%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP376-1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:27 PM UTC 2026
% Result : Unsatisfiable 8.08s 1.75s
% Output : CNFRefutation 8.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 47
% Syntax : Number of formulae : 377 ( 113 unt; 11 def)
% Number of atoms : 1292 ( 697 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 533 ( 172 ~; 361 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?; 79 :)
% 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_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c7 = inverse(sk_c3)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c6 = inverse(sk_c4)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| inverse(sk_c7) = sk_c6 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( sk_c7 = inverse(sk_c3)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c6 = inverse(sk_c4)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c6 = multiply(sk_c1,sk_c7) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
fof(f29,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
fof(f31,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f30]) ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f33,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = inverse(sk_c1) ),
inference(reorient_equations,[],[f32]) ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f35,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f34]) ).
fof(f36,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f37,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f39,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f38]) ).
fof(f40,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = multiply(sk_c5,sk_c6) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = inverse(sk_c3)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c6 = inverse(sk_c4)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c7 = inverse(sk_c3)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f56]) ).
fof(f58,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f59,plain,
( sk_c7 = multiply(sk_c3,sk_c6)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f58]) ).
fof(f60,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f61,plain,
( sk_c6 = inverse(sk_c4)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f60]) ).
fof(f62,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f63,plain,
( sk_c6 = multiply(sk_c4,sk_c5)
| sk_c5 = inverse(sk_c2) ),
inference(reorient_equations,[],[f62]) ).
fof(f64,negated_conjecture,
! [X2,X3,X0,X1] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c5
| multiply(X1,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,plain,
! [X2,X3,X0,X1] :
( sk_c6 != multiply(X3,sk_c5)
| sk_c6 != inverse(X3)
| sk_c7 != multiply(X2,sk_c6)
| sk_c7 != inverse(X2)
| multiply(sk_c6,sk_c7) != sk_c5
| sk_c5 != inverse(X1)
| sk_c7 != multiply(X1,sk_c5)
| sk_c7 != multiply(sk_c5,sk_c6)
| inverse(X0) != sk_c7
| sk_c6 != multiply(X0,sk_c7)
| inverse(sk_c7) != sk_c6 ),
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,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( inverse(sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c1,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_95,negated_conjecture,
( ( multiply(sk_c1,sk_c7) = sk_c6 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_101,negated_conjecture,
( ( multiply(sk_c5,sk_c6) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_102,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c3,sk_c6) = sk_c7 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_105,negated_conjecture,
( ( multiply(sk_c4,sk_c5) = sk_c6 )
| ( multiply(sk_c5,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_106,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c7 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_108,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c4) = sk_c6 )
| ( multiply(sk_c2,sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c5) = sk_c7 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c6,sk_c7) = sk_c5 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_112,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c3) = sk_c7 ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_113,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c3,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_114,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( inverse(sk_c4) = sk_c6 ) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c2) = sk_c5 )
| ( multiply(sk_c4,sk_c5) = sk_c6 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c7) != sk_c6 )
| ( inverse(X3) != sk_c6 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c5 )
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 )
| ( multiply(X3,sk_c5) != sk_c6 )
| ( multiply(X2,sk_c6) != sk_c7 )
| ( multiply(X1,sk_c5) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
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_c5 )
| ( multiply(X0,sk_c5) != sk_c7 ) ),
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_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
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_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_417,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c7) != sk_c6 )
| ( multiply(sk_c5,sk_c6) != sk_c7 )
| ( multiply(sk_c6,sk_c7) != sk_c5 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_418,definition,
iPr_def_14 = multiply(sk_c6,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_419,definition,
iPr_def_15 = multiply(sk_c5,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_420,definition,
iPr_def_16 = inverse(sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_421,definition,
iPr_def_17 = multiply(sk_c4,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_422,definition,
iPr_def_18 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_423,definition,
iPr_def_19 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_424,definition,
iPr_def_20 = multiply(sk_c3,sk_c6),
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 = multiply(sk_c2,sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_427,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_428,definition,
iPr_def_24 = multiply(sk_c1,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_429,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_16 != sk_c6 )
| ( iPr_def_15 != sk_c7 )
| ( iPr_def_14 != sk_c5 ) ),
inference(demodulation,[status(thm)],[c_417,c_420,c_419,c_418]) ).
tcf(c_430,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_416]) ).
