%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP321-1 : 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 : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:50 PM UTC 2026
% Result : Unsatisfiable 10.51s 2.69s
% Output : CNFRefutation 8.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 45
% Syntax : Number of formulae : 460 ( 111 unt; 11 def)
% Number of atoms : 1722 ( 863 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 715 ( 222 ~; 493 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 102 ( 0 sgn 102 !; 0 ?; 82 :)
% 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_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c5)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,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_6) ).
fof(f16,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f30,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f32,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f31]) ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f39,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c7 = inverse(sk_c5)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c3 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c4,sk_c8)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = multiply(sk_c6,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(sk_c6,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c7)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X2)
| multiply(X2,sk_c8) != X1
| sk_c7 != multiply(sk_c8,X1)
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X4] :
( sk_c8 != multiply(sk_c6,sk_c7)
| sk_c7 != inverse(X4)
| sk_c6 != multiply(X4,sk_c7)
| sk_c8 != inverse(X3)
| sk_c7 != multiply(X3,sk_c8)
| sk_c8 != inverse(X2)
| sk_c7 != multiply(sk_c8,multiply(X2,sk_c8))
| inverse(X0) != sk_c7
| sk_c8 != multiply(X0,sk_c7)
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(equality_resolution,[],[f66]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c8 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c4,sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c5,sk_c7) = sk_c6 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c6,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c3 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c3 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c6,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( multiply(X2,sk_c8) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 )
| ( multiply(sk_c8,multiply(X1,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_409,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_116]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_411,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_412,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_413,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c6,sk_c7) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_414,definition,
iPr_def_14 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_415,definition,
iPr_def_15 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_416,definition,
iPr_def_16 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_417,definition,
iPr_def_17 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_418,definition,
iPr_def_18 = multiply(sk_c5,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_419,definition,
iPr_def_19 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_420,definition,
iPr_def_20 = multiply(sk_c4,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_421,definition,
iPr_def_21 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_422,definition,
iPr_def_22 = multiply(sk_c8,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_423,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_424,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_425,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c8 )
| ( iPr_def_14 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_413,c_415,c_414]) ).
tcf(c_426,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_412]) ).
tcf(c_427,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_411]) ).
tcf(c_428,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_410]) ).
tcf(c_429,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_409]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_417]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113,c_418]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112,c_419]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_420]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110,c_421]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105,c_422]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100,c_423]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95,c_424]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_17 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_17 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_18 = sk_c6 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_14 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_460,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_461,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_734,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_433,c_420]) ).
tcf(c_761,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_440,c_420]) ).
tcf(c_855,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_445,c_420]) ).
tcf(c_883,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_434,c_421]) ).
tcf(c_885,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_431,c_421]) ).
tcf(c_906,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,sk_c3) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_434,c_422]) ).
tcf(c_908,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_16,sk_c3) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_431,c_422]) ).
tcf(c_909,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c3) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_430,c_422]) ).
tcf(c_967,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_419,c_84]) ).
tcf(c_968,plain,
multiply(iPr_def_17,sk_c5) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_969,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_970,plain,
multiply(iPr_def_16,sk_c2) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_983,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_446,c_424]) ).
tcf(c_985,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_446,c_441]) ).
tcf(c_988,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_446,c_414]) ).
tcf(c_1008,plain,
! [X0: $i] : inverse(X0) = inverse(X0),
inference(instantiation,[status(thm)],[c_460]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_1033,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(sk_c4,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_448,c_420]) ).
tcf(c_1074,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_449,c_424]) ).
tcf(c_1075,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_449,c_444]) ).
tcf(c_1079,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_449,c_414]) ).
tcf(c_1119,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_450,c_421]) ).
tcf(c_1124,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_450,c_414]) ).
tcf(c_1159,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( inverse(X0) != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_1011]) ).
tcf(c_1188,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_451,c_421]) ).
tcf(c_1196,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_451,c_431]) ).
tcf(c_1339,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_454,c_421]) ).
tcf(c_1345,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_454,c_434]) ).
tcf(c_1433,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_456,c_415]) ).
tcf(c_1454,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = inverse(X0) )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_1463,plain,
! [X0: $i] :
( ( inverse(X0) = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c1) )
| ( inverse(X0) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1159]) ).
tcf(c_1528,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_459,c_415]) ).
tcf(c_1654,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_985,c_418]) ).
