%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP263-1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:38 PM UTC 2026
% Result : Unsatisfiable 36.95s 6.81s
% Output : CNFRefutation 36.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 39
% Syntax : Number of formulae : 331 ( 72 unt; 0 def)
% Number of atoms : 759 ( 705 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 700 ( 272 ~; 428 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 171 ( 0 sgn 171 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c11 = inverse(sk_c3)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f7]) ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(reorient_equations,[],[f14]) ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f24,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f26,plain,
( sk_c11 = inverse(sk_c3)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f28,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f30,plain,
( sk_c10 = inverse(sk_c4)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f32,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c5)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f37,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f38,plain,
( inverse(sk_c7) = sk_c6
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f40,plain,
( sk_c8 = inverse(sk_c6)
| sk_c11 = inverse(sk_c1) ),
inference(reorient_equations,[],[f39]) ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f46,plain,
( sk_c11 = inverse(sk_c3)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f48,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f50,plain,
( sk_c10 = inverse(sk_c4)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c5)
| sk_c9 = multiply(sk_c2,sk_c10) ),
inference(reorient_equations,[],[f53]) ).
fof(f63,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f66,plain,
( sk_c11 = inverse(sk_c3)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f68,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f70,plain,
( sk_c10 = inverse(sk_c4)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_35) ).
fof(f72,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f71]) ).
fof(f73,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f74,plain,
( sk_c8 = inverse(sk_c5)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f73]) ).
fof(f77,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f78,plain,
( inverse(sk_c7) = sk_c6
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f80,plain,
( sk_c8 = inverse(sk_c6)
| sk_c10 = inverse(sk_c2) ),
inference(reorient_equations,[],[f79]) ).
fof(f83,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f84,plain,
( sk_c10 = multiply(sk_c3,sk_c11)
| sk_c11 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_42) ).
fof(f86,plain,
( sk_c11 = inverse(sk_c3)
| sk_c11 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f85]) ).
fof(f87,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f88,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| sk_c11 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f87]) ).
fof(f89,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_44) ).
fof(f90,plain,
( sk_c10 = inverse(sk_c4)
| sk_c11 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f89]) ).
fof(f91,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_45) ).
fof(f92,plain,
( sk_c11 = multiply(sk_c5,sk_c8)
| sk_c11 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f91]) ).
fof(f93,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_46) ).
fof(f94,plain,
( sk_c8 = inverse(sk_c5)
| sk_c11 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f93]) ).
fof(f95,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_47) ).
fof(f96,plain,
( sk_c11 = multiply(sk_c8,sk_c10)
| sk_c11 = multiply(sk_c9,sk_c10) ),
inference(reorient_equations,[],[f95]) ).
fof(f103,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_51) ).
fof(f104,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| sk_c11 != multiply(X5,sk_c10)
| inverse(X4) != X5
| sk_c11 != multiply(X4,X5)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != inverse(X1)
| sk_c9 != multiply(X1,sk_c10)
| inverse(X0) != sk_c11
| sk_c10 != multiply(X0,sk_c11) ),
inference(reorient_equations,[],[f103]) ).
fof(f105,plain,
! [X2,X3,X0,X1,X6,X7,X4] :
( multiply(X6,inverse(X4)) != X7
| inverse(X4) != inverse(X7)
| inverse(X6) != X7
| sk_c11 != multiply(inverse(X4),sk_c10)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != inverse(X1)
| sk_c9 != multiply(X1,sk_c10)
| inverse(X0) != sk_c11
| sk_c10 != multiply(X0,sk_c11) ),
inference(equality_resolution,[],[f104]) ).
fof(f106,plain,
! [X2,X3,X0,X1,X6,X4] :
( inverse(X6) != multiply(X6,inverse(X4))
| inverse(X4) != inverse(inverse(X6))
| sk_c11 != multiply(inverse(X4),sk_c10)
| sk_c11 != multiply(X4,inverse(X4))
| sk_c10 != inverse(X3)
| sk_c9 != multiply(X3,sk_c10)
| sk_c11 != inverse(X2)
| sk_c10 != multiply(X2,sk_c11)
| sk_c11 != multiply(sk_c9,sk_c10)
| sk_c10 != inverse(X1)
| sk_c9 != multiply(X1,sk_c10)
| inverse(X0) != sk_c11
| sk_c10 != multiply(X0,sk_c11) ),
inference(equality_resolution,[],[f105]) ).
tcf(c_103,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_104,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c3,sk_c11) = sk_c10 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c11 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c5,sk_c8) = sk_c11 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_123,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c6) = sk_c8 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( multiply(sk_c2,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_128,negated_conjecture,
( ( multiply(sk_c2,sk_c10) = sk_c9 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c2,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c3) = sk_c11 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_139,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_140,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c5,sk_c8) = sk_c11 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_141,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_143,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_144,negated_conjecture,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_146,negated_conjecture,
( ( multiply(sk_c9,sk_c10) = sk_c11 )
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_147,negated_conjecture,
( ( inverse(sk_c3) = sk_c11 )
| ( multiply(sk_c9,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_148,negated_conjecture,
( ( multiply(sk_c9,sk_c10) = sk_c11 )
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_149,negated_conjecture,
( ( inverse(sk_c4) = sk_c10 )
| ( multiply(sk_c9,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f90]) ).
