%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP337-1 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:03 PM UTC 2026
% Result : Unsatisfiable 34.24s 6.40s
% Output : CNFRefutation 34.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 48
% Syntax : Number of formulae : 507 ( 159 unt; 12 def)
% Number of atoms : 1802 ( 910 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 700 ( 228 ~; 472 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn 120 !; 0 ?; 100 :)
% 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_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = inverse(sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = inverse(sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f31]) ).
fof(f35,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c6 = inverse(sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = inverse(sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c4)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = inverse(sk_c8)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c6 = inverse(sk_c5)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f65]) ).
fof(f67,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_32) ).
fof(f68,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f67]) ).
fof(f69,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_33) ).
fof(f70,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f69]) ).
fof(f71,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_34) ).
fof(f72,plain,
( sk_c6 = inverse(sk_c8)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f71]) ).
fof(f75,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_36) ).
fof(f76,plain,
( sk_c6 = inverse(sk_c5)
| sk_c7 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f75]) ).
fof(f77,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_37) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( sk_c6 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c7 != multiply(X2,sk_c8)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(reorient_equations,[],[f77]) ).
fof(f79,plain,
! [X3,X0,X1,X4] :
( sk_c6 != inverse(X4)
| sk_c7 != multiply(X4,sk_c6)
| sk_c6 != inverse(sk_c8)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != multiply(sk_c7,sk_c6)
| sk_c7 != multiply(inverse(X1),sk_c8)
| sk_c7 != multiply(X1,inverse(X1))
| sk_c8 != multiply(X0,sk_c7)
| inverse(X0) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(equality_resolution,[],[f78]) ).
tcf(c_89,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_90,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c7,sk_c6) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c2,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_116,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_117,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_118,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_119,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_120,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_121,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_122,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_123,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_124,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_125,negated_conjecture,
( ( inverse(sk_c8) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_127,negated_conjecture,
( ( inverse(sk_c5) = sk_c6 )
| ( multiply(sk_c3,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_128,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c6 )
| ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c6) != sk_c7 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(inverse(X1),sk_c8) != sk_c7 )
| ( multiply(X1,inverse(X1)) != sk_c7 ) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_130,plain,
multiply(inverse(sk_c8),sk_c8) = identity,
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_473,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_128]) ).
tcf(c_474,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_128]) ).
tcf(c_475,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_128]) ).
tcf(c_476,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c8) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_128]) ).
tcf(c_477,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c6 )
| ( multiply(sk_c7,sk_c6) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_128]) ).
tcf(c_478,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_479,definition,
iPr_def_15 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_480,definition,
iPr_def_16 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_481,definition,
iPr_def_17 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_482,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_483,definition,
iPr_def_19 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_484,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_485,definition,
iPr_def_21 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_486,definition,
iPr_def_22 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_487,definition,
iPr_def_23 = multiply(sk_c2,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_488,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_489,definition,
iPr_def_25 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_490,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c6 )
| ( iPr_def_15 != sk_c8 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_477,c_480,c_479,c_478]) ).
tcf(c_491,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( multiply(inverse(X0),sk_c8) != sk_c7 )
| ( multiply(X0,inverse(X0)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_476]) ).
tcf(c_492,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_475]) ).
tcf(c_493,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_474]) ).
tcf(c_494,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_473]) ).
tcf(c_495,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_127,c_482,c_481]) ).
tcf(c_497,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_125]) ).
tcf(c_498,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_124,c_484]) ).
tcf(c_499,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_123,c_485]) ).
tcf(c_500,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_122]) ).
tcf(c_501,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_121,c_486]) ).
tcf(c_502,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_120]) ).
tcf(c_503,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_119]) ).
tcf(c_504,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_118]) ).
tcf(c_505,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_117]) ).
tcf(c_506,negated_conjecture,
( ( iPr_def_22 = sk_c3 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_116]) ).
tcf(c_507,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_487]) ).
tcf(c_508,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_114]) ).
tcf(c_509,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_113]) ).
tcf(c_510,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112]) ).
tcf(c_511,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_512,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110]) ).
tcf(c_513,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109,c_488]) ).
tcf(c_515,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_517,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_518,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_519,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103,c_489]) ).
tcf(c_521,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_523,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_524,negated_conjecture,
( ( iPr_def_25 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_525,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_526,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_527,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95]) ).
tcf(c_529,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_530,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_531,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_782,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_495,c_497]) ).
tcf(c_860,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c8) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_502,c_481]) ).
tcf(c_861,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_22,sk_c8) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_501,c_481]) ).
tcf(c_942,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_509,c_507]) ).
tcf(c_961,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_510,c_498]) ).
tcf(c_976,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_507,c_483]) ).
tcf(c_988,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_505,c_487]) ).
tcf(c_989,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_504,c_487]) ).
tcf(c_990,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_503,c_487]) ).
tcf(c_991,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_502,c_487]) ).
tcf(c_992,plain,
( ( sk_c6 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_501,c_487]) ).
tcf(c_1008,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_499,c_488]) ).
tcf(c_1009,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_17) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_498,c_488]) ).
tcf(c_1026,plain,
! [X0: $i,X1: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1027,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1026]) ).
tcf(c_1028,plain,
sk_c6 = sk_c6,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1031,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_484,c_90]) ).
tcf(c_1032,plain,
multiply(iPr_def_16,sk_c8) = identity,
inference(superposition,[status(thm)],[c_480,c_90]) ).
tcf(c_1033,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_482,c_90]) ).
tcf(c_1034,plain,
multiply(iPr_def_25,sk_c1) = identity,
inference(superposition,[status(thm)],[c_489,c_90]) ).
tcf(c_1035,plain,
multiply(iPr_def_22,sk_c2) = identity,
inference(superposition,[status(thm)],[c_486,c_90]) ).
