%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP051-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.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 01:30:13 PM UTC 2026
% Result : Unsatisfiable 189.72s 27.43s
% Output : CNFRefutation 189.72s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f3,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != multiply(multiply(inverse(b2),b2),a2)
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(reorient_equations,[],[f2]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),X2))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = iPr_def_10(X1,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_102]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = iPr_def_10(X1,X2),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_102]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = X0,
inference(demodulation,[status(thm)],[c_51,c_105]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = X0,
inference(demodulation,[status(thm)],[c_51,c_105]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(iPr_def_10(X0,X1),inverse(X1))) = iPr_def_10(inverse(X1),X1),
inference(superposition,[status(thm)],[c_108,c_105]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))) = iPr_def_10(iPr_def_10(X1,X2),inverse(multiply(inverse(X2),X2))),
inference(superposition,[status(thm)],[c_108,c_105]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(iPr_def_10(X0,X1),inverse(multiply(X2,multiply(inverse(X1),X1))))),X0) = iPr_def_10(X2,multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[c_108,c_105]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(iPr_def_10(X0,X1),inverse(X1))) = iPr_def_10(inverse(X1),X1),
inference(superposition,[status(thm)],[c_117,c_105]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))) = iPr_def_10(iPr_def_10(X1,X2),inverse(multiply(inverse(X2),X2))),
inference(superposition,[status(thm)],[c_117,c_105]) ).
tcf(c_126,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(iPr_def_10(X0,X1),inverse(multiply(X2,multiply(inverse(X1),X1))))),X0) = iPr_def_10(X2,multiply(inverse(X1),X1)),
inference(superposition,[status(thm)],[c_117,c_105]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(X1,X2)))),multiply(X0,inverse(multiply(X3,inverse(X2))))) = iPr_def_10(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_105,c_105]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(X1),X1)))),multiply(X0,inverse(multiply(iPr_def_10(X2,X1),inverse(X1))))) = iPr_def_10(inverse(X2),multiply(iPr_def_10(X2,X1),inverse(X1))),
inference(superposition,[status(thm)],[c_123,c_105]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(inverse(multiply(inverse(inverse(X0)),inverse(multiply(X1,X0)))),multiply(inverse(inverse(X0)),inverse(X0))) = multiply(inverse(multiply(iPr_def_10(X2,inverse(X0)),inverse(iPr_def_10(X1,X0)))),X2),
inference(superposition,[status(thm)],[c_105,c_126]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(X1,multiply(inverse(X2),X2))))),multiply(X0,inverse(X3))) = iPr_def_10(inverse(multiply(iPr_def_10(X3,X2),inverse(multiply(X1,multiply(inverse(X2),X2))))),X3),
inference(superposition,[status(thm)],[c_126,c_105]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(multiply(X0,inverse(multiply(inverse(X1),X1))),X1),inverse(multiply(inverse(X1),X1))) = iPr_def_10(X0,inverse(multiply(inverse(X1),X1))),
inference(superposition,[status(thm)],[c_125,c_105]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(inverse(multiply(inverse(inverse(inverse(multiply(inverse(X0),X0)))),inverse(X1))),multiply(inverse(inverse(inverse(multiply(inverse(X0),X0)))),inverse(inverse(multiply(inverse(X0),X0))))) = multiply(inverse(multiply(iPr_def_10(X2,inverse(inverse(multiply(inverse(X0),X0)))),inverse(iPr_def_10(iPr_def_10(X1,X0),inverse(multiply(inverse(X0),X0)))))),X2),
inference(superposition,[status(thm)],[c_125,c_126]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(inverse(multiply(inverse(X2),X2))))),
inference(superposition,[status(thm)],[c_125,c_125]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))) = iPr_def_11(X1,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_175]) ).
tcf(c_179,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = iPr_def_11(X0,X1),
inference(demodulation,[status(thm)],[c_125,c_176]) ).
tcf(c_225,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11(X0,X1),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1))))) = iPr_def_10(X0,X1),
inference(superposition,[status(thm)],[c_179,c_117]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = iPr_def_10(X1,X2),
inference(demodulation,[status(thm)],[c_235,c_106]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = X0,
inference(demodulation,[status(thm)],[c_51,c_239]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(iPr_def_10(X0,X1),inverse(inverse(multiply(inverse(X2),X2))))) = iPr_def_11(multiply(inverse(X1),X1),X2),
inference(superposition,[status(thm)],[c_241,c_176]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(X0),multiply(iPr_def_10(X0,X1),inverse(inverse(multiply(inverse(X2),X2))))) = multiply(inverse(X3),multiply(iPr_def_10(X3,X1),inverse(inverse(multiply(inverse(X2),X2))))),
inference(superposition,[status(thm)],[c_243,c_243]) ).