tcf(c_431,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c6 )
| ( multiply(X0,sk_c5) != sk_c6 ) ),
inference(demodulation,[status(thm)],[c_415]) ).
tcf(c_432,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c5 )
| ( multiply(X0,sk_c5) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_414]) ).
tcf(c_433,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_434,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_115,c_422,c_421]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_114,c_423]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_113,c_424]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_18 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_112,c_425]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_18 = sk_c5 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_111]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_110,c_426]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_442,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_443,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_105]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_447,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_448,negated_conjecture,
( ( iPr_def_15 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_100,c_427]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_23 = sk_c7 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_95,c_428]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_19 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_456,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_20 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_457,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_21 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_458,negated_conjecture,
( ( iPr_def_24 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_459,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_460,negated_conjecture,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_461,negated_conjecture,
( ( iPr_def_20 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_462,negated_conjecture,
( ( iPr_def_21 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_463,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_14 = sk_c5 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_464,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_465,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_705,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c7 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_439,c_440]) ).
tcf(c_766,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c6,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_442,c_418]) ).
tcf(c_824,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_445,c_444]) ).
tcf(c_861,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c7 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_447,c_446]) ).
tcf(c_956,plain,
! [X0: $i,X1: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_465]) ).
tcf(c_957,plain,
! [X0: $i] :
( ( sk_c6 = X0 )
| ( sk_c6 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_956]) ).
tcf(c_958,plain,
sk_c6 = sk_c6,
inference(instantiation,[status(thm)],[c_464]) ).
tcf(c_964,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_437,c_426]) ).
tcf(c_965,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_436,c_426]) ).
tcf(c_966,plain,
( ( sk_c6 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_435,c_426]) ).
tcf(c_967,plain,
( ( sk_c6 = iPr_def_17 )
| ( multiply(sk_c2,iPr_def_18) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_434,c_426]) ).
tcf(c_987,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_465]) ).
tcf(c_989,plain,
( ( sk_c6 = iPr_def_17 )
| ( iPr_def_17 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_957]) ).
tcf(c_990,plain,
( ( sk_c6 = iPr_def_19 )
| ( iPr_def_19 != sk_c6 )
| ( sk_c6 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_957]) ).
tcf(c_1010,plain,
multiply(iPr_def_16,sk_c7) = identity,
inference(superposition,[status(thm)],[c_420,c_84]) ).
tcf(c_1011,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_425,c_84]) ).
tcf(c_1012,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_423,c_84]) ).
tcf(c_1013,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_427,c_84]) ).
tcf(c_1014,plain,
multiply(iPr_def_18,sk_c2) = identity,
inference(superposition,[status(thm)],[c_422,c_84]) ).
tcf(c_1026,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c7 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_450,c_449]) ).
tcf(c_1061,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_19 )
| ( X0 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_987]) ).
tcf(c_1063,plain,
! [X0: $i] :
( ( X0 = sk_c6 )
| ( sk_c6 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_987]) ).
tcf(c_1085,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_451,c_441]) ).
tcf(c_1121,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_452,c_442]) ).
tcf(c_1147,plain,
! [X0: $i,X1: $i] :
( ( X0 = iPr_def_17 )
| ( iPr_def_17 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_465]) ).
tcf(c_1245,plain,
( ( iPr_def_19 = sk_c6 )
| ( iPr_def_19 != iPr_def_19 )
| ( sk_c6 != iPr_def_19 ) ),
inference(instantiation,[status(thm)],[c_1061]) ).
tcf(c_1246,plain,
iPr_def_19 = iPr_def_19,
inference(instantiation,[status(thm)],[c_464]) ).
tcf(c_1253,plain,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_17 != iPr_def_17 )
| ( sk_c6 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1063]) ).
tcf(c_1254,plain,
iPr_def_17 = iPr_def_17,
inference(instantiation,[status(thm)],[c_464]) ).
tcf(c_1491,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_465]) ).
tcf(c_1552,plain,
! [X0: $i,X1: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_465]) ).
tcf(c_1614,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_460,c_459]) ).
tcf(c_1676,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_461,c_456]) ).
tcf(c_1677,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c6 = iPr_def_19 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_461,c_455]) ).
tcf(c_1678,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c6 = iPr_def_17 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_461,c_454]) ).
tcf(c_1685,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_461,c_418]) ).
