%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP432-1 : TPTP v9.3.1. Released v2.6.0.
% 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 01:34:05 PM UTC 2026
% Result : Unsatisfiable 13.11s 7.77s
% Output : CNFRefutation 13.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 2
% Syntax : Number of formulae : 227 ( 227 unt; 0 def)
% Number of atoms : 865 ( 226 equ)
% Maximal formula atoms : 1 ( 3 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 542 ( 0 sgn 542 !; 0 ?; 538 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : multiply(X0,inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0)))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms_3) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X0)))) = X3,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(X0,inverse(multiply(inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),X4))),multiply(multiply(multiply(X5,inverse(X5)),inverse(X3)),X0)))) = X4,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))),multiply(X2,X0)))) = X3,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X0))),multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X5)))))),inverse(multiply(X5,X2))) = X4,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))),multiply(X3,inverse(X3))) = multiply(X4,inverse(multiply(multiply(X1,multiply(X5,inverse(X5))),multiply(X2,X4)))),
inference(superposition,[status(thm)],[c_62,c_51]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : multiply(inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))),multiply(X3,inverse(X3))),multiply(X1,X4))),inverse(multiply(multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X4,X6))),multiply(X7,inverse(X7))),X2))) = X6,
inference(superposition,[status(thm)],[c_62,c_62]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : inverse(multiply(multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))),multiply(X3,inverse(X3))),multiply(X1,X4))) = multiply(X5,inverse(multiply(multiply(multiply(multiply(X6,inverse(X6)),inverse(X2)),multiply(X7,inverse(X7))),multiply(X4,X5)))),
inference(superposition,[status(thm)],[c_62,c_62]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : multiply(X0,inverse(multiply(multiply(X1,multiply(X2,inverse(X2))),multiply(multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X1))),multiply(X5,inverse(X5))),X0)))) = multiply(X4,multiply(X6,inverse(X6))),
inference(superposition,[status(thm)],[c_62,c_62]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : multiply(X0,inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))),multiply(X4,inverse(X4))),multiply(X2,X5))),multiply(multiply(multiply(X6,inverse(X6)),inverse(X3)),X7))),multiply(multiply(multiply(X8,inverse(X8)),inverse(X5)),X0)))) = X7,
inference(superposition,[status(thm)],[c_62,c_60]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X0))),X3))),multiply(multiply(multiply(X4,inverse(X4)),inverse(X2)),X5))),multiply(multiply(multiply(X6,inverse(X6)),inverse(X3)),multiply(multiply(X7,inverse(X7)),inverse(multiply(X8,X9)))))),inverse(multiply(X9,X5))) = X8,
inference(superposition,[status(thm)],[c_60,c_63]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : multiply(inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X4))),multiply(X5,inverse(X5))),multiply(X3,X6))),X0))),multiply(multiply(X7,inverse(X7)),inverse(multiply(X8,X6)))))),inverse(X4)) = X8,
inference(superposition,[status(thm)],[c_62,c_63]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] : inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X0))),multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X5)))))) = multiply(X6,inverse(multiply(inverse(multiply(X5,X2)),multiply(multiply(multiply(X7,inverse(X7)),inverse(X4)),X6)))),
inference(superposition,[status(thm)],[c_63,c_51]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : multiply(X0,inverse(multiply(multiply(multiply(multiply(X1,inverse(X1)),inverse(X2)),multiply(X3,inverse(X3))),multiply(inverse(multiply(X4,multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X6,X4))),multiply(multiply(X7,inverse(X7)),inverse(multiply(X2,X8)))))),X0)))) = inverse(multiply(X8,X6)),
inference(superposition,[status(thm)],[c_63,c_62]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(multiply(X1,multiply(X2,inverse(X2))),multiply(X3,X0)))) = iPr_def_10(X1,X3),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_74]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))),multiply(X3,inverse(X3))) = iPr_def_10(X1,X2),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_74]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,inverse(X1))) = iPr_def_10(X2,iPr_def_10(X0,X2)),
inference(demodulation,[status(thm)],[c_78,c_148,c_149]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(multiply(multiply(X0,inverse(X0)),inverse(X1)),X2) = inverse(multiply(iPr_def_10(X3,X1),multiply(X3,X2))),
inference(demodulation,[status(thm)],[c_77,c_148,c_149]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(iPr_def_10(X0,X1),multiply(X0,X2))),inverse(multiply(iPr_def_10(X2,X3),X1))) = X3,
inference(demodulation,[status(thm)],[c_76,c_149]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(X0,inverse(multiply(inverse(multiply(X1,X2)),multiply(multiply(multiply(X3,inverse(X3)),inverse(X4)),X0)))) = iPr_def_11(X1,X2,X4),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_142]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X0))),multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X5)))))) = iPr_def_11(X5,X2,X4),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_142]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(multiply(multiply(X0,inverse(X0)),inverse(X1)),iPr_def_11(X2,X3,X1)) = inverse(multiply(X2,X3)),
inference(demodulation,[status(thm)],[c_147,c_148,c_166]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(iPr_def_11(X0,inverse(multiply(iPr_def_10(X1,X2),multiply(X1,X0))),X3),inverse(X2)) = X3,
inference(demodulation,[status(thm)],[c_139,c_149,c_166]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : iPr_def_11(inverse(multiply(iPr_def_10(X0,X1),multiply(X0,X2))),multiply(multiply(multiply(X3,inverse(X3)),inverse(X1)),X4),X2) = X4,
inference(demodulation,[status(thm)],[c_104,c_149,c_165]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2))),X1) = X2,
inference(demodulation,[status(thm)],[c_62,c_148]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_11(X0,multiply(multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X0))),X3),X2) = X3,
inference(demodulation,[status(thm)],[c_60,c_165]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_11(X0,X1,X2),inverse(multiply(X0,X1))) = X2,
inference(demodulation,[status(thm)],[c_63,c_166]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,inverse(X1))) = multiply(X0,multiply(X2,inverse(X2))),
inference(superposition,[status(thm)],[c_150,c_150]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_10(X0,X1),multiply(X0,multiply(X2,inverse(X2)))) = multiply(X1,multiply(X3,inverse(X3))),
inference(superposition,[status(thm)],[c_148,c_189]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(iPr_def_10(X0,X1),multiply(X0,X2))),inverse(multiply(multiply(X3,multiply(X4,inverse(X4))),X1))) = iPr_def_10(X3,X2),
inference(superposition,[status(thm)],[c_150,c_163]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : iPr_def_10(multiply(X0,multiply(X1,inverse(X1))),multiply(X2,multiply(X3,inverse(X3)))) = multiply(iPr_def_10(X0,X2),multiply(X4,inverse(X4))),
inference(superposition,[status(thm)],[c_148,c_149]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,iPr_def_10(X2,X1)))) = X2,
inference(superposition,[status(thm)],[c_149,c_51]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : iPr_def_10(multiply(multiply(X0,inverse(X0)),inverse(iPr_def_10(X1,X2))),multiply(multiply(X3,inverse(X3)),inverse(multiply(X1,X2)))) = multiply(X4,inverse(X4)),
inference(superposition,[status(thm)],[c_149,c_189]) ).