tcf(c_1041,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1043,plain,
( ( sk_c6 = iPr_def_16 )
| ( iPr_def_16 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1027]) ).
tcf(c_1044,plain,
( ( sk_c6 = iPr_def_18 )
| ( iPr_def_18 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1027]) ).
tcf(c_1054,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_511,c_488]) ).
tcf(c_1090,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_512,c_500]) ).
tcf(c_1120,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_513,c_483]) ).
tcf(c_1211,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_515,c_513]) ).
tcf(c_1214,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(sk_c7,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_515,c_479]) ).
tcf(c_1305,plain,
iPr_def_16 = iPr_def_16,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_1325,plain,
( ( sk_c8 = iPr_def_15 )
| ( inverse(iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_518,c_480]) ).
tcf(c_1462,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_521,c_519]) ).
tcf(c_1466,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(sk_c7,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_521,c_479]) ).
tcf(c_1475,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_1599,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_25) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_524,c_485]) ).
tcf(c_1766,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_527,c_525]) ).
tcf(c_1769,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_527,c_483]) ).
tcf(c_2095,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_19 )
| ( inverse(sk_c5) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_483,c_492]) ).
tcf(c_2097,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_90,c_492]) ).
tcf(c_2115,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 )
| ( sk_c7 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2095,c_482]) ).
tcf(c_2237,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_488,c_493]) ).
tcf(c_2255,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_25 )
| ( sk_c8 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2237,c_489]) ).
tcf(c_2329,plain,
! [X0: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != iPr_def_16 )
| ( X0 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_1475]) ).
tcf(c_2365,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_21 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_485,c_494]) ).
tcf(c_2366,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_17 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_481,c_494]) ).
tcf(c_2369,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(iPr_def_16) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_1032,c_494]) ).
tcf(c_2383,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_20 )
| ( sk_c7 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2365,c_484]) ).
tcf(c_2533,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_17,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_782,c_478]) ).
tcf(c_2586,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_478,c_91]) ).
tcf(c_2587,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_479,c_91]) ).
tcf(c_2588,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_485,c_91]) ).
tcf(c_2589,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_483,c_91]) ).
tcf(c_2590,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_488,c_91]) ).
tcf(c_2591,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c3,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_487,c_91]) ).
tcf(c_2592,plain,
! [X0: $i] : multiply(sk_c3,multiply(sk_c8,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_481,c_91]) ).
tcf(c_2594,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_90,c_91]) ).
tcf(c_2596,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1031,c_91]) ).
tcf(c_2597,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1032,c_91]) ).
tcf(c_2598,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1033,c_91]) ).
tcf(c_2599,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1034,c_91]) ).
tcf(c_2600,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1035,c_91]) ).
tcf(c_2606,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2600,c_89]) ).
tcf(c_2607,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2599,c_89]) ).
tcf(c_2608,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2598,c_89]) ).
tcf(c_2609,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2597,c_89]) ).
tcf(c_2610,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2596,c_89]) ).
tcf(c_2707,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_1041]) ).
tcf(c_2850,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_23,sk_c6) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_942,c_479]) ).
tcf(c_2851,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_942,c_478]) ).
tcf(c_2930,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_961,c_485]) ).
tcf(c_3073,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1211,c_480]) ).
tcf(c_3209,plain,
( ( iPr_def_24 = iPr_def_25 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1462,c_1211]) ).
tcf(c_3703,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 != iPr_def_16 )
| ( sk_c8 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_1766,c_490]) ).
tcf(c_3903,plain,
multiply(iPr_def_25,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_488,c_2607]) ).
tcf(c_3906,plain,
! [X0: $i] : multiply(iPr_def_25,multiply(iPr_def_24,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3903,c_91]) ).
tcf(c_3914,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c6,
inference(superposition,[status(thm)],[c_483,c_2608]) ).
tcf(c_3927,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_19,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_3914,c_91]) ).
tcf(c_3957,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,multiply(iPr_def_25,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_524,c_2609]) ).
tcf(c_4064,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_485,c_2610]) ).
tcf(c_5077,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c6 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_15) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1090,c_861]) ).
tcf(c_6459,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_25,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1008,c_2607]) ).
tcf(c_6460,plain,
( ( sk_c7 = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_6459,c_3903]) ).
tcf(c_6471,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_25,iPr_def_24) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_1009,c_2607]) ).
tcf(c_6472,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_6471,c_3903]) ).
tcf(c_6499,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_25,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1054,c_2607]) ).
tcf(c_6500,plain,
( ( sk_c7 = iPr_def_23 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_6499,c_3903]) ).
tcf(c_7028,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(iPr_def_21,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_517,c_1214]) ).
tcf(c_7768,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(iPr_def_21,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_523,c_1466]) ).
tcf(c_8203,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_20,iPr_def_21) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1599,c_2610]) ).
tcf(c_8204,plain,
( ( sk_c8 = iPr_def_25 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_8203,c_4064]) ).
tcf(c_8379,plain,
( ( sk_c6 = iPr_def_14 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_1769,c_2608]) ).
tcf(c_8380,plain,
( ( sk_c6 = iPr_def_16 )
| ( sk_c6 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_8379,c_3914]) ).
tcf(c_9544,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_24,sk_c8),
inference(superposition,[status(thm)],[c_478,c_2590]) ).
tcf(c_9545,plain,
multiply(sk_c1,iPr_def_15) = multiply(iPr_def_24,sk_c6),
inference(superposition,[status(thm)],[c_479,c_2590]) ).
tcf(c_10066,plain,
multiply(iPr_def_25,multiply(iPr_def_24,sk_c6)) = iPr_def_15,
inference(superposition,[status(thm)],[c_9545,c_2607]) ).
