%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP232-1 : 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 : n005.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 01:32:04 PM UTC 2026
% Result : Unsatisfiable 15.79s 3.28s
% Output : CNFRefutation 15.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 43
% Syntax : Number of formulae : 363 ( 99 unt; 11 def)
% Number of atoms : 1270 ( 673 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 551 ( 183 ~; 368 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 92 !; 0 ?; 65 :)
% 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,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = inverse(sk_c4)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c8 = inverse(sk_c5)
| inverse(sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c8 = inverse(sk_c4)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f17]) ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = inverse(sk_c5)
| sk_c7 = multiply(sk_c1,sk_c8) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
fof(f28,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f27]) ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f37]) ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
fof(f40,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f39]) ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c2,sk_c3) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c8 = inverse(sk_c4)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c8 = inverse(sk_c5)
| sk_c3 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_30) ).
fof(f64,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f63]) ).
fof(f65,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_31) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(X2,sk_c7)
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| inverse(sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f65]) ).
fof(f67,plain,
! [X3,X0,X1,X4,X5] :
( sk_c8 != inverse(X5)
| multiply(X5,sk_c8) != X4
| sk_c7 != multiply(sk_c8,X4)
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != multiply(X1,inverse(X1))
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| inverse(sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f66]) ).
fof(f68,plain,
! [X3,X0,X1,X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| sk_c8 != multiply(inverse(X1),sk_c7)
| sk_c8 != multiply(X1,inverse(X1))
| inverse(X0) != sk_c8
| sk_c7 != multiply(X0,sk_c8)
| inverse(sk_c8) != sk_c7 ),
inference(equality_resolution,[],[f67]) ).
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_c4) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_88,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_89,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_92,negated_conjecture,
( ( multiply(sk_c1,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_101,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c2,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_104,negated_conjecture,
( ( multiply(sk_c2,sk_c3) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c2,sk_c3) = sk_c8 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c3 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_113,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_114,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_115,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_116,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c8) != sk_c7 )
| ( inverse(X3) != sk_c8 )
| ( inverse(X2) != sk_c8 )
| ( inverse(X0) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 )
| ( multiply(inverse(X1),sk_c7) != sk_c8 )
| ( multiply(X1,inverse(X1)) != sk_c8 )
| ( multiply(sk_c8,multiply(X3,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_405,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_406,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_116]) ).
tcf(c_407,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_408,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_116]) ).
tcf(c_409,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_116]) ).
tcf(c_410,definition,
iPr_def_14 = inverse(sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_411,definition,
iPr_def_15 = multiply(sk_c3,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_412,definition,
iPr_def_16 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_413,definition,
iPr_def_17 = multiply(sk_c5,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_414,definition,
iPr_def_18 = multiply(sk_c8,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_415,definition,
iPr_def_19 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_416,definition,
iPr_def_20 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_417,definition,
iPr_def_21 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_418,definition,
iPr_def_22 = multiply(sk_c2,sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_419,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_420,definition,
iPr_def_24 = multiply(sk_c1,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_421,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_409,c_410]) ).
tcf(c_422,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_408]) ).
tcf(c_423,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_407]) ).
tcf(c_424,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_406]) ).
tcf(c_425,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_405]) ).
tcf(c_426,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_115,c_412,c_411]) ).
tcf(c_427,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_114,c_413]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_113,c_414]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_112,c_415]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_111,c_416]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110,c_417]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_109]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_108]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_21 = sk_c3 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105,c_418]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_17 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_104]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_439,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_440,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_101]) ).
tcf(c_441,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100,c_419]) ).
tcf(c_444,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_445,negated_conjecture,
( ( iPr_def_23 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_96]) ).
tcf(c_446,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_16 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_95,c_420]) ).
tcf(c_449,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_450,negated_conjecture,
( ( iPr_def_24 = sk_c7 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_451,negated_conjecture,
( ( iPr_def_16 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_452,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_453,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_454,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_455,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_456,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_457,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_709,plain,
( ( sk_c8 = iPr_def_15 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_430,c_410]) ).
