%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP265-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:32:38 PM UTC 2026
% Result : Unsatisfiable 1.11s 1.74s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 245 ( 75 unt; 11 def)
% Number of atoms : 743 ( 439 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 377 ( 137 ~; 240 |; 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 : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = inverse(sk_c3)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c4)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f11]) ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c7 = inverse(sk_c5)
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
fof(f26,plain,
( sk_c7 = inverse(sk_c4)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f25]) ).
fof(f33,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c3)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f37]) ).
fof(f41,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
fof(f42,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f41]) ).
fof(f43,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
fof(f44,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f43]) ).
fof(f45,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c7 = inverse(sk_c5)
| sk_c7 = multiply(sk_c2,sk_c8) ),
inference(reorient_equations,[],[f45]) ).
fof(f47,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_22) ).
fof(f48,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f47]) ).
fof(f49,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_23) ).
fof(f50,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f49]) ).
fof(f51,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_24) ).
fof(f52,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f51]) ).
fof(f53,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_25) ).
fof(f54,plain,
( sk_c7 = inverse(sk_c4)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f53]) ).
fof(f55,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c8 = multiply(sk_c7,sk_c6)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c5,sk_c7)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f57]) ).
fof(f59,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_28) ).
fof(f60,plain,
( sk_c7 = inverse(sk_c5)
| sk_c8 = inverse(sk_c2) ),
inference(reorient_equations,[],[f59]) ).
fof(f61,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c7
| multiply(X5,sk_c7) != X4
| multiply(sk_c7,X4) != sk_c8
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c7 != inverse(X5)
| multiply(X5,sk_c7) != X4
| sk_c8 != multiply(sk_c7,X4)
| sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X1,sk_c8)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9) ),
inference(reorient_equations,[],[f61]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X5] :
( sk_c7 != inverse(X5)
| sk_c8 != multiply(sk_c7,multiply(X5,sk_c7))
| sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c8 != inverse(X1)
| sk_c7 != multiply(X1,sk_c8)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9) ),
inference(equality_resolution,[],[f62]) ).
tcf(c_81,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_82,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_84,negated_conjecture,
( ( multiply(sk_c3,sk_c9) = sk_c8 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_91,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_93,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_94,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( inverse(sk_c1) = sk_c9 ) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_98,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c7 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_100,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c7 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_102,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c7 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_103,negated_conjecture,
( ( multiply(sk_c2,sk_c8) = sk_c7 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c5) = sk_c7 )
| ( multiply(sk_c2,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_105,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_106,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_107,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f52]) ).
tcf(c_108,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c4) = sk_c7 ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_109,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c7,sk_c6) = sk_c8 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_110,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( multiply(sk_c5,sk_c7) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_111,negated_conjecture,
( ( inverse(sk_c2) = sk_c8 )
| ( inverse(sk_c5) = sk_c7 ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_112,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X4) != sk_c8 )
| ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c7 )
| ( inverse(X1) != sk_c9 )
| ( inverse(X0) != sk_c9 )
| ( multiply(X4,sk_c8) != sk_c7 )
| ( multiply(X3,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c9) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 )
| ( multiply(sk_c7,multiply(X2,sk_c7)) != sk_c8 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_389,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_112]) ).
tcf(c_390,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_112]) ).
tcf(c_391,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_112]) ).
tcf(c_392,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c8 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_112]) ).
tcf(c_393,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_112]) ).
tcf(c_394,definition,
iPr_def_14 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_395,definition,
iPr_def_15 = inverse(sk_c2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_396,definition,
iPr_def_16 = multiply(sk_c5,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_397,definition,
iPr_def_17 = multiply(sk_c7,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_398,definition,
iPr_def_18 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_399,definition,
iPr_def_19 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_400,definition,
iPr_def_20 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_401,definition,
iPr_def_21 = multiply(sk_c3,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_402,definition,
iPr_def_22 = multiply(sk_c2,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_403,definition,
iPr_def_23 = inverse(sk_c1),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_404,definition,
iPr_def_24 = multiply(sk_c1,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_405,negated_conjecture,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| iPr_def_10 ),
inference(demodulation,[status(thm)],[c_393]) ).