tcf(c_10068,plain,
multiply(sk_c2,iPr_def_17) = multiply(iPr_def_23,sk_c8),
inference(superposition,[status(thm)],[c_481,c_2591]) ).
tcf(c_11769,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2594,c_89]) ).
tcf(c_11787,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_478,c_11769]) ).
tcf(c_11788,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c6,
inference(superposition,[status(thm)],[c_479,c_11769]) ).
tcf(c_11794,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_89,c_11769]) ).
tcf(c_11795,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_90,c_11769]) ).
tcf(c_11931,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2610,c_11769]) ).
tcf(c_11932,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2609,c_11769]) ).
tcf(c_11933,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2608,c_11769]) ).
tcf(c_11934,plain,
! [X0: $i] : multiply(inverse(iPr_def_25),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2607,c_11769]) ).
tcf(c_11935,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2606,c_11769]) ).
tcf(c_11991,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11769,c_11769]) ).
tcf(c_13050,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11795,c_11991]) ).
tcf(c_13070,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_13050,c_2587]) ).
tcf(c_13072,plain,
multiply(sk_c6,identity) = multiply(iPr_def_18,iPr_def_19),
inference(superposition,[status(thm)],[c_13050,c_3927]) ).
tcf(c_13081,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_13050,c_11794]) ).
tcf(c_13086,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_13072,c_3914]) ).
tcf(c_13088,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_13070,c_479]) ).
tcf(c_13254,plain,
( ( iPr_def_16 = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1211,c_2255]) ).
tcf(c_13259,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_518,c_2255]) ).
tcf(c_13361,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_13259,c_8204,c_13259]) ).
tcf(c_13472,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_11931,c_90]) ).
tcf(c_13476,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_11931,c_11769]) ).
tcf(c_13477,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_11931,c_13050]) ).
tcf(c_13496,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( identity = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_2930,c_13472]) ).
tcf(c_13892,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_23 )
| ( multiply(iPr_def_21,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_13496,c_89]) ).
tcf(c_14201,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_13477,c_13050]) ).
tcf(c_14210,plain,
( ~ iPr_def_13
| ( multiply(iPr_def_20,sk_c4) != sk_c7 )
| ( multiply(inverse(iPr_def_20),sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14201,c_491]) ).
tcf(c_14212,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_21 )
| ( sk_c7 != identity ) ),
inference(light_normalisation,[status(thm)],[c_14210,c_485,c_1031,c_14201]) ).
tcf(c_14217,plain,
multiply(sk_c4,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_4064,c_13476]) ).
tcf(c_14408,plain,
multiply(sk_c8,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_11932,c_90]) ).
tcf(c_14412,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_11932,c_11769]) ).
tcf(c_14413,plain,
multiply(sk_c8,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_11932,c_13050]) ).
tcf(c_14474,plain,
multiply(sk_c3,identity) = multiply(iPr_def_17,iPr_def_16),
inference(superposition,[status(thm)],[c_14408,c_2592]) ).
tcf(c_14475,plain,
multiply(sk_c4,identity) = multiply(iPr_def_21,iPr_def_16),
inference(superposition,[status(thm)],[c_14408,c_2588]) ).
tcf(c_14476,plain,
multiply(sk_c7,identity) = multiply(iPr_def_14,iPr_def_16),
inference(superposition,[status(thm)],[c_14408,c_2586]) ).
tcf(c_14684,plain,
inverse(iPr_def_16) = sk_c8,
inference(demodulation,[status(thm)],[c_14413,c_13050]) ).
tcf(c_14804,plain,
multiply(iPr_def_17,iPr_def_16) = sk_c3,
inference(demodulation,[status(thm)],[c_14474,c_13050]) ).
tcf(c_14805,plain,
multiply(inverse(iPr_def_17),sk_c3) = iPr_def_16,
inference(superposition,[status(thm)],[c_14804,c_11769]) ).
tcf(c_14820,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),multiply(sk_c3,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_14805,c_91]) ).
tcf(c_15005,plain,
multiply(inverse(iPr_def_17),sk_c3) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_13050,c_14820]) ).
tcf(c_15102,plain,
multiply(iPr_def_21,iPr_def_16) = sk_c4,
inference(demodulation,[status(thm)],[c_14475,c_13050]) ).
tcf(c_15103,plain,
( ( sk_c4 = iPr_def_15 )
| ( sk_c8 = iPr_def_25 ) ),
inference(demodulation,[status(thm)],[c_7768,c_15102]) ).
tcf(c_15104,plain,
( ( sk_c4 = iPr_def_15 )
| ( sk_c8 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_7028,c_15102]) ).
tcf(c_15114,plain,
multiply(inverse(iPr_def_21),sk_c4) = iPr_def_16,
inference(superposition,[status(thm)],[c_15102,c_11769]) ).
tcf(c_15123,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),multiply(sk_c4,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_15114,c_91]) ).
tcf(c_15129,plain,
multiply(iPr_def_14,iPr_def_16) = sk_c7,
inference(demodulation,[status(thm)],[c_14476,c_13050]) ).
tcf(c_15130,plain,
multiply(inverse(iPr_def_14),sk_c7) = iPr_def_16,
inference(superposition,[status(thm)],[c_15129,c_11769]) ).
tcf(c_15161,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),multiply(sk_c7,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_15130,c_91]) ).
tcf(c_15492,plain,
multiply(inverse(iPr_def_21),iPr_def_21) = multiply(iPr_def_16,sk_c8),
inference(superposition,[status(thm)],[c_14217,c_15123]) ).
tcf(c_15502,plain,
multiply(inverse(iPr_def_21),identity) = multiply(iPr_def_16,iPr_def_20),
inference(superposition,[status(thm)],[c_13472,c_15123]) ).
