%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP209-1 : 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 : n011.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 01:31:48 PM UTC 2026
% Result : Unsatisfiable 7.34s 2.25s
% Output : CNFRefutation 7.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 49
% Syntax : Number of formulae : 392 ( 113 unt; 13 def)
% Number of atoms : 1338 ( 742 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 584 ( 189 ~; 395 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn 112 !; 0 ?; 72 :)
% 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(f7,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c9 = inverse(sk_c6)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = 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_c7,sk_c8)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c7)
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(reorient_equations,[],[f15]) ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c6,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_c6,sk_c9)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c9 = inverse(sk_c6)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = inverse(sk_c7)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c10 = inverse(sk_c5)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c9 = inverse(sk_c6)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c7,sk_c8) = 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_c7,sk_c8)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c7)
| sk_c10 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f43]) ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c10 = inverse(sk_c5)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f49]) ).
fof(f53,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c9 = inverse(sk_c6)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f53]) ).
fof(f57,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c7)
| sk_c9 = multiply(sk_c10,sk_c4) ),
inference(reorient_equations,[],[f57]) ).
fof(f63,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f63]) ).
fof(f67,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c9 = inverse(sk_c6)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c8 = inverse(sk_c7)
| sk_c4 = multiply(sk_c3,sk_c10) ),
inference(reorient_equations,[],[f71]) ).
fof(f75,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c10 = inverse(sk_c5)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
( sk_c10 = multiply(sk_c5,sk_c9)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f77]) ).
fof(f79,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_38) ).
fof(f80,plain,
( sk_c10 = multiply(sk_c6,sk_c9)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f79]) ).
fof(f81,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_39) ).
fof(f82,plain,
( sk_c9 = inverse(sk_c6)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f81]) ).
fof(f83,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_40) ).
fof(f84,plain,
( sk_c9 = multiply(sk_c7,sk_c8)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f83]) ).
fof(f85,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_41) ).
fof(f86,plain,
( sk_c8 = inverse(sk_c7)
| sk_c10 = inverse(sk_c3) ),
inference(reorient_equations,[],[f85]) ).
fof(f89,negated_conjecture,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( multiply(X7,sk_c10) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_43) ).
fof(f90,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( sk_c9 != multiply(X7,sk_c10)
| inverse(X6) != X7
| sk_c9 != multiply(X6,X7)
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2
| sk_c9 != multiply(sk_c10,X2)
| sk_c10 != multiply(X1,sk_c9)
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(reorient_equations,[],[f89]) ).
fof(f91,plain,
! [X2,X3,X0,X6,X7,X4,X5] :
( sk_c9 != multiply(X7,sk_c10)
| inverse(X6) != X7
| sk_c9 != multiply(X6,X7)
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X3)
| multiply(X3,sk_c10) != X2
| sk_c9 != multiply(sk_c10,X2)
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f90]) ).
fof(f92,plain,
! [X3,X0,X6,X7,X4,X5] :
( sk_c9 != multiply(X7,sk_c10)
| inverse(X6) != X7
| sk_c9 != multiply(X6,X7)
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f91]) ).
fof(f93,plain,
! [X3,X0,X6,X4,X5] :
( sk_c9 != multiply(inverse(X6),sk_c10)
| sk_c9 != multiply(X6,inverse(X6))
| sk_c9 != inverse(X5)
| sk_c10 != multiply(X5,sk_c9)
| sk_c10 != multiply(X4,sk_c9)
| sk_c10 != inverse(X4)
| sk_c10 != inverse(X3)
| sk_c9 != multiply(sk_c10,multiply(X3,sk_c10))
| sk_c10 != multiply(inverse(X0),sk_c9)
| sk_c10 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f92]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_96,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_99,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c10 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c10 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c6,sk_c9) = sk_c10 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_116,negated_conjecture,
( ( multiply(sk_c7,sk_c8) = sk_c9 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c2,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c5) = sk_c10 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_120,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c10 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_122,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c10,sk_c4) = sk_c9 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_127,negated_conjecture,
( ( multiply(sk_c3,sk_c10) = sk_c4 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_129,negated_conjecture,
( ( inverse(sk_c6) = sk_c9 )
| ( multiply(sk_c3,sk_c10) = sk_c4 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_130,negated_conjecture,
( ( multiply(sk_c3,sk_c10) = sk_c4 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_131,negated_conjecture,
( ( inverse(sk_c7) = sk_c8 )
| ( multiply(sk_c3,sk_c10) = sk_c4 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_133,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c5) = sk_c10 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_134,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c5,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_135,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c6,sk_c9) = sk_c10 ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_136,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c6) = sk_c9 ) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_137,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( multiply(sk_c7,sk_c8) = sk_c9 ) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_138,negated_conjecture,
( ( inverse(sk_c3) = sk_c10 )
| ( inverse(sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_140,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X3) != sk_c10 )
| ( inverse(X2) != sk_c10 )
| ( inverse(X1) != sk_c9 )
| ( 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,[],[f93]) ).