tcf(c_150,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c11 )
| ( multiply(sk_c9,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_151,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c9,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_152,negated_conjecture,
( ( multiply(sk_c8,sk_c10) = sk_c11 )
| ( multiply(sk_c9,sk_c10) = sk_c11 ) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_156,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( inverse(X5) != sk_c10 )
| ( inverse(X4) != sk_c10 )
| ( inverse(X3) != sk_c11 )
| ( inverse(X2) != sk_c11 )
| ( multiply(sk_c9,sk_c10) != sk_c11 )
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(X5,sk_c10) != sk_c9 )
| ( multiply(X4,sk_c10) != sk_c9 )
| ( multiply(X3,sk_c11) != sk_c10 )
| ( multiply(X2,sk_c11) != sk_c10 )
| ( multiply(inverse(X1),sk_c10) != sk_c11 )
| ( multiply(X1,inverse(X1)) != sk_c11 )
| ( multiply(X0,inverse(X1)) != inverse(X0) ) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_621,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c10) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_156]) ).
tcf(c_622,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c11 )
| ( multiply(X0,sk_c11) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_156]) ).
tcf(c_623,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_12
| ( inverse(inverse(X0)) != inverse(X1) )
| ( multiply(inverse(X1),sk_c10) != sk_c11 )
| ( multiply(X1,inverse(X1)) != sk_c11 )
| ( multiply(X0,inverse(X1)) != inverse(X0) ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_156]) ).
tcf(c_624,negated_conjecture,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c9,sk_c10) != sk_c11 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_156]) ).
tcf(c_625,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_626,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_628,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_631,plain,
sk_c10 = sk_c10,
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_889,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c10) = sk_c11 )
| ( sk_c11 != X0 )
| ( multiply(sk_c9,sk_c10) != X0 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_890,plain,
( ( multiply(sk_c9,sk_c10) = sk_c11 )
| ( sk_c11 != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_889]) ).
tcf(c_892,plain,
! [X0: $i,X1: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_893,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != sk_c11 )
| ( X0 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_892]) ).
tcf(c_894,plain,
sk_c11 = sk_c11,
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_902,plain,
( ( sk_c11 = multiply(identity,sk_c11) )
| ( sk_c11 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_903,plain,
multiply(identity,sk_c11) = sk_c11,
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_905,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_912,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(sk_c5,sk_c8) )
| ( X0 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_892]) ).
tcf(c_913,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c10 != multiply(sk_c5,sk_c8) )
| ( sk_c11 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_912]) ).
tcf(c_918,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(identity,sk_c11) )
| ( X0 != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_892]) ).
tcf(c_919,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c11) )
| ( sk_c11 != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_918]) ).
tcf(c_923,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != multiply(sk_c5,sk_c8) )
| ( X0 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_905]) ).
tcf(c_924,plain,
( ( sk_c10 = sk_c11 )
| ( sk_c10 != multiply(sk_c5,sk_c8) )
| ( sk_c11 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_923]) ).
tcf(c_925,plain,
! [X0: $i] :
( ( X0 = sk_c11 )
| ( sk_c11 != multiply(sk_c8,sk_c10) )
| ( X0 != multiply(sk_c8,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_905]) ).
tcf(c_942,plain,
( ( multiply(sk_c9,sk_c10) = multiply(identity,sk_c11) )
| ( sk_c9 != identity )
| ( sk_c10 != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_627]) ).
tcf(c_979,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(sk_c5,sk_c8) )
| ( X1 != X0 )
| ( multiply(sk_c5,sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_1055,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c3) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_147,c_624]) ).
tcf(c_1059,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,sk_c11) )
| ( X1 != X0 )
| ( multiply(identity,sk_c11) != X0 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_1068,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c4) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_149,c_624]) ).
tcf(c_1118,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_104,c_105]) ).
tcf(c_1152,plain,
( ( multiply(sk_c8,sk_c10) = sk_c11 )
| ( sk_c11 != multiply(sk_c8,sk_c10) )
| ( multiply(sk_c8,sk_c10) != multiply(sk_c8,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_925]) ).
tcf(c_1153,plain,
multiply(sk_c8,sk_c10) = multiply(sk_c8,sk_c10),
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_1193,plain,
( ( sk_c11 = inverse(sk_c1) )
| ( sk_c11 != sk_c11 )
| ( inverse(sk_c1) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_1194,plain,
( ( sk_c11 = multiply(sk_c9,sk_c10) )
| ( sk_c11 != sk_c11 )
| ( multiply(sk_c9,sk_c10) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_893]) ).
tcf(c_1195,plain,
( ~ iPr_def_10
| ( inverse(sk_c4) != sk_c10 )
| ( multiply(sk_c4,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_621]) ).
tcf(c_1196,plain,
( ~ iPr_def_10
| ( inverse(sk_c2) != sk_c10 )
| ( multiply(sk_c2,sk_c10) != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_621]) ).
tcf(c_1223,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c9,sk_c10) = X1 )
| ( X1 != X0 )
| ( multiply(sk_c9,sk_c10) != X0 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_1281,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c3) = sk_c11 ) ),
inference(global_subsumption_just,[status(thm)],[c_1055,c_137,c_147,c_127,c_624,c_1196]) ).
tcf(c_1286,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c4) = sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_1068,c_139,c_129,c_1068,c_1196]) ).
tcf(c_1367,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c11) = X1 )
| ( X1 != X0 )
| ( multiply(identity,sk_c11) != X0 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_1372,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c11) )
| ( X0 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_1059]) ).
tcf(c_1373,plain,
( ( sk_c10 = multiply(identity,sk_c11) )
| ( sk_c10 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_1372]) ).