tcf(c_1690,plain,
( ( identity = iPr_def_14 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_1685,c_1010]) ).
tcf(c_1734,plain,
! [X0: $i] :
( ( X0 = iPr_def_17 )
| ( iPr_def_17 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1147]) ).
tcf(c_1793,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_462,c_457]) ).
tcf(c_1802,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(sk_c5,iPr_def_16) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_462,c_419]) ).
tcf(c_1803,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_462,c_418]) ).
tcf(c_1808,plain,
( ( identity = iPr_def_14 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_1803,c_1010]) ).
tcf(c_1883,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(iPr_def_14,sk_c6) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_463,c_419]) ).
tcf(c_1919,plain,
( ( iPr_def_19 = iPr_def_17 )
| ( iPr_def_19 != sk_c6 )
| ( iPr_def_17 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1734]) ).
tcf(c_1967,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( inverse(iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_705,c_420]) ).
tcf(c_1995,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_15 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_824,c_705]) ).
tcf(c_2089,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_23 )
| ( sk_c7 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_861,c_452]) ).
tcf(c_2090,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_23 )
| ( sk_c7 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_861,c_451]) ).
tcf(c_2191,plain,
( ~ iPr_def_13
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_430]) ).
tcf(c_2193,plain,
( ~ iPr_def_13
| ( sk_c6 != identity )
| ( inverse(iPr_def_16) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_1010,c_430]) ).
tcf(c_2284,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_22 )
| ( inverse(sk_c2) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_426,c_431]) ).
tcf(c_2286,plain,
( ~ iPr_def_12
| ( sk_c6 != identity )
| ( inverse(inverse(sk_c5)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_84,c_431]) ).
tcf(c_2392,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_22 )
| ( inverse(sk_c2) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_426,c_432]) ).
tcf(c_2394,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c5)) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_84,c_432]) ).
tcf(c_2408,plain,
( ~ iPr_def_11
| ( sk_c5 != iPr_def_18 )
| ( sk_c7 != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_2392,c_422]) ).
tcf(c_2536,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c6 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_433]) ).
tcf(c_2757,plain,
! [X0: $i] :
( ( iPr_def_16 = X0 )
| ( iPr_def_16 != sk_c6 )
| ( X0 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_1491]) ).
tcf(c_2793,plain,
! [X0: $i] :
( ( iPr_def_17 = X0 )
| ( iPr_def_17 != iPr_def_17 )
| ( X0 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_1552]) ).
tcf(c_2809,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_17 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1026,c_705]) ).
tcf(c_2811,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1026,c_428]) ).
tcf(c_2975,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_1121,c_1085]) ).
tcf(c_3138,plain,
! [X0: $i] : multiply(sk_c6,multiply(sk_c7,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_3140,plain,
! [X0: $i] : multiply(sk_c4,multiply(sk_c5,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_421,c_85]) ).
tcf(c_3141,plain,
! [X0: $i] : multiply(sk_c1,multiply(sk_c7,X0)) = multiply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_428,c_85]) ).
tcf(c_3142,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c6,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_419,c_85]) ).
tcf(c_3143,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c5,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_426,c_85]) ).
tcf(c_3145,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_3148,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1010,c_85]) ).
tcf(c_3149,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1011,c_85]) ).
tcf(c_3150,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1012,c_85]) ).
tcf(c_3151,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1013,c_85]) ).
tcf(c_3152,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_1014,c_85]) ).
tcf(c_3158,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3152,c_83]) ).
tcf(c_3159,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3151,c_83]) ).
tcf(c_3160,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3150,c_83]) ).
tcf(c_3161,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3149,c_83]) ).
tcf(c_3162,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c7,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_3148,c_83]) ).
tcf(c_3262,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1614,c_418]) ).
tcf(c_3265,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( identity = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3262,c_1010]) ).
tcf(c_3422,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( iPr_def_24 != sk_c6 )
| ( iPr_def_16 != sk_c6 ) ),
inference(instantiation,[status(thm)],[c_2757]) ).
tcf(c_3513,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1793,c_1676]) ).
tcf(c_3591,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1808,c_1690]) ).
tcf(c_4012,plain,
multiply(iPr_def_18,iPr_def_22) = sk_c5,
inference(superposition,[status(thm)],[c_426,c_3158]) ).
tcf(c_4028,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_22,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_4012,c_85]) ).