tcf(c_15513,plain,
multiply(inverse(iPr_def_21),iPr_def_21) = identity,
inference(light_normalisation,[status(thm)],[c_15492,c_1032]) ).
tcf(c_15614,plain,
( ( sk_c8 = iPr_def_25 )
| ( inverse(iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_15103,c_484]) ).
tcf(c_15721,plain,
( ( sk_c8 = iPr_def_24 )
| ( inverse(iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_15104,c_484]) ).
tcf(c_16151,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_11933,c_90]) ).
tcf(c_16156,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_11933,c_13050]) ).
tcf(c_16172,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1120,c_16151]) ).
tcf(c_16174,plain,
( ( identity = iPr_def_19 )
| ( sk_c7 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_976,c_16151]) ).
tcf(c_16413,plain,
( ~ iPr_def_10
| ( inverse(sk_c3) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_2366,c_2383,c_2366,c_6460,c_6472]) ).
tcf(c_16426,plain,
( ( sk_c7 = iPr_def_21 )
| ~ iPr_def_10
| ( inverse(iPr_def_22) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_505,c_16413]) ).
tcf(c_16427,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_10
| ( inverse(iPr_def_22) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_504,c_16413]) ).
tcf(c_16490,plain,
( ( inverse(iPr_def_22) != sk_c8 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_16426,c_2383,c_16426,c_16427]) ).
tcf(c_16491,plain,
( ~ iPr_def_10
| ( inverse(iPr_def_22) != sk_c8 ) ),
inference(renaming,[status(thm)],[c_16490]) ).
tcf(c_17046,plain,
( ( identity = iPr_def_19 )
| ( inverse(iPr_def_24) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_16172,c_480]) ).
tcf(c_17156,plain,
( ( iPr_def_16 = iPr_def_14 )
| ( iPr_def_16 != iPr_def_16 )
| ( iPr_def_14 != iPr_def_16 ) ),
inference(instantiation,[status(thm)],[c_2329]) ).
tcf(c_17412,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_16156,c_13050]) ).
tcf(c_17546,plain,
( ( identity = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_16174,c_478]) ).
tcf(c_17837,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_25,X0)) = X0,
inference(superposition,[status(thm)],[c_11934,c_11769]) ).
tcf(c_17838,plain,
multiply(sk_c1,identity) = inverse(iPr_def_25),
inference(superposition,[status(thm)],[c_11934,c_13050]) ).
tcf(c_18051,plain,
( ~ iPr_def_10
| ( sk_c7 != identity ) ),
inference(ground_joinability,[status(thm)],[c_2369,c_14684]) ).
tcf(c_18079,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_10
| ( identity != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_512,c_18051]) ).
tcf(c_18080,plain,
( ( sk_c7 = iPr_def_21 )
| ~ iPr_def_10
| ( identity != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_511,c_18051]) ).
tcf(c_18081,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_10
| ( identity != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_510,c_18051]) ).
tcf(c_18349,plain,
inverse(iPr_def_25) = sk_c1,
inference(demodulation,[status(thm)],[c_17838,c_13050]) ).
tcf(c_18395,plain,
multiply(sk_c1,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_3903,c_17837]) ).
tcf(c_18526,plain,
( ( identity != iPr_def_23 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_18079,c_2383,c_18081,c_18080]) ).
tcf(c_18527,plain,
( ~ iPr_def_10
| ( identity != iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_18526]) ).
tcf(c_19332,plain,
multiply(sk_c2,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_11935,c_90]) ).
tcf(c_19336,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_11935,c_11769]) ).
tcf(c_19337,plain,
multiply(sk_c2,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_11935,c_13050]) ).
tcf(c_19350,plain,
( ( identity = iPr_def_23 )
| ( sk_c6 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_992,c_19332]) ).
tcf(c_19351,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_991,c_19332]) ).
tcf(c_19352,plain,
( ( identity = iPr_def_23 )
| ( sk_c6 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_990,c_19332]) ).
tcf(c_19353,plain,
( ( identity = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_989,c_19332]) ).
tcf(c_19354,plain,
( ( identity = iPr_def_23 )
| ( sk_c7 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_988,c_19332]) ).
tcf(c_19387,plain,
inverse(iPr_def_22) = sk_c2,
inference(demodulation,[status(thm)],[c_19337,c_13050]) ).
tcf(c_19389,plain,
( ~ iPr_def_10
| ( sk_c8 != sk_c2 ) ),
inference(demodulation,[status(thm)],[c_16491,c_19387]) ).
tcf(c_19399,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_19389,c_2383,c_18527,c_19354,c_19353]) ).
tcf(c_19494,plain,
( ( identity = iPr_def_23 )
| ( multiply(sk_c5,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_19350,c_483]) ).
tcf(c_19500,plain,
( ( identity = iPr_def_23 )
| ( identity = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_19494,c_16151]) ).
tcf(c_19860,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( identity = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_19352,c_19350]) ).
tcf(c_20170,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_17) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_860,c_19336]) ).
tcf(c_20194,plain,
( ( sk_c7 = iPr_def_19 )
| ( multiply(iPr_def_23,sk_c8) = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_20170,c_10068]) ).
tcf(c_20710,plain,
! [X0: $i] :
( ( identity = iPr_def_19 )
| ( multiply(iPr_def_23,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19500,c_89]) ).
tcf(c_20881,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_23,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_19860,c_89]) ).
tcf(c_21407,plain,
multiply(iPr_def_16,iPr_def_20) = inverse(iPr_def_21),
inference(demodulation,[status(thm)],[c_15502,c_13050]) ).
tcf(c_21416,plain,
multiply(sk_c8,inverse(iPr_def_21)) = iPr_def_20,
inference(superposition,[status(thm)],[c_21407,c_14412]) ).