tcf(c_477,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,iPr_def_10(X1,X0),X1) = multiply(X2,inverse(X2)),
inference(superposition,[status(thm)],[c_149,c_190]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(iPr_def_10(X0,multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(X4,inverse(X4))))),multiply(X0,X5))) = iPr_def_10(X3,X5),
inference(superposition,[status(thm)],[c_51,c_162]) ).
tcf(c_489,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : inverse(multiply(iPr_def_10(X0,multiply(multiply(X1,multiply(X2,inverse(X2))),multiply(X3,multiply(X4,inverse(X4))))),multiply(X0,X5))) = iPr_def_10(iPr_def_10(X1,X3),X5),
inference(superposition,[status(thm)],[c_148,c_162]) ).
tcf(c_494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(multiply(X0,multiply(X1,inverse(X1))),multiply(X2,X3))) = iPr_def_10(multiply(multiply(X4,inverse(X4)),inverse(iPr_def_10(X0,X2))),X3),
inference(superposition,[status(thm)],[c_150,c_162]) ).
tcf(c_512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(iPr_def_10(X0,X1),multiply(X0,X2))) = inverse(multiply(iPr_def_10(X3,X1),multiply(X3,X2))),
inference(superposition,[status(thm)],[c_162,c_162]) ).
tcf(c_515,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(iPr_def_10(X0,multiply(X1,X2)),multiply(X0,X1))) = X2,
inference(superposition,[status(thm)],[c_162,c_189]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(iPr_def_10(X0,multiply(X1,X2)),multiply(X0,X1))),iPr_def_10(multiply(multiply(X3,inverse(X3)),inverse(X4)),X2)) = X4,
inference(superposition,[status(thm)],[c_162,c_163]) ).
tcf(c_584,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : iPr_def_11(inverse(multiply(iPr_def_10(X0,multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(X4,inverse(X4))))),multiply(X0,X5))),multiply(X3,X6),X5) = X6,
inference(superposition,[status(thm)],[c_51,c_180]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(X1,inverse(X1))) = iPr_def_12(X0),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_348]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(iPr_def_10(X0,X1),multiply(X0,X2))) = iPr_def_13(X1,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_512]) ).
tcf(c_597,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(X0,X1),iPr_def_12(X0)) = iPr_def_12(X1),
inference(demodulation,[status(thm)],[c_416,c_593]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,iPr_def_10(multiply(multiply(X1,inverse(X1)),inverse(X2)),X0)) = X2,
inference(demodulation,[status(thm)],[c_538,c_515]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_12(X0),iPr_def_12(X1)) = iPr_def_12(iPr_def_10(X0,X1)),
inference(demodulation,[status(thm)],[c_459,c_593]) ).
tcf(c_612,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_13(X0,X1),inverse(multiply(iPr_def_12(X2),X0))) = iPr_def_10(X2,X1),
inference(demodulation,[status(thm)],[c_439,c_593,c_595]) ).
tcf(c_621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(multiply(multiply(X0,inverse(X0)),inverse(iPr_def_10(X1,X2))),X3) = inverse(multiply(iPr_def_12(X1),multiply(X2,X3))),
inference(demodulation,[status(thm)],[c_494,c_593]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(iPr_def_12(X0),multiply(X1,multiply(multiply(X2,inverse(X2)),inverse(multiply(X0,X1)))))) = multiply(X3,inverse(X3)),
inference(demodulation,[status(thm)],[c_474,c_621]) ).
tcf(c_626,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = iPr_def_14,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_14])],[c_625]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(multiply(iPr_def_12(X0),iPr_def_12(X1)),X2) = iPr_def_10(iPr_def_10(X0,X1),X2),
inference(demodulation,[status(thm)],[c_489,c_593,c_595]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(multiply(X0,iPr_def_12(multiply(iPr_def_14,inverse(multiply(X1,X0))))),X2) = iPr_def_10(X1,X2),
inference(demodulation,[status(thm)],[c_488,c_593,c_595,c_626]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_10(X0,X1),multiply(X0,X2),X1) = X2,
inference(demodulation,[status(thm)],[c_584,c_593,c_595,c_626,c_671]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(multiply(iPr_def_12(X1),multiply(X2,X0)))) = iPr_def_10(X1,X2),
inference(demodulation,[status(thm)],[c_148,c_593]) ).
tcf(c_742,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,iPr_def_10(X1,X0)) = iPr_def_12(X1),
inference(demodulation,[status(thm)],[c_150,c_593]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(multiply(multiply(X0,inverse(X0)),inverse(multiply(X1,X2)))) = iPr_def_10(X1,X2),
inference(demodulation,[status(thm)],[c_149,c_593]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i] : iPr_def_12(multiply(iPr_def_14,inverse(multiply(X0,X1)))) = iPr_def_10(X0,X1),
inference(demodulation,[status(thm)],[c_743,c_626]) ).