tcf(c_4033,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c7,
inference(superposition,[status(thm)],[c_428,c_3159]) ).
tcf(c_4067,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_2809,c_1013]) ).
tcf(c_4085,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_22,sk_c1) = identity ) ),
inference(superposition,[status(thm)],[c_2975,c_1013]) ).
tcf(c_4101,plain,
multiply(iPr_def_19,iPr_def_17) = sk_c5,
inference(superposition,[status(thm)],[c_421,c_3160]) ).
tcf(c_4131,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_17,X0)) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_4101,c_85]) ).
tcf(c_4637,plain,
multiply(iPr_def_21,iPr_def_20) = sk_c6,
inference(superposition,[status(thm)],[c_424,c_3161]) ).
tcf(c_4640,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_20,X0)) = multiply(sk_c6,X0),
inference(superposition,[status(thm)],[c_4637,c_85]) ).
tcf(c_4655,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_16,multiply(iPr_def_23,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_452,c_3162]) ).
tcf(c_4656,plain,
! [X0: $i] :
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,multiply(iPr_def_23,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_451,c_3162]) ).
tcf(c_4982,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_19 != iPr_def_17 )
| ( iPr_def_17 != iPr_def_17 ) ),
inference(instantiation,[status(thm)],[c_2793]) ).
tcf(c_9651,plain,
multiply(sk_c4,iPr_def_15) = multiply(iPr_def_17,sk_c6),
inference(superposition,[status(thm)],[c_419,c_3140]) ).
tcf(c_9821,plain,
multiply(iPr_def_19,multiply(iPr_def_17,sk_c6)) = iPr_def_15,
inference(superposition,[status(thm)],[c_9651,c_3160]) ).
tcf(c_9880,plain,
multiply(sk_c5,iPr_def_14) = multiply(iPr_def_15,sk_c7),
inference(superposition,[status(thm)],[c_418,c_3142]) ).
tcf(c_10091,plain,
multiply(sk_c4,multiply(iPr_def_15,sk_c7)) = multiply(iPr_def_17,iPr_def_14),
inference(superposition,[status(thm)],[c_9880,c_3140]) ).
tcf(c_10143,plain,
multiply(sk_c2,multiply(iPr_def_15,sk_c7)) = multiply(iPr_def_22,iPr_def_14),
inference(superposition,[status(thm)],[c_9880,c_3143]) ).
tcf(c_11253,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_3145,c_83]) ).
tcf(c_11275,plain,
multiply(inverse(sk_c6),iPr_def_14) = sk_c7,
inference(superposition,[status(thm)],[c_418,c_11253]) ).
tcf(c_11281,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_11253]) ).
tcf(c_11282,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_11253]) ).
tcf(c_11293,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(inverse(sk_c6),iPr_def_14) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_766,c_11253]) ).
tcf(c_11318,plain,
( ( sk_c6 = iPr_def_16 )
| ( multiply(inverse(iPr_def_14),iPr_def_15) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_1883,c_11253]) ).
tcf(c_11360,plain,
multiply(inverse(iPr_def_16),identity) = sk_c7,
inference(superposition,[status(thm)],[c_1010,c_11253]) ).
tcf(c_11428,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3162,c_11253]) ).
tcf(c_11429,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3161,c_11253]) ).
tcf(c_11430,plain,
! [X0: $i] : multiply(inverse(iPr_def_19),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_3160,c_11253]) ).
tcf(c_11431,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_3159,c_11253]) ).
tcf(c_11432,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_3158,c_11253]) ).
tcf(c_11471,plain,
multiply(inverse(sk_c5),multiply(iPr_def_15,sk_c7)) = iPr_def_14,
inference(superposition,[status(thm)],[c_9880,c_11253]) ).
tcf(c_11473,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11253,c_11253]) ).
tcf(c_12257,plain,
( ~ iPr_def_10
| ( sk_c7 != sk_c6 )
| ( inverse(inverse(identity)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11281,c_433]) ).
tcf(c_12289,plain,
multiply(sk_c7,identity) = sk_c7,
inference(demodulation,[status(thm)],[c_11360,c_11428]) ).
tcf(c_12316,plain,
multiply(sk_c1,sk_c7) = multiply(iPr_def_24,identity),
inference(superposition,[status(thm)],[c_12289,c_3141]) ).