tcf(c_1780,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_17 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1075,c_985]) ).
tcf(c_1856,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_20 )
| ( sk_c8 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_459,c_425]) ).
tcf(c_1859,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_17 )
| ( sk_c8 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_456,c_425]) ).
tcf(c_1948,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_418,c_427]) ).
tcf(c_1950,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_424,c_427]) ).
tcf(c_1952,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_427]) ).
tcf(c_1964,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_24 )
| ( sk_c7 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_1950,c_423]) ).
tcf(c_1971,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_18 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_1948,c_417]) ).
tcf(c_2081,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_18 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_418,c_428]) ).
tcf(c_2082,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_15 )
| ( inverse(sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_415,c_428]) ).
tcf(c_2083,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_424,c_428]) ).
tcf(c_2097,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( sk_c7 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2083,c_423]) ).
tcf(c_2104,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_18 )
| ( sk_c7 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2081,c_417]) ).
tcf(c_2187,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c8 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_83,c_429]) ).
tcf(c_2188,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_84,c_429]) ).
tcf(c_2577,plain,
( ( inverse(sk_c1) = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c1) )
| ( inverse(sk_c1) != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_1463]) ).
tcf(c_2578,plain,
inverse(sk_c1) = inverse(sk_c1),
inference(instantiation,[status(thm)],[c_1008]) ).
tcf(c_2627,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1196,c_418]) ).
tcf(c_2724,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_16 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1345,c_1196]) ).
tcf(c_2842,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_414,c_85]) ).
tcf(c_2844,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c7,X0)) = multiply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2845,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_415,c_85]) ).
tcf(c_2846,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_424,c_85]) ).
tcf(c_2848,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c8,X0)) = multiply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_421,c_85]) ).
tcf(c_2850,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2852,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_967,c_85]) ).
tcf(c_2853,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_968,c_85]) ).
tcf(c_2854,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_969,c_85]) ).
tcf(c_2855,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_970,c_85]) ).
tcf(c_2861,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2855,c_83]) ).
tcf(c_2862,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2854,c_83]) ).
tcf(c_2863,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2853,c_83]) ).
tcf(c_2864,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2852,c_83]) ).
tcf(c_2955,plain,
multiply(iPr_def_16,iPr_def_21) = sk_c8,
inference(superposition,[status(thm)],[c_421,c_2861]) ).
tcf(c_2968,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_21,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2955,c_85]) ).
tcf(c_2970,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_424,c_2862]) ).
tcf(c_2976,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(iPr_def_24,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2970,c_85]) ).
tcf(c_3013,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_24) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_1780,c_2970]) ).
tcf(c_3015,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_22,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_1780,c_969]) ).
tcf(c_3425,plain,
multiply(iPr_def_17,iPr_def_18) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_2863]) ).
tcf(c_3439,plain,
! [X0: $i] : multiply(iPr_def_17,multiply(iPr_def_18,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3425,c_85]) ).
tcf(c_3441,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c8,
inference(superposition,[status(thm)],[c_420,c_2864]) ).
tcf(c_3453,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_20,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3441,c_85]) ).
tcf(c_3502,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_761,c_2864]) ).
tcf(c_3503,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c7 = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_3502,c_3441]) ).
tcf(c_3800,plain,
! [X0: $i] :
( ( inverse(sk_c1) = X0 )
| ( X0 != iPr_def_23 )
| ( inverse(sk_c1) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_1011]) ).
tcf(c_3990,plain,
( ( sk_c7 = iPr_def_23 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_855,c_2864]) ).
tcf(c_3991,plain,
( ( sk_c8 = iPr_def_15 )
| ( sk_c7 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_3990,c_3441]) ).
tcf(c_4328,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_439,c_906]) ).
tcf(c_4334,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_4328,c_2955]) ).
tcf(c_4397,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_4334,c_454]) ).
tcf(c_4409,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_4334,c_434]) ).
tcf(c_4975,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_436,c_908]) ).
tcf(c_4978,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_4975,c_2955]) ).
tcf(c_5001,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_435,c_909]) ).
tcf(c_5003,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_5001,c_2955]) ).
tcf(c_5262,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_4978,c_451]) ).
tcf(c_5274,plain,
( ( iPr_def_16 = iPr_def_22 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_4978,c_431]) ).
tcf(c_5551,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_5262,c_4397]) ).