tcf(c_745,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(multiply(multiply(X0,inverse(X0)),inverse(X1)),X2) = iPr_def_13(X1,X2),
inference(demodulation,[status(thm)],[c_162,c_595]) ).
tcf(c_746,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_11(X0,iPr_def_13(X1,X0),X2),inverse(X1)) = X2,
inference(demodulation,[status(thm)],[c_172,c_595]) ).
tcf(c_747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_11(iPr_def_13(X0,X1),multiply(multiply(multiply(X2,inverse(X2)),inverse(X0)),X3),X1) = X3,
inference(demodulation,[status(thm)],[c_180,c_595]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_13(X0,X1),inverse(multiply(iPr_def_10(X1,X2),X0))) = X2,
inference(demodulation,[status(thm)],[c_163,c_595]) ).
tcf(c_749,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_13(X0,X1),multiply(multiply(iPr_def_14,inverse(X0)),X2),X1) = X2,
inference(demodulation,[status(thm)],[c_747,c_626]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(iPr_def_14,inverse(X0)),X1) = iPr_def_13(X0,X1),
inference(demodulation,[status(thm)],[c_745,c_626]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(multiply(iPr_def_14,inverse(X0)),iPr_def_11(X1,X2,X0)) = inverse(multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_170,c_626]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(iPr_def_14,inverse(multiply(X0,X1))),X0) = X1,
inference(demodulation,[status(thm)],[c_189,c_626]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i] : iPr_def_13(multiply(X0,X1),X0) = X1,
inference(demodulation,[status(thm)],[c_755,c_750]) ).
tcf(c_757,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,iPr_def_11(X1,X2,X0)) = inverse(multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_754,c_750]) ).
tcf(c_1721,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11(X0,inverse(X0),X1),inverse(iPr_def_14)) = X1,
inference(superposition,[status(thm)],[c_626,c_191]) ).
tcf(c_1722,plain,
! [X0: $i] : iPr_def_13(iPr_def_14,X0) = inverse(X0),
inference(superposition,[status(thm)],[c_626,c_756]) ).
tcf(c_1729,plain,
! [X0: $i] : multiply(X0,iPr_def_14) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_626,c_593]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(X0)) = iPr_def_13(iPr_def_12(X1),X1),
inference(superposition,[status(thm)],[c_593,c_756]) ).
tcf(c_1759,plain,
! [X0: $i] : iPr_def_10(iPr_def_14,X0) = iPr_def_13(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_626,c_750]) ).
tcf(c_1779,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X1,X0),X1) = iPr_def_14,
inference(superposition,[status(thm)],[c_477,c_626]) ).
tcf(c_1787,plain,
! [X0: $i] : iPr_def_12(multiply(iPr_def_14,inverse(iPr_def_14))) = iPr_def_10(X0,inverse(X0)),
inference(superposition,[status(thm)],[c_626,c_744]) ).
tcf(c_1788,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,multiply(X1,inverse(X1))) = iPr_def_12(multiply(iPr_def_14,inverse(iPr_def_12(X0)))),
inference(superposition,[status(thm)],[c_593,c_744]) ).
tcf(c_1807,plain,
! [X0: $i,X1: $i] : inverse(iPr_def_12(iPr_def_10(X0,X1))) = iPr_def_13(X1,inverse(X0)),
inference(superposition,[status(thm)],[c_593,c_595]) ).
tcf(c_1856,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(iPr_def_10(X0,X1),X2)) = iPr_def_13(X1,iPr_def_13(X2,X0)),
inference(superposition,[status(thm)],[c_748,c_756]) ).
tcf(c_1870,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(multiply(X0,inverse(X0)),inverse(multiply(X1,iPr_def_10(X2,X1)))) = iPr_def_12(multiply(iPr_def_14,inverse(X2))),
inference(superposition,[status(thm)],[c_470,c_744]) ).
tcf(c_1871,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,iPr_def_10(X1,X0))) = iPr_def_13(X1,multiply(X2,inverse(X2))),
inference(superposition,[status(thm)],[c_470,c_756]) ).
tcf(c_1876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,iPr_def_10(iPr_def_11(X1,iPr_def_10(X2,X1),X2),X0)) = multiply(X3,inverse(X3)),
inference(superposition,[status(thm)],[c_477,c_608]) ).
tcf(c_1878,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,iPr_def_10(X1,X0)) = multiply(X2,iPr_def_10(X1,X2)),
inference(superposition,[status(thm)],[c_470,c_608]) ).
tcf(c_1879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,iPr_def_10(multiply(iPr_def_11(X1,iPr_def_10(X2,X1),X2),inverse(X3)),X0)) = X3,
inference(superposition,[status(thm)],[c_477,c_608]) ).
tcf(c_1880,plain,
! [X0: $i,X1: $i] : multiply(X0,iPr_def_10(multiply(iPr_def_14,inverse(X1)),X0)) = X1,
inference(superposition,[status(thm)],[c_626,c_608]) ).
tcf(c_1886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(multiply(multiply(X0,inverse(X0)),inverse(X1)),X2) = iPr_def_11(iPr_def_10(X2,X3),X1,X3),
inference(superposition,[status(thm)],[c_608,c_715]) ).
tcf(c_1937,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(iPr_def_12(X0),multiply(X1,multiply(X2,inverse(X2)))) = multiply(X3,iPr_def_10(iPr_def_10(X0,X1),X3)),
inference(superposition,[status(thm)],[c_741,c_608]) ).
tcf(c_1954,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,iPr_def_10(X1,X0))) = iPr_def_11(iPr_def_13(iPr_def_14,X2),X1,X2),
inference(superposition,[status(thm)],[c_470,c_749]) ).
tcf(c_1989,plain,
! [X0: $i] : iPr_def_10(iPr_def_14,X0) = inverse(X0),
inference(demodulation,[status(thm)],[c_1759,c_1722]) ).