tcf(c_312,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(iPr_def_10(X0,X1),inverse(inverse(multiply(inverse(X2),X2))))) = iPr_def_12(X1,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_311]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] : iPr_def_11(multiply(X0,inverse(multiply(inverse(X1),X1))),X1) = iPr_def_10(X0,inverse(multiply(inverse(X1),X1))),
inference(demodulation,[status(thm)],[c_165,c_179]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(inverse(multiply(iPr_def_10(inverse(multiply(inverse(X0),X0)),X1),inverse(multiply(X2,multiply(inverse(X1),X1))))),inverse(multiply(inverse(X0),X0))) = iPr_def_11(iPr_def_10(X2,multiply(inverse(X1),X1)),X0),
inference(superposition,[status(thm)],[c_126,c_330]) ).
tcf(c_334,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1))))) = iPr_def_10(multiply(X0,inverse(multiply(inverse(X1),X1))),X1),
inference(superposition,[status(thm)],[c_330,c_225]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(X0,inverse(multiply(inverse(X1),X1))),X1) = X0,
inference(demodulation,[status(thm)],[c_334,c_117]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(iPr_def_10(inverse(multiply(inverse(X0),X0)),X1),inverse(multiply(X2,multiply(inverse(X1),X1))))) = iPr_def_10(iPr_def_10(X2,multiply(inverse(X1),X1)),X0),
inference(superposition,[status(thm)],[c_126,c_335]) ).
tcf(c_347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_11(X1,X2)))),multiply(X0,inverse(multiply(X3,inverse(inverse(multiply(inverse(X2),X2))))))) = iPr_def_10(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(inverse(multiply(inverse(X2),X2))))),
inference(superposition,[status(thm)],[c_176,c_105]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_10(X0,multiply(X1,inverse(inverse(multiply(inverse(X2),X2))))),inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))) = X0,
inference(superposition,[status(thm)],[c_176,c_117]) ).
tcf(c_502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(inverse(multiply(X0,inverse(multiply(multiply(X1,inverse(multiply(inverse(X2),X2))),X2)))),multiply(X0,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(multiply(X0,inverse(X2))))),
inference(superposition,[status(thm)],[c_335,c_127]) ).
tcf(c_533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(X1,X2)))),multiply(X0,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X4,inverse(iPr_def_10(X1,X2)))),multiply(X4,inverse(multiply(X3,inverse(X2))))),
inference(superposition,[status(thm)],[c_127,c_127]) ).
tcf(c_534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(X1,X2)))),multiply(X0,inverse(multiply(X3,inverse(X2))))) = iPr_def_13(X1,X2,X3),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_13])],[c_533]) ).
tcf(c_541,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = iPr_def_13(X1,X2,X0),
inference(demodulation,[status(thm)],[c_127,c_534]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_555,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = iPr_def_10(X1,X2),
inference(demodulation,[status(thm)],[c_551,c_106]) ).
tcf(c_557,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = X0,
inference(demodulation,[status(thm)],[c_51,c_555]) ).
tcf(c_558,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_10(X0,multiply(X1,inverse(inverse(multiply(inverse(X2),X2))))),inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))) = X0,
inference(superposition,[status(thm)],[c_176,c_557]) ).
tcf(c_568,plain,
! [X0: $i,X1: $i] : iPr_def_11(multiply(X0,inverse(multiply(inverse(X1),X1))),X1) = iPr_def_10(X0,inverse(multiply(inverse(X1),X1))),
inference(superposition,[status(thm)],[c_555,c_176]) ).
tcf(c_569,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = iPr_def_11(X0,X1),
inference(superposition,[status(thm)],[c_557,c_568]) ).
tcf(c_574,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11(X0,X1),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1))))) = iPr_def_10(X0,X1),
inference(superposition,[status(thm)],[c_569,c_557]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(iPr_def_10(X0,iPr_def_10(X1,multiply(inverse(X2),X2))),inverse(iPr_def_11(inverse(multiply(inverse(X3),X3)),X3))) = X0,
inference(superposition,[status(thm)],[c_126,c_355]) ).
tcf(c_801,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(X0),multiply(iPr_def_10(X0,X1),inverse(X1))) = iPr_def_13(inverse(X1),X1,iPr_def_10(X0,X1)),
inference(demodulation,[status(thm)],[c_128,c_534]) ).
