%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP212-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 01:31:49 PM UTC 2026
% Result : Unsatisfiable 15.44s 3.26s
% Output : CNFRefutation 15.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 29
% Syntax : Number of formulae : 340 ( 57 unt; 0 def)
% Number of atoms : 829 ( 794 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 855 ( 366 ~; 489 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 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 : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 259 ( 0 sgn 259 !; 0 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f7,plain,
( sk_c8 = inverse(sk_c4)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f9,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f11,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f13,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f15,plain,
( sk_c8 = inverse(sk_c5)
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f17,plain,
( inverse(sk_c8) = sk_c7
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f19,plain,
( sk_c8 = inverse(sk_c4)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f21,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f23,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_11) ).
fof(f25,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_12) ).
fof(f27,plain,
( sk_c8 = inverse(sk_c5)
| sk_c2 = inverse(sk_c1) ),
inference(reorient_equations,[],[f26]) ).
fof(f40,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).
fof(f41,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f40]) ).
fof(f42,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).
fof(f43,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f42]) ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f45,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f44]) ).
fof(f46,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).
fof(f47,plain,
( sk_c7 = multiply(sk_c8,sk_c6)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f46]) ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_23) ).
fof(f49,plain,
( sk_c6 = multiply(sk_c5,sk_c8)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f48]) ).
fof(f50,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_24) ).
fof(f51,plain,
( sk_c8 = inverse(sk_c5)
| sk_c8 = inverse(sk_c3) ),
inference(reorient_equations,[],[f50]) ).
fof(f52,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_25) ).
fof(f53,plain,
( inverse(sk_c8) = sk_c7
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f52]) ).
fof(f54,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f55,plain,
( sk_c8 = inverse(sk_c4)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f54]) ).
fof(f56,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f57,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c3,sk_c7) ),
inference(reorient_equations,[],[f56]) ).
fof(f64,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
| inverse(sk_c8) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_31) ).
fof(f65,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)
| inverse(sk_c8) != sk_c7
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(X1,sk_c7)
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(reorient_equations,[],[f64]) ).
fof(f66,plain,
! [X2,X3,X0,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)
| inverse(sk_c8) != sk_c7
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f65]) ).
fof(f67,plain,
! [X2,X3,X0,X5] :
( sk_c8 != inverse(X5)
| sk_c7 != multiply(sk_c8,multiply(X5,sk_c8))
| sk_c8 != multiply(X3,sk_c7)
| sk_c8 != inverse(X3)
| inverse(sk_c8) != sk_c7
| sk_c8 != multiply(X2,sk_c7)
| sk_c8 != inverse(X2)
| sk_c8 != multiply(inverse(X0),sk_c7)
| sk_c8 != multiply(X0,inverse(X0)) ),
inference(equality_resolution,[],[f66]) ).
tcf(c_83,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_84,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_86,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c8,sk_c6) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_90,negated_conjecture,
( ( multiply(sk_c5,sk_c8) = sk_c6 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_95,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_96,negated_conjecture,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_97,negated_conjecture,
( ( inverse(sk_c5) = sk_c8 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c5,sk_c8) = sk_c6 ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c3) = sk_c8 )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c4) = sk_c8 )
| ( multiply(sk_c3,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_112,negated_conjecture,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f57]) ).
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(X1) != sk_c8 )
| ( multiply(X2,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c7) != sk_c8 )
| ( multiply(inverse(X0),sk_c7) != sk_c8 )
| ( multiply(X0,inverse(X0)) != sk_c8 )
| ( multiply(sk_c8,multiply(X3,sk_c8)) != sk_c7 ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_117,plain,
multiply(identity,sk_c8) = sk_c8,
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_118,plain,
multiply(inverse(sk_c8),sk_c8) = identity,
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_269,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_116]) ).
tcf(c_270,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_271,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_116]) ).
tcf(c_272,negated_conjecture,
( 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_273,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_274,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_275,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X2) = multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = inverse(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_277,plain,
( ( multiply(sk_c8,sk_c8) = multiply(sk_c8,sk_c8) )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_275]) ).
tcf(c_278,plain,
( ( inverse(sk_c8) = inverse(sk_c8) )
| ( sk_c8 != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_276]) ).
tcf(c_279,plain,
sk_c8 = sk_c8,
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_453,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c7) = sk_c8 )
| ( sk_c8 != X1 )
| ( multiply(inverse(X0),sk_c7) != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_481,plain,
! [X0: $i] :
( ( inverse(X0) = sk_c8 )
| ( sk_c8 != inverse(X0) )
| ( inverse(X0) != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_453]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c7) = X2 )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c7) != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(X0),sk_c7) = sk_c8 )
| ( sk_c8 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c7) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_454]) ).
tcf(c_492,plain,
! [X0: $i] :
( ( sk_c8 = sk_c7 )
| ( sk_c7 != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_494,plain,
! [X0: $i] :
( ( sk_c8 = identity )
| ( identity != X0 )
| ( sk_c8 != X0 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_497,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = inverse(X0) )
| ( sk_c8 != X1 )
| ( inverse(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(inverse(X0),sk_c7) )
| ( sk_c8 != X1 )
| ( multiply(inverse(X0),sk_c7) != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_510,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != inverse(X0) )
| ( inverse(X0) != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_483]) ).
tcf(c_513,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c7),sk_c7) = X0 )
| ( X0 != identity )
| ( multiply(inverse(sk_c7),sk_c7) != identity ) ),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(inverse(X0),sk_c7) = X3 )
| ( X3 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c7) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_517,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_519,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_497]) ).
tcf(c_520,plain,
( ( sk_c7 = sk_c8 )
| ( sk_c7 != sk_c7 )
| ( sk_c8 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_519]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk_c7 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_536,plain,
multiply(inverse(sk_c7),sk_c7) = identity,
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_542,plain,
( ( sk_c8 = inverse(sk_c8) )
| ( sk_c8 != sk_c7 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_502]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] :
( ( identity = X0 )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(inverse(X0),sk_c7) )
| ( sk_c8 != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c7) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_505]) ).