tcf(c_738,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,sk_c6) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_426,c_414]) ).
tcf(c_755,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_21,sk_c7) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_434,c_411]) ).
tcf(c_815,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_439,c_413]) ).
tcf(c_875,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_441,c_436]) ).
tcf(c_905,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_14 != X0 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_457]) ).
tcf(c_913,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_438,c_415]) ).
tcf(c_914,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_428,c_415]) ).
tcf(c_924,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_457]) ).
tcf(c_928,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_435,c_418]) ).
tcf(c_929,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_434,c_418]) ).
tcf(c_930,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_433,c_418]) ).
tcf(c_931,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_431,c_418]) ).
tcf(c_942,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_439,c_420]) ).
tcf(c_967,plain,
multiply(iPr_def_14,sk_c8) = identity,
inference(superposition,[status(thm)],[c_410,c_84]) ).
tcf(c_968,plain,
multiply(iPr_def_20,sk_c4) = identity,
inference(superposition,[status(thm)],[c_416,c_84]) ).
tcf(c_969,plain,
multiply(iPr_def_16,sk_c5) = identity,
inference(superposition,[status(thm)],[c_412,c_84]) ).
tcf(c_970,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_419,c_84]) ).
tcf(c_971,plain,
multiply(iPr_def_21,sk_c2) = identity,
inference(superposition,[status(thm)],[c_417,c_84]) ).
tcf(c_975,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( X0 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_924]) ).
tcf(c_1054,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_23) = identity ) ),
inference(superposition,[status(thm)],[c_444,c_967]) ).
tcf(c_1057,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_444,c_439]) ).
tcf(c_1061,plain,
( ( sk_c8 = iPr_def_19 )
| ( inverse(iPr_def_23) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_444,c_410]) ).
tcf(c_1113,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_445,c_440]) ).
tcf(c_1149,plain,
iPr_def_14 = iPr_def_14,
inference(instantiation,[status(thm)],[c_456]) ).
tcf(c_1231,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_24) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_449,c_415]) ).
tcf(c_1306,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_451,c_446]) ).
tcf(c_1308,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_451,c_415]) ).
tcf(c_1355,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c8,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_452,c_414]) ).
tcf(c_1372,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_453,c_415]) ).
tcf(c_1427,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_454,c_449]) ).
tcf(c_1431,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c4,iPr_def_14) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_454,c_415]) ).
tcf(c_1487,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_455,c_450]) ).
tcf(c_1874,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_453,c_421]) ).
tcf(c_1958,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_415,c_423]) ).
tcf(c_1960,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_83,c_423]) ).
tcf(c_1979,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_20 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1958,c_416]) ).
tcf(c_2078,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_420,c_425]) ).
tcf(c_2079,plain,
( ~ iPr_def_10
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_83,c_425]) ).
tcf(c_2081,plain,
( ~ iPr_def_10
| ( sk_c7 != identity )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_967,c_425]) ).
tcf(c_2100,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_24 )
| ( sk_c8 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_2078,c_419]) ).
tcf(c_2249,plain,
( ~ iPr_def_13
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_413,c_422]) ).
tcf(c_2276,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_16 )
| ( multiply(sk_c8,iPr_def_17) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2249,c_412]) ).
tcf(c_2382,plain,
( ~ iPr_def_11
| ( inverse(identity) != sk_c8 )
| ( multiply(inverse(identity),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_83,c_424]) ).
tcf(c_2692,plain,
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_14 != iPr_def_14 )
| ( sk_c7 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_905]) ).
tcf(c_2694,plain,
! [X0: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != iPr_def_14 )
| ( X0 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_924]) ).
tcf(c_2697,plain,
( ( sk_c8 = sk_c7 )
| ( sk_c7 != iPr_def_14 )
| ( sk_c8 != iPr_def_14 ) ),
inference(instantiation,[status(thm)],[c_2694]) ).