tcf(c_529,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_140]) ).
tcf(c_530,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_140]) ).
tcf(c_531,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_140]) ).
tcf(c_532,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_140]) ).
tcf(c_533,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_140]) ).
tcf(c_534,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_140]) ).
tcf(c_535,definition,
iPr_def_15 = multiply(sk_c8,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_536,definition,
iPr_def_16 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_537,definition,
iPr_def_17 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_538,definition,
iPr_def_18 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_539,definition,
iPr_def_19 = inverse(sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_540,definition,
iPr_def_20 = multiply(sk_c6,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_541,definition,
iPr_def_21 = multiply(sk_c5,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_542,definition,
iPr_def_22 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_543,definition,
iPr_def_23 = multiply(sk_c3,sk_c10),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_544,definition,
iPr_def_24 = multiply(sk_c10,sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_545,definition,
iPr_def_25 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_546,definition,
iPr_def_26 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_547,definition,
iPr_def_27 = multiply(sk_c1,sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_27])],[]) ).
tcf(c_548,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_534]) ).
tcf(c_549,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c10 )
| ( multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_533]) ).
tcf(c_550,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c10 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_532]) ).
tcf(c_551,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( multiply(inverse(X0),sk_c9) != sk_c10 )
| ( multiply(X0,inverse(X0)) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_531]) ).
tcf(c_552,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c10 ) ),
inference(demodulation,[status(thm)],[c_530]) ).
tcf(c_553,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(inverse(X0),sk_c10) != sk_c9 )
| ( multiply(X0,inverse(X0)) != sk_c9 ) ),
inference(demodulation,[status(thm)],[c_529]) ).
tcf(c_555,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_138,c_537]) ).
tcf(c_556,negated_conjecture,
( ( iPr_def_18 = sk_c9 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_137,c_538]) ).
tcf(c_557,negated_conjecture,
( ( iPr_def_19 = sk_c9 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_136,c_539]) ).
tcf(c_558,negated_conjecture,
( ( iPr_def_20 = sk_c10 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_135,c_540]) ).
tcf(c_559,negated_conjecture,
( ( iPr_def_21 = sk_c10 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_134,c_541]) ).
tcf(c_560,negated_conjecture,
( ( iPr_def_22 = sk_c10 )
| ( iPr_def_16 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_133,c_542]) ).
tcf(c_562,negated_conjecture,
( ( iPr_def_23 = sk_c4 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_131]) ).
tcf(c_563,negated_conjecture,
( ( iPr_def_23 = sk_c4 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_130]) ).
tcf(c_564,negated_conjecture,
( ( iPr_def_23 = sk_c4 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_129]) ).
tcf(c_566,negated_conjecture,
( ( iPr_def_23 = sk_c4 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_127]) ).
tcf(c_569,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_124]) ).
tcf(c_571,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_573,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_574,negated_conjecture,
( ( iPr_def_24 = sk_c9 )
| ( iPr_def_22 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_576,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_577,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_578,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_115]) ).
tcf(c_579,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_20 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_580,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_581,negated_conjecture,
( ( iPr_def_25 = sk_c10 )
| ( iPr_def_22 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_583,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_584,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_585,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_586,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_20 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_587,negated_conjecture,
( ( iPr_def_26 = sk_c2 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_590,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_591,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_18 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_592,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_19 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_593,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_20 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_594,negated_conjecture,
( ( iPr_def_27 = sk_c10 )
| ( iPr_def_21 = sk_c10 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_596,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_597,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_907,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c10 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_558,c_559]) ).
tcf(c_935,plain,
( ( sk_c10 = iPr_def_16 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_555,c_538]) ).
tcf(c_938,plain,
( ( sk_c10 = iPr_def_16 )
| ( multiply(sk_c6,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_557,c_540]) ).
tcf(c_1022,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c10,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_566,c_544]) ).
tcf(c_1060,plain,
multiply(iPr_def_22,sk_c5) = identity,
inference(superposition,[status(thm)],[c_542,c_96]) ).
tcf(c_1061,plain,
multiply(iPr_def_19,sk_c6) = identity,
inference(superposition,[status(thm)],[c_539,c_96]) ).
tcf(c_1062,plain,
multiply(iPr_def_17,sk_c7) = identity,
inference(superposition,[status(thm)],[c_537,c_96]) ).
tcf(c_1063,plain,
multiply(iPr_def_26,sk_c1) = identity,
inference(superposition,[status(thm)],[c_546,c_96]) ).
tcf(c_1064,plain,
multiply(iPr_def_16,sk_c3) = identity,
inference(superposition,[status(thm)],[c_536,c_96]) ).
tcf(c_1069,plain,
( ( sk_c9 = iPr_def_24 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_569,c_538]) ).
tcf(c_1112,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(sk_c6,iPr_def_24) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_571,c_540]) ).
tcf(c_1172,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_597]) ).