tcf(c_560,plain,
( ( sk_c8 = multiply(sk_c8,sk_c6) )
| ( sk_c8 != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_562,plain,
! [X0: $i] :
( ( sk_c8 = multiply(identity,X0) )
| ( sk_c8 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_563,plain,
( ( sk_c8 = multiply(identity,sk_c8) )
| ( sk_c8 != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_562]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( multiply(X0,X1) = X3 )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_571,plain,
! [X0: $i] :
( ( inverse(X0) = multiply(identity,inverse(X0)) )
| ( inverse(X0) != inverse(X0) )
| ( multiply(identity,inverse(X0)) != inverse(X0) ) ),
inference(instantiation,[status(thm)],[c_510]) ).
tcf(c_572,plain,
( ( inverse(sk_c8) = multiply(identity,inverse(sk_c8)) )
| ( inverse(sk_c8) != inverse(sk_c8) )
| ( multiply(identity,inverse(sk_c8)) != inverse(sk_c8) ) ),
inference(instantiation,[status(thm)],[c_571]) ).
tcf(c_585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(inverse(X0),sk_c7) )
| ( X2 != X1 )
| ( multiply(inverse(X0),sk_c7) != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = multiply(X0,X1) )
| ( X3 != X2 )
| ( multiply(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(inverse(X0),sk_c7) = multiply(X3,X4) )
| ( multiply(X3,X4) != multiply(X1,X2) )
| ( multiply(inverse(X0),sk_c7) != multiply(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_516]) ).
tcf(c_595,plain,
( ( sk_c8 = multiply(sk_c1,sk_c2) )
| ( sk_c8 != sk_c8 )
| ( multiply(sk_c1,sk_c2) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_605,plain,
( ( sk_c8 = inverse(sk_c3) )
| ( sk_c8 != sk_c8 )
| ( inverse(sk_c3) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_502]) ).
tcf(c_609,plain,
( ~ iPr_def_10
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(sk_c3,sk_c7) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_695,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( sk_c8 != inverse(sk_c3) )
| ( inverse(sk_c3) != inverse(sk_c3) ) ),
inference(instantiation,[status(thm)],[c_481]) ).
tcf(c_706,plain,
! [X0: $i] :
( ( multiply(inverse(sk_c7),sk_c7) = multiply(inverse(X0),X0) )
| ( multiply(inverse(sk_c7),sk_c7) != identity )
| ( multiply(inverse(X0),X0) != identity ) ),
inference(instantiation,[status(thm)],[c_513]) ).
tcf(c_707,plain,
( ( multiply(inverse(sk_c7),sk_c7) = multiply(inverse(sk_c8),sk_c8) )
| ( multiply(inverse(sk_c7),sk_c7) != identity )
| ( multiply(inverse(sk_c8),sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_706]) ).
tcf(c_709,plain,
! [X0: $i,X1: $i] :
( ( X0 = identity )
| ( identity != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_274]) ).
tcf(c_710,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_712,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != identity )
| ( X0 != identity ) ),
inference(instantiation,[status(thm)],[c_553]) ).
tcf(c_723,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X0) = X1 )
| ( X1 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_569]) ).
tcf(c_728,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X1) = X2 )
| ( X2 != multiply(X0,X1) )
| ( multiply(X0,X1) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_569]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(X0,X1) = X4 )
| ( X4 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_569]) ).
tcf(c_745,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c4) = identity ) ),
inference(superposition,[status(thm)],[c_105,c_84]) ).
tcf(c_746,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c4) = identity ) ),
inference(superposition,[status(thm)],[c_93,c_84]) ).
tcf(c_747,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c5) = identity ) ),
inference(superposition,[status(thm)],[c_109,c_84]) ).
tcf(c_748,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c5) = identity ) ),
inference(superposition,[status(thm)],[c_97,c_84]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i] :
( ( multiply(inverse(X0),sk_c7) = sk_c8 )
| ( sk_c8 != multiply(identity,X1) )
| ( multiply(inverse(X0),sk_c7) != multiply(identity,X1) ) ),
inference(instantiation,[status(thm)],[c_489]) ).
tcf(c_757,plain,
( ( multiply(inverse(sk_c8),sk_c7) = sk_c8 )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(inverse(sk_c8),sk_c7) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_756]) ).
tcf(c_782,plain,
! [X0: $i] : multiply(identity,inverse(X0)) = inverse(X0),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_783,plain,
multiply(identity,inverse(sk_c8)) = inverse(sk_c8),
inference(instantiation,[status(thm)],[c_782]) ).
tcf(c_809,plain,
! [X0: $i] :
( ( X0 = multiply(inverse(sk_c7),sk_c7) )
| ( X0 != identity )
| ( multiply(inverse(sk_c7),sk_c7) != identity ) ),
inference(instantiation,[status(thm)],[c_585]) ).
tcf(c_818,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(identity,X2) )
| ( multiply(X0,X1) != multiply(identity,X2) ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_825,plain,
! [X0: $i] :
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,multiply(sk_c2,X0)) = multiply(sk_c8,X0) ) ),
inference(superposition,[status(thm)],[c_86,c_85]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i] : multiply(identity,multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_83,c_85]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_84,c_85]) ).
tcf(c_869,plain,
! [X0: $i] :
( ( X0 = multiply(sk_c8,sk_c6) )
| ( X0 != sk_c7 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_593]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i] :
( ( X1 = multiply(identity,X0) )
| ( X1 != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_593]) ).
tcf(c_879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = multiply(X0,X1) )
| ( X4 != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_593]) ).
tcf(c_973,plain,
inverse(sk_c3) = inverse(sk_c3),
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_995,plain,
multiply(identity,identity) = identity,
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_1091,plain,
! [X0: $i,X1: $i] :
( ( multiply(sk_c1,sk_c2) = X1 )
| ( X1 != X0 )
| ( multiply(sk_c1,sk_c2) != X0 ) ),
inference(instantiation,[status(thm)],[c_569]) ).
tcf(c_1120,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(sk_c4,multiply(sk_c7,X0)) = multiply(sk_c8,X0) ) ),
inference(superposition,[status(thm)],[c_88,c_85]) ).
tcf(c_1149,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(identity,sk_c7) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_107,c_838]) ).
tcf(c_1150,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(identity,sk_c7) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_95,c_838]) ).