tcf(c_2715,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_19 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1113,c_1057]) ).
tcf(c_2716,plain,
( ( iPr_def_22 = iPr_def_23 )
| ( iPr_def_16 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1113,c_875]) ).
tcf(c_2820,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c8,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_413,c_85]) ).
tcf(c_2822,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c3,X0)) = multiply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_418,c_85]) ).
tcf(c_2825,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_2827,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_967,c_85]) ).
tcf(c_2828,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_968,c_85]) ).
tcf(c_2829,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_969,c_85]) ).
tcf(c_2830,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_970,c_85]) ).
tcf(c_2831,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_971,c_85]) ).
tcf(c_2837,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2831,c_83]) ).
tcf(c_2838,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2830,c_83]) ).
tcf(c_2839,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2829,c_83]) ).
tcf(c_2840,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2828,c_83]) ).
tcf(c_2841,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c8,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_2827,c_83]) ).
tcf(c_3189,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1487,c_1427]) ).
tcf(c_3190,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( iPr_def_14 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1487,c_1306]) ).
tcf(c_3208,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1487,c_410]) ).
tcf(c_3514,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c3,
inference(superposition,[status(thm)],[c_418,c_2837]) ).
tcf(c_3517,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(iPr_def_22,X0)) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_3514,c_85]) ).
tcf(c_3529,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c8,
inference(superposition,[status(thm)],[c_420,c_2838]) ).
tcf(c_3559,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_24) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_2715,c_3529]) ).
tcf(c_3576,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(iPr_def_22,iPr_def_24) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_2716,c_3529]) ).
tcf(c_3594,plain,
multiply(iPr_def_16,iPr_def_17) = sk_c8,
inference(superposition,[status(thm)],[c_413,c_2839]) ).
tcf(c_3611,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(iPr_def_17,X0)) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_3594,c_85]) ).
tcf(c_3772,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_16,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_427,c_738]) ).
tcf(c_3774,plain,
( ( sk_c8 = iPr_def_18 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3772,c_3594]) ).
tcf(c_3858,plain,
multiply(iPr_def_20,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_415,c_2840]) ).
tcf(c_3861,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(iPr_def_19,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_3858,c_85]) ).
tcf(c_3863,plain,
multiply(iPr_def_14,iPr_def_18) = sk_c6,
inference(superposition,[status(thm)],[c_414,c_2841]) ).
tcf(c_3874,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_14,multiply(iPr_def_23,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_445,c_2841]) ).
tcf(c_4105,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_21,iPr_def_14) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_454,c_755]) ).
tcf(c_4109,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_21,iPr_def_24) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_449,c_755]) ).
tcf(c_4501,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_14,iPr_def_18) = identity ) ),
inference(superposition,[status(thm)],[c_3774,c_967]) ).
tcf(c_4527,plain,
( ( sk_c6 = identity )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_4501,c_3863]) ).
tcf(c_7242,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1231,c_2840]) ).
tcf(c_7243,plain,
( ( sk_c7 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_7242,c_3858]) ).
tcf(c_7550,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1372,c_2840]) ).
tcf(c_7551,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_7550,c_3858]) ).
tcf(c_7578,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1431,c_2840]) ).
tcf(c_7579,plain,
( ( sk_c7 = iPr_def_14 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_7578,c_3858]) ).
tcf(c_8522,plain,
multiply(sk_c5,iPr_def_18) = multiply(iPr_def_17,sk_c6),
inference(superposition,[status(thm)],[c_414,c_2820]) ).
tcf(c_8743,plain,
multiply(sk_c2,iPr_def_15) = multiply(iPr_def_22,sk_c7),
inference(superposition,[status(thm)],[c_411,c_2822]) ).
tcf(c_12867,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_2825,c_83]) ).
tcf(c_12896,plain,
multiply(inverse(sk_c4),iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_415,c_12867]) ).
tcf(c_12901,plain,
multiply(inverse(sk_c3),iPr_def_15) = sk_c7,
inference(superposition,[status(thm)],[c_411,c_12867]) ).