tcf(c_1185,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_573,c_545]) ).
tcf(c_1218,plain,
( ( sk_c10 = iPr_def_22 )
| ( multiply(sk_c5,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_574,c_541]) ).
tcf(c_1308,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1172]) ).
tcf(c_1310,plain,
! [X0: $i] :
( ( X0 = sk_c9 )
| ( sk_c9 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1172]) ).
tcf(c_1319,plain,
( ( sk_c10 = iPr_def_25 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_576,c_538]) ).
tcf(c_1411,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c10 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_578,c_577]) ).
tcf(c_1421,plain,
( ( sk_c10 = iPr_def_25 )
| ( multiply(sk_c6,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_578,c_540]) ).
tcf(c_1467,plain,
( ( iPr_def_19 = sk_c9 )
| ( iPr_def_19 != iPr_def_19 )
| ( sk_c9 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1308]) ).
tcf(c_1468,plain,
iPr_def_19 = iPr_def_19,
inference(instantiation,[status(thm)],[c_596]) ).
tcf(c_1473,plain,
( ( iPr_def_18 = sk_c9 )
| ( iPr_def_18 != iPr_def_18 )
| ( sk_c9 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_1310]) ).
tcf(c_1474,plain,
iPr_def_18 = iPr_def_18,
inference(instantiation,[status(thm)],[c_596]) ).
tcf(c_1486,plain,
( ( sk_c10 = iPr_def_20 )
| ( multiply(sk_c8,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_579,c_535]) ).
tcf(c_1524,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c8,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_580,c_535]) ).
tcf(c_1565,plain,
( ( sk_c10 = iPr_def_22 )
| ( multiply(sk_c8,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_581,c_535]) ).
tcf(c_1608,plain,
( ( sk_c2 = iPr_def_26 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_583,c_538]) ).
tcf(c_1624,plain,
( ( sk_c9 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_584,c_547]) ).
tcf(c_1634,plain,
( ( sk_c9 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_585,c_547]) ).
tcf(c_1646,plain,
( ( sk_c10 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_586,c_547]) ).
tcf(c_1671,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_587,c_547]) ).
tcf(c_1672,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(iPr_def_26,sk_c9) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_587,c_545]) ).
tcf(c_1754,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_18 = X0 )
| ( iPr_def_18 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_597]) ).
tcf(c_1789,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_590,c_538]) ).
tcf(c_1892,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c10 = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_592,c_591]) ).
tcf(c_1904,plain,
( ( sk_c10 = iPr_def_27 )
| ( multiply(sk_c6,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_592,c_540]) ).
tcf(c_1986,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( sk_c10 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_593,c_579]) ).
tcf(c_2041,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( sk_c10 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_594,c_580]) ).
tcf(c_2044,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_27) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_594,c_543]) ).
tcf(c_2045,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c8,iPr_def_27) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_594,c_535]) ).
tcf(c_2149,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c2,X0)) = multiply(iPr_def_27,X0),
inference(superposition,[status(thm)],[c_547,c_97]) ).
tcf(c_2152,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_538,c_97]) ).
tcf(c_2154,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c9,X0)) = multiply(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_545,c_97]) ).
tcf(c_2155,plain,
! [X0: $i] : multiply(sk_c10,multiply(sk_c4,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_544,c_97]) ).
tcf(c_2158,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_96,c_97]) ).
tcf(c_2160,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1060,c_97]) ).
tcf(c_2161,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c6,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1061,c_97]) ).
tcf(c_2162,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1062,c_97]) ).
tcf(c_2163,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1063,c_97]) ).
tcf(c_2164,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1064,c_97]) ).
tcf(c_2166,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2164,c_95]) ).
tcf(c_2167,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2163,c_95]) ).
tcf(c_2168,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2162,c_95]) ).
tcf(c_2169,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c6,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2161,c_95]) ).
tcf(c_2170,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2160,c_95]) ).
tcf(c_2504,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_907,c_543]) ).
tcf(c_2604,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_21 )
| ( inverse(sk_c5) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_541,c_550]) ).
tcf(c_2607,plain,
( ~ iPr_def_13
| ( sk_c10 != sk_c9 )
| ( inverse(identity) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_95,c_550]) ).
tcf(c_2608,plain,
( ~ iPr_def_13
| ( sk_c10 != identity )
| ( inverse(inverse(sk_c9)) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_96,c_550]) ).
tcf(c_2635,plain,
( ~ iPr_def_13
| ( sk_c10 != iPr_def_22 )
| ( sk_c10 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2604,c_542]) ).
tcf(c_2789,plain,
( ~ iPr_def_11
| ( sk_c10 != identity )
| ( inverse(inverse(sk_c9)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_96,c_552]) ).
tcf(c_2996,plain,
( ~ iPr_def_14
| ( inverse(identity) != sk_c10 )
| ( multiply(sk_c10,sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_549]) ).