tcf(c_852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(iPr_def_10(X0,iPr_def_10(X1,multiply(inverse(X2),X2))),inverse(iPr_def_11(inverse(multiply(inverse(X3),X3)),X3))) = X0,
inference(superposition,[status(thm)],[c_121,c_558]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_13(inverse(multiply(iPr_def_10(X0,X1),inverse(multiply(X2,multiply(inverse(X1),X1))))),X0,X3) = iPr_def_10(inverse(multiply(X3,inverse(iPr_def_10(X2,multiply(inverse(X1),X1))))),multiply(X3,inverse(X0))),
inference(superposition,[status(thm)],[c_126,c_541]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_13(iPr_def_10(X0,multiply(X1,inverse(inverse(multiply(inverse(X2),X2))))),inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2)),X3) = iPr_def_10(inverse(multiply(X3,inverse(X0))),multiply(X3,inverse(inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))))),
inference(superposition,[status(thm)],[c_355,c_541]) ).
tcf(c_902,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1))))) = iPr_def_10(multiply(X0,inverse(multiply(inverse(X1),X1))),X1),
inference(superposition,[status(thm)],[c_568,c_574]) ).
tcf(c_915,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(X0,inverse(multiply(inverse(X1),X1))),X1) = X0,
inference(demodulation,[status(thm)],[c_902,c_557]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(X0,inverse(multiply(inverse(iPr_def_10(X1,multiply(inverse(X2),X2))),iPr_def_10(X1,multiply(inverse(X2),X2))))) = multiply(X0,inverse(iPr_def_11(inverse(multiply(inverse(X3),X3)),X3))),
inference(superposition,[status(thm)],[c_915,c_852]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(iPr_def_11(inverse(multiply(inverse(X1),X1)),X1))) = iPr_def_15(X0),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_15])],[c_965]) ).
tcf(c_1054,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_10(X0,X1),inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))) = X0,
inference(superposition,[status(thm)],[c_335,c_756]) ).
tcf(c_1067,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(iPr_def_11(inverse(multiply(inverse(X1),X1)),X1))) = multiply(X0,inverse(multiply(inverse(X2),X2))),
inference(superposition,[status(thm)],[c_335,c_1054]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))))) = iPr_def_10(iPr_def_10(X1,X3),inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))),
inference(superposition,[status(thm)],[c_1054,c_105]) ).
tcf(c_1072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(iPr_def_10(X0,X1),inverse(multiply(X2,iPr_def_11(inverse(multiply(inverse(X3),X3)),X3))))),X0) = iPr_def_10(X2,iPr_def_11(inverse(multiply(inverse(X3),X3)),X3)),
inference(superposition,[status(thm)],[c_1054,c_105]) ).
tcf(c_1075,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(iPr_def_11(inverse(multiply(inverse(X0),X0)),X0)),iPr_def_11(inverse(multiply(inverse(X0),X0)),X0)) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_1054,c_123]) ).
tcf(c_1076,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X1))) = iPr_def_16(X0),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_16])],[c_1067]) ).
tcf(c_1078,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_16(X0),X1) = X0,
inference(demodulation,[status(thm)],[c_335,c_1076]) ).
tcf(c_1079,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,inverse(multiply(inverse(X1),X1))) = iPr_def_11(iPr_def_16(X0),X1),
inference(demodulation,[status(thm)],[c_330,c_1076]) ).
tcf(c_1080,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_10(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_117,c_1076]) ).
tcf(c_1087,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,multiply(inverse(X2),X2))))),iPr_def_16(X0)) = iPr_def_10(X1,multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_1078,c_126]) ).
tcf(c_1088,plain,
! [X0: $i,X1: $i] : multiply(inverse(iPr_def_16(X0)),multiply(X0,inverse(X1))) = iPr_def_10(inverse(X1),X1),
inference(superposition,[status(thm)],[c_1078,c_123]) ).
tcf(c_1126,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(X0,inverse(multiply(X1,X2)))) = iPr_def_16(iPr_def_13(X1,X2,X0)),
inference(superposition,[status(thm)],[c_541,c_1080]) ).
tcf(c_1127,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_13(inverse(X0),X0,iPr_def_10(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_801,c_1080]) ).
tcf(c_1128,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(X0,X1) = iPr_def_10(X0,X2),
inference(superposition,[status(thm)],[c_1080,c_1078]) ).
tcf(c_1130,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_16(iPr_def_13(X0,X1,X2)),multiply(X2,inverse(X1))) = iPr_def_10(X0,X1),
inference(demodulation,[status(thm)],[c_105,c_1126]) ).
tcf(c_1131,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_16(iPr_def_13(X0,multiply(inverse(X1),X1),iPr_def_10(X2,X1))),X2) = iPr_def_10(X0,multiply(inverse(X1),X1)),
inference(demodulation,[status(thm)],[c_126,c_1126]) ).
