%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP285-1 : 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 : n004.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 01:32:43 PM UTC 2026
% Result : Unsatisfiable 3.87s 1.73s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 33
% Syntax : Number of formulae : 275 ( 87 unt; 11 def)
% Number of atoms : 974 ( 498 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 498 ( 206 ~; 292 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).
fof(f6,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).
fof(f8,plain,
( sk_c9 = inverse(sk_c3)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_3) ).
fof(f10,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).
fof(f12,plain,
( sk_c7 = inverse(sk_c4)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).
fof(f14,plain,
( sk_c7 = multiply(sk_c9,sk_c6)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_6) ).
fof(f16,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).
fof(f18,plain,
( sk_c9 = inverse(sk_c5)
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).
fof(f20,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).
fof(f22,plain,
( sk_c9 = inverse(sk_c3)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).
fof(f24,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c8 = multiply(sk_c1,sk_c9) ),
inference(reorient_equations,[],[f23]) ).
fof(f33,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).
fof(f34,plain,
( sk_c8 = multiply(sk_c3,sk_c9)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f33]) ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).
fof(f36,plain,
( sk_c9 = inverse(sk_c3)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f35]) ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).
fof(f38,plain,
( sk_c8 = multiply(sk_c4,sk_c7)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f37]) ).
fof(f45,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).
fof(f46,plain,
( sk_c9 = inverse(sk_c5)
| sk_c9 = inverse(sk_c1) ),
inference(reorient_equations,[],[f45]) ).
fof(f55,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_26) ).
fof(f56,plain,
( sk_c7 = multiply(sk_c9,sk_c6)
| sk_c7 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f55]) ).
fof(f57,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).
fof(f58,plain,
( sk_c6 = multiply(sk_c5,sk_c9)
| sk_c7 = multiply(sk_c2,sk_c9) ),
inference(reorient_equations,[],[f57]) ).
fof(f61,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c9) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4,X5] :
( sk_c9 != inverse(X5)
| multiply(X5,sk_c9) != X4
| sk_c7 != multiply(sk_c9,X4)
| sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c7 != multiply(X1,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(reorient_equations,[],[f61]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X5] :
( sk_c9 != inverse(X5)
| sk_c7 != multiply(sk_c9,multiply(X5,sk_c9))
| sk_c7 != inverse(X3)
| sk_c8 != multiply(X3,sk_c7)
| sk_c9 != inverse(X2)
| sk_c8 != multiply(X2,sk_c9)
| sk_c7 != multiply(X1,sk_c9)
| inverse(X0) != sk_c9
| sk_c8 != multiply(X0,sk_c9)
| multiply(sk_c9,sk_c8) != sk_c7 ),
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_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_85,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_86,negated_conjecture,
( ( multiply(sk_c4,sk_c7) = sk_c8 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_87,negated_conjecture,
( ( inverse(sk_c4) = sk_c7 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_88,negated_conjecture,
( ( multiply(sk_c9,sk_c6) = sk_c7 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_89,negated_conjecture,
( ( multiply(sk_c5,sk_c9) = sk_c6 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_90,negated_conjecture,
( ( inverse(sk_c5) = sk_c9 )
| ( multiply(sk_c9,sk_c8) = sk_c7 ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_91,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_92,negated_conjecture,
( ( inverse(sk_c3) = sk_c9 )
| ( multiply(sk_c1,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_93,negated_conjecture,
( ( multiply(sk_c1,sk_c9) = sk_c8 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_98,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c3,sk_c9) = sk_c8 ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_99,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c3) = sk_c9 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_100,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( multiply(sk_c4,sk_c7) = sk_c8 ) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_104,negated_conjecture,
( ( inverse(sk_c1) = sk_c9 )
| ( inverse(sk_c5) = sk_c9 ) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_109,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c7 )
| ( multiply(sk_c9,sk_c6) = sk_c7 ) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_110,negated_conjecture,
( ( multiply(sk_c2,sk_c9) = sk_c7 )
| ( multiply(sk_c5,sk_c9) = sk_c6 ) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_112,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( inverse(X3) != sk_c7 )
| ( inverse(X2) != sk_c9 )
| ( inverse(X1) != sk_c9 )
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,sk_c8) != sk_c7 )
| ( multiply(X4,sk_c9) != sk_c7 )
| ( multiply(X3,sk_c7) != sk_c8 )
| ( multiply(X1,sk_c9) != sk_c8 )
| ( multiply(X0,sk_c9) != sk_c8 )
| ( multiply(sk_c9,multiply(X2,sk_c9)) != sk_c7 ) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_389,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,sk_c9) != sk_c7 ) ),
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_c9 )
| ( multiply(X0,sk_c9) != 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_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
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_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c7 ) ),
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
| ( multiply(sk_c9,sk_c8) != sk_c7 ) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_112]) ).