tcf(c_1382,plain,
( ( multiply(identity,identity) = multiply(inverse(sk_c7),sk_c7) )
| ( multiply(identity,identity) != identity )
| ( multiply(inverse(sk_c7),sk_c7) != identity ) ),
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_1385,plain,
( ( identity = multiply(inverse(sk_c7),sk_c7) )
| ( identity != identity )
| ( multiply(inverse(sk_c7),sk_c7) != identity ) ),
inference(instantiation,[status(thm)],[c_809]) ).
tcf(c_1502,plain,
! [X0: $i,X1: $i] :
( ( inverse(X0) = X1 )
| ( X1 != multiply(identity,inverse(X0)) )
| ( inverse(X0) != multiply(identity,inverse(X0)) ) ),
inference(instantiation,[status(thm)],[c_483]) ).
tcf(c_1559,plain,
( iPr_def_12
| iPr_def_11
| iPr_def_10
| ( inverse(sk_c1) = sk_c2 ) ),
inference(resolution,[status(thm)],[c_272,c_92]) ).
tcf(c_1710,plain,
! [X0: $i] :
( ( inverse(sk_c8) = X0 )
| ( inverse(sk_c1) = sk_c2 )
| ( X0 != sk_c7 ) ),
inference(resolution,[status(thm)],[c_274,c_92]) ).
tcf(c_1718,plain,
! [X0: $i] :
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = X0 )
| ( X0 != sk_c7 ) ),
inference(resolution,[status(thm)],[c_274,c_107]) ).
tcf(c_1719,plain,
! [X0: $i] :
( ( multiply(sk_c8,sk_c6) = X0 )
| ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( X0 != sk_c7 ) ),
inference(resolution,[status(thm)],[c_274,c_89]) ).
tcf(c_1751,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_274,c_273]) ).
tcf(c_1752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( inverse(X0) = X2 )
| ( X2 != inverse(X1) )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_274,c_276]) ).
tcf(c_1874,plain,
! [X0: $i] :
( ( X0 = identity )
| ( identity != multiply(sk_c1,sk_c2) )
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_709]) ).
tcf(c_1875,plain,
( ( sk_c8 = identity )
| ( identity != multiply(sk_c1,sk_c2) )
| ( sk_c8 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_1874]) ).
tcf(c_1894,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(inverse(sk_c7),sk_c7) = multiply(X1,X2) )
| ( multiply(X1,X2) != multiply(inverse(X0),X0) )
| ( multiply(inverse(sk_c7),sk_c7) != multiply(inverse(X0),X0) ) ),
inference(instantiation,[status(thm)],[c_594]) ).
tcf(c_1897,plain,
( ( multiply(inverse(sk_c7),sk_c7) = multiply(sk_c8,sk_c8) )
| ( multiply(sk_c8,sk_c8) != multiply(inverse(sk_c8),sk_c8) )
| ( multiply(inverse(sk_c7),sk_c7) != multiply(inverse(sk_c8),sk_c8) ) ),
inference(instantiation,[status(thm)],[c_1894]) ).
tcf(c_1983,plain,
( ( sk_c7 = multiply(identity,sk_c7) )
| ( sk_c7 != sk_c7 )
| ( multiply(identity,sk_c7) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_519]) ).
tcf(c_2044,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,X0) = inverse(X1) )
| ( inverse(X1) != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_723]) ).
tcf(c_2047,plain,
! [X0: $i] :
( ( multiply(identity,X0) = identity )
| ( identity != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_723]) ).
tcf(c_2048,plain,
( ( multiply(identity,sk_c8) = identity )
| ( identity != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_2047]) ).
tcf(c_2053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(identity,X0) )
| ( X2 != X1 )
| ( multiply(identity,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_593]) ).
tcf(c_2054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(identity,X0) = X2 )
| ( X2 != X1 )
| ( multiply(identity,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_569]) ).
tcf(c_2055,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(identity,X0) )
| ( sk_c8 != X1 )
| ( multiply(identity,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_2182,plain,
! [X0: $i] :
( ( identity = multiply(identity,X0) )
| ( identity != X0 )
| ( multiply(identity,X0) != X0 ) ),
inference(instantiation,[status(thm)],[c_874]) ).
tcf(c_2277,plain,
identity = identity,
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_2308,plain,
( ( multiply(sk_c3,sk_c7) = sk_c8 )
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_112,c_269]) ).
tcf(c_2311,plain,
( ( inverse(sk_c3) = sk_c8 )
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_106,c_269]) ).
tcf(c_2319,plain,
( ( inverse(sk_c4) = sk_c8 )
| ~ iPr_def_10
| ( inverse(sk_c3) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_111,c_269]) ).
tcf(c_2389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X1,X2) = multiply(inverse(sk_c7),sk_c7) )
| ( multiply(X1,X2) != multiply(inverse(X0),X0) )
| ( multiply(inverse(sk_c7),sk_c7) != multiply(inverse(X0),X0) ) ),
inference(instantiation,[status(thm)],[c_731]) ).
tcf(c_2390,plain,
( ( multiply(sk_c8,sk_c8) = multiply(inverse(sk_c7),sk_c7) )
| ( multiply(sk_c8,sk_c8) != multiply(inverse(sk_c8),sk_c8) )
| ( multiply(inverse(sk_c7),sk_c7) != multiply(inverse(sk_c8),sk_c8) ) ),
inference(instantiation,[status(thm)],[c_2389]) ).
tcf(c_2426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(identity,X4) = multiply(X0,X1) )
| ( multiply(identity,X4) != multiply(X2,X3) )
| ( multiply(X0,X1) != multiply(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_879]) ).
tcf(c_2485,plain,
! [X0: $i] :
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,multiply(sk_c4,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_745,c_85]) ).
tcf(c_2487,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_106,c_2485]) ).
tcf(c_2511,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,multiply(sk_c4,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_746,c_85]) ).
tcf(c_2513,plain,
! [X0: $i] :
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,multiply(sk_c5,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_747,c_85]) ).
tcf(c_2515,plain,
! [X0: $i] :
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,multiply(sk_c5,X0)) = multiply(identity,X0) ) ),
inference(superposition,[status(thm)],[c_748,c_85]) ).
tcf(c_2522,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_94,c_2511]) ).
tcf(c_2529,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = multiply(identity,sk_c8) ) ),
inference(superposition,[status(thm)],[c_108,c_2513]) ).