tcf(c_1167,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(iPr_def_10(X0,inverse(X1)),inverse(iPr_def_10(X2,X1)))),X0) = iPr_def_13(X2,X1,inverse(inverse(X1))),
inference(demodulation,[status(thm)],[c_138,c_1078,c_1126]) ).
tcf(c_1168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(iPr_def_10(X0,X1),inverse(iPr_def_10(X2,X3)))),X0) = iPr_def_13(X2,X3,inverse(inverse(X3))),
inference(superposition,[status(thm)],[c_1128,c_1167]) ).
tcf(c_1199,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_16(iPr_def_13(inverse(X0),X0,iPr_def_10(X1,X2))) = inverse(X1),
inference(superposition,[status(thm)],[c_1128,c_1127]) ).
tcf(c_1215,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_13(inverse(X0),X0,X1)) = inverse(iPr_def_16(X1)),
inference(superposition,[status(thm)],[c_1078,c_1199]) ).
tcf(c_1218,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(inverse(X0),X0,X1) = iPr_def_10(inverse(iPr_def_16(X1)),X2),
inference(superposition,[status(thm)],[c_1215,c_1078]) ).
tcf(c_1230,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(inverse(X0),X0,X1) = iPr_def_13(inverse(X2),X2,X1),
inference(superposition,[status(thm)],[c_1218,c_1218]) ).
tcf(c_1267,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_11(iPr_def_16(X0),X1)) = X0,
inference(superposition,[status(thm)],[c_1079,c_1080]) ).
tcf(c_1268,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_16(X0),X1) = iPr_def_10(X0,X2),
inference(superposition,[status(thm)],[c_1079,c_1128]) ).
tcf(c_1269,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_16(iPr_def_16(X0)),X1) = X0,
inference(superposition,[status(thm)],[c_1079,c_1078]) ).
tcf(c_1305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(X1,multiply(inverse(X2),X2))))),multiply(X0,inverse(X3))) = iPr_def_13(X1,multiply(inverse(X2),X2),iPr_def_10(X3,X2)),
inference(demodulation,[status(thm)],[c_140,c_1078,c_1126]) ).
tcf(c_1307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(X1,X2)))),multiply(X0,inverse(X3))) = iPr_def_13(X1,multiply(inverse(X4),X4),iPr_def_10(X3,X4)),
inference(superposition,[status(thm)],[c_1128,c_1305]) ).
tcf(c_1342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(iPr_def_16(iPr_def_13(X0,iPr_def_11(inverse(multiply(inverse(X1),X1)),X1),iPr_def_10(X2,X3))),X2) = iPr_def_10(X0,iPr_def_11(inverse(multiply(inverse(X1),X1)),X1)),
inference(demodulation,[status(thm)],[c_1072,c_1126]) ).
tcf(c_1355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(iPr_def_10(X0,iPr_def_11(inverse(multiply(inverse(X1),X1)),X1))),multiply(iPr_def_16(iPr_def_13(X0,iPr_def_11(inverse(multiply(inverse(X1),X1)),X1),iPr_def_10(inverse(X2),X3))),inverse(inverse(multiply(inverse(X4),X4))))) = iPr_def_11(X2,X4),
inference(superposition,[status(thm)],[c_1342,c_176]) ).
tcf(c_1450,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_16(iPr_def_11(X0,X1)) = iPr_def_10(X0,X2),
inference(superposition,[status(thm)],[c_1080,c_1267]) ).
tcf(c_1452,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_16(X0),X1) = iPr_def_16(iPr_def_11(X0,X2)),
inference(superposition,[status(thm)],[c_1267,c_1267]) ).
tcf(c_1461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_10(X0,X1),X2) = iPr_def_11(X0,X3),
inference(superposition,[status(thm)],[c_1080,c_1268]) ).
tcf(c_1463,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(iPr_def_16(X0),X1),X2) = iPr_def_11(X0,X3),
inference(superposition,[status(thm)],[c_1267,c_1268]) ).
tcf(c_1517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_16(iPr_def_11(iPr_def_10(X0,X1),X2)) = iPr_def_11(X0,X3),
inference(superposition,[status(thm)],[c_1450,c_1267]) ).
tcf(c_1523,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_16(iPr_def_11(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_1450,c_1080]) ).
tcf(c_1727,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(X1),X1)))),multiply(X0,inverse(multiply(iPr_def_10(X2,X1),inverse(X1))))),inverse(multiply(inverse(multiply(iPr_def_10(X2,X1),inverse(X1))),multiply(iPr_def_10(X2,X1),inverse(X1))))) = inverse(X2),
inference(superposition,[status(thm)],[c_118,c_51]) ).