tcf(c_12902,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_12867]) ).
tcf(c_12903,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_84,c_12867]) ).
tcf(c_13002,plain,
( ( sk_c8 = iPr_def_16 )
| ( multiply(inverse(sk_c4),iPr_def_19) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_1308,c_12867]) ).
tcf(c_13043,plain,
! [X0: $i] : multiply(inverse(iPr_def_14),X0) = multiply(sk_c8,X0),
inference(superposition,[status(thm)],[c_2841,c_12867]) ).
tcf(c_13044,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_2840,c_12867]) ).
tcf(c_13045,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_2839,c_12867]) ).
tcf(c_13046,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_2838,c_12867]) ).
tcf(c_13047,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_2837,c_12867]) ).
tcf(c_13084,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_12867,c_12867]) ).
tcf(c_13711,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_12903,c_13084]) ).
tcf(c_13722,plain,
multiply(sk_c7,identity) = multiply(iPr_def_20,iPr_def_19),
inference(superposition,[status(thm)],[c_13711,c_3861]) ).
tcf(c_13729,plain,
multiply(sk_c8,identity) = multiply(iPr_def_16,iPr_def_17),
inference(superposition,[status(thm)],[c_13711,c_3611]) ).
tcf(c_13734,plain,
multiply(sk_c3,identity) = multiply(iPr_def_21,iPr_def_22),
inference(superposition,[status(thm)],[c_13711,c_3517]) ).
tcf(c_13735,plain,
multiply(sk_c2,sk_c3) = multiply(iPr_def_22,identity),
inference(superposition,[status(thm)],[c_13711,c_2822]) ).
tcf(c_13740,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_13711,c_12902]) ).
tcf(c_13741,plain,
multiply(iPr_def_22,identity) = iPr_def_22,
inference(light_normalisation,[status(thm)],[c_13735,c_418]) ).
tcf(c_13742,plain,
multiply(sk_c3,identity) = sk_c3,
inference(light_normalisation,[status(thm)],[c_13734,c_3514]) ).
tcf(c_13751,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_13722,c_3858]) ).
tcf(c_13777,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(iPr_def_14,sk_c8) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_3529,c_3874]) ).
tcf(c_13788,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_13777,c_967]) ).
tcf(c_14383,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_444,c_2100]) ).
tcf(c_14588,plain,
( ( sk_c8 = iPr_def_19 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_14383,c_7243,c_14383]) ).
tcf(c_15337,plain,
! [X0: $i] :
( ( multiply(X0,iPr_def_17) = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( multiply(X0,iPr_def_17) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_975]) ).
tcf(c_15340,plain,
( ( multiply(sk_c8,iPr_def_17) = sk_c7 )
| ( sk_c7 != iPr_def_18 )
| ( multiply(sk_c8,iPr_def_17) != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_15337]) ).
tcf(c_16297,plain,
( ( identity = iPr_def_24 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_13788,c_410]) ).
tcf(c_18466,plain,
multiply(sk_c8,iPr_def_14) = identity,
inference(superposition,[status(thm)],[c_13043,c_84]) ).
tcf(c_18469,plain,
! [X0: $i] : multiply(sk_c8,multiply(iPr_def_14,X0)) = X0,
inference(superposition,[status(thm)],[c_13043,c_12867]) ).
tcf(c_18470,plain,
multiply(sk_c8,identity) = inverse(iPr_def_14),
inference(superposition,[status(thm)],[c_13043,c_13711]) ).
tcf(c_20108,plain,
multiply(sk_c5,identity) = multiply(iPr_def_17,iPr_def_14),
inference(superposition,[status(thm)],[c_18466,c_2820]) ).
tcf(c_20361,plain,
inverse(iPr_def_14) = sk_c8,
inference(demodulation,[status(thm)],[c_18470,c_13711]) ).
tcf(c_20416,plain,
! [X0: $i] :
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,multiply(iPr_def_14,X0)) = X0 ) ),
inference(superposition,[status(thm)],[c_439,c_18469]) ).