tcf(c_1990,plain,
! [X0: $i] : iPr_def_13(iPr_def_12(X0),X0) = iPr_def_14,
inference(demodulation,[status(thm)],[c_1730,c_626]) ).
tcf(c_1992,plain,
! [X0: $i,X1: $i] : multiply(X0,iPr_def_13(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_1880,c_750]) ).
tcf(c_1994,plain,
! [X0: $i] : iPr_def_10(X0,inverse(X0)) = iPr_def_12(iPr_def_14),
inference(demodulation,[status(thm)],[c_1787,c_626]) ).
tcf(c_1997,plain,
! [X0: $i,X1: $i] : multiply(X0,iPr_def_10(X1,X0)) = iPr_def_16(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_1878]) ).
tcf(c_2007,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X1,X0) = inverse(iPr_def_16(X1)),
inference(demodulation,[status(thm)],[c_1954,c_1722,c_1997]) ).
tcf(c_2008,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,multiply(X1,inverse(X1))) = inverse(iPr_def_16(X0)),
inference(demodulation,[status(thm)],[c_1871,c_1997]) ).
tcf(c_2009,plain,
! [X0: $i] : inverse(iPr_def_16(X0)) = iPr_def_13(X0,iPr_def_14),
inference(demodulation,[status(thm)],[c_2008,c_626]) ).
tcf(c_2011,plain,
! [X0: $i] : iPr_def_12(multiply(iPr_def_14,inverse(iPr_def_12(X0)))) = iPr_def_10(X0,iPr_def_14),
inference(demodulation,[status(thm)],[c_1788,c_626]) ).
tcf(c_2033,plain,
! [X0: $i] : iPr_def_16(multiply(iPr_def_14,inverse(X0))) = X0,
inference(demodulation,[status(thm)],[c_1879,c_1779,c_1997]) ).
tcf(c_2034,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = iPr_def_16(iPr_def_14),
inference(demodulation,[status(thm)],[c_1876,c_1779,c_1997]) ).
tcf(c_2035,plain,
iPr_def_16(iPr_def_14) = iPr_def_14,
inference(demodulation,[status(thm)],[c_2034,c_626]) ).
tcf(c_2045,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_10(X0,X1),X2,X1) = iPr_def_13(X2,X0),
inference(demodulation,[status(thm)],[c_1886,c_626,c_750]) ).
tcf(c_2059,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_12(X0),multiply(X1,multiply(X2,inverse(X2)))) = iPr_def_16(iPr_def_10(X0,X1)),
inference(demodulation,[status(thm)],[c_1937,c_1997]) ).
tcf(c_2060,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_12(X0),iPr_def_12(X1)) = iPr_def_16(iPr_def_10(X0,X1)),
inference(demodulation,[status(thm)],[c_2059,c_593]) ).
tcf(c_2067,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(X0,inverse(X0)),iPr_def_13(X1,iPr_def_14)) = iPr_def_12(multiply(iPr_def_14,inverse(X1))),
inference(demodulation,[status(thm)],[c_1870,c_1997,c_2009]) ).
tcf(c_2068,plain,
! [X0: $i] : iPr_def_10(iPr_def_14,iPr_def_13(X0,iPr_def_14)) = iPr_def_12(multiply(iPr_def_14,inverse(X0))),
inference(demodulation,[status(thm)],[c_2067,c_626]) ).
tcf(c_2141,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(iPr_def_16(iPr_def_10(X0,X1)),X2) = iPr_def_10(iPr_def_10(X0,X1),X2),
inference(demodulation,[status(thm)],[c_650,c_2060]) ).
tcf(c_2142,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_14,iPr_def_13(multiply(X0,X1),iPr_def_14)) = iPr_def_10(X0,X1),
inference(demodulation,[status(thm)],[c_744,c_2068]) ).
tcf(c_2143,plain,
! [X0: $i,X1: $i] : inverse(iPr_def_13(multiply(X0,X1),iPr_def_14)) = iPr_def_10(X0,X1),
inference(demodulation,[status(thm)],[c_2142,c_1989]) ).
tcf(c_2253,plain,
! [X0: $i,X1: $i] : inverse(iPr_def_11(X0,X1,iPr_def_14)) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[c_1722,c_757]) ).
tcf(c_2264,plain,
! [X0: $i] : inverse(iPr_def_10(X0,iPr_def_14)) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_1989,c_742]) ).
tcf(c_2329,plain,
! [X0: $i] : iPr_def_10(inverse(X0),iPr_def_12(iPr_def_14)) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_1994,c_742]) ).
tcf(c_2330,plain,
! [X0: $i] : iPr_def_13(X0,inverse(multiply(iPr_def_14,inverse(X0)))) = iPr_def_12(iPr_def_14),
inference(superposition,[status(thm)],[c_1994,c_750]) ).
tcf(c_2331,plain,
inverse(inverse(iPr_def_14)) = iPr_def_12(iPr_def_14),
inference(superposition,[status(thm)],[c_1994,c_1989]) ).
tcf(c_2335,plain,
! [X0: $i] : iPr_def_10(iPr_def_16(X0),iPr_def_13(X0,iPr_def_14)) = iPr_def_12(iPr_def_14),
inference(superposition,[status(thm)],[c_2009,c_1994]) ).
tcf(c_2338,plain,
! [X0: $i] : multiply(iPr_def_16(X0),iPr_def_13(X0,iPr_def_14)) = iPr_def_14,
inference(superposition,[status(thm)],[c_2009,c_626]) ).
tcf(c_2372,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,X1),iPr_def_12(X0)) = iPr_def_16(X1),
inference(superposition,[status(thm)],[c_742,c_1997]) ).
tcf(c_2383,plain,
! [X0: $i,X1: $i] : iPr_def_13(iPr_def_16(X0),X1) = iPr_def_10(X0,X1),
inference(superposition,[status(thm)],[c_1997,c_756]) ).