tcf(c_1414,negated_conjecture,
( iPr_def_12
| iPr_def_11
| ( multiply(sk_c9,sk_c10) != sk_c11 ) ),
inference(global_subsumption_just,[status(thm)],[c_624,c_138,c_128,c_624,c_1195,c_1196,c_1286]) ).
tcf(c_1557,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_625]) ).
tcf(c_1559,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_1596,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != inverse(sk_c1) )
| ( X0 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_892]) ).
tcf(c_1597,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c10 != inverse(sk_c1) )
| ( sk_c11 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1596]) ).
tcf(c_1631,negated_conjecture,
( iPr_def_12
| iPr_def_11
| ( multiply(sk_c9,sk_c10) != sk_c11 ) ),
inference(global_subsumption_just,[status(thm)],[c_624,c_1414]) ).
tcf(c_1755,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( sk_c11 != multiply(sk_c9,sk_c10) )
| ( X0 != multiply(sk_c9,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_892]) ).
tcf(c_1756,plain,
( ( sk_c11 = sk_c10 )
| ( sk_c10 != multiply(sk_c9,sk_c10) )
| ( sk_c11 != multiply(sk_c9,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_1755]) ).
tcf(c_1776,plain,
( ( multiply(sk_c2,sk_c10) = sk_c9 )
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_128,c_621]) ).
tcf(c_1787,plain,
( ( inverse(sk_c4) = sk_c10 )
| ~ iPr_def_10
| ( inverse(sk_c2) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_129,c_621]) ).
tcf(c_1788,plain,
( ( inverse(sk_c3) = sk_c11 )
| ~ iPr_def_10
| ( inverse(sk_c2) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_127,c_621]) ).
tcf(c_1795,plain,
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( inverse(inverse(sk_c10)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_104,c_621]) ).
tcf(c_1803,plain,
( ~ iPr_def_11
| ( inverse(sk_c1) != sk_c11 )
| ( multiply(sk_c1,sk_c11) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_622]) ).
tcf(c_1937,plain,
( iPr_def_12
| iPr_def_11
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_146,c_1631]) ).
tcf(c_1954,plain,
( iPr_def_12
| iPr_def_11
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(resolution,[status(thm)],[c_148,c_1631]) ).
tcf(c_2004,plain,
! [X0: $i] :
( ( inverse(sk_c5) = X0 )
| ( inverse(sk_c1) = sk_c11 )
| ( X0 != sk_c8 ) ),
inference(resolution,[status(thm)],[c_626,c_121]) ).
tcf(c_2047,plain,
! [X0: $i] :
( ( inverse(sk_c2) = X0 )
| ( inverse(sk_c4) = sk_c10 )
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_626,c_139]) ).
tcf(c_2070,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_626,c_625]) ).
tcf(c_2121,plain,
( ( inverse(sk_c3) = sk_c11 )
| ~ iPr_def_11
| ( inverse(sk_c1) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_107,c_622]) ).
tcf(c_2124,plain,
( ( multiply(sk_c1,sk_c11) = sk_c10 )
| ~ iPr_def_11
| ( inverse(sk_c3) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_106,c_622]) ).
tcf(c_2126,plain,
( ( inverse(sk_c1) = sk_c11 )
| ~ iPr_def_11
| ( inverse(sk_c3) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_116,c_622]) ).
tcf(c_2128,plain,
( ~ iPr_def_11
| ( sk_c10 != identity )
| ( inverse(inverse(sk_c11)) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_104,c_622]) ).
tcf(c_2135,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_2214,plain,
! [X0: $i] :
( ( multiply(sk_c9,sk_c10) = X0 )
| ( X0 != multiply(identity,sk_c11) )
| ( multiply(sk_c9,sk_c10) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_1223]) ).
tcf(c_2215,plain,
( ( multiply(sk_c9,sk_c10) = sk_c10 )
| ( sk_c10 != multiply(identity,sk_c11) )
| ( multiply(sk_c9,sk_c10) != multiply(identity,sk_c11) ) ),
inference(instantiation,[status(thm)],[c_2214]) ).
tcf(c_2230,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1118,c_103]) ).
tcf(c_2257,plain,
( ( multiply(sk_c9,sk_c10) = sk_c11 )
| ( multiply(inverse(sk_c5),sk_c11) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_150,c_2230]) ).
tcf(c_2259,plain,
( ( multiply(sk_c1,sk_c11) = sk_c10 )
| ( multiply(inverse(sk_c5),sk_c11) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_110,c_2230]) ).
tcf(c_2282,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_104,c_2230]) ).
tcf(c_2283,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,X1)),multiply(X0,multiply(X1,X2))) = X2,
inference(superposition,[status(thm)],[c_105,c_2230]) ).
tcf(c_2294,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_2230,c_2230]) ).
tcf(c_2401,plain,
! [X0: $i] :
( ( multiply(identity,sk_c11) = X0 )
| ( X0 != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_1367]) ).
tcf(c_2508,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(sk_c1) )
| ( X1 != X0 )
| ( inverse(sk_c1) != X0 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_2543,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(sk_c9,sk_c10) )
| ( X1 != X0 )
| ( multiply(sk_c9,sk_c10) != X0 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_2544,plain,
( ( sk_c10 = multiply(sk_c9,sk_c10) )
| ( sk_c10 != sk_c10 )
| ( multiply(sk_c9,sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_2543]) ).
tcf(c_2578,plain,
! [X0: $i,X1: $i] :
( ( sk_c10 = inverse(X0) )
| ( sk_c10 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_2579,plain,
( ( sk_c10 = inverse(sk_c10) )
| ( sk_c10 != sk_c10 )
| ( inverse(sk_c10) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_2578]) ).
