%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP255-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n026.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 01:32:36 PM UTC 2026
% Result : Unsatisfiable 0.97s 1.21s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 47
% Syntax : Number of formulae : 357 ( 101 unt; 11 def)
% Number of atoms : 1178 ( 622 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 588 ( 192 ~; 396 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 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 : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 77 ( 0 sgn 77 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = inverse(sk_c5)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c4)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c7 = inverse(sk_c5)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c6 = multiply(sk_c2,sk_c7) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c7 = inverse(sk_c2) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c8 = inverse(sk_c4)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c7 = inverse(sk_c5)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c6 = inverse(sk_c3) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| sk_c6 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = inverse(sk_c4)
| sk_c6 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c6 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c7 = inverse(sk_c5)
| sk_c6 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c7 = multiply(sk_c5,sk_c6)
| sk_c6 = multiply(sk_c3,sk_c8) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| multiply(X2,sk_c8) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( sk_c7 != multiply(X4,sk_c6)
| sk_c7 != inverse(X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| multiply(sk_c7,sk_c8) != sk_c6
| sk_c6 != multiply(X2,sk_c8)
| sk_c6 != inverse(X2)
| sk_c7 != inverse(X1)
| sk_c6 != multiply(X1,sk_c7)
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8) ),
inference(reorient_equations,[],[f64]) ).
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_c7,sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( inverse(sk_c1) = sk_c8 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c2,sk_c7) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_103,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c3) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_111,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c6 )
| ( multiply(sk_c7,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c6 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_115,negated_conjecture,
( ( multiply(sk_c3,sk_c8) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X4) != sk_c6 )
| ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c7,sk_c8) != sk_c6 )
| ( multiply(X4,sk_c8) != sk_c6 )
| ( multiply(X3,sk_c7) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_413,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_414,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_415,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_416,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_417,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_116]) ).
tcf(c_418,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( multiply(sk_c7,sk_c8) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_419,definition,
iPr_def_15 = multiply(sk_c7,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_420,definition,
iPr_def_16 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_421,definition,
iPr_def_17 = multiply(sk_c3,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_422,definition,
iPr_def_18 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_423,definition,
iPr_def_19 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_424,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_425,definition,
iPr_def_21 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_426,definition,
iPr_def_22 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_427,definition,
iPr_def_23 = multiply(sk_c2,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_428,definition,
iPr_def_24 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_429,definition,
iPr_def_25 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_430,negated_conjecture,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_15 != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_418,c_419]) ).
tcf(c_431,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_14
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_417]) ).
tcf(c_432,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c8) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_416]) ).
tcf(c_433,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_415]) ).
tcf(c_434,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_414]) ).
tcf(c_435,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c6) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_413]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_115,c_421,c_420]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_114,c_422]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_113,c_423]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_112,c_424]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110,c_425]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_21 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105,c_426]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_100,c_427]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_23 = sk_c6 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_95,c_428]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_460,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_461,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_16 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90,c_429]) ).
tcf(c_462,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_463,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_464,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_465,negated_conjecture,
( ( iPr_def_25 = sk_c7 )
| ( iPr_def_15 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_466,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_467,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_472,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_466]) ).
tcf(c_738,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_442,c_437]) ).
tcf(c_756,plain,
( ( iPr_def_17 = iPr_def_21 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_443,c_438]) ).
tcf(c_767,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_443,c_420]) ).
tcf(c_768,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_442,c_420]) ).
tcf(c_769,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_441,c_420]) ).
tcf(c_822,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(sk_c5,iPr_def_21) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_445,c_420]) ).
tcf(c_850,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_19) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_448,c_421]) ).
tcf(c_862,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_449,c_421]) ).
tcf(c_945,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_451,c_420]) ).
tcf(c_953,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c7 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_451,c_436]) ).
tcf(c_982,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_447,c_423]) ).
tcf(c_983,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_446,c_423]) ).
tcf(c_1009,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_424,c_84]) ).
tcf(c_1010,plain,
multiply(iPr_def_18,sk_c5) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_1011,plain,
multiply(iPr_def_24,sk_c1) = identity,
inference(superposition,[status(thm)],[c_428,c_84]) ).
tcf(c_1012,plain,
multiply(iPr_def_22,sk_c2) = identity,
inference(superposition,[status(thm)],[c_426,c_84]) ).
tcf(c_1013,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_425,c_84]) ).
tcf(c_1054,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_452,c_420]) ).
tcf(c_1061,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c7 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_452,c_437]) ).