tcf(c_5574,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_5262,c_418]) ).
tcf(c_5649,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_16 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_5274,c_4409]) ).
tcf(c_5862,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_6278,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_451,c_988]) ).
tcf(c_6291,plain,
( ( sk_c7 = iPr_def_17 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6278,c_2970]) ).
tcf(c_6490,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_6291,c_418]) ).
tcf(c_6903,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_454,c_1079]) ).
tcf(c_6918,plain,
( ( sk_c7 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6903,c_2970]) ).
tcf(c_6967,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1119,c_2861]) ).
tcf(c_6968,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_6967,c_2955]) ).
tcf(c_7074,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6918,c_6291]) ).
tcf(c_7220,plain,
( ( sk_c7 = iPr_def_17 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1188,c_2861]) ).
tcf(c_7221,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c7 = iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_7220,c_2955]) ).
tcf(c_7469,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_7074,c_449]) ).
tcf(c_7470,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_23 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_7074,c_446]) ).
tcf(c_7471,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_7074,c_424]) ).
tcf(c_7472,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_7074,c_444]) ).
tcf(c_7473,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_22 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_7074,c_441]) ).
tcf(c_8047,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_21) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1339,c_2861]) ).
tcf(c_8048,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_8047,c_2955]) ).
tcf(c_10138,plain,
! [X0: $i,X1: $i] :
( ( X1 = inverse(sk_c1) )
| ( X1 != X0 )
| ( inverse(sk_c1) != X0 ) ),
inference(instantiation,[status(thm)],[c_1454]) ).
tcf(c_10149,plain,
( ( inverse(sk_c1) = iPr_def_14 )
| ( iPr_def_14 != iPr_def_23 )
| ( inverse(sk_c1) != iPr_def_23 ) ),
inference(instantiation,[status(thm)],[c_3800]) ).
tcf(c_10218,plain,
multiply(sk_c5,iPr_def_14) = multiply(iPr_def_18,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2844]) ).
tcf(c_10318,plain,
multiply(sk_c6,iPr_def_14) = multiply(iPr_def_15,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2845]) ).
tcf(c_10502,plain,
multiply(sk_c1,iPr_def_14) = multiply(iPr_def_24,sk_c8),
inference(superposition,[status(thm)],[c_414,c_2846]) ).
tcf(c_10758,plain,
multiply(sk_c2,iPr_def_22) = multiply(iPr_def_21,sk_c3),
inference(superposition,[status(thm)],[c_422,c_2848]) ).
tcf(c_11226,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_24) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_5649,c_3013]) ).
tcf(c_11242,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_16,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_5649,c_3015]) ).
tcf(c_13310,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_24,sk_c8) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_7471,c_10502]) ).
tcf(c_14248,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2850,c_83]) ).
tcf(c_14253,plain,
multiply(inverse(sk_c7),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_414,c_14248]) ).
tcf(c_14256,plain,
multiply(inverse(sk_c6),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_415,c_14248]) ).
tcf(c_14257,plain,
multiply(inverse(sk_c1),iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_424,c_14248]) ).
tcf(c_14258,plain,
multiply(inverse(sk_c8),iPr_def_22) = sk_c3,
inference(superposition,[status(thm)],[c_422,c_14248]) ).
tcf(c_14260,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_14248]) ).
tcf(c_14261,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_14248]) ).
tcf(c_14414,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2864,c_14248]) ).
tcf(c_14415,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2863,c_14248]) ).
tcf(c_14416,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2862,c_14248]) ).
tcf(c_14417,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2861,c_14248]) ).
tcf(c_14444,plain,
multiply(inverse(sk_c2),multiply(iPr_def_21,sk_c3)) = iPr_def_22,
inference(superposition,[status(thm)],[c_10758,c_14248]) ).
tcf(c_14482,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_14248,c_14248]) ).
tcf(c_15675,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_14261,c_14482]) ).
tcf(c_15691,plain,
multiply(sk_c7,identity) = multiply(iPr_def_17,iPr_def_18),
inference(superposition,[status(thm)],[c_15675,c_3439]) ).
tcf(c_15694,plain,
multiply(sk_c5,sk_c7) = multiply(iPr_def_18,identity),
inference(superposition,[status(thm)],[c_15675,c_2844]) ).