tcf(c_394,definition,
iPr_def_14 = multiply(sk_c9,sk_c8),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_395,definition,
iPr_def_15 = multiply(sk_c2,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_396,definition,
iPr_def_16 = inverse(sk_c5),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_397,definition,
iPr_def_17 = multiply(sk_c5,sk_c9),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_398,definition,
iPr_def_18 = multiply(sk_c9,sk_c6),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_399,definition,
iPr_def_19 = inverse(sk_c4),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_400,definition,
iPr_def_20 = multiply(sk_c4,sk_c7),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_401,definition,
iPr_def_21 = inverse(sk_c3),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_402,definition,
iPr_def_22 = multiply(sk_c3,sk_c9),
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
| ( iPr_def_14 != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_393,c_394]) ).
tcf(c_406,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(sk_c9,multiply(X0,sk_c9)) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_392]) ).
tcf(c_407,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,sk_c7) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_391]) ).
tcf(c_409,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,sk_c9) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_390]) ).
tcf(c_410,negated_conjecture,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,sk_c9) != sk_c7 ) ),
inference(demodulation,[status(thm)],[c_389]) ).
tcf(c_412,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_110,c_397]) ).
tcf(c_413,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_15 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_109,c_398]) ).
tcf(c_418,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_16 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_104,c_403]) ).
tcf(c_422,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_423,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_424,negated_conjecture,
( ( iPr_def_23 = sk_c9 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_429,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_20 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_93]) ).
tcf(c_430,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_21 = sk_c9 ) ),
inference(demodulation,[status(thm)],[c_92]) ).
tcf(c_431,negated_conjecture,
( ( iPr_def_24 = sk_c8 )
| ( iPr_def_22 = sk_c8 ) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_432,negated_conjecture,
( ( iPr_def_16 = sk_c9 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_433,negated_conjecture,
( ( iPr_def_17 = sk_c6 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_89]) ).
tcf(c_434,negated_conjecture,
( ( iPr_def_18 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_435,negated_conjecture,
( ( iPr_def_19 = sk_c7 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_436,negated_conjecture,
( ( iPr_def_20 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_437,negated_conjecture,
( ( iPr_def_21 = sk_c9 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_438,negated_conjecture,
( ( iPr_def_22 = sk_c8 )
| ( iPr_def_14 = sk_c7 ) ),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_439,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_440,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_714,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c9,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_412,c_398]) ).
tcf(c_778,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_23,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_423,c_394]) ).
tcf(c_793,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_424,c_422]) ).
tcf(c_794,plain,
( ( sk_c9 = iPr_def_23 )
| ( multiply(sk_c9,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_424,c_394]) ).
tcf(c_838,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_413,c_400]) ).
tcf(c_864,plain,
! [X0: $i] :
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_14 != X0 )
| ( sk_c7 != X0 ) ),
inference(instantiation,[status(thm)],[c_440]) ).
tcf(c_866,plain,
multiply(iPr_def_21,sk_c3) = identity,
inference(superposition,[status(thm)],[c_401,c_82]) ).
tcf(c_867,plain,
multiply(iPr_def_19,sk_c4) = identity,
inference(superposition,[status(thm)],[c_399,c_82]) ).
tcf(c_868,plain,
multiply(iPr_def_16,sk_c5) = identity,
inference(superposition,[status(thm)],[c_396,c_82]) ).
tcf(c_869,plain,
multiply(iPr_def_23,sk_c1) = identity,
inference(superposition,[status(thm)],[c_403,c_82]) ).
tcf(c_871,plain,
! [X0: $i,X1: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_440]) ).
tcf(c_872,plain,
! [X0: $i] :
( ( sk_c7 = X0 )
| ( sk_c7 != sk_c7 )
| ( X0 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_871]) ).
tcf(c_873,plain,
sk_c7 = sk_c7,
inference(instantiation,[status(thm)],[c_439]) ).
tcf(c_952,plain,
( ( sk_c8 = iPr_def_20 )
| ( multiply(sk_c9,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_429,c_394]) ).