tcf(c_20443,plain,
multiply(sk_c8,sk_c6) = iPr_def_18,
inference(superposition,[status(thm)],[c_3863,c_18469]) ).
tcf(c_20457,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c7 )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_18469,c_422]) ).
tcf(c_20555,plain,
( ~ iPr_def_13
| ( sk_c8 != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_20457,c_20361]) ).
tcf(c_20880,plain,
( ( sk_c8 = iPr_def_20 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_455,c_20555]) ).
tcf(c_20883,plain,
( ( sk_c8 = iPr_def_16 )
| ~ iPr_def_13
| ( sk_c8 != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_451,c_20555]) ).
tcf(c_21468,plain,
multiply(iPr_def_17,iPr_def_14) = sk_c5,
inference(demodulation,[status(thm)],[c_20108,c_13711]) ).
tcf(c_21470,plain,
multiply(inverse(iPr_def_17),sk_c5) = iPr_def_14,
inference(superposition,[status(thm)],[c_21468,c_12867]) ).
tcf(c_21493,plain,
! [X0: $i] : multiply(inverse(iPr_def_17),multiply(sk_c5,X0)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_21470,c_85]) ).
tcf(c_21505,plain,
( ( sk_c8 != iPr_def_14 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_20880,c_1355,c_2276,c_2697,c_7551,c_15340,c_20555,c_20883]) ).
tcf(c_21506,plain,
( ~ iPr_def_13
| ( sk_c8 != iPr_def_14 ) ),
inference(renaming,[status(thm)],[c_21505]) ).
tcf(c_23006,plain,
multiply(inverse(iPr_def_17),iPr_def_17) = multiply(iPr_def_14,sk_c8),
inference(superposition,[status(thm)],[c_413,c_21493]) ).
tcf(c_23020,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(iPr_def_17),iPr_def_17) = multiply(iPr_def_14,iPr_def_22) ) ),
inference(superposition,[status(thm)],[c_815,c_21493]) ).
tcf(c_23033,plain,
multiply(inverse(iPr_def_17),multiply(iPr_def_17,sk_c6)) = multiply(iPr_def_14,iPr_def_18),
inference(superposition,[status(thm)],[c_8522,c_21493]) ).
tcf(c_23039,plain,
multiply(inverse(iPr_def_17),iPr_def_17) = identity,
inference(light_normalisation,[status(thm)],[c_23006,c_967]) ).
tcf(c_23040,plain,
multiply(inverse(iPr_def_17),multiply(iPr_def_17,sk_c6)) = sk_c6,
inference(light_normalisation,[status(thm)],[c_23033,c_3863]) ).
tcf(c_24597,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_20)) != sk_c8 )
| ( multiply(sk_c8,multiply(sk_c4,sk_c8)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_13044,c_422]) ).
tcf(c_24598,plain,
( ~ iPr_def_10
| ( multiply(sk_c4,sk_c8) != sk_c7 )
| ( inverse(inverse(iPr_def_20)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_13044,c_425]) ).
tcf(c_24601,plain,
multiply(sk_c4,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_13044,c_84]) ).
tcf(c_24603,plain,
( ~ iPr_def_12
| ( multiply(sk_c4,sk_c7) != sk_c8 )
| ( inverse(inverse(iPr_def_20)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_13044,c_423]) ).
tcf(c_24604,plain,
! [X0: $i] : multiply(sk_c4,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_13044,c_12867]) ).
tcf(c_24605,plain,
multiply(sk_c4,identity) = inverse(iPr_def_20),
inference(superposition,[status(thm)],[c_13044,c_13711]) ).
tcf(c_24661,plain,
inverse(iPr_def_20) = sk_c4,
inference(demodulation,[status(thm)],[c_24605,c_13711]) ).
tcf(c_24663,plain,
( ( identity = iPr_def_24 )
| ( sk_c4 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_16297,c_24661]) ).