tcf(c_1096,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_23) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_453,c_420]) ).
tcf(c_1097,plain,
( ( iPr_def_21 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_453,c_443]) ).
tcf(c_1102,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_453,c_438]) ).
tcf(c_1155,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_454,c_439]) ).
tcf(c_1201,plain,
( ( iPr_def_17 = iPr_def_23 )
| ( sk_c6 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_455,c_440]) ).
tcf(c_1456,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_461,c_427]) ).
tcf(c_1478,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_25) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_462,c_427]) ).
tcf(c_1513,plain,
( ( sk_c7 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_19) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_463,c_429]) ).
tcf(c_1564,plain,
( ( sk_c7 = iPr_def_25 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_464,c_429]) ).
tcf(c_1916,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_465,c_430]) ).
tcf(c_1923,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_450,c_430]) ).
tcf(c_1931,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_438,c_430]) ).
tcf(c_1932,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_18 )
| ( iPr_def_15 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_437,c_430]) ).
tcf(c_1933,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_16 )
| ( iPr_def_15 != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_436,c_430]) ).
tcf(c_2115,plain,
( ~ iPr_def_14
| ( sk_c7 != iPr_def_25 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_429,c_431]) ).
tcf(c_2119,plain,
( ~ iPr_def_14
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_84,c_431]) ).
tcf(c_2139,plain,
( ~ iPr_def_14
| ( sk_c7 != iPr_def_25 )
| ( sk_c8 != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_2115,c_428]) ).
tcf(c_2258,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_15 )
| ( inverse(sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_419,c_432]) ).
tcf(c_2259,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_17 )
| ( inverse(sk_c3) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_421,c_432]) ).
tcf(c_2274,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_21 )
| ( sk_c6 != iPr_def_17 ) ),
inference(light_normalisation,[status(thm)],[c_2259,c_425]) ).
tcf(c_2383,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_423,c_433]) ).
tcf(c_2386,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c7)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_84,c_433]) ).
tcf(c_2400,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_2383,c_424]) ).
tcf(c_2476,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_23 )
| ( inverse(sk_c2) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_427,c_434]) ).
tcf(c_2488,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_23 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_2476,c_426]) ).
tcf(c_2566,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_16 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_420,c_435]) ).
tcf(c_2568,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c6)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_84,c_435]) ).
tcf(c_2590,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_18 )
| ( sk_c7 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_2566,c_422]) ).
tcf(c_2970,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c8,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_2971,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c7,X0)) = multiply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_423,c_85]) ).
tcf(c_2973,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c7,X0)) = multiply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_427,c_85]) ).
tcf(c_2976,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2978,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1009,c_85]) ).
tcf(c_2979,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1010,c_85]) ).
tcf(c_2980,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1011,c_85]) ).
tcf(c_2981,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1012,c_85]) ).
tcf(c_2982,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1013,c_85]) ).
tcf(c_2989,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2982,c_83]) ).
tcf(c_2990,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2981,c_83]) ).
tcf(c_2991,plain,
! [X0: $i] : multiply(iPr_def_24,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2980,c_83]) ).
tcf(c_2992,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2979,c_83]) ).
tcf(c_2993,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2978,c_83]) ).
tcf(c_3646,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_22 )
| ( iPr_def_22 != X0 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_467]) ).
tcf(c_3647,plain,
( ( sk_c7 = iPr_def_22 )
| ( iPr_def_22 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_3646]) ).
tcf(c_3965,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_17 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1201,c_430]) ).
tcf(c_4363,plain,
multiply(iPr_def_21,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_421,c_2989]) ).
tcf(c_4366,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_17,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_4363,c_85]) ).
tcf(c_4368,plain,
multiply(iPr_def_22,iPr_def_23) = sk_c7,
inference(superposition,[status(thm)],[c_427,c_2990]) ).
tcf(c_4371,plain,
! [X0: $i] : multiply(iPr_def_22,multiply(iPr_def_23,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_4368,c_85]) ).
tcf(c_4401,plain,
multiply(iPr_def_24,iPr_def_25) = sk_c8,
inference(superposition,[status(thm)],[c_429,c_2991]) ).
tcf(c_4492,plain,
( iPr_def_14
| iPr_def_13
| ( iPr_def_17 = iPr_def_23 )
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_3965,c_953,c_1061,c_1102,c_1155,c_2400,c_2590,c_3965]) ).
tcf(c_4493,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_11
| ( iPr_def_17 = iPr_def_23 ) ),
inference(renaming,[status(thm)],[c_4492]) ).