tcf(c_2395,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = iPr_def_13(X0,inverse(iPr_def_16(X1))),
inference(superposition,[status(thm)],[c_2007,c_757]) ).
tcf(c_2399,plain,
! [X0: $i] : multiply(inverse(iPr_def_16(inverse(inverse(X0)))),inverse(iPr_def_14)) = X0,
inference(superposition,[status(thm)],[c_2007,c_1721]) ).
tcf(c_2410,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,inverse(multiply(iPr_def_14,inverse(X1)))) = inverse(iPr_def_12(iPr_def_13(X1,X0))),
inference(superposition,[status(thm)],[c_750,c_1807]) ).
tcf(c_2435,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_13(X0,X1),inverse(multiply(iPr_def_10(X2,iPr_def_14),X0))) = iPr_def_10(multiply(iPr_def_14,inverse(iPr_def_12(X2))),X1),
inference(superposition,[status(thm)],[c_2011,c_612]) ).
tcf(c_2462,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X1,X0) = iPr_def_13(X1,iPr_def_14),
inference(superposition,[status(thm)],[c_1989,c_2045]) ).
tcf(c_2488,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,iPr_def_13(X1,X0)) = inverse(iPr_def_13(X1,iPr_def_14)),
inference(superposition,[status(thm)],[c_1992,c_2143]) ).
tcf(c_2493,plain,
! [X0: $i] : inverse(iPr_def_13(iPr_def_12(X0),iPr_def_14)) = iPr_def_10(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_1729,c_2143]) ).
tcf(c_2513,plain,
! [X0: $i] : multiply(iPr_def_13(inverse(inverse(X0)),iPr_def_14),inverse(iPr_def_14)) = X0,
inference(demodulation,[status(thm)],[c_2399,c_2009]) ).
tcf(c_2516,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(X0),X1)) = iPr_def_13(X0,iPr_def_13(X1,iPr_def_14)),
inference(demodulation,[status(thm)],[c_2395,c_2009]) ).
tcf(c_2545,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_13(X0,X1),inverse(iPr_def_13(X0,X2))) = iPr_def_13(iPr_def_12(X2),X1),
inference(demodulation,[status(thm)],[c_2435,c_750,c_1722,c_1856]) ).
tcf(c_3633,plain,
! [X0: $i] : iPr_def_13(iPr_def_12(iPr_def_14),inverse(inverse(X0))) = inverse(iPr_def_12(iPr_def_12(X0))),
inference(superposition,[status(thm)],[c_2329,c_1807]) ).
tcf(c_3642,plain,
multiply(iPr_def_16(iPr_def_12(iPr_def_14)),iPr_def_14) = iPr_def_14,
inference(superposition,[status(thm)],[c_1990,c_2338]) ).
tcf(c_3666,plain,
! [X0: $i] : multiply(iPr_def_16(iPr_def_16(X0)),iPr_def_10(X0,iPr_def_14)) = iPr_def_14,
inference(superposition,[status(thm)],[c_2383,c_2338]) ).
tcf(c_3671,plain,
iPr_def_10(iPr_def_16(iPr_def_12(iPr_def_14)),iPr_def_14) = iPr_def_12(iPr_def_14),
inference(superposition,[status(thm)],[c_1990,c_2335]) ).
tcf(c_3761,plain,
! [X0: $i,X1: $i] : iPr_def_16(multiply(iPr_def_14,inverse(multiply(X0,X1)))) = iPr_def_11(X0,X1,iPr_def_14),
inference(superposition,[status(thm)],[c_2253,c_2033]) ).
tcf(c_3835,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_13(X0,X1),inverse(iPr_def_13(X0,iPr_def_14))) = iPr_def_16(X1),
inference(superposition,[status(thm)],[c_2488,c_1997]) ).
tcf(c_3855,plain,
iPr_def_12(iPr_def_16(iPr_def_12(iPr_def_14))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_3642,c_1729]) ).
tcf(c_3864,plain,
! [X0: $i] : iPr_def_13(iPr_def_12(iPr_def_14),X0) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_3835,c_2545]) ).
tcf(c_3867,plain,
! [X0: $i] : inverse(iPr_def_12(iPr_def_12(X0))) = iPr_def_16(inverse(inverse(X0))),
inference(demodulation,[status(thm)],[c_3633,c_3864]) ).
tcf(c_3883,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,X1,iPr_def_14) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_3761,c_2033]) ).
tcf(c_4047,plain,
! [X0: $i] : multiply(iPr_def_10(iPr_def_16(iPr_def_12(iPr_def_14)),X0),iPr_def_14) = iPr_def_16(X0),
inference(superposition,[status(thm)],[c_3855,c_2372]) ).
tcf(c_4051,plain,
! [X0: $i] : iPr_def_12(iPr_def_10(iPr_def_16(iPr_def_12(iPr_def_14)),X0)) = iPr_def_10(iPr_def_14,iPr_def_12(X0)),
inference(superposition,[status(thm)],[c_3855,c_610]) ).
tcf(c_4059,plain,
! [X0: $i] : inverse(iPr_def_13(iPr_def_12(iPr_def_14),iPr_def_14)) = iPr_def_10(X0,iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_3864,c_2488]) ).
tcf(c_4092,plain,
iPr_def_13(iPr_def_14,inverse(iPr_def_16(iPr_def_12(iPr_def_14)))) = inverse(iPr_def_12(iPr_def_12(iPr_def_14))),
inference(superposition,[status(thm)],[c_3671,c_1807]) ).
tcf(c_4097,plain,
iPr_def_12(iPr_def_16(iPr_def_12(iPr_def_14))) = inverse(iPr_def_12(iPr_def_14)),
inference(superposition,[status(thm)],[c_3671,c_2264]) ).
tcf(c_4248,plain,
inverse(iPr_def_12(iPr_def_14)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_4097,c_3855]) ).
tcf(c_4263,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_16(X0)) = inverse(iPr_def_14),
inference(demodulation,[status(thm)],[c_4059,c_1989,c_2493]) ).