tcf(c_2694,plain,
( iPr_def_12
| ( inverse(sk_c3) = sk_c11 ) ),
inference(global_subsumption_just,[status(thm)],[c_1281,c_137,c_117,c_147,c_624,c_1788,c_2121]) ).
tcf(c_2723,negated_conjecture,
( iPr_def_12
| ( multiply(sk_c9,sk_c10) != sk_c11 ) ),
inference(global_subsumption_just,[status(thm)],[c_624,c_1414,c_1803,c_2126,c_2124,c_2694]) ).
tcf(c_2773,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_2282,c_2294]) ).
tcf(c_2786,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_2294,c_104]) ).
tcf(c_3166,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_2135]) ).
tcf(c_3167,plain,
( ( identity = sk_c10 )
| ( identity != identity )
| ( sk_c10 != identity ) ),
inference(instantiation,[status(thm)],[c_3166]) ).
tcf(c_3206,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c3,sk_c11) = identity ) ),
inference(superposition,[status(thm)],[c_137,c_2786]) ).
tcf(c_3207,plain,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c3,sk_c11) = identity ) ),
inference(superposition,[status(thm)],[c_117,c_2786]) ).
tcf(c_3208,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_139,c_2786]) ).
tcf(c_3209,plain,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_119,c_2786]) ).
tcf(c_3210,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c5,sk_c8) = identity ) ),
inference(superposition,[status(thm)],[c_141,c_2786]) ).
tcf(c_3211,plain,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c5,sk_c8) = identity ) ),
inference(superposition,[status(thm)],[c_121,c_2786]) ).
tcf(c_3489,plain,
( iPr_def_12
| ( multiply(sk_c3,sk_c11) = sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_1937,c_146,c_2723]) ).
tcf(c_3499,plain,
( iPr_def_12
| ~ iPr_def_11
| ( inverse(sk_c3) != sk_c11 ) ),
inference(resolution,[status(thm)],[c_3489,c_622]) ).
tcf(c_3541,plain,
( ( sk_c11 = multiply(sk_c5,sk_c8) )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(resolution,[status(thm)],[c_2070,c_120]) ).
tcf(c_3542,plain,
( ( sk_c11 = multiply(sk_c5,sk_c8) )
| ( inverse(sk_c2) = sk_c10 ) ),
inference(resolution,[status(thm)],[c_2070,c_140]) ).
tcf(c_3550,plain,
( ( sk_c11 = multiply(sk_c8,sk_c10) )
| ( multiply(sk_c9,sk_c10) = sk_c11 ) ),
inference(resolution,[status(thm)],[c_2070,c_152]) ).
tcf(c_3576,plain,
( ( sk_c11 = multiply(sk_c9,sk_c10) )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(resolution,[status(thm)],[c_2070,c_151]) ).
tcf(c_3796,plain,
( ( sk_c10 = identity )
| ( inverse(sk_c2) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_3206,c_136]) ).
tcf(c_3821,plain,
( ( sk_c10 = identity )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_3207,c_116]) ).
tcf(c_4087,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c2) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_3208,c_138]) ).
tcf(c_4119,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_3209,c_118]) ).
tcf(c_4845,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_2282,c_2773]) ).
tcf(c_4847,plain,
( ~ iPr_def_11
| ( sk_c10 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2128,c_4845]) ).
tcf(c_4848,plain,
( ~ iPr_def_10
| ( sk_c9 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1795,c_4845]) ).
tcf(c_4860,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_4845,c_104]) ).
tcf(c_4864,plain,
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c3,sk_c11) = identity ) ),
inference(superposition,[status(thm)],[c_117,c_4860]) ).
tcf(c_4865,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_139,c_4860]) ).
tcf(c_4867,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c5,sk_c8) = identity ) ),
inference(superposition,[status(thm)],[c_141,c_4860]) ).
tcf(c_4877,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_4860,c_105]) ).
tcf(c_5058,plain,
( ( multiply(sk_c9,sk_c10) = sk_c11 )
| ( multiply(sk_c8,multiply(sk_c10,inverse(sk_c11))) = identity ) ),
inference(superposition,[status(thm)],[c_152,c_4877]) ).
tcf(c_5215,plain,
( iPr_def_12
| ( multiply(sk_c4,sk_c10) = sk_c9 ) ),
inference(global_subsumption_just,[status(thm)],[c_1954,c_1803,c_1954,c_2121,c_2124,c_3821,c_4847]) ).
tcf(c_5228,plain,
( iPr_def_12
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c10 ) ),
inference(resolution,[status(thm)],[c_5215,c_621]) ).
tcf(c_5244,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_5256,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_3499,c_1803,c_2121,c_2124,c_3821,c_4847]) ).
tcf(c_5260,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_5228,c_1196,c_1787,c_1776,c_4087,c_4848]) ).
tcf(c_5282,plain,
( ( sk_c10 = identity )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_4864,c_116]) ).
tcf(c_5318,plain,
( ( sk_c10 = identity )
| ( multiply(sk_c1,sk_c11) = identity ) ),
inference(superposition,[status(thm)],[c_5282,c_4860]) ).
tcf(c_5399,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c2) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_4865,c_138]) ).
tcf(c_5421,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c2,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_5399,c_4860]) ).
tcf(c_5606,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c5) )
| ( inverse(sk_c1) = sk_c11 )
| ( X0 != sk_c8 ) ),
inference(resolution,[status(thm)],[c_2004,c_2070]) ).
tcf(c_5626,plain,
( ( sk_c10 = identity )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_5318,c_111]) ).