tcf(c_12317,plain,
multiply(sk_c6,sk_c7) = multiply(iPr_def_14,identity),
inference(superposition,[status(thm)],[c_12289,c_3138]) ).
tcf(c_12320,plain,
multiply(iPr_def_14,identity) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_12317,c_418]) ).
tcf(c_12321,plain,
multiply(iPr_def_24,identity) = iPr_def_24,
inference(light_normalisation,[status(thm)],[c_12316,c_428]) ).
tcf(c_12419,plain,
multiply(inverse(iPr_def_24),iPr_def_24) = identity,
inference(superposition,[status(thm)],[c_12321,c_11253]) ).
tcf(c_12740,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11282,c_11473]) ).
tcf(c_12771,plain,
multiply(sk_c6,identity) = multiply(iPr_def_21,iPr_def_20),
inference(superposition,[status(thm)],[c_12740,c_4640]) ).
tcf(c_12774,plain,
multiply(sk_c5,identity) = multiply(iPr_def_19,iPr_def_17),
inference(superposition,[status(thm)],[c_12740,c_4131]) ).
tcf(c_12778,plain,
multiply(sk_c5,identity) = multiply(iPr_def_18,iPr_def_22),
inference(superposition,[status(thm)],[c_12740,c_4028]) ).
tcf(c_12783,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_12740,c_11281]) ).
tcf(c_12784,plain,
multiply(sk_c5,identity) = sk_c5,
inference(light_normalisation,[status(thm)],[c_12778,c_4012]) ).
tcf(c_12828,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( inverse(iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3265,c_12783]) ).
tcf(c_12922,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c6 = iPr_def_19 ) ),
inference(global_subsumption_just,[status(thm)],[c_1677,c_455,c_460,c_958,c_990,c_3422]) ).
tcf(c_13212,plain,
( ( iPr_def_16 = iPr_def_24 )
| ( sk_c6 = iPr_def_17 ) ),
inference(global_subsumption_just,[status(thm)],[c_1678,c_454,c_459,c_958,c_989,c_3422]) ).
tcf(c_13240,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_16 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_13212,c_12922]) ).
tcf(c_13586,plain,
multiply(sk_c7,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_11428,c_84]) ).
tcf(c_13589,plain,
( ~ iPr_def_11
| ( multiply(sk_c7,sk_c5) != sk_c7 )
| ( inverse(inverse(iPr_def_16)) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_11428,c_432]) ).
tcf(c_13593,plain,
multiply(sk_c7,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_11428,c_12740]) ).
tcf(c_13652,plain,
multiply(sk_c1,identity) = multiply(iPr_def_24,iPr_def_16),
inference(superposition,[status(thm)],[c_13586,c_3141]) ).
tcf(c_13653,plain,
multiply(sk_c6,identity) = multiply(iPr_def_14,iPr_def_16),
inference(superposition,[status(thm)],[c_13586,c_3138]) ).
tcf(c_13720,plain,
inverse(iPr_def_16) = sk_c7,
inference(demodulation,[status(thm)],[c_13593,c_12740]) ).
tcf(c_14369,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_2090,c_2089]) ).
tcf(c_14417,plain,
multiply(iPr_def_24,iPr_def_16) = sk_c1,
inference(demodulation,[status(thm)],[c_13652,c_12740]) ).
tcf(c_14420,plain,
multiply(inverse(iPr_def_24),sk_c1) = iPr_def_16,
inference(superposition,[status(thm)],[c_14417,c_11253]) ).
tcf(c_14431,plain,
! [X0: $i] : multiply(inverse(iPr_def_24),multiply(sk_c1,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_14420,c_85]) ).
tcf(c_14439,plain,
multiply(iPr_def_14,iPr_def_16) = sk_c6,
inference(demodulation,[status(thm)],[c_13653,c_12740]) ).
tcf(c_14444,plain,
multiply(inverse(iPr_def_14),sk_c6) = iPr_def_16,
inference(superposition,[status(thm)],[c_14439,c_11253]) ).
tcf(c_14484,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),multiply(sk_c6,X0)) = multiply(iPr_def_16,X0),
inference(superposition,[status(thm)],[c_14444,c_85]) ).
tcf(c_14730,plain,
multiply(inverse(iPr_def_24),iPr_def_24) = multiply(iPr_def_16,sk_c7),
inference(superposition,[status(thm)],[c_428,c_14431]) ).