tcf(c_406,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c7 )
| ( multiply(sk_c7,multiply(X0,sk_c7)) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_392]) ).
tcf(c_407,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c8 )
| ( multiply(X0,sk_c8) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_391]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_390]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_389]) ).
tcf(c_411,negated_conjecture,
( ( iPr_def_15 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_111,c_395,c_394]) ).
tcf(c_412,negated_conjecture,
( ( iPr_def_16 = sk_c6 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_110,c_396]) ).
tcf(c_413,negated_conjecture,
( ( iPr_def_17 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_109,c_397]) ).
tcf(c_414,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_108,c_398]) ).
tcf(c_415,negated_conjecture,
( ( iPr_def_19 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_107,c_399]) ).
tcf(c_416,negated_conjecture,
( ( iPr_def_20 = sk_c9 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_106,c_400]) ).
tcf(c_417,negated_conjecture,
( ( iPr_def_21 = sk_c8 )
| ( iPr_def_15 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_105,c_401]) ).
tcf(c_418,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_104,c_402]) ).
tcf(c_419,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_16 = sk_c6 ) ),
inference(demodulation,[status(thm)],[c_103]) ).
tcf(c_420,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_17 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_102]) ).
tcf(c_422,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_423,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_424,negated_conjecture,
( ( iPr_def_22 = sk_c7 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_428,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_94]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90,c_404]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_18 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_19 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_703,plain,
( ( sk_c8 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_414,c_399]) ).
tcf(c_715,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_418,c_399]) ).
tcf(c_736,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c7,iPr_def_16) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_419,c_397]) ).
tcf(c_745,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_420,c_399]) ).
tcf(c_793,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c5,iPr_def_22) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_422,c_396]) ).
tcf(c_818,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_424,c_399]) ).
tcf(c_850,plain,
( ( sk_c7 = iPr_def_22 )
| ( multiply(sk_c3,iPr_def_20) = iPr_def_21 ) ),
inference(superposition,[status(thm)],[c_423,c_401]) ).
tcf(c_884,plain,
multiply(iPr_def_20,sk_c3) = identity,
inference(superposition,[status(thm)],[c_400,c_82]) ).
tcf(c_885,plain,
multiply(iPr_def_18,sk_c4) = identity,
inference(superposition,[status(thm)],[c_398,c_82]) ).
tcf(c_886,plain,
multiply(iPr_def_14,sk_c5) = identity,
inference(superposition,[status(thm)],[c_394,c_82]) ).
tcf(c_887,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_403,c_82]) ).
tcf(c_888,plain,
multiply(iPr_def_15,sk_c2) = identity,
inference(superposition,[status(thm)],[c_395,c_82]) ).
tcf(c_955,plain,
( ( sk_c7 = iPr_def_18 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_428,c_404]) ).
tcf(c_975,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_429,c_404]) ).
tcf(c_995,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_430,c_404]) ).
tcf(c_1022,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c1,iPr_def_23) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_431,c_404]) ).
tcf(c_1150,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_435,c_399]) ).
tcf(c_1200,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_436,c_402]) ).
tcf(c_1246,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(sk_c1,iPr_def_20) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_437,c_404]) ).
tcf(c_1285,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(sk_c2,iPr_def_24) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_438,c_402]) ).
tcf(c_1312,plain,
! [X0: $i] : multiply(sk_c7,multiply(sk_c6,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_397,c_83]) ).
tcf(c_1316,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_82,c_83]) ).
tcf(c_1318,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_884,c_83]) ).
tcf(c_1319,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_885,c_83]) ).
tcf(c_1320,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_886,c_83]) ).