tcf(c_15695,plain,
multiply(sk_c7,identity) = multiply(iPr_def_23,iPr_def_24),
inference(superposition,[status(thm)],[c_15675,c_2976]) ).
tcf(c_15697,plain,
multiply(sk_c8,identity) = multiply(iPr_def_16,iPr_def_21),
inference(superposition,[status(thm)],[c_15675,c_2968]) ).
tcf(c_15702,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_15675,c_14260]) ).
tcf(c_15703,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_15697,c_2955]) ).
tcf(c_15705,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_15695,c_2970]) ).
tcf(c_15706,plain,
multiply(iPr_def_18,identity) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_15694,c_418]) ).
tcf(c_16057,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_7470,c_7469]) ).
tcf(c_16546,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_7473,c_7472]) ).
tcf(c_16754,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_449,c_1964]) ).
tcf(c_16755,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_12
| ( sk_c6 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_446,c_1964]) ).
tcf(c_16984,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_12
| ( iPr_def_14 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_459,c_16754]) ).
tcf(c_17013,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_12
| ( iPr_def_14 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_456,c_16755]) ).
tcf(c_17029,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_20 )
| ~ iPr_def_12
| ( iPr_def_14 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_2724,c_16984]) ).
tcf(c_17678,plain,
( ( sk_c7 = iPr_def_20 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_449,c_2097]) ).
tcf(c_17679,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_446,c_2097]) ).
tcf(c_17843,plain,
( ( sk_c7 = iPr_def_17 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_17679,c_7221,c_17679]) ).
tcf(c_18076,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_16546,c_5649]) ).
tcf(c_18951,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_2104,c_2104,c_17843]) ).
tcf(c_18984,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11
| ( iPr_def_18 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_450,c_18951]) ).
tcf(c_19146,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_18984,c_2097,c_3991,c_6968]) ).
tcf(c_19236,plain,
multiply(sk_c4,iPr_def_19) = identity,
inference(superposition,[status(thm)],[c_14414,c_84]) ).
tcf(c_19240,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_19)) != sk_c8 )
| ( multiply(sk_c4,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_14414,c_429]) ).
tcf(c_19242,plain,
multiply(sk_c4,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_14414,c_15675]) ).
tcf(c_19243,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_20 )
| ( inverse(inverse(iPr_def_19)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_19240,c_420]) ).
tcf(c_19257,plain,
( ( identity = iPr_def_20 )
| ( sk_c7 = iPr_def_23 ) ),
inference(demodulation,[status(thm)],[c_1033,c_19236]) ).
tcf(c_19259,plain,
( ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_734,c_19236]) ).
tcf(c_19630,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_19257,c_424]) ).
tcf(c_19767,plain,
! [X0: $i] :
( ( X0 = sk_c8 )
| ( sk_c8 != iPr_def_15 )
| ( X0 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_5862]) ).
tcf(c_19768,plain,
( ( sk_c7 = sk_c8 )
| ( sk_c8 != iPr_def_15 )
| ( sk_c7 != iPr_def_15 ) ),
inference(instantiation,[status(thm)],[c_19767]) ).
tcf(c_20227,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( identity = iPr_def_20 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_19259,c_453]) ).
tcf(c_20232,plain,
( ( identity = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_19259,c_421]) ).
tcf(c_20486,plain,
inverse(iPr_def_19) = sk_c4,
inference(demodulation,[status(thm)],[c_19242,c_15675]) ).
tcf(c_20739,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( identity = iPr_def_20 )
| ( multiply(sk_c4,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_20227,c_420]) ).
tcf(c_20750,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_20739,c_19236]) ).
tcf(c_20897,plain,
multiply(sk_c5,iPr_def_17) = identity,
inference(superposition,[status(thm)],[c_14415,c_84]) ).
tcf(c_20902,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_17,X0)) = X0,
inference(superposition,[status(thm)],[c_14415,c_14248]) ).
tcf(c_20903,plain,
multiply(sk_c5,identity) = inverse(iPr_def_17),
inference(superposition,[status(thm)],[c_14415,c_15675]) ).
tcf(c_20915,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_6490,c_20897]) ).
tcf(c_20917,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_5574,c_20897]) ).
tcf(c_20918,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_2627,c_20897]) ).
tcf(c_20919,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( identity = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1654,c_20897]) ).
tcf(c_21073,plain,
inverse(iPr_def_17) = sk_c5,
inference(demodulation,[status(thm)],[c_20903,c_15675]) ).