tcf(c_5628,plain,
( ( sk_c10 = identity )
| ( inverse(sk_c3) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_5318,c_107]) ).
tcf(c_5666,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_5421,c_129]) ).
tcf(c_5790,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c2) )
| ( inverse(sk_c4) = sk_c10 )
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_2047,c_2070]) ).
tcf(c_6075,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(sk_c1) )
| ( X1 != inverse(X0) )
| ( inverse(sk_c1) != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_2508]) ).
tcf(c_6076,plain,
! [X0: $i] :
( ( inverse(sk_c1) = inverse(X0) )
| ( sk_c1 != X0 ) ),
inference(instantiation,[status(thm)],[c_628]) ).
tcf(c_6077,plain,
( ( sk_c10 = inverse(sk_c1) )
| ( sk_c10 != inverse(sk_c10) )
| ( inverse(sk_c1) != inverse(sk_c10) ) ),
inference(instantiation,[status(thm)],[c_6075]) ).
tcf(c_6078,plain,
( ( inverse(sk_c1) = inverse(sk_c10) )
| ( sk_c1 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_6076]) ).
tcf(c_6168,plain,
( ( sk_c11 = identity )
| ( inverse(sk_c2) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_4867,c_140]) ).
tcf(c_6183,plain,
( ( sk_c11 = identity )
| ( multiply(sk_c2,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_6168,c_4860]) ).
tcf(c_6359,plain,
! [X0: $i] :
( ( sk_c11 = X0 )
| ( inverse(sk_c5) = sk_c8 )
| ( X0 != multiply(sk_c9,sk_c10) ) ),
inference(resolution,[status(thm)],[c_3576,c_626]) ).
tcf(c_6360,plain,
( ( sk_c11 = sk_c10 )
| ( inverse(sk_c5) = sk_c8 )
| ( sk_c10 != multiply(sk_c9,sk_c10) ) ),
inference(instantiation,[status(thm)],[c_6359]) ).
tcf(c_6462,plain,
! [X0: $i] :
( ( sk_c11 = identity )
| ( multiply(sk_c2,multiply(sk_c10,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_6183,c_105]) ).
tcf(c_6655,plain,
( ( sk_c11 = multiply(sk_c8,sk_c10) )
| ( sk_c11 = multiply(sk_c9,sk_c10) ) ),
inference(resolution,[status(thm)],[c_3550,c_2070]) ).
tcf(c_7643,plain,
( ( identity = sk_c11 )
| ( identity != identity )
| ( sk_c11 != identity ) ),
inference(instantiation,[status(thm)],[c_3166]) ).
tcf(c_7647,plain,
( ( multiply(identity,sk_c11) = identity )
| ( identity != sk_c11 )
| ( multiply(identity,sk_c11) != sk_c11 ) ),
inference(instantiation,[status(thm)],[c_2401]) ).
tcf(c_7659,plain,
( ( identity = multiply(sk_c5,sk_c8) )
| ( identity != identity )
| ( multiply(sk_c5,sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_3166]) ).
tcf(c_7661,plain,
( ( identity = sk_c11 )
| ( identity != multiply(sk_c5,sk_c8) )
| ( sk_c11 != multiply(sk_c5,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_923]) ).
tcf(c_9700,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_104,c_2773]) ).
tcf(c_9841,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(inverse(X0)) != inverse(identity) )
| ( multiply(X0,identity) != inverse(X0) )
| ( multiply(identity,inverse(identity)) != sk_c11 )
| ( multiply(inverse(identity),sk_c10) != sk_c11 ) ),
inference(superposition,[status(thm)],[c_9700,c_623]) ).
tcf(c_9864,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != X0 )
| ( multiply(identity,identity) != sk_c11 )
| ( multiply(identity,sk_c10) != sk_c11 )
| ( inverse(inverse(X0)) != identity ) ),
inference(light_normalisation,[status(thm)],[c_9841,c_2773,c_9700]) ).
tcf(c_9865,plain,
! [X0: $i] :
( ~ iPr_def_12
| ( sk_c11 != identity )
| ( sk_c11 != sk_c10 )
| ( inverse(X0) != X0 )
| ( inverse(inverse(X0)) != identity ) ),
inference(demodulation,[status(thm)],[c_9864,c_103]) ).
tcf(c_9886,plain,
( ~ iPr_def_12
| ( sk_c11 != identity )
| ( sk_c11 != sk_c10 )
| ( inverse(identity) != identity ) ),
inference(superposition,[status(thm)],[c_9700,c_9865]) ).
tcf(c_9887,plain,
( ~ iPr_def_12
| ( sk_c11 != identity )
| ( sk_c11 != sk_c10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9886,c_9700]) ).
tcf(c_9936,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_2282,c_2773]) ).
tcf(c_9949,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( inverse(sk_c6) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_143,c_9936]) ).
tcf(c_9950,plain,
( ( inverse(sk_c6) = sk_c7 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_123,c_9936]) ).
tcf(c_9954,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_9936,c_104]) ).
tcf(c_9973,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_9954,c_105]) ).
tcf(c_9975,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_9954,c_105]) ).
tcf(c_9986,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_9973,c_103]) ).
tcf(c_10000,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c11 )
| ( multiply(sk_c7,multiply(sk_c6,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_123,c_9986]) ).
tcf(c_10001,plain,
! [X0: $i] :
( ( inverse(sk_c2) = sk_c10 )
| ( multiply(sk_c6,multiply(sk_c8,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_144,c_9986]) ).
tcf(c_10004,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_9936,c_9986]) ).