tcf(c_2538,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c6) = multiply(identity,sk_c8) ) ),
inference(superposition,[status(thm)],[c_96,c_2515]) ).
tcf(c_2552,plain,
( ( inverse(sk_c3) = sk_c8 )
| ~ iPr_def_10
| ( inverse(sk_c4) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_106,c_269]) ).
tcf(c_2572,plain,
( ( inverse(sk_c3) = sk_c8 )
| ~ iPr_def_12
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_108,c_271]) ).
tcf(c_2573,plain,
( ( inverse(sk_c1) = sk_c2 )
| ~ iPr_def_12
| ( inverse(sk_c5) != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_96,c_271]) ).
tcf(c_3024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( multiply(X0,X2) = X4 )
| ( X4 != multiply(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_275,c_274]) ).
tcf(c_3041,plain,
( ( sk_c7 = multiply(sk_c8,sk_c6) )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(resolution,[status(thm)],[c_1751,c_89]) ).
tcf(c_3051,plain,
( ( sk_c8 = inverse(sk_c3) )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(resolution,[status(thm)],[c_1751,c_104]) ).
tcf(c_3053,plain,
( ( sk_c8 = inverse(sk_c3) )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(resolution,[status(thm)],[c_1751,c_109]) ).
tcf(c_3361,plain,
( ( sk_c8 = identity )
| ( identity != multiply(inverse(sk_c7),sk_c7) )
| ( sk_c8 != multiply(inverse(sk_c7),sk_c7) ) ),
inference(instantiation,[status(thm)],[c_494]) ).
tcf(c_4078,plain,
( ( inverse(sk_c3) = sk_c8 )
| ~ iPr_def_10 ),
inference(global_subsumption_just,[status(thm)],[c_2552,c_105,c_609,c_2319,c_2311,c_2308]) ).
tcf(c_4080,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_4078,c_609,c_2319,c_2308,c_4078]) ).
tcf(c_4101,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c8) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_2487,c_1149]) ).
tcf(c_4151,negated_conjecture,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_269,c_4080]) ).
tcf(c_4169,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c8) != sk_c7 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_272,c_4151]) ).
tcf(c_4170,plain,
( iPr_def_12
| iPr_def_11
| ( inverse(sk_c1) = sk_c2 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1559,c_4151]) ).
tcf(c_4171,plain,
( ( inverse(sk_c1) = sk_c2 )
| iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_4170,c_97,c_95,c_2573,c_4170]) ).
tcf(c_4172,plain,
( iPr_def_11
| ( inverse(sk_c1) = sk_c2 ) ),
inference(renaming,[status(thm)],[c_4171]) ).
tcf(c_4228,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c8) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_2522,c_1150]) ).
tcf(c_4320,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c6) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_2529,c_83]) ).
tcf(c_4425,plain,
( ( sk_c8 = sk_c7 )
| ( inverse(sk_c3) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_4320,c_107]) ).
tcf(c_4547,plain,
( iPr_def_12
| iPr_def_11
| ( sk_c8 = inverse(sk_c3) ) ),
inference(resolution,[status(thm)],[c_3051,c_4169]) ).
tcf(c_4549,plain,
! [X0: $i] :
( ( sk_c8 = inverse(sk_c3) )
| ( inverse(sk_c8) = X0 )
| ( X0 != sk_c7 ) ),
inference(resolution,[status(thm)],[c_3051,c_274]) ).
tcf(c_4585,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c6) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_2538,c_83]) ).
tcf(c_4768,plain,
! [X0: $i] :
( ( sk_c8 = inverse(sk_c3) )
| ( inverse(sk_c5) = X0 )
| ( X0 != sk_c8 ) ),
inference(resolution,[status(thm)],[c_3053,c_274]) ).
tcf(c_4797,plain,
( ( sk_c8 = sk_c7 )
| ( inverse(sk_c1) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_4585,c_95]) ).
tcf(c_4806,plain,
multiply(identity,sk_c7) = sk_c7,
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_5232,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = multiply(identity,inverse(X0)) )
| ( X2 != X1 )
| ( multiply(identity,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_2053]) ).
tcf(c_5271,plain,
! [X0: $i] :
( ( X0 = inverse(sk_c8) )
| ( inverse(sk_c1) = sk_c2 )
| ( X0 != sk_c7 ) ),
inference(resolution,[status(thm)],[c_1710,c_1751]) ).
tcf(c_5342,plain,
! [X0: $i] :
( ( sk_c8 = multiply(identity,identity) )
| ( sk_c8 != X0 )
| ( multiply(identity,identity) != X0 ) ),
inference(instantiation,[status(thm)],[c_2055]) ).
tcf(c_5843,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( multiply(X0,X2) = multiply(inverse(X1),X1) )
| ( X2 != X1 )
| ( X0 != inverse(X1) ) ),
inference(instantiation,[status(thm)],[c_275]) ).
tcf(c_5844,plain,
( ( multiply(sk_c8,sk_c8) = multiply(inverse(sk_c8),sk_c8) )
| ( sk_c8 != sk_c8 )
| ( sk_c8 != inverse(sk_c8) ) ),
inference(instantiation,[status(thm)],[c_5843]) ).
tcf(c_6055,plain,
multiply(identity,sk_c7) = sk_c7,
inference(global_subsumption_just,[status(thm)],[c_1149,c_4806]) ).
tcf(c_6088,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(inverse(sk_c4),sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_106,c_839]) ).
tcf(c_6089,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(inverse(sk_c4),sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_94,c_839]) ).
tcf(c_6262,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_105,c_6088]) ).
tcf(c_6278,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c8) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_6262,c_83]) ).
tcf(c_6286,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(inverse(sk_c8),sk_c7) = multiply(identity,sk_c8) ) ),
inference(superposition,[status(thm)],[c_6278,c_839]) ).
tcf(c_6524,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_93,c_6089]) ).
tcf(c_6547,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c8,sk_c8) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_6524,c_6055]) ).
tcf(c_7076,plain,
( ( identity = multiply(identity,identity) )
| ( identity != identity )
| ( multiply(identity,identity) != identity ) ),
inference(instantiation,[status(thm)],[c_2182]) ).