tcf(c_4264,plain,
! [X0: $i] : iPr_def_12(iPr_def_10(iPr_def_16(iPr_def_12(iPr_def_14)),X0)) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_4047,c_1729]) ).
tcf(c_4267,plain,
iPr_def_16(inverse(inverse(iPr_def_14))) = inverse(iPr_def_14),
inference(demodulation,[status(thm)],[c_4092,c_1722,c_2009,c_3864,c_3867]) ).
tcf(c_4268,plain,
iPr_def_16(iPr_def_12(iPr_def_14)) = inverse(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_4267,c_2331]) ).
tcf(c_4273,plain,
! [X0: $i] : iPr_def_10(iPr_def_14,iPr_def_12(X0)) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_4051,c_4264]) ).
tcf(c_4274,plain,
! [X0: $i] : inverse(iPr_def_12(X0)) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_4273,c_1989]) ).
tcf(c_4439,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,inverse(X1)) = iPr_def_16(iPr_def_10(X1,X0)),
inference(demodulation,[status(thm)],[c_1807,c_4274]) ).
tcf(c_4574,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11(X0,iPr_def_13(iPr_def_12(iPr_def_14),X0),X1),iPr_def_14) = X1,
inference(superposition,[status(thm)],[c_4248,c_746]) ).
tcf(c_4590,plain,
iPr_def_13(iPr_def_12(iPr_def_14),iPr_def_14) = inverse(inverse(iPr_def_14)),
inference(superposition,[status(thm)],[c_4268,c_2009]) ).
tcf(c_4595,plain,
inverse(inverse(iPr_def_14)) = iPr_def_16(iPr_def_14),
inference(demodulation,[status(thm)],[c_4590,c_3864]) ).
tcf(c_4596,plain,
iPr_def_12(iPr_def_14) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_4595,c_2035,c_2331]) ).
tcf(c_4619,plain,
! [X0: $i,X1: $i] : iPr_def_12(iPr_def_11(X0,iPr_def_16(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_4574,c_1729,c_3864]) ).
tcf(c_4640,plain,
! [X0: $i] : iPr_def_13(iPr_def_14,X0) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_3864,c_4596]) ).
tcf(c_4642,plain,
! [X0: $i] : iPr_def_13(X0,inverse(multiply(iPr_def_14,inverse(X0)))) = iPr_def_14,
inference(demodulation,[status(thm)],[c_2330,c_4596]) ).
tcf(c_4649,plain,
! [X0: $i] : iPr_def_16(iPr_def_13(X0,X0)) = iPr_def_14,
inference(demodulation,[status(thm)],[c_4642,c_2410,c_4274]) ).
tcf(c_4650,plain,
! [X0: $i] : inverse(X0) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_1722,c_4640]) ).
tcf(c_4655,plain,
! [X0: $i] : multiply(iPr_def_13(inverse(iPr_def_16(X0)),iPr_def_14),inverse(iPr_def_14)) = X0,
inference(demodulation,[status(thm)],[c_2513,c_4650]) ).
tcf(c_4656,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_16(X0),X1,X0) = iPr_def_13(X1,iPr_def_14),
inference(demodulation,[status(thm)],[c_2462,c_4650]) ).
tcf(c_4658,plain,
! [X0: $i] : iPr_def_16(multiply(iPr_def_14,iPr_def_16(X0))) = X0,
inference(demodulation,[status(thm)],[c_2033,c_4650]) ).
tcf(c_4659,plain,
! [X0: $i] : iPr_def_10(iPr_def_14,X0) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_1989,c_4650]) ).
tcf(c_4668,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_14) = iPr_def_16(iPr_def_16(X0)),
inference(demodulation,[status(thm)],[c_2009,c_4650]) ).
tcf(c_4670,plain,
! [X0: $i] : iPr_def_16(iPr_def_10(X0,iPr_def_14)) = iPr_def_12(X0),
inference(demodulation,[status(thm)],[c_2264,c_4650]) ).
tcf(c_4672,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_13(multiply(X0,X1),iPr_def_14)) = iPr_def_10(X0,X1),
inference(demodulation,[status(thm)],[c_2143,c_4650]) ).
tcf(c_4673,plain,
! [X0: $i] : iPr_def_13(iPr_def_14,inverse(X0)) = iPr_def_12(X0),
inference(demodulation,[status(thm)],[c_4670,c_4439]) ).
tcf(c_4677,plain,
! [X0: $i] : multiply(iPr_def_13(iPr_def_13(X0,iPr_def_14),iPr_def_14),iPr_def_16(iPr_def_14)) = X0,
inference(demodulation,[status(thm)],[c_4655,c_4650,c_4668]) ).
tcf(c_4678,plain,
! [X0: $i] : multiply(iPr_def_13(iPr_def_13(X0,iPr_def_14),iPr_def_14),iPr_def_14) = X0,
inference(light_normalisation,[status(thm)],[c_4677,c_2035]) ).
tcf(c_4679,plain,
! [X0: $i] : iPr_def_12(iPr_def_13(iPr_def_13(X0,iPr_def_14),iPr_def_14)) = X0,
inference(demodulation,[status(thm)],[c_4678,c_1729]) ).
tcf(c_7069,plain,
! [X0: $i] : multiply(iPr_def_10(iPr_def_14,X0),iPr_def_14) = iPr_def_16(X0),
inference(superposition,[status(thm)],[c_4596,c_2372]) ).
tcf(c_7072,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(iPr_def_14,X0),iPr_def_14) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_4596,c_597]) ).
tcf(c_7084,plain,
! [X0: $i] : iPr_def_10(iPr_def_16(X0),iPr_def_14) = iPr_def_12(X0),
inference(demodulation,[status(thm)],[c_7072,c_4659]) ).
tcf(c_7085,plain,
! [X0: $i] : iPr_def_12(iPr_def_16(X0)) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_7069,c_1729,c_4659]) ).