tcf(c_3097,plain,
! [X0: $i] :
( ( iPr_def_18 = X0 )
| ( iPr_def_18 != sk_c9 )
| ( X0 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_1754]) ).
tcf(c_3186,plain,
( ~ iPr_def_10
| ( inverse(identity) != sk_c9 )
| ( multiply(inverse(identity),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_95,c_553]) ).
tcf(c_3622,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(sk_c8,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1411,c_535]) ).
tcf(c_3893,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_27,sk_c4) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1892,c_544]) ).
tcf(c_4229,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_2041,c_1986]) ).
tcf(c_4728,plain,
multiply(iPr_def_16,iPr_def_23) = sk_c10,
inference(superposition,[status(thm)],[c_543,c_2166]) ).
tcf(c_4731,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_23,X0)) = multiply(sk_c10,X0),
inference(superposition,[status(thm)],[c_4728,c_97]) ).
tcf(c_4733,plain,
multiply(iPr_def_26,iPr_def_27) = sk_c2,
inference(superposition,[status(thm)],[c_547,c_2167]) ).
tcf(c_4797,plain,
! [X0: $i] : multiply(iPr_def_26,multiply(iPr_def_27,X0)) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_4733,c_97]) ).
tcf(c_4799,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c8,
inference(superposition,[status(thm)],[c_538,c_2168]) ).
tcf(c_4805,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_18,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4799,c_97]) ).
tcf(c_4807,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c9,
inference(superposition,[status(thm)],[c_540,c_2169]) ).
tcf(c_4833,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4807,c_97]) ).
tcf(c_4995,plain,
multiply(iPr_def_22,iPr_def_21) = sk_c9,
inference(superposition,[status(thm)],[c_541,c_2170]) ).
tcf(c_5010,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_21,X0)) = multiply(sk_c9,X0),
inference(superposition,[status(thm)],[c_4995,c_97]) ).
tcf(c_5198,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(iPr_def_25,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_580,c_1022]) ).
tcf(c_6426,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(iPr_def_26,iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_587,c_1185]) ).
tcf(c_6542,plain,
( ( sk_c10 = iPr_def_22 )
| ( multiply(iPr_def_22,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1218,c_2170]) ).
tcf(c_6543,plain,
( ( sk_c9 = iPr_def_24 )
| ( sk_c10 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_6542,c_4995]) ).
tcf(c_9532,plain,
multiply(sk_c1,iPr_def_25) = multiply(iPr_def_27,sk_c9),
inference(superposition,[status(thm)],[c_545,c_2149]) ).
tcf(c_9956,plain,
multiply(sk_c7,iPr_def_15) = multiply(iPr_def_18,sk_c10),
inference(superposition,[status(thm)],[c_535,c_2152]) ).
tcf(c_10618,plain,
( ~ iPr_def_14
| ( inverse(sk_c4) != sk_c10 )
| ( multiply(iPr_def_24,sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_2155,c_549]) ).
tcf(c_12203,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2158,c_95]) ).
tcf(c_12213,plain,
multiply(inverse(sk_c8),iPr_def_15) = sk_c10,
inference(superposition,[status(thm)],[c_535,c_12203]) ).
tcf(c_12214,plain,
multiply(inverse(sk_c2),iPr_def_25) = sk_c9,
inference(superposition,[status(thm)],[c_545,c_12203]) ).
tcf(c_12215,plain,
multiply(inverse(sk_c10),iPr_def_24) = sk_c4,
inference(superposition,[status(thm)],[c_544,c_12203]) ).
tcf(c_12217,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_95,c_12203]) ).
tcf(c_12218,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_96,c_12203]) ).
tcf(c_12318,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_3622,c_12203]) ).
tcf(c_12320,plain,
( ( sk_c10 = iPr_def_22 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1565,c_12203]) ).
tcf(c_12321,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1524,c_12203]) ).
tcf(c_12322,plain,
( ( sk_c10 = iPr_def_20 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1486,c_12203]) ).
tcf(c_12351,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_2045,c_12203]) ).
tcf(c_12362,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2170,c_12203]) ).
tcf(c_12363,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_2169,c_12203]) ).
tcf(c_12364,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2168,c_12203]) ).
tcf(c_12365,plain,
! [X0: $i] : multiply(inverse(iPr_def_26),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2167,c_12203]) ).
tcf(c_12366,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2166,c_12203]) ).
tcf(c_12388,plain,
multiply(inverse(iPr_def_16),sk_c10) = iPr_def_23,
inference(superposition,[status(thm)],[c_4728,c_12203]) ).
tcf(c_12402,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(inverse(iPr_def_25),iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_5198,c_12203]) ).
tcf(c_12414,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_12203,c_12203]) ).
tcf(c_13259,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_12218,c_12414]) ).
tcf(c_13268,plain,
multiply(sk_c2,identity) = multiply(iPr_def_26,iPr_def_27),
inference(superposition,[status(thm)],[c_13259,c_4797]) ).