tcf(c_969,plain,
( ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != sk_c7 )
| ( sk_c7 != sk_c7 ) ),
inference(instantiation,[status(thm)],[c_872]) ).
tcf(c_1025,plain,
( ( sk_c8 = iPr_def_22 )
| ( multiply(sk_c9,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_431,c_394]) ).
tcf(c_1098,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c9,iPr_def_17) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_433,c_398]) ).
tcf(c_1120,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_18) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_434,c_400]) ).
tcf(c_1143,plain,
( ( iPr_def_14 = sk_c7 )
| ( iPr_def_14 != iPr_def_18 )
| ( sk_c7 != iPr_def_18 ) ),
inference(instantiation,[status(thm)],[c_864]) ).
tcf(c_1160,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(sk_c4,iPr_def_19) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_435,c_400]) ).
tcf(c_1315,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c7 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_438,c_436]) ).
tcf(c_1366,plain,
! [X0: $i] : multiply(sk_c5,multiply(sk_c9,X0)) = multiply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_397,c_83]) ).
tcf(c_1368,plain,
! [X0: $i] : multiply(sk_c2,multiply(sk_c9,X0)) = multiply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_395,c_83]) ).
tcf(c_1370,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_82,c_83]) ).
tcf(c_1372,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_866,c_83]) ).
tcf(c_1373,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_867,c_83]) ).
tcf(c_1374,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_868,c_83]) ).
tcf(c_1375,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = multiply(identity,X0),
inference(superposition,[status(thm)],[c_869,c_83]) ).
tcf(c_1377,plain,
! [X0: $i] : multiply(iPr_def_23,multiply(sk_c1,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1375,c_81]) ).
tcf(c_1378,plain,
! [X0: $i] : multiply(iPr_def_16,multiply(sk_c5,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1374,c_81]) ).
tcf(c_1379,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(sk_c4,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1373,c_81]) ).
tcf(c_1380,plain,
! [X0: $i] : multiply(iPr_def_21,multiply(sk_c3,X0)) = X0,
inference(light_normalisation,[status(thm)],[c_1372,c_81]) ).
tcf(c_1802,plain,
( ~ iPr_def_10
| ( sk_c7 != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_395,c_410]) ).
tcf(c_1805,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10
| ( multiply(X0,multiply(X1,sk_c9)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_83,c_410]) ).
tcf(c_1867,plain,
( ~ iPr_def_12
| ( sk_c8 != iPr_def_20 )
| ( inverse(sk_c4) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_400,c_407]) ).
tcf(c_1868,plain,
( ~ iPr_def_12
| ( sk_c8 != sk_c7 )
| ( inverse(identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_81,c_407]) ).
tcf(c_1869,plain,
( ~ iPr_def_12
| ( sk_c8 != identity )
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_82,c_407]) ).
tcf(c_1886,plain,
( ~ iPr_def_12
| ( sk_c7 != iPr_def_19 )
| ( sk_c8 != iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_1867,c_399]) ).
tcf(c_2021,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_22 )
| ( inverse(sk_c3) != sk_c9 ) ),
inference(superposition,[status(thm)],[c_402,c_409]) ).
tcf(c_2031,plain,
! [X0: $i] :
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_11
| ( inverse(X0) != sk_c9 )
| ( multiply(X0,iPr_def_23) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_423,c_409]) ).
tcf(c_2047,plain,
( ~ iPr_def_11
| ( sk_c8 != iPr_def_22 )
| ( sk_c9 != iPr_def_21 ) ),
inference(light_normalisation,[status(thm)],[c_2021,c_401]) ).
tcf(c_2138,plain,
( ~ iPr_def_13
| ( inverse(inverse(sk_c9)) != sk_c9 )
| ( multiply(sk_c9,identity) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_82,c_406]) ).
tcf(c_2141,plain,
! [X0: $i] :
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_13
| ( inverse(X0) != sk_c9 )
| ( multiply(iPr_def_23,multiply(X0,iPr_def_23)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_793,c_406]) ).
tcf(c_3153,plain,
multiply(iPr_def_23,iPr_def_24) = sk_c9,
inference(superposition,[status(thm)],[c_404,c_1377]) ).
tcf(c_3167,plain,
multiply(iPr_def_16,iPr_def_17) = sk_c9,
inference(superposition,[status(thm)],[c_397,c_1378]) ).
tcf(c_3183,plain,
multiply(iPr_def_19,iPr_def_20) = sk_c7,
inference(superposition,[status(thm)],[c_400,c_1379]) ).