tcf(c_7275,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(inverse(sk_c8),sk_c7) = multiply(identity,sk_c8) ) ),
inference(superposition,[status(thm)],[c_6547,c_839]) ).
tcf(c_7743,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != multiply(identity,sk_c7) )
| ( X0 != multiply(identity,sk_c7) ) ),
inference(instantiation,[status(thm)],[c_497]) ).
tcf(c_8459,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,identity) = multiply(X0,X1) )
| ( multiply(identity,identity) != multiply(inverse(sk_c7),sk_c7) )
| ( multiply(X0,X1) != multiply(inverse(sk_c7),sk_c7) ) ),
inference(instantiation,[status(thm)],[c_2426]) ).
tcf(c_8460,plain,
( ( multiply(identity,identity) = multiply(sk_c8,sk_c8) )
| ( multiply(identity,identity) != multiply(inverse(sk_c7),sk_c7) )
| ( multiply(sk_c8,sk_c8) != multiply(inverse(sk_c7),sk_c7) ) ),
inference(instantiation,[status(thm)],[c_8459]) ).
tcf(c_9065,plain,
( ( multiply(identity,sk_c7) = inverse(sk_c8) )
| ( inverse(sk_c8) != sk_c7 )
| ( multiply(identity,sk_c7) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_2044]) ).
tcf(c_9066,plain,
( ( sk_c7 = inverse(sk_c8) )
| ( sk_c7 != sk_c7 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_519]) ).
tcf(c_9105,plain,
( ( sk_c8 = inverse(sk_c8) )
| ( sk_c8 != multiply(sk_c8,sk_c6) )
| ( inverse(sk_c8) != multiply(sk_c8,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_502]) ).
tcf(c_9284,plain,
( ( sk_c8 = sk_c7 )
| ( sk_c7 != multiply(sk_c8,sk_c6) )
| ( sk_c8 != multiply(sk_c8,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_492]) ).
tcf(c_11010,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = multiply(X0,X1) )
| ( sk_c7 != multiply(identity,sk_c7) )
| ( multiply(X0,X1) != multiply(identity,sk_c7) ) ),
inference(instantiation,[status(thm)],[c_7743]) ).
tcf(c_11011,plain,
( ( sk_c7 = multiply(sk_c8,sk_c8) )
| ( sk_c7 != multiply(identity,sk_c7) )
| ( multiply(sk_c8,sk_c8) != multiply(identity,sk_c7) ) ),
inference(instantiation,[status(thm)],[c_11010]) ).
tcf(c_12128,plain,
! [X0: $i,X1: $i] :
( ( inverse(X1) = multiply(sk_c8,sk_c6) )
| ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( X1 != X0 )
| ( inverse(X0) != sk_c7 ) ),
inference(resolution,[status(thm)],[c_1752,c_1719]) ).
tcf(c_12131,plain,
( ( inverse(sk_c8) = multiply(sk_c8,sk_c6) )
| ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( sk_c8 != sk_c8 )
| ( inverse(sk_c8) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_12128]) ).
tcf(c_13888,plain,
! [X0: $i] :
( ( inverse(X0) = identity )
| ( identity != multiply(identity,inverse(X0)) )
| ( inverse(X0) != multiply(identity,inverse(X0)) ) ),
inference(instantiation,[status(thm)],[c_1502]) ).
tcf(c_13889,plain,
( ( inverse(sk_c8) = identity )
| ( identity != multiply(identity,inverse(sk_c8)) )
| ( inverse(sk_c8) != multiply(identity,inverse(sk_c8)) ) ),
inference(instantiation,[status(thm)],[c_13888]) ).
tcf(c_15065,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != multiply(sk_c8,sk_c6) )
| ( multiply(X0,X1) != multiply(sk_c8,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_570]) ).
tcf(c_15066,plain,
( ( sk_c8 = multiply(sk_c8,sk_c8) )
| ( sk_c8 != multiply(sk_c8,sk_c6) )
| ( multiply(sk_c8,sk_c8) != multiply(sk_c8,sk_c6) ) ),
inference(instantiation,[status(thm)],[c_15065]) ).
tcf(c_15584,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(identity,identity) )
| ( sk_c8 != multiply(X0,X1) )
| ( multiply(identity,identity) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_5342]) ).
tcf(c_15585,plain,
( ( sk_c8 = multiply(identity,identity) )
| ( sk_c8 != multiply(sk_c8,sk_c8) )
| ( multiply(identity,identity) != multiply(sk_c8,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_15584]) ).
tcf(c_15712,plain,
( ( sk_c8 = identity )
| ( identity != multiply(identity,identity) )
| ( sk_c8 != multiply(identity,identity) ) ),
inference(instantiation,[status(thm)],[c_494]) ).
tcf(c_16842,plain,
! [X0: $i] :
( ( sk_c8 = multiply(sk_c8,sk_c6) )
| ( sk_c8 != X0 )
| ( multiply(sk_c8,sk_c6) != X0 ) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_16843,plain,
( ( sk_c8 = multiply(sk_c8,sk_c6) )
| ( sk_c8 != sk_c8 )
| ( multiply(sk_c8,sk_c6) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_16842]) ).
tcf(c_17423,plain,
( ( sk_c8 = sk_c7 )
| ( sk_c7 != inverse(sk_c8) )
| ( sk_c8 != inverse(sk_c8) ) ),
inference(instantiation,[status(thm)],[c_492]) ).
tcf(c_17801,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(X2,X3) = multiply(sk_c8,sk_c6) )
| ( X3 != X1 )
| ( X2 != X0 )
| ( multiply(X0,X1) != sk_c7 ) ),
inference(resolution,[status(thm)],[c_3024,c_1718]) ).
tcf(c_17806,plain,
( ( inverse(sk_c3) = sk_c8 )
| ( multiply(sk_c8,sk_c8) = multiply(sk_c8,sk_c6) )
| ( sk_c8 != sk_c8 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_17801]) ).
tcf(c_17958,plain,
multiply(identity,sk_c7) = sk_c7,
inference(global_subsumption_just,[status(thm)],[c_1149,c_4806]) ).
tcf(c_17979,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(inverse(sk_c1),sk_c8) = multiply(identity,sk_c2) ) ),
inference(superposition,[status(thm)],[c_86,c_839]) ).