tcf(c_13269,plain,
multiply(sk_c1,sk_c2) = multiply(iPr_def_27,identity),
inference(superposition,[status(thm)],[c_13259,c_2149]) ).
tcf(c_13270,plain,
multiply(sk_c9,identity) = multiply(iPr_def_22,iPr_def_21),
inference(superposition,[status(thm)],[c_13259,c_5010]) ).
tcf(c_13271,plain,
multiply(sk_c2,sk_c9) = multiply(iPr_def_25,identity),
inference(superposition,[status(thm)],[c_13259,c_2154]) ).
tcf(c_13274,plain,
multiply(sk_c9,identity) = multiply(iPr_def_19,iPr_def_20),
inference(superposition,[status(thm)],[c_13259,c_4833]) ).
tcf(c_13275,plain,
multiply(sk_c8,identity) = multiply(iPr_def_17,iPr_def_18),
inference(superposition,[status(thm)],[c_13259,c_4805]) ).
tcf(c_13280,plain,
multiply(sk_c10,identity) = multiply(iPr_def_16,iPr_def_23),
inference(superposition,[status(thm)],[c_13259,c_4731]) ).
tcf(c_13286,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_13259,c_12217]) ).
tcf(c_13287,plain,
multiply(sk_c10,identity) = sk_c10,
inference(light_normalisation,[status(thm)],[c_13280,c_4728]) ).
tcf(c_13292,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_13275,c_4799]) ).
tcf(c_13293,plain,
multiply(sk_c9,identity) = sk_c9,
inference(light_normalisation,[status(thm)],[c_13274,c_4807]) ).
tcf(c_13296,plain,
multiply(iPr_def_25,identity) = iPr_def_25,
inference(light_normalisation,[status(thm)],[c_13271,c_545]) ).
tcf(c_13298,plain,
multiply(iPr_def_27,identity) = iPr_def_27,
inference(light_normalisation,[status(thm)],[c_13269,c_547]) ).
tcf(c_13299,plain,
multiply(sk_c2,identity) = sk_c2,
inference(light_normalisation,[status(thm)],[c_13268,c_4733]) ).
tcf(c_13308,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_13286,c_96]) ).
tcf(c_17767,plain,
multiply(sk_c5,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_12362,c_96]) ).
tcf(c_17768,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c9 )
| ( multiply(sk_c5,sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_12362,c_552]) ).
tcf(c_17769,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_22)) != sk_c10 )
| ( multiply(sk_c5,sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_12362,c_550]) ).
tcf(c_17772,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_22)) != sk_c10 )
| ( multiply(sk_c10,multiply(sk_c5,sk_c10)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_12362,c_549]) ).
tcf(c_17773,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_12362,c_12203]) ).
tcf(c_17774,plain,
multiply(sk_c5,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_12362,c_13259]) ).
tcf(c_17779,plain,
( ~ iPr_def_11
| ( sk_c10 != iPr_def_21 )
| ( inverse(inverse(iPr_def_22)) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_17768,c_541]) ).
tcf(c_17797,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(superposition,[status(thm)],[c_17767,c_2170]) ).
tcf(c_17802,plain,
inverse(iPr_def_22) = sk_c5,
inference(demodulation,[status(thm)],[c_17774,c_13259]) ).
tcf(c_17806,plain,
( ~ iPr_def_12
| ( multiply(iPr_def_22,sk_c5) != sk_c10 )
| ( multiply(inverse(iPr_def_22),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_17802,c_551]) ).
tcf(c_17808,plain,
( ~ iPr_def_12
| ( sk_c10 != iPr_def_21 )
| ( sk_c10 != identity ) ),
inference(light_normalisation,[status(thm)],[c_17806,c_541,c_1060,c_17802]) ).
tcf(c_17824,plain,
multiply(sk_c5,sk_c9) = iPr_def_21,
inference(superposition,[status(thm)],[c_4995,c_17773]) ).
tcf(c_18015,plain,
multiply(sk_c6,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_12363,c_96]) ).
tcf(c_18021,plain,
! [X0: $i] : multiply(sk_c6,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_12363,c_12203]) ).
tcf(c_18040,plain,
( ( identity = iPr_def_20 )
| ( sk_c10 = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_1904,c_18015]) ).
tcf(c_18041,plain,
( ( identity = iPr_def_20 )
| ( sk_c10 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1421,c_18015]) ).
tcf(c_18042,plain,
( ( identity = iPr_def_20 )
| ( sk_c10 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_938,c_18015]) ).
tcf(c_18054,plain,
multiply(iPr_def_19,identity) = iPr_def_19,
inference(superposition,[status(thm)],[c_18015,c_2169]) ).
tcf(c_18200,plain,
( ( identity = iPr_def_20 )
| ( multiply(iPr_def_27,sk_c4) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_18040,c_544]) ).
tcf(c_18372,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_18041,c_18040]) ).
tcf(c_18416,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c8,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_18041,c_535]) ).
tcf(c_18598,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_18042,c_543]) ).