tcf(c_3188,plain,
multiply(iPr_def_21,iPr_def_22) = sk_c9,
inference(superposition,[status(thm)],[c_402,c_1380]) ).
tcf(c_3498,plain,
( ( sk_c9 = iPr_def_21 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_430,c_778]) ).
tcf(c_3508,plain,
( ( sk_c9 = iPr_def_21 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3498,c_3153]) ).
tcf(c_3550,plain,
( ( sk_c9 = iPr_def_14 )
| ( multiply(iPr_def_21,sk_c8) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3508,c_394]) ).
tcf(c_3757,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c9 = iPr_def_14 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3508,c_794]) ).
tcf(c_3775,plain,
( ( sk_c9 = iPr_def_23 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_3757,c_3188]) ).
tcf(c_3929,plain,
( ( sk_c7 = iPr_def_15 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_838,c_1379]) ).
tcf(c_3930,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c7 = iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_3929,c_3183]) ).
tcf(c_4300,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c9 = iPr_def_14 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3775,c_952]) ).
tcf(c_4330,plain,
( ( sk_c8 = iPr_def_20 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4300,c_3153]) ).
tcf(c_4378,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c9 = iPr_def_14 )
| ( multiply(iPr_def_23,iPr_def_24) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_3775,c_1025]) ).
tcf(c_4408,plain,
( ( sk_c8 = iPr_def_22 )
| ( sk_c9 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4378,c_3153]) ).
tcf(c_4502,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_1120,c_1379]) ).
tcf(c_4503,plain,
( ( sk_c7 = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4502,c_3183]) ).
tcf(c_4515,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_19,iPr_def_20) = iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_1160,c_1379]) ).
tcf(c_4516,plain,
( ( sk_c7 = iPr_def_19 )
| ( sk_c7 = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_4515,c_3183]) ).
tcf(c_4768,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,iPr_def_17) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_397,c_1805]) ).
tcf(c_4769,plain,
! [X0: $i] :
( ~ iPr_def_10
| ( multiply(X0,iPr_def_24) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_404,c_1805]) ).
tcf(c_4873,plain,
( ( sk_c7 = iPr_def_15 )
| ~ iPr_def_10
| ( sk_c7 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_714,c_4768]) ).
tcf(c_4897,plain,
~ iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_4769,c_1802,c_3930,c_4873]) ).
tcf(c_4899,plain,
( iPr_def_13
| iPr_def_12
| iPr_def_11
| ( sk_c7 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_405,c_4897]) ).
tcf(c_5935,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( sk_c9 = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4408,c_4330]) ).
tcf(c_6365,plain,
multiply(sk_c5,iPr_def_14) = multiply(iPr_def_17,sk_c8),
inference(superposition,[status(thm)],[c_394,c_1366]) ).
tcf(c_7468,plain,
multiply(sk_c2,iPr_def_14) = multiply(iPr_def_15,sk_c8),
inference(superposition,[status(thm)],[c_394,c_1368]) ).
tcf(c_8629,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( iPr_def_14 = iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_5935,c_793]) ).
tcf(c_10812,plain,
( ( sk_c9 = iPr_def_14 )
| ( multiply(iPr_def_21,iPr_def_22) = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_4408,c_3550]) ).
tcf(c_10829,plain,
sk_c9 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_10812,c_3188]) ).
tcf(c_10839,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_14,X0)) = multiply(iPr_def_17,X0),
inference(demodulation,[status(thm)],[c_1366,c_10829]) ).
tcf(c_10852,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_14,iPr_def_17) = iPr_def_18 ) ),
inference(demodulation,[status(thm)],[c_1098,c_10829]) ).
tcf(c_10884,plain,
multiply(iPr_def_16,iPr_def_17) = iPr_def_14,
inference(demodulation,[status(thm)],[c_3167,c_10829]) ).
tcf(c_10892,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != iPr_def_14 )
| ( multiply(X0,iPr_def_14) != sk_c8 ) ),
inference(demodulation,[status(thm)],[c_409,c_10829]) ).
tcf(c_10896,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_437,c_10829]) ).
tcf(c_10897,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_432,c_10829]) ).
tcf(c_10898,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c8 = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_430,c_10829]) ).
tcf(c_10899,plain,
multiply(sk_c1,iPr_def_14) = iPr_def_24,
inference(demodulation,[status(thm)],[c_404,c_10829]) ).