tcf(c_10048,plain,
( ( sk_c8 = sk_c7 )
| ( inverse(sk_c2) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_9949,c_144]) ).
tcf(c_10057,plain,
( ( sk_c8 = sk_c7 )
| ( multiply(sk_c2,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_10048,c_9954]) ).
tcf(c_10065,plain,
( ( sk_c8 = sk_c7 )
| ( inverse(sk_c1) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_9950,c_124]) ).
tcf(c_10073,plain,
( ( sk_c8 = sk_c7 )
| ( multiply(sk_c1,sk_c11) = identity ) ),
inference(superposition,[status(thm)],[c_10065,c_9954]) ).
tcf(c_10549,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))) = identity,
inference(superposition,[status(thm)],[c_105,c_9975]) ).
tcf(c_10577,plain,
( ( multiply(sk_c9,sk_c10) = sk_c11 )
| ( multiply(sk_c8,multiply(sk_c10,inverse(sk_c11))) = identity ) ),
inference(superposition,[status(thm)],[c_152,c_9975]) ).
tcf(c_10588,plain,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,multiply(sk_c10,inverse(sk_c9))) = identity ) ),
inference(superposition,[status(thm)],[c_131,c_9975]) ).
tcf(c_10638,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X0))) = multiply(X1,identity),
inference(superposition,[status(thm)],[c_9975,c_9986]) ).
tcf(c_10764,plain,
( ( sk_c8 = sk_c7 )
| ( sk_c9 = identity )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_10057,c_129]) ).
tcf(c_10768,plain,
! [X0: $i] :
( ( sk_c8 = sk_c7 )
| ( multiply(sk_c2,multiply(sk_c10,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_10057,c_105]) ).
tcf(c_10783,plain,
( ( sk_c8 = sk_c7 )
| ( sk_c10 = identity )
| ( inverse(sk_c3) = sk_c11 ) ),
inference(superposition,[status(thm)],[c_10073,c_107]) ).
tcf(c_12362,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(inverse(multiply(X0,X1)),X0)),identity) = X1,
inference(superposition,[status(thm)],[c_104,c_2283]) ).
tcf(c_14299,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c2) )
| ( X0 != sk_c10 )
| ( inverse(sk_c2) != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_5244]) ).
tcf(c_14984,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(demodulation,[status(thm)],[c_12362,c_2773]) ).
tcf(c_15622,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X0))) = X1,
inference(demodulation,[status(thm)],[c_10638,c_2773]) ).
tcf(c_15725,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(X0,X1))))) = X2,
inference(superposition,[status(thm)],[c_15622,c_105]) ).
tcf(c_16173,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c11 )
| ~ iPr_def_12
| ( inverse(inverse(sk_c5)) != inverse(X0) )
| ( multiply(sk_c5,inverse(X0)) != sk_c8 )
| ( multiply(inverse(X0),sk_c10) != sk_c11 )
| ( multiply(X0,inverse(X0)) != sk_c11 ) ),
inference(resolution,[status(thm)],[c_5606,c_623]) ).
tcf(c_16337,plain,
! [X0: $i] :
( ( sk_c11 = identity )
| ( identity != X0 )
| ( sk_c11 != X0 ) ),
inference(instantiation,[status(thm)],[c_1559]) ).
tcf(c_16340,plain,
( ( sk_c11 = identity )
| ( identity != sk_c10 )
| ( sk_c11 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_16337]) ).
tcf(c_16351,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c5,sk_c8) )
| ( X0 != identity )
| ( multiply(sk_c5,sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_979]) ).
tcf(c_16353,plain,
( ( sk_c10 = multiply(sk_c5,sk_c8) )
| ( sk_c10 != identity )
| ( multiply(sk_c5,sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_16351]) ).
tcf(c_16363,plain,
! [X0: $i] :
( ( X0 = multiply(identity,sk_c11) )
| ( X0 != identity )
| ( multiply(identity,sk_c11) != identity ) ),
inference(instantiation,[status(thm)],[c_1059]) ).
tcf(c_16365,plain,
( ( sk_c10 = multiply(identity,sk_c11) )
| ( sk_c10 != identity )
| ( multiply(identity,sk_c11) != identity ) ),
inference(instantiation,[status(thm)],[c_16363]) ).
tcf(c_16420,plain,
inverse(sk_c1) = sk_c11,
inference(global_subsumption_just,[status(thm)],[c_16173,c_624,c_890,c_903,c_913,c_924,c_942,c_1373,c_1557,c_2215,c_3167,c_3211,c_3541,c_3821,c_4119,c_5256,c_5260,c_9887,c_16340,c_16353]) ).
tcf(c_16476,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c2) )
| ( X0 != sk_c10 ) ),
inference(global_subsumption_just,[status(thm)],[c_5790,c_624,c_890,c_903,c_913,c_924,c_942,c_1196,c_1557,c_1787,c_1776,c_1803,c_2121,c_2124,c_2215,c_3167,c_3210,c_3542,c_3796,c_3821,c_4087,c_4848,c_4847,c_7647,c_7659,c_7661,c_9887,c_14299,c_16340,c_16353,c_16365]) ).
tcf(c_16488,plain,
! [X0: $i] :
( ( inverse(sk_c2) = X0 )
| ( X0 != sk_c10 ) ),
inference(resolution,[status(thm)],[c_16476,c_2070]) ).
tcf(c_16489,plain,
( ( inverse(sk_c2) = sk_c10 )
| ( sk_c10 != sk_c10 ) ),
inference(instantiation,[status(thm)],[c_16488]) ).