tcf(c_7106,plain,
! [X0: $i] : multiply(iPr_def_14,iPr_def_13(iPr_def_13(X0,X0),iPr_def_14)) = iPr_def_14,
inference(superposition,[status(thm)],[c_4649,c_2338]) ).
tcf(c_7113,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_16(X0)) = iPr_def_12(iPr_def_14),
inference(superposition,[status(thm)],[c_4659,c_742]) ).
tcf(c_7128,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_16(X0)) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_7113,c_4263,c_4596]) ).
tcf(c_7133,plain,
! [X0: $i] : iPr_def_13(X0,X0) = iPr_def_14,
inference(demodulation,[status(thm)],[c_7106,c_1992]) ).
tcf(c_7151,plain,
! [X0: $i] : multiply(X0,iPr_def_14) = X0,
inference(superposition,[status(thm)],[c_7133,c_1992]) ).
tcf(c_7204,plain,
! [X0: $i] : iPr_def_12(X0) = X0,
inference(superposition,[status(thm)],[c_4658,c_7085]) ).
tcf(c_7219,plain,
! [X0: $i,X1: $i] : iPr_def_13(iPr_def_13(X0,iPr_def_14),X1) = iPr_def_10(iPr_def_16(X0),X1),
inference(superposition,[status(thm)],[c_4668,c_2383]) ).
tcf(c_7226,plain,
! [X0: $i] : iPr_def_16(inverse(X0)) = iPr_def_12(X0),
inference(superposition,[status(thm)],[c_4673,c_4640]) ).
tcf(c_7233,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_12(X0),X1,iPr_def_14) = iPr_def_13(X1,iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_7084,c_2045]) ).
tcf(c_7235,plain,
! [X0: $i] : multiply(iPr_def_14,iPr_def_12(X0)) = iPr_def_16(iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_7084,c_1997]) ).
tcf(c_7241,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,iPr_def_14),X1) = iPr_def_13(X1,X0),
inference(superposition,[status(thm)],[c_3883,c_2045]) ).
tcf(c_7242,plain,
! [X0: $i,X1: $i] : iPr_def_12(iPr_def_13(iPr_def_16(iPr_def_10(X0,X1)),X0)) = X1,
inference(superposition,[status(thm)],[c_2045,c_4619]) ).
tcf(c_7273,plain,
! [X0: $i] : iPr_def_12(iPr_def_13(X0,iPr_def_14)) = multiply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_756,c_4679]) ).
tcf(c_7281,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(iPr_def_13(iPr_def_13(X0,iPr_def_14),iPr_def_14),X1),X0) = iPr_def_16(X1),
inference(superposition,[status(thm)],[c_4679,c_2372]) ).
tcf(c_7296,plain,
! [X0: $i] : iPr_def_13(iPr_def_14,iPr_def_16(iPr_def_16(X0))) = iPr_def_10(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_3666,c_756]) ).
tcf(c_7318,plain,
! [X0: $i] : iPr_def_16(inverse(inverse(iPr_def_16(X0)))) = inverse(iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_7085,c_3867]) ).
tcf(c_7408,plain,
! [X0: $i] : iPr_def_16(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_7226,c_7204]) ).
tcf(c_7409,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_14) = X0,
inference(demodulation,[status(thm)],[c_7408,c_4650,c_4668]) ).
tcf(c_7461,plain,
! [X0: $i] : multiply(iPr_def_14,X0) = X0,
inference(demodulation,[status(thm)],[c_7273,c_7204,c_7409]) ).
tcf(c_7465,plain,
! [X0: $i] : iPr_def_16(iPr_def_16(X0)) = X0,
inference(demodulation,[status(thm)],[c_7235,c_7204,c_7461]) ).
tcf(c_7481,plain,
! [X0: $i] : iPr_def_13(iPr_def_13(X0,iPr_def_14),iPr_def_14) = iPr_def_13(X0,iPr_def_14),
inference(demodulation,[status(thm)],[c_7318,c_4650,c_4668]) ).
tcf(c_7487,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_14) = iPr_def_13(iPr_def_14,X0),
inference(demodulation,[status(thm)],[c_7296,c_7465]) ).
tcf(c_7488,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_14) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_7487,c_4640]) ).
tcf(c_7499,plain,
! [X0: $i,X1: $i] : iPr_def_13(iPr_def_16(iPr_def_10(X0,X1)),X0) = X1,
inference(demodulation,[status(thm)],[c_7242,c_7204]) ).
tcf(c_7500,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(X0,X1),X0) = X1,
inference(demodulation,[status(thm)],[c_7499,c_2141]) ).
tcf(c_7501,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_16(X0),X1) = iPr_def_13(X1,X0),
inference(demodulation,[status(thm)],[c_7241,c_7488]) ).
tcf(c_7520,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,X1,iPr_def_14) = iPr_def_13(X1,iPr_def_16(X0)),
inference(demodulation,[status(thm)],[c_7233,c_7204]) ).
tcf(c_7521,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,iPr_def_16(X1)) = multiply(X1,X0),
inference(demodulation,[status(thm)],[c_7520,c_3883]) ).
tcf(c_7523,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_16(X0),X1) = iPr_def_13(X0,X1),
inference(demodulation,[status(thm)],[c_7219,c_7409]) ).
tcf(c_7541,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,X1),X0) = iPr_def_16(X1),
inference(demodulation,[status(thm)],[c_7281,c_7409,c_7481]) ).
tcf(c_7663,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,iPr_def_10(X1,X0)) = X1,
inference(demodulation,[status(thm)],[c_742,c_7204]) ).
tcf(c_7804,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,iPr_def_10(X1,X2)) = iPr_def_11(X2,X0,X1),
inference(superposition,[status(thm)],[c_7500,c_2045]) ).
tcf(c_7853,plain,
! [X0: $i,X1: $i] : multiply(X0,iPr_def_16(X1)) = iPr_def_10(X1,iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_7521,c_2383]) ).
tcf(c_7862,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,iPr_def_13(X1,X0)) = iPr_def_16(X1),
inference(superposition,[status(thm)],[c_7523,c_7663]) ).