tcf(c_1321,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_887,c_83]) ).
tcf(c_1323,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1321,c_81]) ).
tcf(c_1324,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1320,c_81]) ).
tcf(c_1325,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1319,c_81]) ).
tcf(c_1326,plain,
! [X0: $i] : multiply(iPr_def_20,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1318,c_81]) ).
tcf(c_1354,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_888,c_83]) ).
tcf(c_1355,plain,
! [X0: $i] : multiply(iPr_def_15,multiply(sk_c2,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1354,c_81]) ).
tcf(c_1517,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_81,c_407]) ).
tcf(c_1518,plain,
( ~ iPr_def_12
| ( sk_c7 != identity )
| ( inverse(inverse(sk_c8)) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_82,c_407]) ).
tcf(c_1636,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_19 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_399,c_409]) ).
tcf(c_1637,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_16 )
| ( inverse(sk_c5) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_396,c_409]) ).
tcf(c_1638,plain,
( ~ iPr_def_11
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_81,c_409]) ).
tcf(c_1653,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_14 )
| ( sk_c8 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_1637,c_394]) ).
tcf(c_1657,plain,
( ~ iPr_def_11
| ( sk_c7 != iPr_def_18 )
| ( sk_c8 != iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_1636,c_398]) ).
tcf(c_1754,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_24 )
| ( inverse(sk_c1) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_404,c_410]) ).
tcf(c_1755,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_21 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_401,c_410]) ).
tcf(c_1771,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_21 )
| ( sk_c9 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_1755,c_400]) ).
tcf(c_1775,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_24 )
| ( sk_c9 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_1754,c_403]) ).
tcf(c_1883,plain,
( ~ iPr_def_13
| ( inverse(sk_c4) != sk_c7 )
| ( multiply(sk_c7,iPr_def_19) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_399,c_406]) ).
tcf(c_1884,plain,
( ~ iPr_def_13
| ( inverse(sk_c5) != sk_c7 )
| ( multiply(sk_c7,iPr_def_16) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_396,c_406]) ).
tcf(c_1885,plain,
( ~ iPr_def_13
| ( inverse(identity) != sk_c7 )
| ( multiply(sk_c7,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_81,c_406]) ).
tcf(c_1900,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( multiply(sk_c7,iPr_def_16) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1884,c_394]) ).
tcf(c_1904,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_18 )
| ( multiply(sk_c7,iPr_def_19) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1883,c_398]) ).
tcf(c_2200,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c9,
inference(superposition,[status(thm)],[c_404,c_1323]) ).
tcf(c_2211,plain,
multiply(iPr_def_14,iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_396,c_1324]) ).
tcf(c_2226,plain,
! [X0: $i] : multiply(iPr_def_14,multiply(iPr_def_16,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2211,c_83]) ).
tcf(c_2230,plain,
multiply(iPr_def_18,iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_399,c_1325]) ).
tcf(c_2236,plain,
! [X0: $i] : multiply(iPr_def_18,multiply(iPr_def_19,X0)) = multiply(sk_c7,X0),
inference(superposition,[status(thm)],[c_2230,c_83]) ).
tcf(c_2244,plain,
multiply(iPr_def_20,iPr_def_21) = sk_c9,
inference(superposition,[status(thm)],[c_401,c_1326]) ).
tcf(c_2457,plain,
multiply(iPr_def_15,iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_402,c_1355]) ).
tcf(c_3396,plain,
( ( sk_c9 = iPr_def_20 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_995,c_1323]) ).
tcf(c_3397,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3396,c_2200]) ).
tcf(c_3427,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_1022,c_1323]) ).
tcf(c_3428,plain,
( ( sk_c8 = iPr_def_21 )
| ( sk_c9 = iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_3427,c_2200]) ).
tcf(c_3938,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(iPr_def_18,iPr_def_19) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1150,c_1325]) ).