tcf(c_4534,plain,
multiply(iPr_def_18,iPr_def_16) = sk_c6,
inference(superposition,[status(thm)],[c_420,c_2992]) ).
tcf(c_4546,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_16,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4534,c_85]) ).
tcf(c_4548,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_423,c_2993]) ).
tcf(c_4551,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_4548,c_85]) ).
tcf(c_4729,plain,
( ( sk_c6 = iPr_def_15 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_822,c_2992]) ).
tcf(c_4730,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c6 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4729,c_4534]) ).
tcf(c_4935,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_21,iPr_def_17) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_850,c_2989]) ).
tcf(c_4936,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_4935,c_4363]) ).
tcf(c_5043,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(iPr_def_21,iPr_def_17) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_862,c_2989]) ).
tcf(c_5044,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_5043,c_4363]) ).
tcf(c_5228,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_945,c_2992]) ).
tcf(c_5229,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_5228,c_4534]) ).
tcf(c_5240,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_982,c_2993]) ).
tcf(c_5241,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5240,c_4548]) ).
tcf(c_5252,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_983,c_2993]) ).
tcf(c_5253,plain,
( ( sk_c7 = iPr_def_22 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_5252,c_4548]) ).
tcf(c_5310,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1054,c_2992]) ).
tcf(c_5311,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_5310,c_4534]) ).
tcf(c_5326,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_18,iPr_def_16) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1096,c_2992]) ).
tcf(c_5327,plain,
( ( sk_c6 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_5326,c_4534]) ).
tcf(c_6102,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1456,c_2990]) ).
tcf(c_6103,plain,
( ( sk_c7 = iPr_def_25 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6102,c_4368]) ).
tcf(c_6164,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(iPr_def_22,iPr_def_23) = iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_1478,c_2990]) ).
tcf(c_6165,plain,
( ( sk_c7 = iPr_def_25 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_6164,c_4368]) ).
tcf(c_6224,plain,
( ( sk_c7 = iPr_def_25 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1513,c_2991]) ).
tcf(c_6225,plain,
( ( sk_c7 = iPr_def_25 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_6224,c_4401]) ).
tcf(c_6311,plain,
( ( sk_c7 = iPr_def_25 )
| ( multiply(iPr_def_24,iPr_def_25) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1564,c_2991]) ).
tcf(c_6312,plain,
( ( sk_c7 = iPr_def_25 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_6311,c_4401]) ).
tcf(c_7673,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_19,sk_c8),
inference(superposition,[status(thm)],[c_419,c_2971]) ).
tcf(c_7945,plain,
multiply(sk_c2,iPr_def_15) = multiply(iPr_def_23,sk_c8),
inference(superposition,[status(thm)],[c_419,c_2973]) ).
tcf(c_9242,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2976,c_83]) ).
tcf(c_9249,plain,
multiply(inverse(sk_c7),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_419,c_9242]) ).
tcf(c_9254,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_9242]) ).
tcf(c_9255,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_9242]) ).
tcf(c_9259,plain,
( ( sk_c7 = iPr_def_16 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_769,c_9242]) ).
tcf(c_9260,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_768,c_9242]) ).
tcf(c_9261,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_767,c_9242]) ).
tcf(c_9374,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2993,c_9242]) ).
tcf(c_9375,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2992,c_9242]) ).
tcf(c_9376,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2991,c_9242]) ).
tcf(c_9377,plain,
! [X0: $i] : multiply(inverse(iPr_def_22),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2990,c_9242]) ).
tcf(c_9378,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_2989,c_9242]) ).
tcf(c_9399,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_9242,c_9242]) ).
tcf(c_9557,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_9261,c_422,c_4534]) ).
tcf(c_9560,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c7 = iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_9260,c_422,c_4534]) ).
tcf(c_9563,plain,
( ( sk_c6 = iPr_def_21 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_9259,c_422,c_4534]) ).
tcf(c_9930,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_9255,c_9399]) ).
tcf(c_9942,plain,
multiply(sk_c7,sk_c8) = multiply(iPr_def_15,identity),
inference(superposition,[status(thm)],[c_9930,c_2970]) ).
tcf(c_9944,plain,
multiply(sk_c7,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_9930,c_4551]) ).
tcf(c_9947,plain,
multiply(sk_c6,identity) = multiply(iPr_def_18,iPr_def_16),
inference(superposition,[status(thm)],[c_9930,c_4546]) ).