tcf(c_21443,plain,
multiply(iPr_def_21,inverse(iPr_def_21)) = multiply(sk_c4,iPr_def_20),
inference(superposition,[status(thm)],[c_21416,c_2588]) ).
tcf(c_21444,plain,
multiply(iPr_def_14,inverse(iPr_def_21)) = multiply(sk_c7,iPr_def_20),
inference(superposition,[status(thm)],[c_21416,c_2586]) ).
tcf(c_21447,plain,
multiply(iPr_def_21,inverse(iPr_def_21)) = identity,
inference(light_normalisation,[status(thm)],[c_21443,c_13472]) ).
tcf(c_21918,plain,
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( multiply(inverse(iPr_def_21),sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_21447,c_491]) ).
tcf(c_23132,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_20710,c_17546]) ).
tcf(c_23555,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_20881,c_2850]) ).
tcf(c_23561,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_20881,c_2851]) ).
tcf(c_24120,plain,
( ( identity = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_16) = identity ) ),
inference(superposition,[status(thm)],[c_23132,c_14408]) ).
tcf(c_24183,plain,
( ( identity = iPr_def_19 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_24120,c_15129]) ).
tcf(c_24411,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_23555,c_1766]) ).
tcf(c_24640,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_14,iPr_def_16) = identity ) ),
inference(superposition,[status(thm)],[c_23561,c_14408]) ).
tcf(c_24675,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_23561,c_1462]) ).
tcf(c_24677,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_23561,c_1211]) ).
tcf(c_24707,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_24640,c_15129]) ).
tcf(c_25557,plain,
( ( identity = iPr_def_19 )
| ( multiply(sk_c1,identity) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_24183,c_488]) ).
tcf(c_25987,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( inverse(iPr_def_16) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_24411,c_17412]) ).
tcf(c_26004,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( sk_c8 = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_25987,c_14684]) ).
tcf(c_26036,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_24675,c_18349]) ).
tcf(c_26469,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(sk_c1,identity) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_24707,c_488]) ).
tcf(c_27363,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( multiply(sk_c8,sk_c6) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_26004,c_483]) ).
tcf(c_32396,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(sk_c1,sk_c7) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_26036,c_15130]) ).
tcf(c_32397,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_32396,c_18395]) ).
tcf(c_32432,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_24677,c_32397]) ).
tcf(c_32473,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_16) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_32397,c_3073]) ).
tcf(c_32479,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c8 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_32473,c_14684]) ).
tcf(c_32741,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_16) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_32432,c_17412]) ).
tcf(c_32758,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c8 = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_32741,c_14684]) ).
tcf(c_33690,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_17,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_32479,c_2533]) ).
tcf(c_33731,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c3 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_33690,c_14804]) ).
tcf(c_33992,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(sk_c8,sk_c6) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_32758,c_483]) ).
tcf(c_33993,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(sk_c8) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_32758,c_482]) ).
tcf(c_34256,plain,
( ( identity = iPr_def_19 )
| ( sk_c1 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_25557,c_13050]) ).
tcf(c_34303,plain,
( ( identity = iPr_def_19 )
| ( inverse(iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_34256,c_489]) ).
tcf(c_34388,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_34303,c_17046]) ).
tcf(c_34468,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_33731,c_506]) ).
tcf(c_34469,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_33731,c_505]) ).
tcf(c_34471,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_33731,c_503]) ).
tcf(c_34473,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_33731,c_502]) ).
tcf(c_34474,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c6 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_33731,c_501]) ).
tcf(c_34805,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_25 )
| ( multiply(iPr_def_19,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_34388,c_89]) ).
tcf(c_34993,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_34468,c_1462,c_2115,c_3703,c_13254,c_14212,c_19399,c_24707,c_34468,c_34469,c_34471,c_34473,c_34474]) ).
tcf(c_35005,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_14) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_34993,c_19387]) ).
tcf(c_35456,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c1 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_26469,c_13050]) ).
tcf(c_35503,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_24) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_35456,c_489]) ).
tcf(c_35857,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c1 = sk_c2 ) ),
inference(superposition,[status(thm)],[c_35005,c_26036]) ).
tcf(c_36518,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( multiply(inverse(sk_c8),iPr_def_19) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_27363,c_11769]) ).
tcf(c_36870,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(sk_c1) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_35857,c_486]) ).
tcf(c_36871,plain,
( ( iPr_def_22 = iPr_def_25 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_36870,c_489]) ).
tcf(c_37029,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_16 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_36871,c_3209]) ).
tcf(c_37951,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( inverse(iPr_def_22) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_37029,c_35503]) ).
tcf(c_37998,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c2 = iPr_def_25 ) ),
inference(light_normalisation,[status(thm)],[c_37951,c_19387]) ).
tcf(c_38104,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( multiply(iPr_def_25,sk_c3) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_37998,c_487]) ).
tcf(c_38254,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(inverse(sk_c8),iPr_def_19) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_33992,c_11769]) ).
tcf(c_41032,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_25,iPr_def_22) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_503,c_38104]) ).
tcf(c_43180,plain,
multiply(inverse(iPr_def_14),multiply(iPr_def_14,inverse(iPr_def_21))) = multiply(iPr_def_16,iPr_def_20),
inference(superposition,[status(thm)],[c_21444,c_15161]) ).
tcf(c_43186,plain,
multiply(inverse(iPr_def_14),sk_c7) = multiply(iPr_def_16,identity),
inference(superposition,[status(thm)],[c_13050,c_15161]) ).
tcf(c_43224,plain,
multiply(inverse(iPr_def_14),multiply(iPr_def_14,inverse(iPr_def_21))) = inverse(iPr_def_21),
inference(light_normalisation,[status(thm)],[c_43180,c_21407]) ).
tcf(c_45261,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_11991,c_90]) ).
tcf(c_45264,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_11991,c_11769]) ).