tcf(c_3939,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c8 = iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_3938,c_2230]) ).
tcf(c_3973,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(iPr_def_15,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1200,c_1355]) ).
tcf(c_3974,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_3973,c_2457]) ).
tcf(c_3996,plain,
( ( sk_c8 = iPr_def_24 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_1246,c_1323]) ).
tcf(c_3997,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c9 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_3996,c_2200]) ).
tcf(c_4019,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(iPr_def_15,iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1285,c_1355]) ).
tcf(c_4020,plain,
( ( sk_c8 = iPr_def_24 )
| ( sk_c8 = iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_4019,c_2457]) ).
tcf(c_5146,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1316,c_81]) ).
tcf(c_5154,plain,
multiply(inverse(sk_c4),iPr_def_19) = sk_c7,
inference(superposition,[status(thm)],[c_399,c_5146]) ).
tcf(c_5156,plain,
multiply(inverse(sk_c5),iPr_def_16) = sk_c7,
inference(superposition,[status(thm)],[c_396,c_5146]) ).
tcf(c_5157,plain,
multiply(inverse(sk_c2),iPr_def_22) = sk_c8,
inference(superposition,[status(thm)],[c_402,c_5146]) ).
tcf(c_5158,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_81,c_5146]) ).
tcf(c_5159,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_82,c_5146]) ).
tcf(c_5177,plain,
( ( sk_c8 = iPr_def_21 )
| ( multiply(inverse(sk_c4),iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_818,c_5146]) ).
tcf(c_5180,plain,
( ( sk_c8 = iPr_def_17 )
| ( multiply(inverse(sk_c4),iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_745,c_5146]) ).
tcf(c_5181,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(inverse(sk_c4),iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_715,c_5146]) ).
tcf(c_5188,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c5),iPr_def_16) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_793,c_5146]) ).
tcf(c_5221,plain,
( ( sk_c8 = iPr_def_19 )
| ( multiply(inverse(sk_c2),iPr_def_22) = iPr_def_24 ) ),
inference(superposition,[status(thm)],[c_1200,c_5146]) ).
tcf(c_5230,plain,
! [X0: $i] : multiply(inverse(iPr_def_20),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1326,c_5146]) ).
tcf(c_5231,plain,
! [X0: $i] : multiply(inverse(iPr_def_18),X0) = multiply(sk_c4,X0),
inference(superposition,[status(thm)],[c_1325,c_5146]) ).
tcf(c_5233,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1323,c_5146]) ).
tcf(c_5234,plain,
! [X0: $i] : multiply(inverse(iPr_def_15),X0) = multiply(sk_c2,X0),
inference(superposition,[status(thm)],[c_1355,c_5146]) ).
tcf(c_5267,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_5146,c_5146]) ).
tcf(c_5624,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_5159,c_5267]) ).
tcf(c_5636,plain,
multiply(sk_c7,identity) = multiply(iPr_def_18,iPr_def_19),
inference(superposition,[status(thm)],[c_5624,c_2236]) ).
tcf(c_5639,plain,
multiply(sk_c7,sk_c6) = multiply(iPr_def_17,identity),
inference(superposition,[status(thm)],[c_5624,c_1312]) ).
tcf(c_5640,plain,
multiply(sk_c7,identity) = multiply(iPr_def_14,iPr_def_16),
inference(superposition,[status(thm)],[c_5624,c_2226]) ).
tcf(c_5648,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_5624,c_5158]) ).
tcf(c_5651,plain,
multiply(sk_c7,identity) = sk_c7,
inference(light_normalisation,[status(thm)],[c_5640,c_2211]) ).
tcf(c_5652,plain,
multiply(iPr_def_17,identity) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_5639,c_397]) ).
tcf(c_5676,plain,
multiply(identity,identity) = identity,
inference(superposition,[status(thm)],[c_5648,c_82]) ).
