c9 ) ),
inference(superposition,[status(thm)],[c_100420,c_70061]) ).
tcf(c_100454,plain,
multiply(sk_c3,sk_c9) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_77119,c_137,c_342,c_681,c_7176,c_96076]) ).
tcf(c_100467,plain,
multiply(sk_c10,sk_c10) = multiply(identity,sk_c9),
inference(superposition,[status(thm)],[c_100454,c_68480]) ).
tcf(c_100468,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_100467,c_100424,c_97712,c_96062,c_96050,c_68947,c_42764,c_42758,c_37160,c_19629,c_12698,c_8155,c_5435,c_3496,c_2623,c_2521,c_2243,c_1307,c_1148,c_1040,c_734,c_726,c_708,c_681,c_342,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.59 % Computer : n004.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Wed Sep 23 14:09:13 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.63 Running first-order theorem proving
% 0.14/5.63 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.64
% 0.14/5.64 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.64
% 0.14/5.64 % Detected problem language: tptp
% 0.14/5.65 % Proving...
% 28.86/10.04 % SZS status Started for theBenchmark.p
% 28.86/10.04 % SZS status Unsatisfiable for theBenchmark.p
% 28.86/10.04
% 28.86/10.04 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 28.86/10.04
% 28.86/10.04 % ------ iProver source info
% 28.86/10.04
% 28.86/10.04 % git: date: 2026-07-19 20:42:38 +0200
% 28.86/10.04 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 28.86/10.04 % git: non_committed_changes: false
% 28.86/10.04
% 28.86/10.04 % ------ Parsing...% successful
% 28.86/10.04
% 28.86/10.04
% 28.86/10.04 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 28.86/10.04
% 28.86/10.04 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 28.86/10.04
% 28.86/10.04 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 28.86/10.04
% 28.86/10.04 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 28.86/10.04 % ------ Proving...
% 28.86/10.04 % ------ Problem Properties
% 28.86/10.04
% 28.86/10.04 %
% 28.86/10.04 % clauses 48
% 28.86/10.04 % conjectures 45
% 28.86/10.04 % EPR 1
% 28.86/10.04 % Horn 7
% 28.86/10.04 % unary 3
% 28.86/10.04 % binary 40
% 28.86/10.04 % lits 99
% 28.86/10.04 % lits eq 91
% 28.86/10.04 % fd_pure 0
% 28.86/10.04 % fd_pseudo 0
% 28.86/10.04 % fd_cond 0
% 28.86/10.04 % fd_pseudo_cond 0
% 28.86/10.04 % AC symbols 0
% 28.86/10.04
% 28.86/10.04 % ------ Input Options Time Limit: Unbounded
% 28.86/10.04
% 28.86/10.04
% 28.86/10.04 % ------
% 28.86/10.04 % Current options:
% 28.86/10.04 % ------
% 28.86/10.04
% 28.86/10.04
% 28.86/10.04 %
% 28.86/10.04
% 28.86/10.04 % ------ Proving...
% 28.86/10.04 %
% 28.86/10.04
% 28.86/10.04 % SZS status Unsatisfiable for theBenchmark.p
% 28.86/10.04
% 28.86/10.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.86/10.04
% 28.86/10.04
%------------------------------------------------------------------------------