tcf(c_10900,plain,
multiply(sk_c3,iPr_def_14) = iPr_def_22,
inference(demodulation,[status(thm)],[c_402,c_10829]) ).
tcf(c_10902,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( sk_c8 = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_424,c_10829]) ).
tcf(c_10903,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_21 ) ),
inference(demodulation,[status(thm)],[c_423,c_10829]) ).
tcf(c_10909,plain,
multiply(sk_c5,iPr_def_14) = iPr_def_17,
inference(demodulation,[status(thm)],[c_397,c_10829]) ).
tcf(c_10910,plain,
multiply(sk_c2,iPr_def_14) = iPr_def_15,
inference(demodulation,[status(thm)],[c_395,c_10829]) ).
tcf(c_10911,plain,
multiply(iPr_def_14,sk_c8) = iPr_def_14,
inference(demodulation,[status(thm)],[c_394,c_10829]) ).
tcf(c_10912,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( iPr_def_14 = iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_418,c_10829]) ).
tcf(c_10921,plain,
multiply(iPr_def_15,sk_c8) = iPr_def_15,
inference(demodulation,[status(thm)],[c_7468,c_10910]) ).
tcf(c_10922,plain,
multiply(iPr_def_17,sk_c8) = iPr_def_17,
inference(demodulation,[status(thm)],[c_6365,c_10909]) ).
tcf(c_11079,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_21 )
| ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_10896,c_407]) ).
tcf(c_11127,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_12
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_14) != sk_c8 ) ),
inference(superposition,[status(thm)],[c_10897,c_407]) ).
tcf(c_11542,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_1370,c_81]) ).
tcf(c_11548,plain,
! [X0: $i] : multiply(inverse(identity),X0) = X0,
inference(superposition,[status(thm)],[c_81,c_11542]) ).
tcf(c_11549,plain,
! [X0: $i] : multiply(inverse(inverse(X0)),identity) = X0,
inference(superposition,[status(thm)],[c_82,c_11542]) ).
tcf(c_11577,plain,
! [X0: $i] : multiply(inverse(iPr_def_21),X0) = multiply(sk_c3,X0),
inference(superposition,[status(thm)],[c_1380,c_11542]) ).
tcf(c_11579,plain,
! [X0: $i] : multiply(inverse(iPr_def_16),X0) = multiply(sk_c5,X0),
inference(superposition,[status(thm)],[c_1378,c_11542]) ).
tcf(c_11580,plain,
! [X0: $i] : multiply(inverse(iPr_def_23),X0) = multiply(sk_c1,X0),
inference(superposition,[status(thm)],[c_1377,c_11542]) ).
tcf(c_11606,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(X0)),X1) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_11542,c_11542]) ).
tcf(c_11679,plain,
! [X0: $i] : multiply(X0,identity) = X0,
inference(demodulation,[status(thm)],[c_11549,c_11606]) ).
tcf(c_11693,plain,
inverse(identity) = identity,
inference(superposition,[status(thm)],[c_11679,c_11548]) ).
tcf(c_11728,plain,
multiply(inverse(iPr_def_14),iPr_def_14) = sk_c8,
inference(superposition,[status(thm)],[c_10911,c_11542]) ).
tcf(c_11743,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_15,iPr_def_20) = iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_436,c_10921]) ).
tcf(c_11750,plain,
multiply(inverse(iPr_def_15),iPr_def_15) = sk_c8,
inference(superposition,[status(thm)],[c_10921,c_11542]) ).
tcf(c_11794,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(inverse(iPr_def_15),iPr_def_15) = iPr_def_20 ) ),
inference(superposition,[status(thm)],[c_11743,c_11542]) ).
tcf(c_11796,plain,
( ( sk_c7 = iPr_def_14 )
| ( sk_c8 = iPr_def_20 ) ),
inference(light_normalisation,[status(thm)],[c_11794,c_11750]) ).
tcf(c_11882,plain,
( ( sk_c7 = iPr_def_14 )
| ( multiply(iPr_def_17,iPr_def_20) = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_436,c_10922]) ).
tcf(c_12315,plain,
sk_c8 = identity,
inference(demodulation,[status(thm)],[c_11728,c_82]) ).
tcf(c_12330,plain,
( ( iPr_def_14 = iPr_def_23 )
| ( identity = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_10902,c_12315]) ).
tcf(c_12332,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( identity = iPr_def_24 ) ),
inference(demodulation,[status(thm)],[c_10898,c_12315]) ).