tcf(c_6411,plain,
( ( sk_c8 = iPr_def_24 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_432,c_1653]) ).
tcf(c_6542,plain,
( ( sk_c8 = iPr_def_24 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_6411,c_1657,c_3939,c_3974]) ).
tcf(c_6660,plain,
( ~ iPr_def_10
| ( sk_c8 != iPr_def_21 ) ),
inference(global_subsumption_just,[status(thm)],[c_1771,c_1775,c_1771,c_3397,c_3997]) ).
tcf(c_6662,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_6660,c_1775,c_3428,c_4020,c_6660]) ).
tcf(c_6664,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11 ),
inference(backward_subsumption_resolution,[status(thm)],[c_405,c_6662]) ).
tcf(c_6770,plain,
multiply(sk_c3,iPr_def_20) = identity,
inference(superposition,[status(thm)],[c_5230,c_82]) ).
tcf(c_6776,plain,
! [X0: $i] : multiply(sk_c3,multiply(iPr_def_20,X0)) = X0,
inference(superposition,[status(thm)],[c_5230,c_5146]) ).
tcf(c_6789,plain,
( ( identity = iPr_def_21 )
| ( sk_c7 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_850,c_6770]) ).
tcf(c_6843,plain,
multiply(sk_c3,sk_c9) = iPr_def_21,
inference(superposition,[status(thm)],[c_2244,c_6776]) ).
tcf(c_6856,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1517,c_5648]) ).
tcf(c_7025,plain,
( ~ iPr_def_11
| ( sk_c7 != identity )
| ( sk_c8 != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_1638,c_5648]) ).
tcf(c_7412,plain,
( ( identity = iPr_def_21 )
| ( multiply(sk_c4,iPr_def_22) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_6789,c_399]) ).
tcf(c_7553,plain,
multiply(sk_c4,iPr_def_18) = identity,
inference(superposition,[status(thm)],[c_5231,c_82]) ).
tcf(c_7557,plain,
( ~ iPr_def_11
| ( inverse(inverse(iPr_def_18)) != sk_c7 )
| ( multiply(sk_c4,sk_c7) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_5231,c_409]) ).
tcf(c_7560,plain,
multiply(sk_c4,identity) = inverse(iPr_def_18),
inference(superposition,[status(thm)],[c_5231,c_5624]) ).
tcf(c_7564,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_19 )
| ( inverse(inverse(iPr_def_18)) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_7557,c_399]) ).
tcf(c_7572,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_1150,c_7553]) ).
tcf(c_7573,plain,
( ( identity = iPr_def_19 )
| ( sk_c8 = iPr_def_15 ) ),
inference(demodulation,[status(thm)],[c_703,c_7553]) ).
tcf(c_7842,plain,
( ( iPr_def_15 = iPr_def_24 )
| ( identity = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_7573,c_7572]) ).
tcf(c_7920,plain,
( ( identity = iPr_def_21 )
| ( multiply(inverse(sk_c4),iPr_def_19) = iPr_def_22 ) ),
inference(superposition,[status(thm)],[c_7412,c_5146]) ).
tcf(c_7925,plain,
inverse(iPr_def_18) = sk_c4,
inference(demodulation,[status(thm)],[c_7560,c_5624]) ).
tcf(c_8842,plain,
( ~ iPr_def_13
| ( sk_c7 != identity )
| ( multiply(sk_c7,sk_c7) != sk_c8 ) ),
inference(light_normalisation,[status(thm)],[c_1885,c_5648]) ).
tcf(c_9417,plain,
multiply(sk_c1,iPr_def_23) = identity,
inference(superposition,[status(thm)],[c_5233,c_82]) ).
tcf(c_9436,plain,
( ( identity = iPr_def_24 )
| ( sk_c8 = iPr_def_19 ) ),
inference(demodulation,[status(thm)],[c_975,c_9417]) ).