tcf(c_24664,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( sk_c4 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_3208,c_24661]) ).
tcf(c_24666,plain,
( ( sk_c4 = iPr_def_14 )
| ( sk_c8 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_709,c_24661]) ).
tcf(c_24676,plain,
( ~ iPr_def_11
| ( multiply(iPr_def_20,sk_c4) != sk_c8 )
| ( multiply(inverse(iPr_def_20),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_24661,c_424]) ).
tcf(c_24678,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_19 )
| ( sk_c8 != identity ) ),
inference(light_normalisation,[status(thm)],[c_24676,c_415,c_968,c_24661]) ).
tcf(c_28275,plain,
multiply(sk_c4,sk_c7) = iPr_def_19,
inference(superposition,[status(thm)],[c_3858,c_24604]) ).
tcf(c_28389,plain,
( ( identity = iPr_def_24 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_24663,c_415]) ).
tcf(c_28437,plain,
( ( iPr_def_14 = iPr_def_24 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_24664,c_415]) ).
tcf(c_29243,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(iPr_def_14,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_24666,c_914]) ).
tcf(c_29250,plain,
( ( sk_c6 = iPr_def_19 )
| ( sk_c8 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_29243,c_3863]) ).
tcf(c_29313,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_29250,c_4527]) ).
tcf(c_29491,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_29313,c_440]) ).
tcf(c_31359,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_19 )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_28389,c_423]) ).
tcf(c_31364,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_19 ) ),
inference(ground_joinability,[status(thm)],[c_31359,c_20361]) ).
tcf(c_31565,plain,
( ( iPr_def_14 = iPr_def_24 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_19 )
| ( inverse(iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_28437,c_423]) ).
tcf(c_31570,plain,
( ( iPr_def_14 = iPr_def_24 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_19 ) ),
inference(ground_joinability,[status(thm)],[c_31565,c_20361]) ).
tcf(c_31585,plain,
multiply(sk_c5,iPr_def_16) = identity,
inference(superposition,[status(thm)],[c_13045,c_84]) ).
tcf(c_31588,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_13045,c_12867]) ).
tcf(c_31589,plain,
multiply(sk_c5,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_13045,c_13711]) ).
tcf(c_31630,plain,
inverse(iPr_def_16) = sk_c5,
inference(demodulation,[status(thm)],[c_31589,c_13711]) ).
tcf(c_31656,plain,
multiply(sk_c5,sk_c8) = iPr_def_17,
inference(superposition,[status(thm)],[c_3594,c_31588]) ).
tcf(c_32881,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,identity) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1054,c_20416]) ).
tcf(c_33907,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_13046,c_13711]) ).
tcf(c_34271,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_33907,c_13711]) ).
tcf(c_34277,plain,
( ( sk_c1 = iPr_def_14 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_1061,c_34271]) ).
tcf(c_36120,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_14,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_34277,c_942]) ).
tcf(c_36125,plain,
( ( sk_c8 = iPr_def_19 )
| ( inverse(iPr_def_14) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_34277,c_419]) ).
tcf(c_36347,plain,
( ( iPr_def_15 = iPr_def_22 )
| ( identity = iPr_def_19 )
| ( multiply(iPr_def_20,iPr_def_14) = identity ) ),
inference(superposition,[status(thm)],[c_29491,c_18466]) ).
tcf(c_39989,plain,
multiply(sk_c2,iPr_def_21) = identity,
inference(superposition,[status(thm)],[c_13047,c_84]) ).
tcf(c_39992,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_21,X0)) = X0,
inference(superposition,[status(thm)],[c_13047,c_12867]) ).
tcf(c_39993,plain,
multiply(sk_c2,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_13047,c_13711]) ).
tcf(c_40006,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_931,c_39989]) ).
tcf(c_40007,plain,
( ( identity = iPr_def_22 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_930,c_39989]) ).
tcf(c_40008,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_929,c_39989]) ).