tcf(c_12340,plain,
( ( identity = iPr_def_24 )
| ( identity = iPr_def_22 ) ),
inference(demodulation,[status(thm)],[c_431,c_12315]) ).
tcf(c_13097,plain,
multiply(sk_c3,identity) = inverse(iPr_def_21),
inference(superposition,[status(thm)],[c_11577,c_11679]) ).
tcf(c_13119,plain,
inverse(iPr_def_21) = sk_c3,
inference(demodulation,[status(thm)],[c_13097,c_11679]) ).
tcf(c_13212,plain,
( ~ iPr_def_12
| ( sk_c7 != identity ) ),
inference(light_normalisation,[status(thm)],[c_1868,c_11693,c_12315]) ).
tcf(c_13239,plain,
( ( sk_c7 = iPr_def_14 )
| ~ iPr_def_12
| ( identity != iPr_def_19 ) ),
inference(superposition,[status(thm)],[c_435,c_13212]) ).
tcf(c_13303,plain,
( ( sk_c7 = iPr_def_14 )
| ~ iPr_def_12 ),
inference(global_subsumption_just,[status(thm)],[c_13239,c_1886,c_4516,c_11796]) ).
tcf(c_13365,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_16,X0)) = X0,
inference(superposition,[status(thm)],[c_11579,c_11542]) ).
tcf(c_13366,plain,
multiply(sk_c5,identity) = inverse(iPr_def_16),
inference(superposition,[status(thm)],[c_11579,c_11679]) ).
tcf(c_13383,plain,
inverse(iPr_def_16) = sk_c5,
inference(demodulation,[status(thm)],[c_13366,c_11679]) ).
tcf(c_13439,plain,
( ~ iPr_def_12
| ( inverse(inverse(sk_c7)) != sk_c7 ) ),
inference(ground_joinability,[status(thm)],[c_1869,c_12315]) ).
tcf(c_13713,plain,
multiply(sk_c1,identity) = inverse(iPr_def_23),
inference(superposition,[status(thm)],[c_11580,c_11679]) ).
tcf(c_13746,plain,
inverse(iPr_def_23) = sk_c1,
inference(demodulation,[status(thm)],[c_13713,c_11679]) ).
tcf(c_13748,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_10912,c_13746]) ).
tcf(c_13749,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_10903,c_13746]) ).
tcf(c_13750,plain,
( ( iPr_def_20 = iPr_def_22 )
| ( inverse(iPr_def_14) = sk_c1 ) ),
inference(superposition,[status(thm)],[c_8629,c_13746]) ).
tcf(c_13798,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( inverse(X0) != iPr_def_14 )
| ( multiply(X0,iPr_def_14) != identity ) ),
inference(light_normalisation,[status(thm)],[c_10892,c_12315]) ).
tcf(c_13814,plain,
( ~ iPr_def_11
| ( identity != iPr_def_24 )
| ( inverse(sk_c1) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_10899,c_13798]) ).
tcf(c_13815,plain,
( ~ iPr_def_11
| ( identity != iPr_def_22 )
| ( inverse(sk_c3) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_10900,c_13798]) ).
tcf(c_13822,plain,
( ~ iPr_def_11
| ( iPr_def_14 != iPr_def_21 )
| ( identity != iPr_def_22 ) ),
inference(light_normalisation,[status(thm)],[c_13815,c_401]) ).
tcf(c_13826,plain,
( ~ iPr_def_11
| ( iPr_def_14 != iPr_def_23 )
| ( identity != iPr_def_24 ) ),
inference(light_normalisation,[status(thm)],[c_13814,c_403]) ).
tcf(c_14195,plain,
( ~ iPr_def_13
| ( inverse(inverse(iPr_def_14)) != iPr_def_14 )
| ( multiply(iPr_def_14,identity) != sk_c7 ) ),
inference(light_normalisation,[status(thm)],[c_2138,c_10829]) ).
tcf(c_14196,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(inverse(iPr_def_14)) != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_14195,c_11679]) ).
tcf(c_14550,plain,
( ( sk_c9 = iPr_def_21 )
| ~ iPr_def_11 ),
inference(global_subsumption_just,[status(thm)],[c_2031,c_10903,c_12340,c_12332,c_12330,c_13826,c_13822]) ).
tcf(c_14552,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_14550,c_2047,c_10902,c_12340,c_12332,c_13826,c_13822,c_14550]) ).
tcf(c_14558,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c7 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4899,c_14552]) ).