tcf(c_14940,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_14369,c_2975]) ).
tcf(c_15389,plain,
multiply(inverse(iPr_def_14),iPr_def_14) = multiply(iPr_def_16,sk_c7),
inference(superposition,[status(thm)],[c_418,c_14484]) ).
tcf(c_15772,plain,
( ~ iPr_def_10
| ( multiply(sk_c3,sk_c6) != sk_c7 )
| ( inverse(inverse(iPr_def_21)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11429,c_433]) ).
tcf(c_15773,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_11429,c_11253]) ).
tcf(c_15774,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_11429,c_12740]) ).
tcf(c_15808,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_15774,c_12740]) ).
tcf(c_16196,plain,
multiply(sk_c3,sk_c6) = iPr_def_20,
inference(superposition,[status(thm)],[c_4637,c_15773]) ).
tcf(c_16849,plain,
( ~ iPr_def_12
| ( multiply(sk_c4,sk_c5) != sk_c6 )
| ( inverse(inverse(iPr_def_19)) != sk_c6 ) ),
inference(superposition,[status(thm)],[c_11430,c_431]) ).
tcf(c_16851,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_19,X0)) = X0,
inference(superposition,[status(thm)],[c_11430,c_11253]) ).
tcf(c_16852,plain,
multiply(sk_c4,identity) = inverse(iPr_def_19),
inference(superposition,[status(thm)],[c_11430,c_12740]) ).
tcf(c_16856,plain,
( ~ iPr_def_12
| ( sk_c6 != iPr_def_17 )
| ( inverse(inverse(iPr_def_19)) != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_16849,c_421]) ).
tcf(c_16897,plain,
( ( sk_c7 = iPr_def_21 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_4033,c_4655]) ).
tcf(c_16912,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_16897,c_1010]) ).
tcf(c_16958,plain,
( ( sk_c7 = iPr_def_20 )
| ( multiply(iPr_def_16,sk_c7) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_4033,c_4656]) ).
tcf(c_16973,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_16958,c_1010]) ).
tcf(c_17418,plain,
inverse(iPr_def_19) = sk_c4,
inference(demodulation,[status(thm)],[c_16852,c_12740]) ).
tcf(c_17427,plain,
multiply(sk_c4,identity) = sk_c4,
inference(superposition,[status(thm)],[c_1012,c_16851]) ).
tcf(c_17433,plain,
multiply(sk_c4,sk_c5) = iPr_def_17,
inference(superposition,[status(thm)],[c_4101,c_16851]) ).
tcf(c_18100,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_16973,c_16912]) ).
tcf(c_18469,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_18100,c_3591]) ).
tcf(c_18497,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_14,iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_18469,c_14417]) ).
tcf(c_18531,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c6 = sk_c1 ) ),
inference(light_normalisation,[status(thm)],[c_18497,c_14439]) ).
tcf(c_19586,plain,
( ~ iPr_def_13
| ( multiply(sk_c1,sk_c7) != sk_c6 )
| ( inverse(inverse(iPr_def_23)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11431,c_430]) ).
tcf(c_19587,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_11431,c_84]) ).
tcf(c_19592,plain,
( ~ iPr_def_10
| ( multiply(sk_c1,sk_c6) != sk_c7 )
| ( inverse(inverse(iPr_def_23)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_11431,c_433]) ).
tcf(c_19593,plain,
! [X0: $i] : multiply(sk_c1,multiply(iPr_def_23,X0)) = X0,
inference(superposition,[status(thm)],[c_11431,c_11253]) ).
tcf(c_19594,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_11431,c_12740]) ).
tcf(c_19614,plain,
( ~ iPr_def_13
| ( sk_c6 != iPr_def_24 )
| ( inverse(inverse(iPr_def_23)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_19586,c_428]) ).
tcf(c_19618,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( identity = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_2811,c_19587]) ).
tcf(c_19753,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_19618,c_3265]) ).
tcf(c_20135,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_19594,c_12740]) ).
tcf(c_20160,plain,
multiply(sk_c1,sk_c7) = iPr_def_24,
inference(superposition,[status(thm)],[c_4033,c_19593]) ).
tcf(c_20260,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_16) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_19753,c_14417]) ).
tcf(c_20296,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = sk_c1 ) ),
inference(light_normalisation,[status(thm)],[c_20260,c_14439]) ).