tcf(c_9949,plain,
multiply(sk_c7,identity) = multiply(iPr_def_22,iPr_def_23),
inference(superposition,[status(thm)],[c_9930,c_4371]) ).
tcf(c_9950,plain,
multiply(sk_c8,identity) = multiply(iPr_def_21,iPr_def_17),
inference(superposition,[status(thm)],[c_9930,c_4366]) ).
tcf(c_9956,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_9930,c_9254]) ).
tcf(c_9957,plain,
multiply(sk_c8,identity) = sk_c8,
inference(light_normalisation,[status(thm)],[c_9950,c_4363]) ).
tcf(c_9958,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_9949,c_4368]) ).
tcf(c_9960,plain,
multiply(sk_c6,identity) = sk_c6,
inference(light_normalisation,[status(thm)],[c_9947,c_4534]) ).
tcf(c_9965,plain,
multiply(iPr_def_15,identity) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_9942,c_419]) ).
tcf(c_10074,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_9956,c_84]) ).
tcf(c_10127,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_14
| ( sk_c7 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_458,c_2139]) ).
tcf(c_10128,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_14
| ( sk_c7 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_457,c_2139]) ).
tcf(c_10129,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_14
| ( sk_c7 != iPr_def_25 ) ),
inference(superposition,[status(thm)],[c_456,c_2139]) ).
tcf(c_10236,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_14 ),
inference(global_subsumption_just,[status(thm)],[c_10128,c_6165,c_10128]) ).
tcf(c_10258,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_14 ),
inference(global_subsumption_just,[status(thm)],[c_10129,c_6103,c_10129]) ).
tcf(c_10321,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_13
| ( iPr_def_17 != iPr_def_21 )
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_442,c_2274]) ).
tcf(c_10323,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_440,c_2274]) ).
tcf(c_10325,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_438,c_2274]) ).
tcf(c_10326,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_437,c_2274]) ).
tcf(c_10327,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_13
| ( sk_c6 != iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_436,c_2274]) ).
tcf(c_10510,plain,
( ( sk_c6 = iPr_def_15 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_10323,c_4730,c_10323]) ).
tcf(c_10729,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_10326,c_738,c_9560,c_10321]) ).
tcf(c_10735,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_10327,c_9563,c_10327]) ).
tcf(c_11078,plain,
( ( iPr_def_21 = iPr_def_23 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1097,c_2400]) ).
tcf(c_11080,plain,
( ( iPr_def_17 = iPr_def_21 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_756,c_2400]) ).
tcf(c_11082,plain,
( ( sk_c7 = iPr_def_25 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_463,c_2400]) ).
tcf(c_11088,plain,
( ( sk_c7 = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_448,c_2400]) ).
tcf(c_11136,plain,
( ( sk_c7 = iPr_def_25 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_11082,c_6312,c_11082]) ).
tcf(c_11142,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_25 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1916,c_11136]) ).
tcf(c_11149,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_11
| ( sk_c7 = iPr_def_25 ) ),
inference(global_subsumption_just,[status(thm)],[c_11142,c_1916,c_2590,c_6103,c_6165,c_11136]) ).
tcf(c_11168,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_9374,c_84]) ).
tcf(c_11172,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_20)) != sk_c8 )
| ( multiply(sk_c4,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_9374,c_433]) ).
tcf(c_11174,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_9374,c_9242]) ).
tcf(c_11175,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_9374,c_9930]) ).
tcf(c_11179,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_19 )
| ( inverse(inverse(iPr_def_20)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_11172,c_423]) ).
tcf(c_11196,plain,
( ( sk_c7 = iPr_def_22 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_11088,c_5044,c_11088]) ).
tcf(c_11202,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_22 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1923,c_11196]) ).
tcf(c_11308,plain,
( iPr_def_14
| iPr_def_13
| iPr_def_11
| ( sk_c7 = iPr_def_22 ) ),
inference(global_subsumption_just,[status(thm)],[c_11202,c_472,c_430,c_450,c_2590,c_3647,c_5241,c_5253,c_11196]) ).
tcf(c_11344,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_447,c_2488]) ).
tcf(c_11345,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_11
| ( sk_c6 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_446,c_2488]) ).
tcf(c_11399,plain,
( ( sk_c7 = iPr_def_18 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_11344,c_5311,c_11344]) ).
tcf(c_11405,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_11175,c_9930]) ).
tcf(c_11410,plain,
multiply(sk_c4,sk_c7) = iPr_def_19,
inference(superposition,[status(thm)],[c_4548,c_11174]) ).