tcf(c_45265,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_11991,c_13050]) ).
tcf(c_45266,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_45265,c_13050]) ).
tcf(c_45318,plain,
! [X0: $i] :
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( multiply(inverse(X0),sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_491,c_45261]) ).
tcf(c_45322,plain,
( ~ iPr_def_12
| ( sk_c7 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2097,c_45266]) ).
tcf(c_45348,plain,
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( multiply(inverse(sk_c8),sk_c8) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_45318]) ).
tcf(c_45380,plain,
inverse(sk_c8) = iPr_def_16,
inference(superposition,[status(thm)],[c_14684,c_45266]) ).
tcf(c_45392,plain,
inverse(sk_c5) = iPr_def_18,
inference(superposition,[status(thm)],[c_17412,c_45266]) ).
tcf(c_46414,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(multiply(X0,X1)))) = identity,
inference(superposition,[status(thm)],[c_45261,c_91]) ).
tcf(c_46422,plain,
multiply(iPr_def_16,identity) = inverse(sk_c8),
inference(superposition,[status(thm)],[c_45261,c_2609]) ).
tcf(c_46429,plain,
multiply(iPr_def_19,inverse(sk_c6)) = multiply(sk_c5,identity),
inference(superposition,[status(thm)],[c_45261,c_2589]) ).
tcf(c_46430,plain,
multiply(iPr_def_15,inverse(sk_c6)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_45261,c_2587]) ).
tcf(c_46442,plain,
multiply(sk_c6,inverse(iPr_def_19)) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_45261,c_3927]) ).
tcf(c_46447,plain,
multiply(sk_c7,inverse(iPr_def_24)) = multiply(iPr_def_25,identity),
inference(superposition,[status(thm)],[c_45261,c_3906]) ).
tcf(c_46449,plain,
multiply(iPr_def_24,inverse(sk_c7)) = multiply(sk_c1,identity),
inference(superposition,[status(thm)],[c_45261,c_2590]) ).
tcf(c_46465,plain,
multiply(iPr_def_25,identity) = inverse(sk_c1),
inference(superposition,[status(thm)],[c_45261,c_2607]) ).
tcf(c_47212,plain,
! [X0: $i] : multiply(X0,inverse(multiply(iPr_def_25,X0))) = multiply(sk_c1,identity),
inference(superposition,[status(thm)],[c_46414,c_17837]) ).
tcf(c_47334,plain,
! [X0: $i] : multiply(X0,inverse(multiply(iPr_def_25,X0))) = multiply(iPr_def_24,inverse(sk_c7)),
inference(light_normalisation,[status(thm)],[c_47212,c_46449]) ).
tcf(c_50296,plain,
( ( identity = iPr_def_19 )
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_24183,c_45322]) ).
tcf(c_50298,plain,
( ( identity = iPr_def_23 )
| ~ iPr_def_12
| ( identity != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_19351,c_45322]) ).
tcf(c_50323,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_12
| ( identity != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_508,c_45322]) ).
tcf(c_50461,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_50323,c_50296,c_50323,c_50298]) ).
tcf(c_50467,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2115,c_50461]) ).
tcf(c_50906,plain,
multiply(sk_c7,sk_c8) = iPr_def_14,
inference(superposition,[status(thm)],[c_11787,c_45264]) ).
tcf(c_50907,plain,
multiply(sk_c7,sk_c6) = iPr_def_15,
inference(superposition,[status(thm)],[c_11788,c_45264]) ).
tcf(c_55234,plain,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_16 != iPr_def_14 )
| ( sk_c6 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2707]) ).
tcf(c_59645,plain,
multiply(iPr_def_19,inverse(sk_c6)) = sk_c5,
inference(demodulation,[status(thm)],[c_46429,c_13050]) ).
tcf(c_59688,plain,
multiply(inverse(iPr_def_19),sk_c5) = inverse(sk_c6),
inference(superposition,[status(thm)],[c_59645,c_11769]) ).
tcf(c_59690,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( inverse(sk_c6) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_59645,c_34805]) ).
tcf(c_60235,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( sk_c6 = iPr_def_16 ) ),
inference(global_subsumption_just,[status(thm)],[c_41032,c_1028,c_1043,c_1305,c_8380,c_17156,c_32432,c_55234]) ).
tcf(c_60281,plain,
( ( iPr_def_16 = iPr_def_18 )
| ( iPr_def_15 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_60235,c_23555]) ).
tcf(c_60511,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(inverse(iPr_def_19),sk_c8) = inverse(sk_c6) ) ),
inference(superposition,[status(thm)],[c_32758,c_59688]) ).
tcf(c_60514,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),multiply(sk_c5,X0)) = multiply(inverse(sk_c6),X0),
inference(superposition,[status(thm)],[c_59688,c_91]) ).
tcf(c_60615,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( inverse(iPr_def_16) = sk_c5 ) ),
inference(superposition,[status(thm)],[c_60281,c_17412]) ).
tcf(c_60632,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( sk_c8 = sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_60615,c_14684]) ).
tcf(c_61041,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( multiply(sk_c8,sk_c6) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_60632,c_483]) ).
tcf(c_61697,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( sk_c8 = iPr_def_25 )
| ( multiply(sk_c8,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_519,c_61041]) ).
tcf(c_61934,plain,
multiply(inverse(sk_c6),identity) = multiply(inverse(iPr_def_19),sk_c5),
inference(superposition,[status(thm)],[c_13050,c_60514]) ).
tcf(c_62487,plain,
multiply(iPr_def_15,inverse(sk_c6)) = sk_c7,
inference(demodulation,[status(thm)],[c_46430,c_13050]) ).
tcf(c_62523,plain,
multiply(inverse(iPr_def_15),sk_c7) = inverse(sk_c6),
inference(superposition,[status(thm)],[c_62487,c_11769]) ).