tcf(c_1730,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(multiply(inverse(X2),X2))))),inverse(multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(inverse(X2),X2))))) = multiply(inverse(multiply(X3,inverse(multiply(X1,X2)))),multiply(X3,inverse(X2))),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_1734,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,X2)))),multiply(X0,inverse(X2))) = iPr_def_10(X1,X2),
inference(demodulation,[status(thm)],[c_1730,c_106]) ).
tcf(c_1736,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = X0,
inference(demodulation,[status(thm)],[c_51,c_1734]) ).
tcf(c_1737,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_10(X0,multiply(X1,inverse(inverse(multiply(inverse(X2),X2))))),inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))) = X0,
inference(superposition,[status(thm)],[c_176,c_1736]) ).
tcf(c_1738,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(X0),multiply(iPr_def_10(X0,X1),inverse(inverse(multiply(inverse(X2),X2))))) = iPr_def_11(multiply(inverse(X1),X1),X2),
inference(superposition,[status(thm)],[c_1736,c_176]) ).
tcf(c_1747,plain,
! [X0: $i,X1: $i] : iPr_def_11(multiply(X0,inverse(multiply(inverse(X1),X1))),X1) = iPr_def_10(X0,inverse(multiply(inverse(X1),X1))),
inference(superposition,[status(thm)],[c_1734,c_176]) ).
tcf(c_1748,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(X0,X1),inverse(multiply(inverse(X1),X1))) = iPr_def_11(X0,X1),
inference(superposition,[status(thm)],[c_1736,c_1747]) ).
tcf(c_1753,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_11(X0,X1),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1))))) = iPr_def_10(X0,X1),
inference(superposition,[status(thm)],[c_1748,c_1736]) ).
tcf(c_1780,plain,
! [X0: $i,X1: $i] : iPr_def_11(multiply(inverse(X0),X0),X1) = iPr_def_12(X0,X1),
inference(demodulation,[status(thm)],[c_1738,c_312]) ).
tcf(c_1782,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(multiply(X0,inverse(inverse(multiply(inverse(X1),X1)))),X2) = iPr_def_11(iPr_def_11(inverse(multiply(inverse(X1),X1)),X1),X2),
inference(superposition,[status(thm)],[c_176,c_1780]) ).
tcf(c_1783,plain,
! [X0: $i] : iPr_def_10(inverse(inverse(multiply(inverse(X0),X0))),inverse(multiply(inverse(X0),X0))) = iPr_def_12(inverse(multiply(inverse(X0),X0)),X0),
inference(superposition,[status(thm)],[c_1780,c_1747]) ).
tcf(c_1785,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(iPr_def_10(X0,X1)),multiply(iPr_def_11(X0,X1),inverse(inverse(multiply(inverse(X2),X2))))) = iPr_def_12(inverse(multiply(inverse(X1),X1)),X2),
inference(superposition,[status(thm)],[c_1748,c_312]) ).
tcf(c_1800,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(multiply(X0,inverse(iPr_def_12(inverse(multiply(inverse(X1),X1)),X1)))),multiply(X0,inverse(multiply(iPr_def_12(inverse(multiply(inverse(X1),X1)),X1),inverse(inverse(multiply(inverse(X1),X1))))))),inverse(multiply(inverse(multiply(iPr_def_12(inverse(multiply(inverse(X1),X1)),X1),inverse(inverse(multiply(inverse(X1),X1))))),multiply(iPr_def_12(inverse(multiply(inverse(X1),X1)),X1),inverse(inverse(multiply(inverse(X1),X1))))))) = inverse(inverse(inverse(multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[c_1783,c_1727]) ).
tcf(c_1802,plain,
! [X0: $i,X1: $i] : multiply(multiply(inverse(multiply(X0,inverse(iPr_def_12(inverse(multiply(inverse(X1),X1)),X1)))),multiply(X0,inverse(multiply(iPr_def_12(inverse(multiply(inverse(X1),X1)),X1),inverse(inverse(multiply(inverse(X1),X1))))))),inverse(iPr_def_11(inverse(multiply(inverse(X1),X1)),X1))) = inverse(inverse(inverse(multiply(inverse(X1),X1)))),
inference(demodulation,[status(thm)],[c_1800,c_120,c_1748]) ).
tcf(c_1818,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_11(iPr_def_11(inverse(multiply(inverse(X0),X0)),X0),X1) = iPr_def_12(iPr_def_10(X2,multiply(inverse(X3),X3)),X1),
inference(superposition,[status(thm)],[c_121,c_1782]) ).