tcf(c_11445,plain,
multiply(sk_c5,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_9375,c_84]) ).
tcf(c_11448,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_18)) != sk_c7 )
| ( multiply(sk_c5,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_9375,c_434]) ).
tcf(c_11450,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_18)) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_9375,c_435]) ).
tcf(c_11451,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_9375,c_9242]) ).
tcf(c_11452,plain,
multiply(sk_c5,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_9375,c_9930]) ).
tcf(c_11472,plain,
( ( sk_c7 = iPr_def_16 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_11345,c_5229,c_11345]) ).
tcf(c_11719,plain,
inverse(iPr_def_18) = sk_c5,
inference(demodulation,[status(thm)],[c_11452,c_9930]) ).
tcf(c_11735,plain,
multiply(sk_c5,sk_c6) = iPr_def_16,
inference(superposition,[status(thm)],[c_4534,c_11451]) ).
tcf(c_11809,plain,
( ~ iPr_def_14
| ( inverse(inverse(iPr_def_24)) != sk_c8 )
| ( multiply(sk_c1,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_9376,c_431]) ).
tcf(c_11810,plain,
multiply(sk_c1,iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_9376,c_84]) ).
tcf(c_11816,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_24,X0)) = X0,
inference(superposition,[status(thm)],[c_9376,c_9242]) ).
tcf(c_11817,plain,
multiply(sk_c1,identity) = inverse(iPr_def_24),
inference(superposition,[status(thm)],[c_9376,c_9930]) ).
tcf(c_11827,plain,
( ~ iPr_def_14
| ( sk_c7 != iPr_def_25 )
| ( inverse(inverse(iPr_def_24)) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_11809,c_429]) ).
tcf(c_12658,plain,
inverse(iPr_def_24) = sk_c1,
inference(demodulation,[status(thm)],[c_11817,c_9930]) ).
tcf(c_12662,plain,
multiply(sk_c1,identity) = sk_c1,
inference(superposition,[status(thm)],[c_1011,c_11816]) ).
tcf(c_12663,plain,
multiply(sk_c1,sk_c8) = iPr_def_25,
inference(superposition,[status(thm)],[c_4401,c_11816]) ).
tcf(c_13045,plain,
multiply(sk_c2,iPr_def_22) = identity,
inference(superposition,[status(thm)],[c_9377,c_84]) ).
tcf(c_13048,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_22)) != sk_c7 )
| ( multiply(sk_c2,sk_c7) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_9377,c_434]) ).
tcf(c_13050,plain,
( ~ iPr_def_10
| ( inverse(inverse(iPr_def_22)) != sk_c7 )
| ( multiply(sk_c2,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_9377,c_435]) ).
tcf(c_13051,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_22,X0)) = X0,
inference(superposition,[status(thm)],[c_9377,c_9242]) ).
tcf(c_13052,plain,
multiply(sk_c2,identity) = inverse(iPr_def_22),
inference(superposition,[status(thm)],[c_9377,c_9930]) ).
tcf(c_13060,plain,
( ~ iPr_def_11
| ( sk_c6 != iPr_def_23 )
| ( inverse(inverse(iPr_def_22)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_13048,c_427]) ).
tcf(c_13271,plain,
( ~ iPr_def_13
| ( inverse(sk_c7) != sk_c6 ) ),
inference(global_subsumption_just,[status(thm)],[c_2258,c_2258,c_10510]) ).
tcf(c_14605,plain,
inverse(iPr_def_22) = sk_c2,
inference(demodulation,[status(thm)],[c_13052,c_9930]) ).
tcf(c_14612,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1012,c_13051]) ).
tcf(c_14613,plain,
multiply(sk_c2,sk_c7) = iPr_def_23,
inference(superposition,[status(thm)],[c_4368,c_13051]) ).
tcf(c_15886,plain,
( iPr_def_12
| ( iPr_def_15 != iPr_def_17 )
| ( sk_c8 = iPr_def_19 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1931,c_1931,c_2488,c_4936,c_5327,c_6225,c_9557,c_10127,c_10325]) ).
tcf(c_15887,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c8 = iPr_def_19 )
| ( iPr_def_15 != iPr_def_17 ) ),
inference(renaming,[status(thm)],[c_15886]) ).
tcf(c_15896,plain,
( iPr_def_12
| ( iPr_def_15 != iPr_def_17 )
| ( sk_c7 = iPr_def_18 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1932,c_1932,c_5311,c_6165,c_9560,c_10128,c_10326,c_11344]) ).