tcf(c_22159,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( inverse(sk_c6) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_20296,c_427]) ).
tcf(c_22353,plain,
multiply(sk_c2,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_11432,c_84]) ).
tcf(c_22356,plain,
( ~ iPr_def_11
| ( multiply(sk_c2,sk_c5) != sk_c7 )
| ( inverse(inverse(iPr_def_18)) != sk_c5 ) ),
inference(superposition,[status(thm)],[c_11432,c_432]) ).
tcf(c_22359,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_18,X0)) = X0,
inference(superposition,[status(thm)],[c_11432,c_11253]) ).
tcf(c_22360,plain,
multiply(sk_c2,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_11432,c_12740]) ).
tcf(c_22368,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_22 )
| ( inverse(inverse(iPr_def_18)) != sk_c5 ) ),
inference(light_normalisation,[status(thm)],[c_22356,c_426]) ).
tcf(c_22375,plain,
( ( identity = iPr_def_22 )
| ( sk_c6 = iPr_def_17 ) ),
inference(demodulation,[status(thm)],[c_967,c_22353]) ).
tcf(c_22376,plain,
( ( identity = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_966,c_22353]) ).
tcf(c_22377,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_965,c_22353]) ).
tcf(c_22378,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_964,c_22353]) ).
tcf(c_22528,plain,
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2191,c_12783]) ).
tcf(c_22555,plain,
( ( iPr_def_17 = iPr_def_19 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_16 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_1614,c_22528]) ).
tcf(c_22634,plain,
( ~ iPr_def_13
| ( sk_c6 != identity ) ),
inference(ground_joinability,[status(thm)],[c_2193,c_13720]) ).
tcf(c_23170,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22376,c_22375]) ).
tcf(c_23783,plain,
inverse(iPr_def_18) = sk_c2,
inference(demodulation,[status(thm)],[c_22360,c_12740]) ).
tcf(c_23792,plain,
multiply(sk_c2,identity) = sk_c2,
inference(superposition,[status(thm)],[c_1014,c_22359]) ).
tcf(c_23799,plain,
multiply(sk_c2,sk_c5) = iPr_def_22,
inference(superposition,[status(thm)],[c_4012,c_22359]) ).
tcf(c_23975,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_22378,c_22377]) ).
tcf(c_24546,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c7 = iPr_def_21 )
| ( inverse(iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_457,c_22159]) ).
tcf(c_24548,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = iPr_def_19 )
| ( inverse(iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_455,c_22159]) ).
tcf(c_24549,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = iPr_def_17 )
| ( inverse(iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_454,c_22159]) ).
tcf(c_24610,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_17 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_23170,c_19618]) ).
tcf(c_24616,plain,
! [X0: $i] :
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_23170,c_83]) ).
tcf(c_27487,plain,
( ( iPr_def_22 = iPr_def_24 )
| ( iPr_def_20 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_23975,c_18100]) ).
tcf(c_27492,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_21 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_23975,c_83]) ).
tcf(c_27609,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_16 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_24610,c_13240]) ).
tcf(c_28508,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_16 = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_27487,c_3513]) ).
tcf(c_28868,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( inverse(iPr_def_16) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_27609,c_1967]) ).
tcf(c_28874,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( iPr_def_15 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_27609,c_1995]) ).
tcf(c_28877,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c7 = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_28868,c_13720]) ).
tcf(c_29049,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( sk_c7 != sk_c6 ) ),
inference(light_normalisation,[status(thm)],[c_2536,c_12783]) ).
tcf(c_29078,plain,
( ( iPr_def_17 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_16 )
| ( sk_c7 != identity ) ),
inference(superposition,[status(thm)],[c_1614,c_29049]) ).
tcf(c_29612,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( iPr_def_15 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_28508,c_14940]) ).
tcf(c_30425,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( inverse(iPr_def_24) = iPr_def_23 ) ),
inference(global_subsumption_just,[status(thm)],[c_24546,c_1245,c_1246,c_1253,c_1254,c_1919,c_4982,c_24549,c_24548]) ).
tcf(c_30438,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_23,iPr_def_24) = identity ) ),
inference(superposition,[status(thm)],[c_30425,c_84]) ).
tcf(c_30448,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c7 = identity ) ),
inference(light_normalisation,[status(thm)],[c_30438,c_4033]) ).