tcf(c_1825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : iPr_def_12(iPr_def_10(X0,multiply(inverse(X1),X1)),X2) = iPr_def_12(iPr_def_10(X3,multiply(inverse(X4),X4)),X2),
inference(superposition,[status(thm)],[c_1818,c_1818]) ).
tcf(c_1922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(iPr_def_10(X0,iPr_def_10(X1,multiply(inverse(X2),X2))),inverse(iPr_def_11(inverse(multiply(inverse(X3),X3)),X3))) = X0,
inference(superposition,[status(thm)],[c_121,c_1737]) ).
tcf(c_1934,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_10(X0,inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1))))) = iPr_def_10(multiply(X0,inverse(multiply(inverse(X1),X1))),X1),
inference(superposition,[status(thm)],[c_1747,c_1753]) ).
tcf(c_1935,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_12(X0,X1),inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1))))) = iPr_def_10(multiply(inverse(X0),X0),X1),
inference(superposition,[status(thm)],[c_1780,c_1753]) ).
tcf(c_1947,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(X0,inverse(multiply(inverse(X1),X1))),X1) = X0,
inference(demodulation,[status(thm)],[c_1934,c_1736]) ).
tcf(c_1957,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(X1),X1)))),multiply(X0,inverse(multiply(X2,inverse(X1))))),inverse(multiply(inverse(multiply(X2,inverse(X1))),multiply(X2,inverse(X1))))) = inverse(multiply(X2,inverse(multiply(inverse(X1),X1)))),
inference(superposition,[status(thm)],[c_1947,c_1727]) ).
tcf(c_1958,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_10(X0,X1),inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))) = X0,
inference(superposition,[status(thm)],[c_1947,c_1922]) ).
tcf(c_1966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_12(iPr_def_10(X0,multiply(inverse(X1),X1)),X2) = iPr_def_12(X3,X2),
inference(superposition,[status(thm)],[c_1947,c_1825]) ).
tcf(c_1983,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))),multiply(X0,inverse(multiply(X2,inverse(inverse(multiply(inverse(X1),X1))))))),inverse(iPr_def_11(inverse(multiply(inverse(X1),X1)),X1))) = inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))),
inference(superposition,[status(thm)],[c_176,c_1957]) ).
tcf(c_1988,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),X1))))),multiply(X0,inverse(X2))),inverse(multiply(inverse(X2),X2))) = inverse(multiply(iPr_def_10(X2,X1),inverse(multiply(inverse(multiply(inverse(X1),X1)),multiply(inverse(X1),X1))))),
inference(superposition,[status(thm)],[c_1736,c_1957]) ).
tcf(c_1999,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_15(multiply(inverse(multiply(X0,inverse(iPr_def_12(inverse(multiply(inverse(X1),X1)),X1)))),multiply(X0,inverse(multiply(X2,inverse(inverse(multiply(inverse(X1),X1)))))))) = inverse(multiply(X2,inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X1),X1)))))),
inference(demodulation,[status(thm)],[c_1983,c_1783,c_966]) ).
tcf(c_2015,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(X0,X1) = iPr_def_12(X2,X1),
inference(superposition,[status(thm)],[c_1966,c_1966]) ).
tcf(c_2078,plain,
! [X0: $i,X1: $i] : iPr_def_15(iPr_def_10(X0,X1)) = X0,
inference(demodulation,[status(thm)],[c_1958,c_966]) ).
tcf(c_2079,plain,
! [X0: $i,X1: $i] : iPr_def_15(iPr_def_11(X0,X1)) = iPr_def_10(X0,X1),
inference(superposition,[status(thm)],[c_1748,c_2078]) ).
tcf(c_2080,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(inverse(X1),X1))) = iPr_def_15(X0),
inference(superposition,[status(thm)],[c_1947,c_2078]) ).
tcf(c_2083,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_15(X0),X1) = X0,
inference(demodulation,[status(thm)],[c_1947,c_2080]) ).
tcf(c_2089,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(X0,X1) = iPr_def_10(X0,X2),
inference(superposition,[status(thm)],[c_2078,c_2083]) ).
tcf(c_2127,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(inverse(X0),X0),X1) = iPr_def_15(iPr_def_12(X0,X1)),
inference(superposition,[status(thm)],[c_1780,c_2079]) ).
tcf(c_2132,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(X0,X1),X2) = iPr_def_11(X0,X1),
inference(superposition,[status(thm)],[c_2079,c_2083]) ).
tcf(c_2211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_10(X0,X1),X2) = iPr_def_11(X0,X3),
inference(superposition,[status(thm)],[c_2089,c_2132]) ).