tcf(c_14619,plain,
( iPr_def_13
| iPr_def_12
| ( sk_c7 = iPr_def_14 )
| ( iPr_def_14 != iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_434,c_14558]) ).
tcf(c_14769,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c1) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_13748,c_14196]) ).
tcf(c_14774,plain,
( ( iPr_def_14 = iPr_def_16 )
| ~ iPr_def_13
| ( iPr_def_14 != iPr_def_23 )
| ( sk_c7 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_14769,c_403]) ).
tcf(c_14824,plain,
( ( iPr_def_14 = iPr_def_21 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c1) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_13749,c_14196]) ).
tcf(c_14829,plain,
( ( iPr_def_14 = iPr_def_21 )
| ~ iPr_def_13
| ( iPr_def_14 != iPr_def_23 )
| ( sk_c7 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_14824,c_403]) ).
tcf(c_14844,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c1) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_13750,c_14196]) ).
tcf(c_14846,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_13
| ( iPr_def_14 != iPr_def_23 )
| ( sk_c7 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_14844,c_403]) ).
tcf(c_15054,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_21 )
| ( multiply(X0,iPr_def_14) != sk_c8 )
| ( inverse(X0) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_11079,c_4899,c_10903,c_10896,c_11079,c_12340,c_12332,c_12330,c_13826,c_13822,c_14829]) ).
tcf(c_15055,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_21 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_14) != sk_c8 ) ),
inference(renaming,[status(thm)],[c_15054]) ).
tcf(c_15057,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_21 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_14) != identity ) ),
inference(light_normalisation,[status(thm)],[c_15055,c_12315]) ).
tcf(c_15068,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( inverse(inverse(iPr_def_14)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_82,c_15057]) ).
tcf(c_15138,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ( multiply(X0,iPr_def_14) != sk_c8 )
| ( inverse(X0) != sk_c7 ) ),
inference(global_subsumption_just,[status(thm)],[c_11127,c_10912,c_10897,c_11127,c_14558,c_14774]) ).
tcf(c_15139,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_14) != sk_c8 ) ),
inference(renaming,[status(thm)],[c_15138]) ).
tcf(c_15141,plain,
! [X0: $i] :
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(X0) != sk_c7 )
| ( multiply(X0,iPr_def_14) != identity ) ),
inference(light_normalisation,[status(thm)],[c_15139,c_12315]) ).
tcf(c_15152,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( inverse(inverse(iPr_def_14)) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_82,c_15141]) ).
tcf(c_15285,plain,
( ( iPr_def_20 = iPr_def_22 )
| ~ iPr_def_13 ),
inference(global_subsumption_just,[status(thm)],[c_2141,c_1315,c_8629,c_14846]) ).
tcf(c_17632,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( inverse(sk_c1) != sk_c7 ) ),
inference(superposition,[status(thm)],[c_13749,c_15068]) ).
tcf(c_17634,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( sk_c7 != iPr_def_23 ) ),
inference(light_normalisation,[status(thm)],[c_17632,c_403]) ).
tcf(c_17654,plain,
( ( iPr_def_14 = iPr_def_21 )
| ( iPr_def_14 != iPr_def_23 ) ),
inference(superposition,[status(thm)],[c_10896,c_17634]) ).
tcf(c_17684,plain,
iPr_def_14 = iPr_def_21,
inference(global_subsumption_just,[status(thm)],[c_17654,c_10903,c_17654]) ).
tcf(c_17703,plain,
inverse(iPr_def_14) = sk_c3,
inference(demodulation,[status(thm)],[c_13119,c_17684]) ).
tcf(c_17710,plain,
inverse(sk_c3) = iPr_def_14,
inference(demodulation,[status(thm)],[c_401,c_17684]) ).
tcf(c_17726,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_14 )
| ( inverse(sk_c3) != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_14196,c_17703]) ).
tcf(c_17728,plain,
( ~ iPr_def_13
| ( sk_c7 != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17726,c_17710]) ).
tcf(c_17965,plain,
( ( iPr_def_14 = iPr_def_16 )
| ( sk_c7 != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_15152,c_17703,c_17710]) ).
tcf(c_17968,plain,
iPr_def_14 = iPr_def_16,
inference(forward_subsumption_resolution,[status(thm)],[c_17965,c_10897]) ).
tcf(c_17982,plain,
! [X0: $i] : multiply(sk_c5,multiply(iPr_def_14,X0)) = X0,
inference(demodulation,[status(thm)],[c_13365,c_17968]) ).