tcf(c_7875,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_10(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7663,c_7541]) ).
tcf(c_7907,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,inverse(iPr_def_10(X0,X1))) = iPr_def_16(X1),
inference(superposition,[status(thm)],[c_7500,c_4439]) ).
tcf(c_7911,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_13(X0,inverse(X1)),X2) = iPr_def_13(X2,iPr_def_10(X1,X0)),
inference(superposition,[status(thm)],[c_4439,c_7501]) ).
tcf(c_7918,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(iPr_def_13(X0,inverse(X1)),X2) = iPr_def_10(iPr_def_10(X1,X0),X2),
inference(superposition,[status(thm)],[c_4439,c_2383]) ).
tcf(c_7925,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,X1,iPr_def_16(X0)) = iPr_def_13(X1,iPr_def_14),
inference(superposition,[status(thm)],[c_7465,c_4656]) ).
tcf(c_8008,plain,
! [X0: $i,X1: $i] : iPr_def_16(multiply(X0,X1)) = iPr_def_10(X0,X1),
inference(superposition,[status(thm)],[c_7409,c_4672]) ).
tcf(c_8044,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,X1,iPr_def_16(X0)) = X1,
inference(demodulation,[status(thm)],[c_7925,c_7409]) ).
tcf(c_8046,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,multiply(X0,X1)) = iPr_def_16(X1),
inference(demodulation,[status(thm)],[c_7907,c_4439,c_4650,c_7521]) ).
tcf(c_8100,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(X0,X1),X2) = iPr_def_13(multiply(X0,X1),X2),
inference(demodulation,[status(thm)],[c_7918,c_4650,c_7521]) ).
tcf(c_8101,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_13(X0,inverse(X1)),X2) = iPr_def_11(X0,X2,X1),
inference(demodulation,[status(thm)],[c_7911,c_7804]) ).
tcf(c_8102,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = iPr_def_11(X1,X2,X0),
inference(demodulation,[status(thm)],[c_8101,c_4650,c_7521]) ).
tcf(c_8194,plain,
multiply(a3,multiply(b3,c3)) != iPr_def_11(b3,c3,a3),
inference(demodulation,[status(thm)],[c_52,c_8102]) ).
tcf(c_8252,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_16(X0),X1,X0) = X1,
inference(superposition,[status(thm)],[c_7465,c_8044]) ).
tcf(c_8715,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X0))))),multiply(multiply(multiply(X3,inverse(X3)),inverse(X2)),X4))),multiply(multiply(multiply(X5,inverse(X5)),inverse(iPr_def_14)),multiply(multiply(X6,inverse(X6)),inverse(multiply(X7,X8)))))),inverse(multiply(X8,X4))) = X7,
inference(superposition,[status(thm)],[c_7151,c_129]) ).
tcf(c_8849,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_11(X0,X1,X2),iPr_def_10(X0,X1)) = X2,
inference(demodulation,[status(thm)],[c_8715,c_2516,c_3883,c_4650,c_7128,c_7488,c_7501,c_7523,c_7663,c_7804,c_7875,c_7853,c_7862,c_8008,c_8100,c_8102,c_8252]) ).
tcf(c_9161,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(iPr_def_11(X0,X1,X2),X2) = iPr_def_16(iPr_def_10(X0,X1)),
inference(superposition,[status(thm)],[c_8849,c_8046]) ).
tcf(c_9242,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(iPr_def_11(X0,X1,X2),X2) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_9161,c_7875]) ).
tcf(c_9542,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,X2)) = iPr_def_11(X1,X2,X0),
inference(superposition,[status(thm)],[c_9242,c_1992]) ).
tcf(c_9782,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_8194,c_9542]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP432-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n004.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.39 % DateTime : Wed Sep 23 14:45:15 UTC 2026
% 0.11/5.40 % CPUTime :
% 0.16/5.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.43 Running UEQ theorem proving
% 0.16/5.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.45
% 0.16/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 13.11/7.77 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 13.11/7.77 % SZS status Started for theBenchmark.p
% 13.11/7.77 % SZS status Unsatisfiable for theBenchmark.p
% 13.11/7.77
% 13.11/7.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 13.11/7.77
% 13.11/7.77 % ------ iProver source info
% 13.11/7.77
% 13.11/7.77 % git: date: 2026-07-19 20:42:38 +0200
% 13.11/7.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 13.11/7.77 % git: non_committed_changes: false
% 13.11/7.77
% 13.11/7.77 % ------ Parsing...% successful
% 13.11/7.77
% 13.11/7.77
% 13.11/7.77 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 13.11/7.77 % ------ Proving...
% 13.11/7.77 % ------ Problem Properties
% 13.11/7.77
% 13.11/7.77 %
% 13.11/7.77 % clauses 2
% 13.11/7.77 % conjectures 1
% 13.11/7.77 % EPR 0
% 13.11/7.77 % Horn 2
% 13.11/7.77 % unary 2
% 13.11/7.77 % binary 0
% 13.11/7.77 % lits 2
% 13.11/7.77 % lits eq 2
% 13.11/7.77 % fd_pure 0
% 13.11/7.77 % fd_pseudo 0
% 13.11/7.77 % fd_cond 0
% 13.11/7.77 % fd_pseudo_cond 0
% 13.11/7.77 % AC symbols 0
% 13.11/7.77
% 13.11/7.77 % ------ Input Options Time Limit: Unbounded
% 13.11/7.77
% 13.11/7.77
% 13.11/7.77 % ------
% 13.11/7.77 % Current options:
% 13.11/7.77 % ------
% 13.11/7.77
% 13.11/7.77
% 13.11/7.77 %
% 13.11/7.77
% 13.11/7.77 % ------ Proving...
% 13.11/7.77 %
% 13.11/7.77
% 13.11/7.77 % SZS status Unsatisfiable for theBenchmark.p
% 13.11/7.77
% 13.11/7.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 13.11/7.79
% 13.11/7.79
%------------------------------------------------------------------------------