tcf(c_17999,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(inverse(sk_c3),sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_110,c_839]) ).
tcf(c_18000,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_83,c_839]) ).
tcf(c_18001,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_84,c_839]) ).
tcf(c_18026,plain,
! [X0: $i] : multiply(inverse(inverse(identity)),X0) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_18000,c_839]) ).
tcf(c_18061,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(identity,X1)) = multiply(multiply(identity,X0),X1),
inference(superposition,[status(thm)],[c_18001,c_85]) ).
tcf(c_18073,plain,
multiply(identity,inverse(identity)) = identity,
inference(superposition,[status(thm)],[c_18026,c_84]) ).
tcf(c_18102,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = multiply(identity,sk_c2) ) ),
inference(superposition,[status(thm)],[c_92,c_17979]) ).
tcf(c_18113,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_18102,c_83]) ).
tcf(c_18149,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_18073,c_83]) ).
tcf(c_18150,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(inverse(identity),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_18073,c_270]) ).
tcf(c_18513,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_104,c_17999]) ).
tcf(c_18530,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c8) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_18513,c_17958]) ).
tcf(c_18834,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c1,sk_c2) = multiply(sk_c8,sk_c8) ) ),
inference(superposition,[status(thm)],[c_18113,c_825]) ).
tcf(c_21085,plain,
! [X0: $i,X1: $i] : multiply(multiply(identity,X0),X1) = multiply(inverse(inverse(X0)),X1),
inference(superposition,[status(thm)],[c_83,c_18061]) ).
tcf(c_21355,plain,
! [X0: $i,X1: $i] :
( ( identity = multiply(identity,inverse(X0)) )
| ( identity != X1 )
| ( multiply(identity,inverse(X0)) != X1 ) ),
inference(instantiation,[status(thm)],[c_5232]) ).
tcf(c_22115,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = multiply(sk_c8,sk_c6) )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(X0,X1) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_869]) ).
tcf(c_22116,plain,
( ( multiply(sk_c8,sk_c8) = multiply(sk_c8,sk_c6) )
| ( multiply(sk_c8,sk_c6) != sk_c7 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_22115]) ).
tcf(c_23566,plain,
! [X0: $i] : multiply(multiply(identity,X0),inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_21085,c_84]) ).
tcf(c_23937,plain,
! [X0: $i,X1: $i] :
( ( multiply(identity,sk_c7) = X1 )
| ( X1 != X0 )
| ( multiply(identity,sk_c7) != X0 ) ),
inference(instantiation,[status(thm)],[c_2054]) ).
tcf(c_26453,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c8,sk_c8) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_18834,c_86]) ).
tcf(c_26771,plain,
( ( sk_c8 = sk_c7 )
| ( inverse(sk_c8) = sk_c7 ) ),
inference(superposition,[status(thm)],[c_26453,c_18530]) ).
tcf(c_28561,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_83,c_23566]) ).
tcf(c_29677,plain,
! [X0: $i] :
( ( sk_c8 = inverse(sk_c3) )
| ( X0 = inverse(sk_c8) )
| ( X0 != sk_c7 ) ),
inference(resolution,[status(thm)],[c_4549,c_1751]) ).
tcf(c_29678,plain,
( ( sk_c8 = inverse(sk_c3) )
| ( sk_c8 = inverse(sk_c8) )
| ( sk_c8 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_29677]) ).
tcf(c_29729,plain,
( ( inverse(sk_c1) = sk_c2 )
| ( multiply(sk_c4,sk_c8) = identity ) ),
inference(superposition,[status(thm)],[c_93,c_28561]) ).
tcf(c_29750,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(inverse(X0),sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_28561,c_270]) ).
tcf(c_29795,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(inverse(sk_c8),sk_c7) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_29750]) ).
tcf(c_30309,plain,
sk_c8 = inverse(sk_c3),
inference(global_subsumption_just,[status(thm)],[c_4768,c_117,c_118,c_107,c_279,c_536,c_560,c_563,c_605,c_707,c_757,c_995,c_1382,c_2277,c_2390,c_2572,c_3053,c_4101,c_4425,c_4547,c_5844,c_6286,c_7076,c_8460,c_15066,c_15585,c_15712,c_17806,c_29678,c_29795]) ).
tcf(c_30313,plain,
inverse(sk_c1) = sk_c2,
inference(global_subsumption_just,[status(thm)],[c_5271,c_117,c_118,c_92,c_95,c_279,c_536,c_542,c_563,c_707,c_757,c_995,c_1382,c_2277,c_2390,c_4172,c_4228,c_4585,c_4797,c_5844,c_7076,c_7275,c_8460,c_15066,c_15585,c_15712,c_16843,c_22116,c_29795]) ).
tcf(c_32635,plain,
! [X0: $i] :
( ( inverse(sk_c8) = sk_c7 )
| ( sk_c7 != X0 )
| ( inverse(sk_c8) != X0 ) ),
inference(instantiation,[status(thm)],[c_527]) ).
tcf(c_32636,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( sk_c7 != sk_c8 )
| ( inverse(sk_c8) != sk_c8 ) ),
inference(instantiation,[status(thm)],[c_32635]) ).
tcf(c_36604,plain,
! [X0: $i] :
( ( identity = multiply(identity,inverse(X0)) )
| ( identity != identity )
| ( multiply(identity,inverse(X0)) != identity ) ),
inference(instantiation,[status(thm)],[c_21355]) ).
tcf(c_36605,plain,
( ( identity = multiply(identity,inverse(sk_c8)) )
| ( identity != identity )
| ( multiply(identity,inverse(sk_c8)) != identity ) ),
inference(instantiation,[status(thm)],[c_36604]) ).
tcf(c_37111,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(X0,X1) )
| ( sk_c8 != sk_c7 )
| ( multiply(X0,X1) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_517]) ).
tcf(c_37112,plain,
( ( sk_c8 = multiply(sk_c8,sk_c8) )
| ( sk_c8 != sk_c7 )
| ( multiply(sk_c8,sk_c8) != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_37111]) ).