tcf(c_21083,plain,
multiply(sk_c5,sk_c7) = iPr_def_18,
inference(superposition,[status(thm)],[c_3425,c_20902]) ).
tcf(c_21105,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c8 != iPr_def_15 )
| ( sk_c7 = iPr_def_20 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1856,c_1856,c_8048,c_17678]) ).
tcf(c_21106,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_20 )
| ( sk_c8 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_21105]) ).
tcf(c_21141,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_20 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_454,c_21106]) ).
tcf(c_21578,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c8 != iPr_def_15 )
| ( sk_c7 = iPr_def_17 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1859,c_1859,c_7221,c_17679]) ).
tcf(c_21579,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_17 )
| ( sk_c8 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_21578]) ).
tcf(c_21616,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_17 )
| ( iPr_def_15 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_451,c_21579]) ).
tcf(c_21793,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_20915,c_446]) ).
tcf(c_21794,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_14) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_20915,c_424]) ).
tcf(c_21798,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c6,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_20915,c_415]) ).
tcf(c_21802,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_15,sk_c8) = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_21798,c_10318]) ).
tcf(c_21808,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_24,sk_c8) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_21794,c_10502]) ).
tcf(c_22353,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_16 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_20918,c_20750]) ).
tcf(c_23177,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( identity = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_21793,c_418]) ).
tcf(c_23189,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_23177,c_20897]) ).
tcf(c_23653,plain,
( ~ iPr_def_11
| ( inverse(sk_c6) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_2082,c_2082,c_19146]) ).
tcf(c_23665,plain,
( ( sk_c6 = iPr_def_14 )
| ~ iPr_def_11
| ( inverse(iPr_def_18) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_457,c_23653]) ).
tcf(c_23668,plain,
( ( sk_c8 = iPr_def_24 )
| ~ iPr_def_11
| ( inverse(iPr_def_18) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_452,c_23653]) ).
tcf(c_23669,plain,
( ( sk_c7 = iPr_def_23 )
| ~ iPr_def_11
| ( inverse(iPr_def_18) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_447,c_23653]) ).
tcf(c_23789,plain,
( ( inverse(iPr_def_18) != sk_c7 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_23665,c_2097,c_23669,c_23668]) ).
tcf(c_23790,plain,
( ~ iPr_def_11
| ( inverse(iPr_def_18) != sk_c7 ) ),
inference(renaming,[status(thm)],[c_23789]) ).
tcf(c_23984,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_23)) != sk_c7 )
| ( multiply(sk_c1,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_14416,c_428]) ).
tcf(c_23986,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_14416,c_84]) ).
tcf(c_23991,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_14416,c_14248]) ).
tcf(c_23992,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_14416,c_15675]) ).
tcf(c_24004,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_24 )
| ( inverse(inverse(iPr_def_23)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_23984,c_424]) ).
tcf(c_24011,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_19630,c_23986]) ).
tcf(c_24013,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_1074,c_23986]) ).
tcf(c_24014,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_983,c_23986]) ).
tcf(c_24069,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_23992,c_15675]) ).
tcf(c_24072,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_16057,c_24069]) ).
tcf(c_24073,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_22) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_1780,c_24069]) ).
tcf(c_24090,plain,
multiply(sk_c1,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_2970,c_23991]) ).
tcf(c_24474,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( sk_c7 != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2187,c_15702]) ).
tcf(c_25402,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_24014,c_24013]) ).
tcf(c_25463,plain,
( ( identity = iPr_def_24 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_24014,c_418]) ).
tcf(c_25472,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_25463,c_20897]) ).
tcf(c_28913,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_24) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_25402,c_15702]) ).
tcf(c_28915,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_25402,c_83]) ).
tcf(c_28955,plain,
! [X0: $i] :
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_24,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_25472,c_83]) ).
tcf(c_28978,plain,
multiply(sk_c2,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_14417,c_84]) ).
tcf(c_28983,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_14417,c_14248]) ).
tcf(c_28984,plain,
multiply(sk_c2,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_14417,c_15675]) ).
tcf(c_29000,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_885,c_28978]) ).
tcf(c_29001,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_883,c_28978]) ).
tcf(c_29802,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c5,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_29000,c_418]) ).