tcf(c_15897,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_18 )
| ( iPr_def_15 != iPr_def_17 ) ),
inference(renaming,[status(thm)],[c_15896]) ).
tcf(c_15948,plain,
( iPr_def_12
| ( iPr_def_15 != iPr_def_17 )
| ( sk_c7 = iPr_def_16 )
| iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_1933,c_1933,c_5229,c_6103,c_9563,c_10129,c_10327,c_11345]) ).
tcf(c_15949,plain,
( iPr_def_12
| iPr_def_10
| ( sk_c7 = iPr_def_16 )
| ( iPr_def_15 != iPr_def_17 ) ),
inference(renaming,[status(thm)],[c_15948]) ).
tcf(c_17867,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_21)) != sk_c6 )
| ( multiply(sk_c3,sk_c8) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_9378,c_432]) ).
tcf(c_17869,plain,
multiply(sk_c3,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_9378,c_84]) ).
tcf(c_17875,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_9378,c_9242]) ).
tcf(c_17876,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_9378,c_9930]) ).
tcf(c_17984,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(superposition,[status(thm)],[c_17869,c_2989]) ).
tcf(c_18946,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_17876,c_9930]) ).
tcf(c_18957,plain,
multiply(sk_c3,sk_c8) = iPr_def_17,
inference(superposition,[status(thm)],[c_4363,c_17875]) ).
tcf(c_19979,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_18957,c_18946,c_17984,c_17867,c_15949,c_15897,c_15887,c_14613,c_14612,c_14605,c_13271,c_13060,c_13050,c_13045,c_12663,c_12662,c_12658,c_11827,c_11810,c_11735,c_11719,c_11472,c_11450,c_11448,c_11452,c_11445,c_11410,c_11405,c_11399,c_11308,c_11196,c_11179,c_11172,c_11168,c_11149,c_11136,c_11080,c_11078,c_10735,c_10729,c_10258,c_10236,c_9965,c_9960,c_9958,c_9957,c_9950,c_9947,c_9944,c_9942,c_9956,c_9249,c_7945,c_7673,c_10074,c_4493,c_2590,c_2568,c_2386,c_2274,c_2258,c_2119,c_465,c_464,c_460,c_459,c_458,c_457,c_456,c_455,c_454,c_450,c_449,c_445,c_444,c_440,c_439,c_438,c_437,c_436,c_430,c_428,c_426,c_425,c_424,c_422]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP255-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:19:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.97/1.21 % SZS status Started for theBenchmark.p
% 0.97/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.97/1.21
% 0.97/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.97/1.21
% 0.97/1.21 % ------ iProver source info
% 0.97/1.21
% 0.97/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 0.97/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.97/1.21 % git: non_committed_changes: false
% 0.97/1.21
% 0.97/1.21 % ------ Parsing...% successful
% 0.97/1.21
% 0.97/1.21
% 0.97/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.97/1.21
% 0.97/1.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.97/1.21
% 0.97/1.21 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.97/1.21
% 0.97/1.21 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.97/1.21 % ------ Proving...
% 0.97/1.21 % ------ Problem Properties
% 0.97/1.21
% 0.97/1.21 %
% 0.97/1.21 % clauses 50
% 0.97/1.21 % conjectures 36
% 0.97/1.21 % EPR 31
% 0.97/1.21 % Horn 19
% 0.97/1.21 % unary 14
% 0.97/1.21 % binary 30
% 0.97/1.21 % lits 95
% 0.97/1.21 % lits eq 85
% 0.97/1.21 % fd_pure 0
% 0.97/1.21 % fd_pseudo 0
% 0.97/1.21 % fd_cond 0
% 0.97/1.21 % fd_pseudo_cond 0
% 0.97/1.21 % AC symbols 0
% 0.97/1.21
% 0.97/1.21 % ------ Schedule dynamic 5 is on
% 0.97/1.21
% 0.97/1.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.97/1.21
% 0.97/1.21
% 0.97/1.21 % ------
% 0.97/1.21 % Current options:
% 0.97/1.21 % ------
% 0.97/1.21
% 0.97/1.21
% 0.97/1.21 %
% 0.97/1.21
% 0.97/1.21 % ------ Proving...
% 0.97/1.21 %
% 0.97/1.21
% 0.97/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 0.97/1.21
% 0.97/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.97/1.22
% 0.97/1.22
%------------------------------------------------------------------------------