tcf(c_40009,plain,
( ( identity = iPr_def_22 )
| ( sk_c8 = iPr_def_20 ) ),
inference(demodulation,[status(thm)],[c_928,c_39989]) ).
tcf(c_40373,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10
| ( iPr_def_14 != iPr_def_18 ) ),
inference(global_subsumption_just,[status(thm)],[c_1874,c_421,c_1149,c_1874,c_2692]) ).
tcf(c_40414,plain,
multiply(iPr_def_21,identity) = iPr_def_21,
inference(superposition,[status(thm)],[c_39989,c_2837]) ).
tcf(c_40561,plain,
( ( identity = iPr_def_22 )
| ( inverse(iPr_def_16) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_40006,c_410]) ).
tcf(c_40564,plain,
( ( identity = iPr_def_22 )
| ( sk_c5 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_40561,c_31630]) ).
tcf(c_40778,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_40007,c_415]) ).
tcf(c_41007,plain,
( ( identity = iPr_def_22 )
| ~ iPr_def_12
| ( sk_c8 != iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_40008,c_1979]) ).
tcf(c_41290,plain,
inverse(iPr_def_21) = sk_c2,
inference(demodulation,[status(thm)],[c_39993,c_13711]) ).
tcf(c_41300,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_15) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_755,c_39992]) ).
tcf(c_41305,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_15) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4105,c_39992]) ).
tcf(c_41308,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_15) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_4109,c_39992]) ).
tcf(c_41324,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_41308,c_8743]) ).
tcf(c_41333,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c7) = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_41305,c_8743]) ).
tcf(c_41345,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_22,sk_c7) = sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_41300,c_8743]) ).
tcf(c_41443,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_40009,c_40008]) ).
tcf(c_41444,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( identity = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_40009,c_40006]) ).
tcf(c_41526,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c5,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_40009,c_413]) ).
tcf(c_41527,plain,
( ( identity = iPr_def_22 )
| ( inverse(iPr_def_20) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_40009,c_410]) ).
tcf(c_41534,plain,
( ( identity = iPr_def_22 )
| ( sk_c4 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_41527,c_24661]) ).
tcf(c_41723,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1960,c_13740]) ).
tcf(c_41840,plain,
( ~ iPr_def_10
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2079,c_13740]) ).
tcf(c_41893,plain,
( ~ iPr_def_10
| ( sk_c7 != identity ) ),
inference(ground_joinability,[status(thm)],[c_2081,c_20361]) ).
tcf(c_42349,plain,
! [X0: $i] :
( ( iPr_def_19 = iPr_def_20 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_41443,c_83]) ).
tcf(c_42386,plain,
! [X0: $i] :
( ( iPr_def_16 = iPr_def_20 )
| ( multiply(iPr_def_22,X0) = X0 ) ),
inference(superposition,[status(thm)],[c_41444,c_83]) ).
tcf(c_42934,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_14,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_41534,c_40778]) ).
tcf(c_42952,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_14,sk_c7) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_41534,c_415]) ).
tcf(c_42957,plain,
( ( identity = iPr_def_22 )
| ( sk_c6 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_42934,c_3863]) ).
tcf(c_44594,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( identity = iPr_def_22 )
| ( sk_c3 = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_42957,c_432]) ).
tcf(c_46378,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( identity = iPr_def_22 )
| ( multiply(sk_c2,iPr_def_21) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_44594,c_418]) ).
tcf(c_46383,plain,
( ( iPr_def_17 = iPr_def_19 )
| ( identity = iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_46378,c_39989]) ).
tcf(c_46564,plain,
( ( identity = iPr_def_22 )
| ( multiply(iPr_def_14,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_40564,c_41526]) ).
tcf(c_46571,plain,
( ( identity = iPr_def_22 )
| ( multiply(inverse(iPr_def_17),iPr_def_17) = multiply(iPr_def_14,iPr_def_20) ) ),
inference(superposition,[status(thm)],[c_41526,c_21493]) ).
tcf(c_49270,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_42349,c_3559]) ).