tcf(c_16796,plain,
inverse(sk_c1) = sk_c11,
inference(global_subsumption_just,[status(thm)],[c_10000,c_16420]) ).
tcf(c_16840,plain,
multiply(sk_c1,sk_c11) = identity,
inference(superposition,[status(thm)],[c_16796,c_9954]) ).
tcf(c_16841,plain,
inverse(sk_c11) = sk_c1,
inference(superposition,[status(thm)],[c_16796,c_9936]) ).
tcf(c_16847,plain,
inverse(sk_c2) = sk_c10,
inference(global_subsumption_just,[status(thm)],[c_10001,c_631,c_16489]) ).
tcf(c_16901,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c10,X0)) = X0,
inference(superposition,[status(thm)],[c_16847,c_9986]) ).
tcf(c_16902,plain,
multiply(sk_c2,sk_c10) = identity,
inference(superposition,[status(thm)],[c_16847,c_9954]) ).
tcf(c_16903,plain,
inverse(sk_c10) = sk_c2,
inference(superposition,[status(thm)],[c_16847,c_9936]) ).
tcf(c_16951,plain,
( ( inverse(sk_c4) = sk_c10 )
| ( sk_c9 = identity ) ),
inference(global_subsumption_just,[status(thm)],[c_10764,c_5666]) ).
tcf(c_16952,plain,
( ( sk_c9 = identity )
| ( inverse(sk_c4) = sk_c10 ) ),
inference(renaming,[status(thm)],[c_16951]) ).
tcf(c_16960,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c4,sk_c10) = identity ) ),
inference(superposition,[status(thm)],[c_16952,c_9954]) ).
tcf(c_17112,plain,
( ( inverse(sk_c3) = sk_c11 )
| ( sk_c10 = identity ) ),
inference(global_subsumption_just,[status(thm)],[c_10783,c_5628]) ).
tcf(c_17113,plain,
( ( sk_c10 = identity )
| ( inverse(sk_c3) = sk_c11 ) ),
inference(renaming,[status(thm)],[c_17112]) ).
tcf(c_17121,plain,
( ( sk_c10 = identity )
| ( multiply(sk_c3,sk_c11) = identity ) ),
inference(superposition,[status(thm)],[c_17113,c_9954]) ).
tcf(c_17534,plain,
( ( sk_c9 = identity )
| ( multiply(sk_c2,sk_c10) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_16960,c_128]) ).
tcf(c_17586,plain,
sk_c9 = identity,
inference(light_normalisation,[status(thm)],[c_17534,c_16902]) ).
tcf(c_17636,plain,
! [X0: $i] : multiply(sk_c9,X0) = X0,
inference(demodulation,[status(thm)],[c_103,c_17586]) ).
tcf(c_17637,plain,
multiply(sk_c9,sk_c10) = sk_c10,
inference(instantiation,[status(thm)],[c_17636]) ).
tcf(c_17671,plain,
inverse(sk_c5) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_10588,c_631,c_624,c_890,c_1196,c_1557,c_1787,c_1776,c_1803,c_2121,c_2124,c_2544,c_3167,c_3821,c_4087,c_4848,c_4847,c_5626,c_6360,c_9887,c_16340,c_17637]) ).
tcf(c_17673,plain,
( ( multiply(sk_c8,sk_c11) = sk_c8 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_2259,c_17671]) ).
tcf(c_17675,plain,
( ( multiply(sk_c8,sk_c11) = sk_c8 )
| ( multiply(sk_c9,sk_c10) = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_2257,c_17671]) ).
tcf(c_17795,plain,
( ( sk_c10 = sk_c9 )
| ( multiply(sk_c3,sk_c11) = sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_17121,c_17586]) ).
tcf(c_17805,plain,
( ( sk_c10 = sk_c9 )
| ( multiply(sk_c1,sk_c11) = sk_c10 ) ),
inference(superposition,[status(thm)],[c_17795,c_106]) ).
tcf(c_17825,plain,
sk_c10 = sk_c9,
inference(light_normalisation,[status(thm)],[c_17805,c_16840,c_17586]) ).
tcf(c_17832,plain,
sk_c10 = identity,
inference(demodulation,[status(thm)],[c_17586,c_17825]) ).
tcf(c_17838,plain,
( ( multiply(sk_c8,sk_c10) = sk_c11 )
| ( multiply(sk_c10,sk_c10) = sk_c11 ) ),
inference(demodulation,[status(thm)],[c_152,c_17825]) ).
tcf(c_17872,plain,
multiply(sk_c8,sk_c10) = sk_c11,
inference(global_subsumption_just,[status(thm)],[c_17838,c_631,c_624,c_890,c_1152,c_1153,c_1196,c_1557,c_1756,c_1787,c_1776,c_1803,c_2121,c_2124,c_2544,c_3167,c_3821,c_4087,c_4848,c_4847,c_6655,c_9887,c_16340,c_17637,c_17832]) ).
tcf(c_18014,plain,
multiply(sk_c8,sk_c11) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_17673,c_631,c_624,c_890,c_894,c_1194,c_1196,c_1557,c_1756,c_1787,c_1776,c_1803,c_2121,c_2124,c_2544,c_3167,c_3821,c_4087,c_4848,c_4847,c_9887,c_16340,c_17637,c_17675,c_17832]) ).
tcf(c_18016,plain,
inverse(multiply(inverse(sk_c8),sk_c8)) = sk_c11,
inference(superposition,[status(thm)],[c_18014,c_14984]) ).
tcf(c_18018,plain,
multiply(inverse(sk_c8),sk_c8) = sk_c11,
inference(superposition,[status(thm)],[c_18014,c_10004]) ).