tcf(c_62614,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(inverse(iPr_def_15),iPr_def_21) = inverse(sk_c6) ) ),
inference(superposition,[status(thm)],[c_523,c_62523]) ).
tcf(c_62616,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(inverse(iPr_def_15),iPr_def_21) = inverse(sk_c6) ) ),
inference(superposition,[status(thm)],[c_517,c_62523]) ).
tcf(c_62626,plain,
( ~ iPr_def_11
| ( inverse(sk_c6) != sk_c8 )
| ( inverse(inverse(iPr_def_15)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_62523,c_493]) ).
tcf(c_62628,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),multiply(sk_c7,X0)) = multiply(inverse(sk_c6),X0),
inference(superposition,[status(thm)],[c_62523,c_91]) ).
tcf(c_63242,plain,
( ( sk_c8 = iPr_def_25 )
| ( multiply(iPr_def_20,iPr_def_21) = inverse(sk_c6) ) ),
inference(superposition,[status(thm)],[c_15614,c_62614]) ).
tcf(c_63249,plain,
( ( sk_c8 = iPr_def_25 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_63242,c_4064]) ).
tcf(c_63362,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(iPr_def_20,iPr_def_21) = inverse(sk_c6) ) ),
inference(superposition,[status(thm)],[c_15721,c_62616]) ).
tcf(c_63370,plain,
( ( sk_c8 = iPr_def_24 )
| ( inverse(sk_c6) = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_63362,c_4064]) ).
tcf(c_64300,plain,
multiply(sk_c6,inverse(iPr_def_19)) = iPr_def_18,
inference(demodulation,[status(thm)],[c_46442,c_13050]) ).
tcf(c_64359,plain,
multiply(iPr_def_15,inverse(iPr_def_19)) = multiply(sk_c7,iPr_def_18),
inference(superposition,[status(thm)],[c_64300,c_2587]) ).
tcf(c_66523,plain,
multiply(sk_c7,inverse(iPr_def_24)) = iPr_def_25,
inference(demodulation,[status(thm)],[c_46447,c_13050]) ).
tcf(c_66553,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_17,inverse(iPr_def_24)) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_500,c_66523]) ).
tcf(c_66805,plain,
multiply(iPr_def_24,inverse(sk_c7)) = sk_c1,
inference(demodulation,[status(thm)],[c_46449,c_13050]) ).
tcf(c_66843,plain,
multiply(inverse(iPr_def_24),sk_c1) = inverse(sk_c7),
inference(superposition,[status(thm)],[c_66805,c_11769]) ).
tcf(c_69678,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),multiply(sk_c1,X0)) = multiply(inverse(sk_c7),X0),
inference(superposition,[status(thm)],[c_66843,c_91]) ).
tcf(c_70176,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_17,iPr_def_16) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1325,c_66553]) ).
tcf(c_70184,plain,
( ( sk_c3 = iPr_def_25 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_70176,c_14804]) ).
tcf(c_71004,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_25,sk_c8) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_70184,c_481]) ).
tcf(c_74096,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_17) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_71004,c_3957]) ).
tcf(c_77319,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c8) = sk_c7 )
| ( sk_c7 != X1 )
| ( multiply(inverse(X0),sk_c8) != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_77322,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_77344,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_77350,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_532]) ).
tcf(c_77358,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_77322]) ).
tcf(c_77400,plain,
! [X0: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_77350]) ).
tcf(c_77401,plain,
iPr_def_17 = iPr_def_17,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_77501,plain,
! [X0: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_77350]) ).
tcf(c_77509,plain,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_17 != iPr_def_17 )
| ( sk_c7 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_77400]) ).
tcf(c_77682,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_23 )
| ( X0 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_77344]) ).
tcf(c_77696,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( iPr_def_23 != sk_c7 )
| ( iPr_def_17 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_77501]) ).
tcf(c_78096,plain,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_23 != iPr_def_23 )
| ( sk_c7 != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_77682]) ).
tcf(c_78097,plain,
iPr_def_23 = iPr_def_23,
inference(instantiation,[status(thm)],[c_531]) ).
tcf(c_94433,plain,
multiply(inverse(sk_c6),identity) = multiply(inverse(iPr_def_15),sk_c7),
inference(superposition,[status(thm)],[c_13050,c_62628]) ).
tcf(c_95214,plain,
multiply(inverse(iPr_def_24),multiply(iPr_def_24,sk_c8)) = multiply(inverse(sk_c7),iPr_def_14),
inference(superposition,[status(thm)],[c_9544,c_69678]) ).
tcf(c_95215,plain,
multiply(inverse(iPr_def_24),multiply(iPr_def_24,sk_c6)) = multiply(inverse(sk_c7),iPr_def_15),
inference(superposition,[status(thm)],[c_9545,c_69678]) ).
tcf(c_95237,plain,
multiply(inverse(iPr_def_24),multiply(iPr_def_24,sk_c6)) = sk_c6,
inference(light_normalisation,[status(thm)],[c_95215,c_11788]) ).
tcf(c_95238,plain,
multiply(inverse(iPr_def_24),multiply(iPr_def_24,sk_c8)) = sk_c8,
inference(light_normalisation,[status(thm)],[c_95214,c_11787]) ).
tcf(c_96826,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( sk_c8 = iPr_def_25 )
| ( multiply(iPr_def_16,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_61697,c_2609]) ).
tcf(c_97426,plain,
( ( multiply(inverse(sk_c8),sk_c8) = sk_c7 )
| ( sk_c7 != identity )
| ( multiply(inverse(sk_c8),sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_77319]) ).
tcf(c_97512,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c6 = iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_5077,c_495,c_507,c_1028,c_1044,c_77696]) ).