tcf(c_49447,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c8 = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_42386,c_3576]) ).
tcf(c_50559,plain,
( ( identity = iPr_def_22 )
| ( multiply(sk_c8,iPr_def_19) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_42952,c_18469]) ).
tcf(c_51480,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_49270,c_410]) ).
tcf(c_52261,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( inverse(iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3189,c_51480]) ).
tcf(c_52268,plain,
( ( iPr_def_19 = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_52261,c_20361]) ).
tcf(c_53186,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( inverse(iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_49447,c_410]) ).
tcf(c_54106,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( inverse(iPr_def_14) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3190,c_53186]) ).
tcf(c_54114,plain,
( ( iPr_def_16 = iPr_def_20 )
| ( sk_c8 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_54106,c_20361]) ).
tcf(c_57090,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(identity,sk_c7) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_2382,c_13740]) ).
tcf(c_57091,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_57090,c_83]) ).
tcf(c_58399,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_57091,c_54114,c_52268,c_50559,c_46571,c_46564,c_46383,c_41893,c_41840,c_41723,c_41345,c_41333,c_41324,c_41290,c_41007,c_40414,c_40373,c_40009,c_40008,c_36347,c_36125,c_36120,c_32881,c_31656,c_31630,c_31585,c_31570,c_31364,c_28275,c_24678,c_24661,c_24603,c_24598,c_24597,c_24601,c_23040,c_23039,c_23033,c_23020,c_23006,c_21506,c_20443,c_20361,c_18470,c_14588,c_13751,c_13742,c_13741,c_13734,c_13729,c_13722,c_13740,c_13002,c_12901,c_12896,c_8743,c_7579,c_1355,c_913,c_453,c_437,c_430,c_429,c_428,c_427,c_426,c_421,c_416,c_410]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 14:12:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 15.79/3.28 % SZS status Started for theBenchmark.p
% 15.79/3.28 % SZS status Unsatisfiable for theBenchmark.p
% 15.79/3.28
% 15.79/3.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.79/3.28
% 15.79/3.28 % ------ iProver source info
% 15.79/3.28
% 15.79/3.28 % git: date: 2026-07-19 20:42:38 +0200
% 15.79/3.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.79/3.28 % git: non_committed_changes: false
% 15.79/3.28
% 15.79/3.28 % ------ Parsing...% successful
% 15.79/3.28
% 15.79/3.28
% 15.79/3.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.79/3.28
% 15.79/3.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 15.79/3.28
% 15.79/3.28 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.79/3.28
% 15.79/3.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 15.79/3.28 % ------ Proving...
% 15.79/3.28 % ------ Problem Properties
% 15.79/3.28
% 15.79/3.28 %
% 15.79/3.28 % clauses 49
% 15.79/3.28 % conjectures 35
% 15.79/3.28 % EPR 31
% 15.79/3.28 % Horn 18
% 15.79/3.28 % unary 14
% 15.79/3.28 % binary 30
% 15.79/3.28 % lits 91
% 15.79/3.28 % lits eq 83
% 15.79/3.28 % fd_pure 0
% 15.79/3.28 % fd_pseudo 0
% 15.79/3.28 % fd_cond 0
% 15.79/3.28 % fd_pseudo_cond 0
% 15.79/3.28 % AC symbols 0
% 15.79/3.28
% 15.79/3.28 % ------ Schedule dynamic 5 is on
% 15.79/3.28
% 15.79/3.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 15.79/3.28
% 15.79/3.28
% 15.79/3.28 % ------
% 15.79/3.28 % Current options:
% 15.79/3.28 % ------
% 15.79/3.28
% 15.79/3.28
% 15.79/3.28 %
% 15.79/3.28
% 15.79/3.28 % ------ Proving...
% 15.79/3.28 %
% 15.79/3.28
% 15.79/3.28 % SZS status Unsatisfiable for theBenchmark.p
% 15.79/3.28
% 15.79/3.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.79/3.29
% 15.79/3.29
%------------------------------------------------------------------------------