tcf(c_38348,plain,
inverse(sk_c1) = sk_c2,
inference(global_subsumption_just,[status(thm)],[c_29729,c_117,c_118,c_92,c_95,c_279,c_536,c_542,c_563,c_707,c_757,c_995,c_1382,c_2277,c_2390,c_4172,c_4228,c_4585,c_4797,c_5844,c_7076,c_7275,c_8460,c_15066,c_15585,c_15712,c_16843,c_22116,c_29795]) ).
tcf(c_38355,plain,
multiply(sk_c1,sk_c2) = identity,
inference(superposition,[status(thm)],[c_38348,c_28561]) ).
tcf(c_38737,plain,
! [X0: $i] :
( ( multiply(sk_c1,sk_c2) = X0 )
| ( X0 != identity )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_1091]) ).
tcf(c_38738,plain,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( sk_c8 != identity )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_38737]) ).
tcf(c_41193,plain,
( ( identity = multiply(sk_c1,sk_c2) )
| ( identity != identity )
| ( multiply(sk_c1,sk_c2) != identity ) ),
inference(instantiation,[status(thm)],[c_712]) ).
tcf(c_41514,plain,
! [X0: $i,X1: $i] :
( ( multiply(X0,X1) = sk_c7 )
| ( sk_c7 != multiply(X0,X1) )
| ( multiply(X0,X1) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_728]) ).
tcf(c_41515,plain,
( ( multiply(sk_c8,sk_c8) = sk_c7 )
| ( sk_c7 != multiply(sk_c8,sk_c8) )
| ( multiply(sk_c8,sk_c8) != multiply(sk_c8,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_41514]) ).
tcf(c_42260,plain,
! [X0: $i] :
( ( multiply(identity,sk_c7) = X0 )
| ( X0 != inverse(sk_c8) )
| ( multiply(identity,sk_c7) != inverse(sk_c8) ) ),
inference(instantiation,[status(thm)],[c_23937]) ).
tcf(c_42261,plain,
( ( multiply(identity,sk_c7) = sk_c8 )
| ( sk_c8 != inverse(sk_c8) )
| ( multiply(identity,sk_c7) != inverse(sk_c8) ) ),
inference(instantiation,[status(thm)],[c_42260]) ).
tcf(c_45315,plain,
! [X0: $i] :
( ( sk_c8 = multiply(sk_c8,sk_c6) )
| ( sk_c8 != multiply(identity,X0) )
| ( multiply(sk_c8,sk_c6) != multiply(identity,X0) ) ),
inference(instantiation,[status(thm)],[c_818]) ).
tcf(c_45316,plain,
( ( sk_c8 = multiply(sk_c8,sk_c6) )
| ( sk_c8 != multiply(identity,sk_c8) )
| ( multiply(sk_c8,sk_c6) != multiply(identity,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_45315]) ).
tcf(c_50488,plain,
! [X0: $i,X1: $i] :
( ( sk_c8 = multiply(inverse(sk_c7),sk_c7) )
| ( sk_c8 != multiply(X0,X1) )
| ( multiply(inverse(sk_c7),sk_c7) != multiply(X0,X1) ) ),
inference(instantiation,[status(thm)],[c_557]) ).
tcf(c_50489,plain,
( ( sk_c8 = multiply(inverse(sk_c7),sk_c7) )
| ( sk_c8 != multiply(sk_c8,sk_c8) )
| ( multiply(inverse(sk_c7),sk_c7) != multiply(sk_c8,sk_c8) ) ),
inference(instantiation,[status(thm)],[c_50488]) ).
tcf(c_55466,plain,
! [X0: $i] :
( ( identity = X0 )
| ( identity != multiply(sk_c1,sk_c2) )
| ( X0 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_553]) ).
tcf(c_55467,plain,
( ( identity = sk_c8 )
| ( identity != multiply(sk_c1,sk_c2) )
| ( sk_c8 != multiply(sk_c1,sk_c2) ) ),
inference(instantiation,[status(thm)],[c_55466]) ).
tcf(c_60990,plain,
( ~ iPr_def_11
| ( sk_c8 != identity )
| ( multiply(identity,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_18149,c_18150]) ).
tcf(c_64340,plain,
( ( sk_c8 = inverse(sk_c8) )
| ( sk_c8 != identity )
| ( inverse(sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_502]) ).
tcf(c_64342,plain,
! [X0: $i] :
( ( inverse(sk_c8) = X0 )
| ( X0 != identity )
| ( inverse(sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_483]) ).
tcf(c_64343,plain,
( ( inverse(sk_c8) = sk_c8 )
| ( sk_c8 != identity )
| ( inverse(sk_c8) != identity ) ),
inference(instantiation,[status(thm)],[c_64342]) ).
tcf(c_66336,negated_conjecture,
inverse(sk_c1) = sk_c2,
inference(global_subsumption_just,[status(thm)],[c_92,c_30313]) ).
tcf(c_66338,negated_conjecture,
inverse(sk_c3) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_104,c_695,c_973,c_30309]) ).
tcf(c_66344,plain,
multiply(sk_c2,sk_c1) = identity,
inference(superposition,[status(thm)],[c_66336,c_84]) ).
tcf(c_66345,plain,
multiply(sk_c8,sk_c3) = identity,
inference(superposition,[status(thm)],[c_66338,c_84]) ).
tcf(c_66397,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_66344,c_85]) ).
tcf(c_66398,plain,
! [X0: $i] : multiply(sk_c8,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_66345,c_85]) ).
tcf(c_66425,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = multiply(identity,sk_c2) ) ),
inference(superposition,[status(thm)],[c_86,c_66397]) ).
tcf(c_66435,plain,
( ~ iPr_def_12
| ( inverse(sk_c3) != sk_c8 )
| ( multiply(identity,sk_c8) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_66398,c_271]) ).
tcf(c_66471,plain,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(inverse(sk_c4),sk_c8) = multiply(identity,sk_c7) ) ),
inference(superposition,[status(thm)],[c_88,c_839]) ).
tcf(c_66474,plain,
( ( multiply(sk_c1,sk_c2) = sk_c8 )
| ( multiply(inverse(sk_c5),sk_c6) = multiply(identity,sk_c8) ) ),
inference(superposition,[status(thm)],[c_90,c_839]) ).
tcf(c_66489,plain,
multiply(inverse(sk_c2),identity) = multiply(identity,sk_c1),
inference(superposition,[status(thm)],[c_66344,c_839]) ).