tcf(c_17984,plain,
inverse(iPr_def_14) = sk_c5,
inference(demodulation,[status(thm)],[c_13383,c_17968]) ).
tcf(c_17986,plain,
multiply(iPr_def_14,iPr_def_17) = iPr_def_14,
inference(demodulation,[status(thm)],[c_10884,c_17968]) ).
tcf(c_17989,plain,
sk_c3 = sk_c5,
inference(light_normalisation,[status(thm)],[c_17984,c_17703]) ).
tcf(c_17990,plain,
! [X0: $i] : multiply(iPr_def_17,X0) = X0,
inference(demodulation,[status(thm)],[c_10839,c_17982]) ).
tcf(c_17993,plain,
( ( iPr_def_17 = iPr_def_20 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_11882,c_17990]) ).
tcf(c_18005,plain,
( ( iPr_def_14 = iPr_def_18 )
| ( sk_c7 = iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_10852,c_17986]) ).
tcf(c_18010,plain,
multiply(sk_c3,iPr_def_14) = iPr_def_17,
inference(demodulation,[status(thm)],[c_10909,c_17989]) ).
tcf(c_18017,plain,
iPr_def_17 = iPr_def_22,
inference(demodulation,[status(thm)],[c_10900,c_18010]) ).
tcf(c_18026,plain,
( ( iPr_def_17 = iPr_def_20 )
| ~ iPr_def_13 ),
inference(demodulation,[status(thm)],[c_15285,c_18017]) ).
tcf(c_18082,plain,
~ iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_18026,c_873,c_969,c_1143,c_4503,c_17728,c_18005]) ).
tcf(c_18084,plain,
( iPr_def_12
| ( sk_c7 != iPr_def_14 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_14558,c_18082]) ).
tcf(c_18093,plain,
sk_c7 = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_17993,c_13303,c_14619,c_18005,c_18082]) ).
tcf(c_18100,plain,
( ~ iPr_def_12
| ( inverse(inverse(iPr_def_14)) != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_13439,c_18093]) ).
tcf(c_18118,plain,
~ iPr_def_12,
inference(ground_joinability,[status(thm)],[c_18100,c_17703,c_17710]) ).
tcf(c_18132,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18118,c_18093,c_18084]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP285-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 14:21:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.87/1.73 % SZS status Started for theBenchmark.p
% 3.87/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 3.87/1.73
% 3.87/1.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.87/1.73
% 3.87/1.73 % ------ iProver source info
% 3.87/1.73
% 3.87/1.73 % git: date: 2026-07-19 20:42:38 +0200
% 3.87/1.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.87/1.73 % git: non_committed_changes: false
% 3.87/1.73
% 3.87/1.73 % ------ Parsing...% successful
% 3.87/1.73
% 3.87/1.73
% 3.87/1.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.87/1.73
% 3.87/1.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.87/1.73
% 3.87/1.73 % ------ Preprocessing... gs_s sp: 5 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.87/1.73
% 3.87/1.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.87/1.73 % ------ Proving...
% 3.87/1.73 % ------ Problem Properties
% 3.87/1.73
% 3.87/1.73 %
% 3.87/1.73 % clauses 47
% 3.87/1.73 % conjectures 33
% 3.87/1.73 % EPR 29
% 3.87/1.73 % Horn 18
% 3.87/1.73 % unary 14
% 3.87/1.73 % binary 29
% 3.87/1.73 % lits 86
% 3.87/1.73 % lits eq 78
% 3.87/1.73 % fd_pure 0
% 3.87/1.73 % fd_pseudo 0
% 3.87/1.73 % fd_cond 0
% 3.87/1.73 % fd_pseudo_cond 0
% 3.87/1.73 % AC symbols 0
% 3.87/1.73
% 3.87/1.73 % ------ Schedule dynamic 5 is on
% 3.87/1.73
% 3.87/1.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.87/1.73
% 3.87/1.73
% 3.87/1.73 % ------
% 3.87/1.73 % Current options:
% 3.87/1.73 % ------
% 3.87/1.73
% 3.87/1.73
% 3.87/1.73 %
% 3.87/1.73
% 3.87/1.73 % ------ Proving...
% 3.87/1.73 %
% 3.87/1.73
% 3.87/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 3.87/1.73
% 3.87/1.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.87/1.74
% 3.87/1.74
%------------------------------------------------------------------------------