tcf(c_2225,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_15(X0),X1) = iPr_def_10(X0,X2),
inference(superposition,[status(thm)],[c_2083,c_2211]) ).
tcf(c_2234,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_15(iPr_def_11(X0,X1)) = iPr_def_10(X0,X2),
inference(superposition,[status(thm)],[c_2211,c_2078]) ).
tcf(c_2236,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1) = iPr_def_11(X0,X2),
inference(superposition,[status(thm)],[c_2211,c_2211]) ).
tcf(c_2241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_10(multiply(inverse(X0),X0),X1),X2) = iPr_def_12(X0,X3),
inference(superposition,[status(thm)],[c_2211,c_1780]) ).
tcf(c_2250,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(X0,X1) = iPr_def_12(X0,X2),
inference(demodulation,[status(thm)],[c_2241,c_2083,c_2127]) ).
tcf(c_2281,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,inverse(iPr_def_11(inverse(multiply(inverse(X1),X1)),X2))) = iPr_def_15(X0),
inference(superposition,[status(thm)],[c_2236,c_966]) ).
tcf(c_2284,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(multiply(inverse(X0),X0),X1) = iPr_def_12(X0,X2),
inference(superposition,[status(thm)],[c_2236,c_1780]) ).
tcf(c_2309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_12(X0,X1) = iPr_def_12(X2,X3),
inference(superposition,[status(thm)],[c_2250,c_2015]) ).
tcf(c_2338,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_15(iPr_def_15(X0)),X1) = X0,
inference(superposition,[status(thm)],[c_2225,c_2083]) ).
tcf(c_2478,plain,
! [X0: $i,X1: $i] : iPr_def_15(iPr_def_15(iPr_def_11(X0,X1))) = X0,
inference(superposition,[status(thm)],[c_2234,c_2078]) ).
tcf(c_2479,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_15(iPr_def_11(X0,X1)) = iPr_def_15(iPr_def_11(X0,X2)),
inference(superposition,[status(thm)],[c_2234,c_2234]) ).
tcf(c_2612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_11(multiply(inverse(X0),X0),X1) = iPr_def_12(X2,X3),
inference(superposition,[status(thm)],[c_2284,c_2309]) ).
tcf(c_2802,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(iPr_def_11(inverse(multiply(inverse(X2),X2)),X2))))) = iPr_def_10(iPr_def_10(X1,X3),X4),
inference(superposition,[status(thm)],[c_1070,c_1128]) ).
tcf(c_2826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_11(X1,X2)))),multiply(X0,inverse(multiply(X3,inverse(inverse(multiply(inverse(X2),X2))))))) = iPr_def_10(inverse(multiply(X3,inverse(X1))),X4),
inference(superposition,[status(thm)],[c_347,c_1128]) ).
tcf(c_3097,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_15(iPr_def_15(iPr_def_12(X0,X1))) = multiply(inverse(X2),X2),
inference(superposition,[status(thm)],[c_2612,c_2478]) ).
tcf(c_3195,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(superposition,[status(thm)],[c_3097,c_3097]) ).
tcf(c_3207,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_19,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_19])],[c_3195]) ).
tcf(c_3215,plain,
! [X0: $i] : multiply(X0,inverse(iPr_def_19)) = iPr_def_15(X0),
inference(demodulation,[status(thm)],[c_2080,c_3207]) ).
tcf(c_3218,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_12(X0,X1) = iPr_def_11(iPr_def_19,X2),
inference(demodulation,[status(thm)],[c_2612,c_3207]) ).
tcf(c_3393,plain,
! [X0: $i] : multiply(X0,inverse(iPr_def_19)) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_1076,c_3207]) ).
tcf(c_3396,plain,
( ( multiply(inverse(b1),b1) != iPr_def_19 )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(demodulation,[status(thm)],[c_52,c_3207]) ).
tcf(c_3397,plain,
( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
| ( multiply(multiply(inverse(b2),b2),a2) != a2 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3396,c_3207]) ).
tcf(c_3404,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_15(X1)))),multiply(X0,inverse(inverse(iPr_def_19)))) = iPr_def_10(X1,inverse(iPr_def_19)),
inference(superposition,[status(thm)],[c_3215,c_1734]) ).
tcf(c_3405,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,iPr_def_19)))),iPr_def_15(X0)) = iPr_def_10(X1,iPr_def_19),
inference(superposition,[status(thm)],[c_3215,c_1734]) ).
tcf(c_3406,plain,
iPr_def_15(inverse(inverse(iPr_def_19))) = iPr_def_19,
inference(superposition,[status(thm)],[c_3215,c_3207]) ).