tcf(c_18023,plain,
inverse(sk_c11) = sk_c11,
inference(light_normalisation,[status(thm)],[c_18016,c_18018]) ).
tcf(c_18157,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c10,X0)) = multiply(identity,X0),
inference(global_subsumption_just,[status(thm)],[c_10768,c_624,c_890,c_894,c_902,c_903,c_919,c_1196,c_1557,c_1787,c_1776,c_1803,c_2121,c_2124,c_3167,c_3821,c_4087,c_4848,c_4847,c_6462,c_7643,c_7647,c_9887,c_16340,c_16365,c_17637,c_17832]) ).
tcf(c_18160,plain,
! [X0: $i] : multiply(sk_c10,X0) = X0,
inference(light_normalisation,[status(thm)],[c_18157,c_16901,c_17832]) ).
tcf(c_18519,plain,
multiply(sk_c8,multiply(sk_c10,inverse(sk_c11))) = identity,
inference(global_subsumption_just,[status(thm)],[c_10577,c_631,c_624,c_890,c_894,c_1194,c_1196,c_1557,c_1756,c_1787,c_1776,c_1803,c_2121,c_2124,c_2544,c_3167,c_3821,c_4087,c_4848,c_4847,c_5058,c_9887,c_16340,c_17637,c_17832]) ).
tcf(c_18521,plain,
multiply(sk_c8,multiply(sk_c10,sk_c11)) = sk_c10,
inference(light_normalisation,[status(thm)],[c_18519,c_17832,c_18023]) ).
tcf(c_18522,plain,
sk_c10 = sk_c8,
inference(demodulation,[status(thm)],[c_18521,c_18014,c_18160]) ).
tcf(c_18531,plain,
multiply(sk_c10,sk_c10) = sk_c11,
inference(demodulation,[status(thm)],[c_17872,c_18522]) ).
tcf(c_18766,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))) = sk_c10,
inference(light_normalisation,[status(thm)],[c_10549,c_17832]) ).
tcf(c_18782,plain,
! [X0: $i] : multiply(inverse(X0),X0) = sk_c10,
inference(superposition,[status(thm)],[c_15725,c_18766]) ).
tcf(c_18827,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1))) = sk_c10,
inference(superposition,[status(thm)],[c_18766,c_2283]) ).
tcf(c_18839,plain,
inverse(sk_c10) = sk_c10,
inference(demodulation,[status(thm)],[c_18827,c_18782]) ).
tcf(c_18940,plain,
sk_c1 = sk_c11,
inference(light_normalisation,[status(thm)],[c_16841,c_18023]) ).
tcf(c_18942,plain,
sk_c10 = sk_c2,
inference(light_normalisation,[status(thm)],[c_16903,c_18839]) ).
tcf(c_18971,plain,
sk_c11 = sk_c10,
inference(light_normalisation,[status(thm)],[c_16902,c_17832,c_18531,c_18942]) ).
tcf(c_18973,plain,
sk_c1 = sk_c10,
inference(demodulation,[status(thm)],[c_18940,c_18971]) ).
tcf(c_18978,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18973,c_18839,c_17832,c_17637,c_16420,c_16340,c_9887,c_6078,c_6077,c_5260,c_5256,c_3167,c_2579,c_1597,c_1557,c_1193,c_894,c_890,c_624,c_631]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP263-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 14:19:17 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 36.95/6.81 % SZS status Started for theBenchmark.p
% 36.95/6.81 % SZS status Unsatisfiable for theBenchmark.p
% 36.95/6.81
% 36.95/6.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 36.95/6.81
% 36.95/6.81 % ------ iProver source info
% 36.95/6.81
% 36.95/6.81 % git: date: 2026-07-19 20:42:38 +0200
% 36.95/6.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 36.95/6.81 % git: non_committed_changes: false
% 36.95/6.81
% 36.95/6.81 % ------ Parsing...% successful
% 36.95/6.81
% 36.95/6.81
% 36.95/6.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 36.95/6.81
% 36.95/6.81 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 36.95/6.81
% 36.95/6.81 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 36.95/6.81
% 36.95/6.81 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 36.95/6.81 % ------ Proving...
% 36.95/6.81 % ------ Problem Properties
% 36.95/6.81
% 36.95/6.81 %
% 36.95/6.81 % clauses 57
% 36.95/6.81 % conjectures 54
% 36.95/6.81 % EPR 0
% 36.95/6.81 % Horn 6
% 36.95/6.81 % unary 3
% 36.95/6.81 % binary 50
% 36.95/6.81 % lits 118
% 36.95/6.81 % lits eq 112
% 36.95/6.81 % fd_pure 0
% 36.95/6.81 % fd_pseudo 0
% 36.95/6.81 % fd_cond 0
% 36.95/6.81 % fd_pseudo_cond 0
% 36.95/6.81 % AC symbols 0
% 36.95/6.81
% 36.95/6.81 % ------ Input Options Time Limit: Unbounded
% 36.95/6.81
% 36.95/6.81
% 36.95/6.81 % ------
% 36.95/6.81 % Current options:
% 36.95/6.81 % ------
% 36.95/6.81
% 36.95/6.81
% 36.95/6.81 %
% 36.95/6.81
% 36.95/6.81 % ------ Proving...
% 36.95/6.81 %
% 36.95/6.81
% 36.95/6.81 % SZS status Unsatisfiable for theBenchmark.p
% 36.95/6.81
% 36.95/6.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 36.95/6.82
% 36.95/6.82
%------------------------------------------------------------------------------