tcf(c_97553,plain,
( ( iPr_def_17 = iPr_def_23 )
| ~ iPr_def_12 ),
inference(superposition,[status(thm)],[c_97512,c_50467]) ).
tcf(c_97607,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_18 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_97512,c_529]) ).
tcf(c_97813,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c7 = iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_97607,c_6460,c_6500,c_77401,c_77509,c_77696,c_78096,c_78097]) ).
tcf(c_97926,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( multiply(iPr_def_21,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_97813,c_478]) ).
tcf(c_98160,plain,
( ( sk_c7 = identity )
| ( identity != iPr_def_19 )
| ( sk_c7 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_77358]) ).
tcf(c_98590,plain,
~ iPr_def_12,
inference(global_subsumption_just,[status(thm)],[c_97553,c_45322,c_50296,c_50461,c_98160]) ).
tcf(c_100156,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c8 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_97926,c_13892]) ).
tcf(c_103917,plain,
( ~ iPr_def_13
| ( sk_c7 != identity ) ),
inference(global_subsumption_just,[status(thm)],[c_21918,c_130,c_45348,c_97426]) ).
tcf(c_103927,plain,
( ( identity = iPr_def_19 )
| ~ iPr_def_13 ),
inference(superposition,[status(thm)],[c_24183,c_103917]) ).
tcf(c_103929,plain,
( ( identity = iPr_def_23 )
| ~ iPr_def_13
| ( identity != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_19351,c_103917]) ).
tcf(c_103947,plain,
( ( sk_c8 = iPr_def_25 )
| ~ iPr_def_13
| ( identity != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_523,c_103917]) ).
tcf(c_103954,plain,
( ( sk_c7 = iPr_def_19 )
| ~ iPr_def_13
| ( identity != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_508,c_103917]) ).
tcf(c_104063,plain,
~ iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_103947,c_98160,c_103917,c_103927,c_103954,c_103929]) ).
tcf(c_104260,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( inverse(sk_c5) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_59690,c_45266]) ).
tcf(c_104266,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( sk_c6 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_104260,c_45392]) ).
tcf(c_104322,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_15)) != sk_c8 ) ),
inference(global_subsumption_just,[status(thm)],[c_62626,c_2255,c_62626,c_63249,c_63370]) ).
tcf(c_104324,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_104322,c_45266]) ).
tcf(c_104327,plain,
~ iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_104324,c_13361]) ).
tcf(c_104477,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( iPr_def_14 = iPr_def_18 )
| ( sk_c7 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_104266,c_526]) ).
tcf(c_107742,plain,
( ( iPr_def_16 = iPr_def_25 )
| ( iPr_def_14 = iPr_def_18 )
| ( multiply(inverse(iPr_def_14),iPr_def_19) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_104477,c_15130]) ).
tcf(c_113410,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_107742,c_104327,c_104063,c_100156,c_98590,c_96826,c_95215,c_95214,c_94433,c_95237,c_74096,c_66805,c_66523,c_64359,c_62523,c_61934,c_60511,c_95238,c_50907,c_50906,c_47334,c_47212,c_46465,c_46447,c_46422,c_45380,c_43224,c_43186,c_43180,c_38254,c_36518,c_33993,c_23561,c_23132,c_21447,c_21443,c_20194,c_19399,c_18395,c_17412,c_15513,c_15492,c_15129,c_15102,c_15005,c_14804,c_14684,c_14408,c_14217,c_14201,c_13088,c_13086,c_13072,c_13081,c_10066,c_530,c_500,c_499,c_498,c_497,c_490]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 14:32:32 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 34.24/6.40 % SZS status Started for theBenchmark.p
% 34.24/6.40 % SZS status Unsatisfiable for theBenchmark.p
% 34.24/6.40
% 34.24/6.40 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 34.24/6.40
% 34.24/6.40 % ------ iProver source info
% 34.24/6.40
% 34.24/6.40 % git: date: 2026-07-19 20:42:38 +0200
% 34.24/6.40 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 34.24/6.40 % git: non_committed_changes: false
% 34.24/6.40
% 34.24/6.40 % ------ Parsing...% successful
% 34.24/6.40
% 34.24/6.40
% 34.24/6.40 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 34.24/6.40
% 34.24/6.40 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 34.24/6.40
% 34.24/6.40 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 34.24/6.40
% 34.24/6.40 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 34.24/6.40 % ------ Proving...
% 34.24/6.40 % ------ Problem Properties
% 34.24/6.40
% 34.24/6.40 %
% 34.24/6.40 % clauses 56
% 34.24/6.40 % conjectures 41
% 34.24/6.40 % EPR 37
% 34.24/6.40 % Horn 19
% 34.24/6.40 % unary 15
% 34.24/6.40 % binary 36
% 34.24/6.40 % lits 106
% 34.24/6.40 % lits eq 98
% 34.24/6.40 % fd_pure 0
% 34.24/6.40 % fd_pseudo 0
% 34.24/6.40 % fd_cond 0
% 34.24/6.40 % fd_pseudo_cond 0
% 34.24/6.40 % AC symbols 0
% 34.24/6.40
% 34.24/6.40 % ------ Schedule dynamic 5 is on
% 34.24/6.40
% 34.24/6.40 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 34.24/6.40
% 34.24/6.40
% 34.24/6.40 % ------
% 34.24/6.40 % Current options:
% 34.24/6.40 % ------
% 34.24/6.40
% 34.24/6.40
% 34.24/6.40 %
% 34.24/6.40
% 34.24/6.40 % ------ Proving...
% 34.24/6.40 %
% 34.24/6.40
% 34.24/6.40 % SZS status Unsatisfiable for theBenchmark.p
% 34.24/6.40
% 34.24/6.40 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 34.50/6.41
% 34.50/6.41
%------------------------------------------------------------------------------