tcf(c_18787,plain,
multiply(sk_c6,identity) = sk_c6,
inference(superposition,[status(thm)],[c_1061,c_18021]) ).
tcf(c_18788,plain,
multiply(sk_c6,sk_c9) = iPr_def_20,
inference(superposition,[status(thm)],[c_4807,c_18021]) ).
tcf(c_18929,plain,
( ~ iPr_def_13
| ( sk_c10 != identity )
| ( sk_c10 != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_2607,c_13286]) ).
tcf(c_18961,plain,
( ( sk_c10 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c10 != iPr_def_24 )
| ( sk_c10 != identity ) ),
inference(superposition,[status(thm)],[c_573,c_18929]) ).
tcf(c_19214,plain,
multiply(sk_c7,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_12364,c_96]) ).
tcf(c_19220,plain,
! [X0: $i] : multiply(sk_c7,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_12364,c_12203]) ).
tcf(c_19221,plain,
multiply(sk_c7,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_12364,c_13259]) ).
tcf(c_19237,plain,
( ( identity = iPr_def_18 )
| ( sk_c10 = iPr_def_27 ) ),
inference(demodulation,[status(thm)],[c_1789,c_19214]) ).
tcf(c_19238,plain,
( ( identity = iPr_def_18 )
| ( sk_c2 = iPr_def_26 ) ),
inference(demodulation,[status(thm)],[c_1608,c_19214]) ).
tcf(c_19239,plain,
( ( identity = iPr_def_18 )
| ( sk_c10 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_1319,c_19214]) ).
tcf(c_19240,plain,
( ( identity = iPr_def_18 )
| ( sk_c9 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1069,c_19214]) ).
tcf(c_19241,plain,
( ( identity = iPr_def_18 )
| ( sk_c10 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_935,c_19214]) ).
tcf(c_19270,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(superposition,[status(thm)],[c_19214,c_2168]) ).
tcf(c_19273,plain,
inverse(iPr_def_17) = sk_c7,
inference(demodulation,[status(thm)],[c_19221,c_13259]) ).
tcf(c_19510,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_27,sk_c4) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_19237,c_544]) ).
tcf(c_19724,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_26) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_19238,c_547]) ).
tcf(c_19793,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_19239,c_19237]) ).
tcf(c_19839,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c8,iPr_def_25) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_19239,c_535]) ).
tcf(c_19962,plain,
( ( identity = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c10 != iPr_def_24 )
| ( sk_c10 != identity ) ),
inference(superposition,[status(thm)],[c_19240,c_18929]) ).
tcf(c_19994,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c6,iPr_def_24) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_19240,c_540]) ).
tcf(c_20120,plain,
multiply(sk_c7,sk_c8) = iPr_def_18,
inference(superposition,[status(thm)],[c_4799,c_19220]) ).
tcf(c_20286,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c3,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_19241,c_543]) ).
tcf(c_20410,plain,
( ( iPr_def_25 = iPr_def_27 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_19793,c_18372]) ).
tcf(c_20644,plain,
( ( identity = iPr_def_20 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_18416,c_12203]) ).
tcf(c_21507,plain,
multiply(sk_c1,iPr_def_26) = identity,
inference(superposition,[status(thm)],[c_12365,c_96]) ).
tcf(c_21513,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_26,X0)) = X0,
inference(superposition,[status(thm)],[c_12365,c_12203]) ).
tcf(c_21514,plain,
multiply(sk_c1,identity) = inverse(iPr_def_26),
inference(superposition,[status(thm)],[c_12365,c_13259]) ).
tcf(c_21531,plain,
( ( identity = iPr_def_27 )
| ( sk_c10 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_1671,c_21507]) ).
tcf(c_21532,plain,
( ( identity = iPr_def_27 )
| ( sk_c10 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1646,c_21507]) ).
tcf(c_21533,plain,
( ( identity = iPr_def_27 )
| ( sk_c9 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1634,c_21507]) ).
tcf(c_21534,plain,
( ( identity = iPr_def_27 )
| ( sk_c9 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1624,c_21507]) ).
tcf(c_21573,plain,
multiply(iPr_def_26,identity) = iPr_def_26,
inference(superposition,[status(thm)],[c_21507,c_2167]) ).
tcf(c_23161,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_21532,c_21531]) ).
tcf(c_23566,plain,
( ( identity = iPr_def_27 )
| ( multiply(sk_c6,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_21533,c_540]) ).
tcf(c_23569,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_23566,c_18015]) ).
tcf(c_23637,plain,
inverse(iPr_def_26) = sk_c1,
inference(demodulation,[status(thm)],[c_21514,c_13259]) ).
tcf(c_23671,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_25) = sk_c9 ) ),
inference(superposition,[status(thm)],[c_1672,c_21513]) ).
tcf(c_23679,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_25) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_6426,c_21513]) ).
tcf(c_23700,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(iPr_def_27,sk_c9) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_23679,c_9532]) ).