tcf(c_29809,plain,
( ( identity = iPr_def_21 )
| ( identity = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_29802,c_20897]) ).
tcf(c_30017,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( identity = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_29001,c_29000]) ).
tcf(c_30276,plain,
inverse(iPr_def_16) = sk_c2,
inference(demodulation,[status(thm)],[c_28984,c_15675]) ).
tcf(c_30284,plain,
multiply(sk_c2,sk_c8) = iPr_def_21,
inference(superposition,[status(thm)],[c_2955,c_28983]) ).
tcf(c_30379,plain,
( ( iPr_def_21 = iPr_def_24 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_29809,c_25472]) ).
tcf(c_30385,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_18 = iPr_def_21 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_29809,c_20919]) ).
tcf(c_30387,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_21 )
| ( identity = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_29809,c_20917]) ).
tcf(c_31500,plain,
( ( iPr_def_21 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_30017,c_25402]) ).
tcf(c_31511,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_21) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_30017,c_15702]) ).
tcf(c_32029,plain,
( ( iPr_def_21 = iPr_def_22 )
| ( iPr_def_17 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_31500,c_5551]) ).
tcf(c_32308,plain,
( ( identity = iPr_def_21 )
| ( identity = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_20232,c_28978]) ).
tcf(c_32332,plain,
( ( iPr_def_21 = iPr_def_24 )
| ( identity = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_32308,c_24011]) ).
tcf(c_32812,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_32029,c_16546]) ).
tcf(c_33113,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_33261,plain,
( ( iPr_def_21 = iPr_def_24 )
| ( iPr_def_18 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_32332,c_30379]) ).
tcf(c_33620,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_23 )
| ( multiply(iPr_def_15,iPr_def_19) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_448,c_21802]) ).
tcf(c_34516,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( iPr_def_16 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_33261,c_22353]) ).
tcf(c_34549,plain,
( ( iPr_def_18 = iPr_def_20 )
| ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c7,iPr_def_21) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_33261,c_1124]) ).
tcf(c_41816,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_21) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_32029,c_24073]) ).
tcf(c_41818,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_5649,c_24073]) ).
tcf(c_41821,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c1 = sk_c2 ) ),
inference(light_normalisation,[status(thm)],[c_41818,c_30276]) ).
tcf(c_41955,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_28915,c_13310]) ).
tcf(c_42063,plain,
( ( identity = iPr_def_18 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_28955,c_21808]) ).
tcf(c_42813,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c7,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_42063,c_414]) ).
tcf(c_46439,plain,
! [X0: $i] :
( ( X0 = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c1) )
| ( X0 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_33113]) ).
tcf(c_46440,plain,
( ( sk_c7 = iPr_def_23 )
| ( iPr_def_23 != inverse(sk_c1) )
| ( sk_c7 != inverse(sk_c1) ) ),
inference(instantiation,[status(thm)],[c_46439]) ).
tcf(c_46781,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c1) )
| ( X0 != iPr_def_14 )
| ( inverse(sk_c1) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_10138]) ).
tcf(c_46782,plain,
( ( sk_c7 = inverse(sk_c1) )
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c1) != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_46781]) ).
tcf(c_47547,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_16) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_2724,c_28913]) ).
tcf(c_47550,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c2 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_47547,c_30276]) ).
tcf(c_47651,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c1 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_41821,c_47550]) ).
tcf(c_47750,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_47651,c_423]) ).
tcf(c_47751,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c2 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_47750,c_30276]) ).
tcf(c_47881,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c1 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_47751,c_41821]) ).
tcf(c_48765,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_23,sk_c7) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_47881,c_424]) ).
tcf(c_50291,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( inverse(iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_32812,c_31511]) ).
tcf(c_50762,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c1 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_41816,c_31511]) ).
tcf(c_52162,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c1 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_50291,c_24072]) ).
tcf(c_52642,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_52162,c_424]) ).
tcf(c_52926,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_21) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_31500,c_11226]) ).
tcf(c_52940,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_52926,c_2955]) ).
tcf(c_53071,plain,
( ( identity = iPr_def_18 )
| ( sk_c7 = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_33620,c_423,c_2577,c_2578,c_10149,c_20915,c_23189,c_46440,c_46782]) ).
tcf(c_53178,plain,
( ( identity = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_53071,c_424]) ).
tcf(c_53681,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_52940,c_41955]) ).