tcf(c_9437,plain,
( ( identity = iPr_def_24 )
| ( sk_c7 = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_955,c_9417]) ).
tcf(c_10157,plain,
( ( identity = iPr_def_24 )
| ~ iPr_def_11
| ( sk_c8 != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_9437,c_1657]) ).
tcf(c_10184,plain,
( ( identity = iPr_def_24 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_9437,c_399]) ).
tcf(c_10192,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_19 ) ),
inference(light_normalisation,[status(thm)],[c_10184,c_7553]) ).
tcf(c_11334,plain,
multiply(sk_c2,iPr_def_15) = identity,
inference(superposition,[status(thm)],[c_5234,c_82]) ).
tcf(c_11340,plain,
! [X0: $i] : multiply(sk_c2,multiply(iPr_def_15,X0)) = X0,
inference(superposition,[status(thm)],[c_5234,c_5146]) ).
tcf(c_11341,plain,
multiply(sk_c2,identity) = inverse(iPr_def_15),
inference(superposition,[status(thm)],[c_5234,c_5624]) ).
tcf(c_11390,plain,
inverse(iPr_def_15) = sk_c2,
inference(demodulation,[status(thm)],[c_11341,c_5624]) ).
tcf(c_11395,plain,
multiply(sk_c2,sk_c8) = iPr_def_22,
inference(superposition,[status(thm)],[c_2457,c_11340]) ).
tcf(c_11984,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_11395,c_11390,c_11334,c_10192,c_10157,c_9436,c_8842,c_7925,c_7920,c_7842,c_7564,c_7025,c_6856,c_6843,c_6770,c_6664,c_6542,c_5652,c_5651,c_5640,c_5639,c_5636,c_5221,c_5188,c_5181,c_5180,c_5177,c_5157,c_5156,c_5154,c_5676,c_1904,c_1900,c_1518,c_736,c_417,c_416,c_415,c_414,c_413,c_412,c_411,c_398,c_395]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP265-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 14:18:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 1.11/1.74 % SZS status Started for theBenchmark.p
% 1.11/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.11/1.74
% 1.11/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.11/1.74
% 1.11/1.74 % ------ iProver source info
% 1.11/1.74
% 1.11/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.11/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.11/1.74 % git: non_committed_changes: false
% 1.11/1.74
% 1.11/1.74 % ------ Parsing...% successful
% 1.11/1.74
% 1.11/1.74
% 1.11/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.11/1.74
% 1.11/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.11/1.74
% 1.11/1.74 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.11/1.74
% 1.11/1.74 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.11/1.74 % ------ Proving...
% 1.11/1.74 % ------ Problem Properties
% 1.11/1.74
% 1.11/1.74 %
% 1.11/1.74 % clauses 47
% 1.11/1.74 % conjectures 33
% 1.11/1.74 % EPR 29
% 1.11/1.74 % Horn 18
% 1.11/1.74 % unary 14
% 1.11/1.74 % binary 28
% 1.11/1.74 % lits 86
% 1.11/1.74 % lits eq 78
% 1.11/1.74 % fd_pure 0
% 1.11/1.74 % fd_pseudo 0
% 1.11/1.74 % fd_cond 0
% 1.11/1.74 % fd_pseudo_cond 0
% 1.11/1.74 % AC symbols 0
% 1.11/1.74
% 1.11/1.74 % ------ Schedule dynamic 5 is on
% 1.11/1.74
% 1.11/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.11/1.74
% 1.11/1.74
% 1.11/1.74 % ------
% 1.11/1.74 % Current options:
% 1.11/1.74 % ------
% 1.11/1.74
% 1.11/1.74
% 1.11/1.74 %
% 1.11/1.74
% 1.11/1.74 % ------ Proving...
% 1.11/1.74 %
% 1.11/1.74
% 1.11/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.11/1.74
% 1.11/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.11/1.74
% 1.11/1.74
%------------------------------------------------------------------------------