tcf(c_23718,plain,
( ( sk_c10 = iPr_def_21 )
| ( multiply(iPr_def_27,sk_c9) = sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_23671,c_9532]) ).
tcf(c_23870,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( identity = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_21534,c_21533]) ).
tcf(c_23916,plain,
( ( identity = iPr_def_27 )
| ( multiply(sk_c6,iPr_def_18) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_21534,c_540]) ).
tcf(c_24131,plain,
! [X0: $i] :
( ( identity = iPr_def_20 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_23569,c_95]) ).
tcf(c_24543,plain,
( ( identity = iPr_def_27 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_19724,c_21507]) ).
tcf(c_24562,plain,
( ( identity = iPr_def_18 )
| ( inverse(iPr_def_27) = iPr_def_27 ) ),
inference(superposition,[status(thm)],[c_24543,c_13286]) ).
tcf(c_24564,plain,
! [X0: $i] :
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_24543,c_95]) ).
tcf(c_24676,plain,
! [X0: $i] :
( ( iPr_def_18 = iPr_def_19 )
| ( multiply(iPr_def_27,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_23870,c_95]) ).
tcf(c_24803,plain,
multiply(sk_c3,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_12366,c_96]) ).
tcf(c_24808,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_16)) != sk_c10 )
| ( multiply(sk_c10,multiply(sk_c3,sk_c10)) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_12366,c_549]) ).
tcf(c_24809,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_12366,c_12203]) ).
tcf(c_24810,plain,
multiply(sk_c3,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_12366,c_13259]) ).
tcf(c_24827,plain,
( ( identity = iPr_def_23 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_18598,c_24803]) ).
tcf(c_24830,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_2504,c_24803]) ).
tcf(c_24931,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_24827,c_23569]) ).
tcf(c_25130,plain,
inverse(iPr_def_16) = sk_c3,
inference(demodulation,[status(thm)],[c_24810,c_13259]) ).
tcf(c_25133,plain,
( ~ iPr_def_10
| ( multiply(iPr_def_16,sk_c3) != sk_c9 )
| ( multiply(inverse(iPr_def_16),sk_c10) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_25130,c_553]) ).
tcf(c_25134,plain,
( ~ iPr_def_12
| ( multiply(iPr_def_16,sk_c3) != sk_c10 )
| ( multiply(inverse(iPr_def_16),sk_c9) != sk_c10 ) ),
inference(superposition,[status(thm)],[c_25130,c_551]) ).
tcf(c_25136,plain,
( ~ iPr_def_12
| ( sk_c10 != identity )
| ( multiply(sk_c3,sk_c9) != sk_c10 ) ),
inference(light_normalisation,[status(thm)],[c_25134,c_1064,c_25130]) ).
tcf(c_25144,plain,
multiply(sk_c3,identity) = sk_c3,
inference(superposition,[status(thm)],[c_1064,c_24809]) ).
tcf(c_25152,plain,
multiply(sk_c3,sk_c10) = iPr_def_23,
inference(superposition,[status(thm)],[c_4728,c_24809]) ).
tcf(c_25249,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_24830,c_23161]) ).
tcf(c_26329,plain,
( ( identity = iPr_def_18 )
| ( multiply(inverse(sk_c8),iPr_def_15) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_19839,c_12203]) ).
tcf(c_26379,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_19994,c_2169]) ).
tcf(c_26435,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_25249,c_4229]) ).
tcf(c_27423,plain,
( ( identity = iPr_def_23 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_20286,c_24803]) ).
tcf(c_27449,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_27423,c_24543]) ).
tcf(c_28860,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( iPr_def_19 != sk_c9 )
| ( iPr_def_18 != sk_c9 ) ),
inference(instantiation,[status(thm)],[c_3097]) ).
tcf(c_29014,plain,
( ( iPr_def_23 = iPr_def_27 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_27449,c_24931]) ).
tcf(c_29118,plain,
( ( iPr_def_23 = iPr_def_25 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_29014,c_20410]) ).
tcf(c_29727,plain,
( ( identity = iPr_def_27 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_23916,c_2169]) ).
tcf(c_30193,plain,
( ( identity = iPr_def_20 )
| ( sk_c4 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_24131,c_18200]) ).
tcf(c_31093,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( identity = iPr_def_20 )
| ( sk_c9 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_30193,c_564]) ).
tcf(c_31706,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( identity = iPr_def_20 )
| ( multiply(sk_c6,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_31093,c_540]) ).
tcf(c_31709,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_31706,c_18015]) ).
tcf(c_32102,plain,
( ~ iPr_def_14
| ( sk_c10 != identity )
| ( multiply(sk_c10,sk_c10) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_2996,c_13286]) ).
tcf(c_32159,plain,
( ( identity = iPr_def_18 )
| ~ iPr_def_14
| ( sk_c10 != identity )
| ( multiply(iPr_def_27,iPr_def_27) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_19237,c_32102]) ).