tcf(c_30753,plain,
( ( iPr_def_17 = iPr_def_19 )
| ~ iPr_def_11
| ( identity != iPr_def_22 )
| ( sk_c5 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_30448,c_2408]) ).
tcf(c_30801,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(sk_c6,identity) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_30448,c_418]) ).
tcf(c_31319,plain,
( ( iPr_def_15 = iPr_def_16 )
| ( multiply(iPr_def_20,iPr_def_20) = sk_c6 ) ),
inference(superposition,[status(thm)],[c_29612,c_4637]) ).
tcf(c_31754,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_24616,c_4067]) ).
tcf(c_31834,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c1 = identity ) ),
inference(superposition,[status(thm)],[c_27492,c_4085]) ).
tcf(c_32563,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_30801,c_12740]) ).
tcf(c_32694,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_32563,c_418]) ).
tcf(c_33421,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( sk_c6 = identity ) ),
inference(superposition,[status(thm)],[c_31754,c_20296]) ).
tcf(c_33998,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_28877,c_32694]) ).
tcf(c_34204,plain,
( ( iPr_def_20 = iPr_def_21 )
| ( sk_c6 = identity ) ),
inference(superposition,[status(thm)],[c_31834,c_18531]) ).
tcf(c_34886,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_34204,c_33998,c_33421,c_31319,c_30753,c_30448,c_29612,c_29078,c_28874,c_23799,c_23792,c_23783,c_22634,c_22555,c_22528,c_22368,c_22353,c_20160,c_20135,c_19614,c_19592,c_19587,c_17433,c_17427,c_17418,c_16856,c_16849,c_16196,c_15808,c_15772,c_15389,c_14730,c_14444,c_14439,c_13720,c_13653,c_13589,c_12828,c_12784,c_12774,c_12771,c_12783,c_12419,c_12320,c_12317,c_12257,c_11471,c_11318,c_11293,c_11275,c_10143,c_10091,c_9821,c_2394,c_2286,c_2284,c_1802,c_1614,c_460,c_458,c_455,c_453,c_450,c_448,c_447,c_446,c_445,c_444,c_443,c_440,c_438,c_437,c_436,c_435,c_434,c_429,c_427,c_425,c_423,c_422,c_420]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP376-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.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 14:39:54 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 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...
% 8.08/1.75 % SZS status Started for theBenchmark.p
% 8.08/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 8.08/1.75
% 8.08/1.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.08/1.75
% 8.08/1.75 % ------ iProver source info
% 8.08/1.75
% 8.08/1.75 % git: date: 2026-07-19 20:42:38 +0200
% 8.08/1.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.08/1.75 % git: non_committed_changes: false
% 8.08/1.75
% 8.08/1.75 % ------ Parsing...% successful
% 8.08/1.75
% 8.08/1.75
% 8.08/1.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.08/1.75
% 8.08/1.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.08/1.75
% 8.08/1.75 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.08/1.75
% 8.08/1.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.08/1.75 % ------ Proving...
% 8.08/1.75 % ------ Problem Properties
% 8.08/1.75
% 8.08/1.75 %
% 8.08/1.75 % clauses 49
% 8.08/1.75 % conjectures 35
% 8.08/1.75 % EPR 31
% 8.08/1.75 % Horn 18
% 8.08/1.75 % unary 14
% 8.08/1.75 % binary 30
% 8.08/1.75 % lits 93
% 8.08/1.75 % lits eq 85
% 8.08/1.75 % fd_pure 0
% 8.08/1.75 % fd_pseudo 0
% 8.08/1.75 % fd_cond 0
% 8.08/1.75 % fd_pseudo_cond 0
% 8.08/1.75 % AC symbols 0
% 8.08/1.75
% 8.08/1.75 % ------ Schedule dynamic 5 is on
% 8.08/1.75
% 8.08/1.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 8.08/1.75
% 8.08/1.75
% 8.08/1.75 % ------
% 8.08/1.75 % Current options:
% 8.08/1.75 % ------
% 8.08/1.75
% 8.08/1.75
% 8.08/1.75 %
% 8.08/1.75
% 8.08/1.75 % ------ Proving...
% 8.08/1.75 %
% 8.08/1.75
% 8.08/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 8.08/1.75
% 8.08/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.08/1.76
% 8.08/1.76
%------------------------------------------------------------------------------