tcf(c_54477,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_53681,c_7074]) ).
tcf(c_59784,plain,
( ( identity = iPr_def_18 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_53071,c_42813]) ).
tcf(c_60329,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( multiply(iPr_def_16,iPr_def_21) = identity ) ),
inference(superposition,[status(thm)],[c_50762,c_11242]) ).
tcf(c_60341,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c8 = identity ) ),
inference(light_normalisation,[status(thm)],[c_60329,c_2955]) ).
tcf(c_60492,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = identity ) ),
inference(superposition,[status(thm)],[c_60341,c_52940]) ).
tcf(c_66052,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_449,c_48765]) ).
tcf(c_70513,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_14482,c_84]) ).
tcf(c_70518,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_14482,c_14248]) ).
tcf(c_70519,plain,
! [X0: $i] : multiply(X0,identity) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_14482,c_15675]) ).
tcf(c_70520,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_70519,c_15675]) ).
tcf(c_70559,plain,
( ~ iPr_def_10
| ( sk_c7 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2188,c_70520]) ).
tcf(c_70561,plain,
( ~ iPr_def_12
| ( sk_c6 != identity ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1952,c_70520]) ).
tcf(c_70596,plain,
inverse(sk_c1) = iPr_def_23,
inference(superposition,[status(thm)],[c_24069,c_70520]) ).
tcf(c_70599,plain,
inverse(sk_c5) = iPr_def_17,
inference(superposition,[status(thm)],[c_21073,c_70520]) ).
tcf(c_70600,plain,
inverse(sk_c4) = iPr_def_19,
inference(superposition,[status(thm)],[c_20486,c_70520]) ).
tcf(c_70601,plain,
inverse(sk_c2) = iPr_def_16,
inference(superposition,[status(thm)],[c_30276,c_70520]) ).
tcf(c_70841,plain,
multiply(iPr_def_21,inverse(sk_c8)) = multiply(sk_c2,identity),
inference(superposition,[status(thm)],[c_70513,c_2848]) ).
tcf(c_70843,plain,
multiply(iPr_def_14,inverse(sk_c8)) = multiply(sk_c7,identity),
inference(superposition,[status(thm)],[c_70513,c_2842]) ).
tcf(c_70848,plain,
multiply(sk_c8,inverse(iPr_def_20)) = multiply(iPr_def_19,identity),
inference(superposition,[status(thm)],[c_70513,c_3453]) ).
tcf(c_70859,plain,
multiply(iPr_def_15,inverse(sk_c7)) = multiply(sk_c6,identity),
inference(superposition,[status(thm)],[c_70513,c_2845]) ).
tcf(c_70872,plain,
multiply(iPr_def_19,identity) = inverse(sk_c4),
inference(superposition,[status(thm)],[c_70513,c_2864]) ).
tcf(c_70873,plain,
multiply(iPr_def_17,identity) = inverse(sk_c5),
inference(superposition,[status(thm)],[c_70513,c_2863]) ).
tcf(c_71613,plain,
( ( iPr_def_17 = iPr_def_20 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_60492,c_70559]) ).
tcf(c_74713,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_52642,c_1528]) ).
tcf(c_74715,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( iPr_def_15 = iPr_def_24 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_52642,c_1433]) ).
tcf(c_75113,plain,
multiply(sk_c7,sk_c8) = iPr_def_14,
inference(superposition,[status(thm)],[c_14253,c_70518]) ).
tcf(c_75114,plain,
multiply(sk_c6,sk_c7) = iPr_def_15,
inference(superposition,[status(thm)],[c_14256,c_70518]) ).
tcf(c_75166,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c8 )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_70518,c_426]) ).
tcf(c_75216,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c8 ) ),
inference(ground_joinability,[status(thm)],[c_75166,c_70520]) ).
tcf(c_76626,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_66052,c_17029,c_18076,c_21141,c_52940,c_71613,c_74713,c_75216]) ).
tcf(c_76764,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_76626,c_441]) ).
tcf(c_76984,plain,
( ( sk_c7 = iPr_def_17 )
| ( iPr_def_17 = iPr_def_20 ) ),
inference(global_subsumption_just,[status(thm)],[c_76764,c_17013,c_21616,c_52940,c_54477,c_71613,c_74715,c_75216]) ).
tcf(c_76985,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_17 ) ),
inference(renaming,[status(thm)],[c_76984]) ).