tcf(c_66499,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),multiply(identity,X1)) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_839,c_839]) ).
tcf(c_66520,plain,
! [X0: $i] : multiply(inverse(sk_c2),multiply(identity,X0)) = multiply(multiply(identity,sk_c1),X0),
inference(superposition,[status(thm)],[c_66489,c_85]) ).
tcf(c_66620,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c2 ) ),
inference(superposition,[status(thm)],[c_66425,c_83]) ).
tcf(c_66707,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(inverse(sk_c2),sk_c2) = multiply(identity,sk_c8) ) ),
inference(superposition,[status(thm)],[c_66620,c_839]) ).
tcf(c_66766,plain,
! [X0: $i] : multiply(multiply(identity,sk_c1),X0) = multiply(inverse(sk_c2),X0),
inference(superposition,[status(thm)],[c_83,c_66520]) ).
tcf(c_66871,plain,
! [X0: $i] : multiply(inverse(sk_c2),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_83,c_66766]) ).
tcf(c_66896,plain,
multiply(sk_c1,sk_c2) = identity,
inference(superposition,[status(thm)],[c_66871,c_84]) ).
tcf(c_66915,plain,
( ( sk_c8 = identity )
| ( inverse(sk_c5) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_66896,c_91]) ).
tcf(c_66916,plain,
( ( sk_c8 = identity )
| ( inverse(sk_c4) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_66896,c_87]) ).
tcf(c_67524,plain,
( ~ iPr_def_12
| ( multiply(identity,sk_c8) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_66435,c_695,c_973,c_30309,c_66435]) ).
tcf(c_67526,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_67524]) ).
tcf(c_67552,plain,
( ( sk_c8 = identity )
| ( multiply(sk_c8,sk_c8) = multiply(identity,sk_c7) )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_66916,c_66471]) ).
tcf(c_67808,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(identity,multiply(X0,X1)),
inference(superposition,[status(thm)],[c_83,c_66499]) ).
tcf(c_67880,plain,
( ( inverse(sk_c8) = sk_c7 )
| ( multiply(identity,sk_c8) = identity ) ),
inference(superposition,[status(thm)],[c_66707,c_84]) ).
tcf(c_67883,plain,
( ( sk_c8 = identity )
| ( multiply(sk_c8,sk_c6) = multiply(identity,sk_c8) )
| ( multiply(sk_c1,sk_c2) = sk_c8 ) ),
inference(superposition,[status(thm)],[c_66915,c_66474]) ).
tcf(c_67929,plain,
multiply(sk_c1,sk_c2) = sk_c8,
inference(global_subsumption_just,[status(thm)],[c_1120,c_117,c_118,c_86,c_277,c_279,c_536,c_563,c_707,c_710,c_1385,c_1897,c_1983,c_2277,c_3041,c_3361,c_4806,c_5844,c_9105,c_9284,c_11011,c_12131,c_37112,c_38355,c_38738,c_41515,c_45316,c_50489,c_67552,c_67883]) ).
tcf(c_67995,plain,
multiply(identity,sk_c8) = identity,
inference(global_subsumption_just,[status(thm)],[c_67880,c_117,c_279,c_595,c_2048,c_2277,c_38355,c_41193,c_55467,c_67929]) ).
tcf(c_68003,plain,
! [X0: $i] : multiply(identity,multiply(sk_c8,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_67995,c_85]) ).
tcf(c_68307,plain,
! [X0: $i] : multiply(identity,multiply(X0,inverse(X0))) = identity,
inference(superposition,[status(thm)],[c_67808,c_84]) ).
tcf(c_68372,plain,
multiply(identity,inverse(sk_c8)) = identity,
inference(superposition,[status(thm)],[c_68307,c_68003]) ).
tcf(c_68484,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_68372,c_67929,c_67526,c_64340,c_64343,c_60990,c_42261,c_41193,c_38355,c_36605,c_32636,c_26771,c_17423,c_13889,c_9066,c_9065,c_4806,c_4169,c_2277,c_1875,c_783,c_710,c_595,c_572,c_520,c_279,c_278]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP212-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 14:07:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 15.44/3.26 % SZS status Started for theBenchmark.p
% 15.44/3.26 % SZS status Unsatisfiable for theBenchmark.p
% 15.44/3.26
% 15.44/3.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.44/3.26
% 15.44/3.26 % ------ iProver source info
% 15.44/3.26
% 15.44/3.26 % git: date: 2026-07-19 20:42:38 +0200
% 15.44/3.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.44/3.26 % git: non_committed_changes: false
% 15.44/3.26
% 15.44/3.26 % ------ Parsing...% successful
% 15.44/3.26
% 15.44/3.26
% 15.44/3.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.44/3.26
% 15.44/3.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 15.44/3.26
% 15.44/3.26 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.44/3.26
% 15.44/3.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 15.44/3.26 % ------ Proving...
% 15.44/3.26 % ------ Problem Properties
% 15.44/3.26
% 15.44/3.26 %
% 15.44/3.26 % clauses 37
% 15.44/3.26 % conjectures 34
% 15.44/3.26 % EPR 0
% 15.44/3.26 % Horn 6
% 15.44/3.26 % unary 3
% 15.44/3.26 % binary 30
% 15.44/3.26 % lits 76
% 15.44/3.26 % lits eq 70
% 15.44/3.26 % fd_pure 0
% 15.44/3.26 % fd_pseudo 0
% 15.44/3.26 % fd_cond 0
% 15.44/3.26 % fd_pseudo_cond 0
% 15.44/3.26 % AC symbols 0
% 15.44/3.26
% 15.44/3.26 % ------ Input Options Time Limit: Unbounded
% 15.44/3.26
% 15.44/3.26
% 15.44/3.26 % ------
% 15.44/3.26 % Current options:
% 15.44/3.26 % ------
% 15.44/3.26
% 15.44/3.26
% 15.44/3.26 %
% 15.44/3.26
% 15.44/3.26 % ------ Proving...
% 15.44/3.26 %
% 15.44/3.26
% 15.44/3.26 % SZS status Unsatisfiable for theBenchmark.p
% 15.44/3.26
% 15.44/3.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.44/3.27
% 15.44/3.27
%------------------------------------------------------------------------------