tcf(c_33103,plain,
( ( identity = iPr_def_18 )
| ( sk_c4 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_24564,c_19510]) ).
tcf(c_33340,plain,
( ( iPr_def_18 = iPr_def_19 )
| ( sk_c4 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_24676,c_3893]) ).
tcf(c_33825,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c10,iPr_def_24) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_33103,c_544]) ).
tcf(c_33831,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_33103,c_562]) ).
tcf(c_33944,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_33340,c_564]) ).
tcf(c_33945,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_19 )
| ( sk_c9 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_33340,c_563]) ).
tcf(c_34801,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( identity = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_33831,c_538]) ).
tcf(c_34806,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_34801,c_19214]) ).
tcf(c_34813,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_33944,c_1467,c_1468,c_1473,c_1474,c_28860,c_33945,c_33944]) ).
tcf(c_39484,plain,
( ( iPr_def_23 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_34806,c_31709]) ).
tcf(c_39829,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( sk_c9 = iPr_def_19 )
| ( multiply(sk_c6,iPr_def_23) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_39484,c_1112]) ).
tcf(c_41548,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_27,iPr_def_27) = identity ) ),
inference(superposition,[status(thm)],[c_24562,c_96]) ).
tcf(c_42400,plain,
( ~ iPr_def_10
| ( sk_c9 != identity )
| ( multiply(identity,sk_c10) != sk_c9 ) ),
inference(light_normalisation,[status(thm)],[c_3186,c_13286]) ).
tcf(c_46466,plain,
( ( identity = iPr_def_18 )
| ( multiply(inverse(sk_c10),iPr_def_24) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_33825,c_12203]) ).
tcf(c_46800,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_46466,c_42400,c_41548,c_39829,c_34813,c_34806,c_32159,c_29727,c_29118,c_27449,c_26435,c_26379,c_26329,c_25152,c_25144,c_25136,c_25133,c_25130,c_24808,c_24803,c_24543,c_23870,c_23718,c_23700,c_23637,c_21573,c_21531,c_20644,c_20120,c_19962,c_19793,c_19273,c_19270,c_19214,c_18961,c_18788,c_18787,c_18054,c_18015,c_17824,c_17808,c_17802,c_17797,c_17779,c_17772,c_17769,c_17767,c_13299,c_13298,c_13296,c_13293,c_13292,c_13287,c_13280,c_13275,c_13274,c_13270,c_13268,c_13286,c_12402,c_12388,c_12351,c_12322,c_12321,c_12320,c_12318,c_12215,c_12214,c_12213,c_10618,c_9956,c_9532,c_6543,c_5198,c_2789,c_2635,c_2608,c_2044,c_1892,c_13308,c_1064,c_560,c_559,c_558,c_557,c_556,c_555,c_542,c_536,c_548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP209-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:08:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 7.34/2.25 % SZS status Started for theBenchmark.p
% 7.34/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 7.34/2.25
% 7.34/2.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.34/2.25
% 7.34/2.25 % ------ iProver source info
% 7.34/2.25
% 7.34/2.25 % git: date: 2026-07-19 20:42:38 +0200
% 7.34/2.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.34/2.25 % git: non_committed_changes: false
% 7.34/2.25
% 7.34/2.25 % ------ Parsing...% successful
% 7.34/2.25
% 7.34/2.25
% 7.34/2.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.34/2.25
% 7.34/2.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 7.34/2.25
% 7.34/2.25 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.34/2.25
% 7.34/2.25 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 7.34/2.25 % ------ Proving...
% 7.34/2.25 % ------ Problem Properties
% 7.34/2.25
% 7.34/2.25 %
% 7.34/2.25 % clauses 64
% 7.34/2.25 % conjectures 48
% 7.34/2.25 % EPR 43
% 7.34/2.25 % Horn 21
% 7.34/2.25 % unary 16
% 7.34/2.25 % binary 42
% 7.34/2.25 % lits 120
% 7.34/2.25 % lits eq 110
% 7.34/2.25 % fd_pure 0
% 7.34/2.25 % fd_pseudo 0
% 7.34/2.25 % fd_cond 0
% 7.34/2.25 % fd_pseudo_cond 0
% 7.34/2.25 % AC symbols 0
% 7.34/2.25
% 7.34/2.25 % ------ Schedule dynamic 5 is on
% 7.34/2.25
% 7.34/2.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.34/2.25
% 7.34/2.25
% 7.34/2.25 % ------
% 7.34/2.25 % Current options:
% 7.34/2.25 % ------
% 7.34/2.25
% 7.34/2.25
% 7.34/2.25 %
% 7.34/2.25
% 7.34/2.25 % ------ Proving...
% 7.34/2.25 %
% 7.34/2.25
% 7.34/2.25 % SZS status Unsatisfiable for theBenchmark.p
% 7.34/2.25
% 7.34/2.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.34/2.26
% 7.34/2.26
%------------------------------------------------------------------------------