tcf(c_77028,plain,
iPr_def_17 = iPr_def_20,
inference(superposition,[status(thm)],[c_76985,c_76626]) ).
tcf(c_77299,plain,
multiply(sk_c4,sk_c8) = iPr_def_17,
inference(demodulation,[status(thm)],[c_420,c_77028]) ).
tcf(c_77667,plain,
multiply(inverse(sk_c4),iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_77299,c_14248]) ).
tcf(c_77669,plain,
( ~ iPr_def_13
| ( inverse(sk_c4) != sk_c8 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_77299,c_426]) ).
tcf(c_77716,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_19 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_77669,c_70600]) ).
tcf(c_77745,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_5003,c_75216]) ).
tcf(c_77756,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_450,c_75216]) ).
tcf(c_77758,plain,
( ( sk_c7 = iPr_def_23 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_445,c_75216]) ).
tcf(c_78062,plain,
( ( sk_c8 = iPr_def_15 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_77756,c_3503,c_77745]) ).
tcf(c_78156,plain,
( ( sk_c7 != iPr_def_15 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_77758,c_19768,c_75216,c_78062]) ).
tcf(c_78157,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_15 ) ),
inference(renaming,[status(thm)],[c_78156]) ).
tcf(c_82333,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_78157,c_77716,c_77667,c_77299,c_77028,c_75114,c_75113,c_70873,c_70872,c_70859,c_70848,c_70843,c_70841,c_70601,c_70600,c_70599,c_70596,c_70561,c_70559,c_59784,c_53178,c_53071,c_34549,c_34516,c_30387,c_30385,c_30284,c_30276,c_28984,c_28978,c_24474,c_24090,c_24069,c_24004,c_23986,c_23790,c_21083,c_21073,c_20897,c_20486,c_19243,c_19236,c_15706,c_15705,c_15703,c_15695,c_15691,c_15702,c_14444,c_14258,c_14257,c_14253,c_10758,c_10218,c_2104,c_1971,c_459,c_458,c_457,c_455,c_452,c_447,c_442,c_437,c_434,c_433,c_432,c_430,c_425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP321-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 14:27:48 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 10.51/2.69 % SZS status Started for theBenchmark.p
% 10.51/2.69 % SZS status Unsatisfiable for theBenchmark.p
% 10.51/2.69
% 10.51/2.69 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.51/2.69
% 10.51/2.69 % ------ iProver source info
% 10.51/2.69
% 10.51/2.69 % git: date: 2026-07-19 20:42:38 +0200
% 10.51/2.69 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.51/2.69 % git: non_committed_changes: false
% 10.51/2.69
% 10.51/2.69 % ------ Parsing...% successful
% 10.51/2.69
% 10.51/2.69
% 10.51/2.69 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.51/2.69
% 10.51/2.69 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.51/2.69
% 10.51/2.69 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.51/2.69
% 10.51/2.69 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.51/2.69 % ------ Proving...
% 10.51/2.69 % ------ Problem Properties
% 10.51/2.69
% 10.51/2.69 %
% 10.51/2.69 % clauses 49
% 10.51/2.69 % conjectures 35
% 10.51/2.69 % EPR 31
% 10.51/2.69 % Horn 18
% 10.51/2.69 % unary 14
% 10.51/2.69 % binary 30
% 10.51/2.69 % lits 92
% 10.51/2.69 % lits eq 84
% 10.51/2.69 % fd_pure 0
% 10.51/2.69 % fd_pseudo 0
% 10.51/2.69 % fd_cond 0
% 10.51/2.69 % fd_pseudo_cond 0
% 10.51/2.69 % AC symbols 0
% 10.51/2.69
% 10.51/2.69 % ------ Schedule dynamic 5 is on
% 10.51/2.69
% 10.51/2.69 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.51/2.69
% 10.51/2.69
% 10.51/2.69 % ------
% 10.51/2.69 % Current options:
% 10.51/2.69 % ------
% 10.51/2.69
% 10.51/2.69
% 10.51/2.69 %
% 10.51/2.69
% 10.51/2.69 % ------ Proving...
% 10.51/2.69 %
% 10.51/2.69
% 10.51/2.69 % SZS status Unsatisfiable for theBenchmark.p
% 10.51/2.69
% 10.51/2.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.67/2.70
%------------------------------------------------------------------------------