tcf(c_3412,plain,
! [X0: $i] : iPr_def_10(iPr_def_19,X0) = inverse(inverse(iPr_def_19)),
inference(superposition,[status(thm)],[c_3406,c_2083]) ).
tcf(c_3423,plain,
( ( multiply(iPr_def_19,a2) != a2 )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(demodulation,[status(thm)],[c_3397,c_3207]) ).
tcf(c_3511,plain,
iPr_def_16(inverse(inverse(iPr_def_19))) = iPr_def_19,
inference(superposition,[status(thm)],[c_3207,c_3393]) ).
tcf(c_3516,plain,
! [X0: $i] : iPr_def_11(iPr_def_16(iPr_def_19),X0) = inverse(inverse(iPr_def_19)),
inference(superposition,[status(thm)],[c_3511,c_1269]) ).
tcf(c_3518,plain,
! [X0: $i] : iPr_def_10(iPr_def_19,X0) = inverse(inverse(iPr_def_19)),
inference(superposition,[status(thm)],[c_3511,c_1078]) ).
tcf(c_4024,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(iPr_def_16(X0)),multiply(X0,inverse(X1))) = iPr_def_10(inverse(X1),X2),
inference(superposition,[status(thm)],[c_1088,c_1128]) ).
tcf(c_4100,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_16(iPr_def_13(X0,iPr_def_19,X1)),iPr_def_16(X1)) = iPr_def_10(X0,iPr_def_19),
inference(demodulation,[status(thm)],[c_1087,c_1126,c_3207]) ).
tcf(c_4104,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_16(iPr_def_13(inverse(X0),X0,X1)),iPr_def_16(X1)) = iPr_def_10(inverse(iPr_def_19),iPr_def_19),
inference(superposition,[status(thm)],[c_1230,c_4100]) ).
tcf(c_4115,plain,
iPr_def_10(inverse(iPr_def_19),iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4104,c_1215,c_3207]) ).
tcf(c_4571,plain,
! [X0: $i] : iPr_def_10(inverse(iPr_def_19),X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_4115,c_1128]) ).
tcf(c_4580,plain,
inverse(iPr_def_19) = iPr_def_16(iPr_def_19),
inference(superposition,[status(thm)],[c_4571,c_1080]) ).
tcf(c_4586,plain,
! [X0: $i] : iPr_def_11(iPr_def_16(iPr_def_19),X0) = inverse(iPr_def_16(iPr_def_19)),
inference(demodulation,[status(thm)],[c_3516,c_4580]) ).
tcf(c_4587,plain,
! [X0: $i] : iPr_def_10(iPr_def_19,X0) = inverse(iPr_def_16(iPr_def_19)),
inference(demodulation,[status(thm)],[c_3518,c_4580]) ).
tcf(c_4588,plain,
iPr_def_16(inverse(iPr_def_16(iPr_def_19))) = iPr_def_19,
inference(demodulation,[status(thm)],[c_3511,c_4580]) ).
tcf(c_4589,plain,
! [X0: $i] : multiply(X0,iPr_def_16(iPr_def_19)) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_3393,c_4580]) ).
tcf(c_4594,plain,
! [X0: $i] : iPr_def_16(iPr_def_13(iPr_def_16(iPr_def_19),iPr_def_19,X0)) = inverse(iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_4580,c_1215]) ).
tcf(c_4766,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(iPr_def_11(iPr_def_16(iPr_def_19),X0)),iPr_def_11(iPr_def_16(iPr_def_19),X0)) = multiply(inverse(X1),X1),
inference(light_normalisation,[status(thm)],[c_1075,c_3207,c_4580]) ).
tcf(c_4767,plain,
iPr_def_10(inverse(inverse(iPr_def_16(iPr_def_19))),inverse(iPr_def_16(iPr_def_19))) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4766,c_3207,c_4586]) ).
tcf(c_4780,plain,
! [X0: $i] : iPr_def_10(inverse(inverse(iPr_def_16(iPr_def_19))),X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_4767,c_1128]) ).
tcf(c_4782,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(inverse(inverse(iPr_def_16(iPr_def_19)))))) = iPr_def_10(iPr_def_10(X1,X2),X3),
inference(demodulation,[status(thm)],[c_2802,c_3207,c_4580,c_4586]) ).
tcf(c_4806,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(inverse(inverse(iPr_def_16(iPr_def_19))),X0),X1) = iPr_def_19,
inference(superposition,[status(thm)],[c_4782,c_3207]) ).
tcf(c_4818,plain,
! [X0: $i] : iPr_def_10(iPr_def_19,X0) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4806,c_4780]) ).
tcf(c_4829,plain,
inverse(iPr_def_16(iPr_def_19)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4587,c_4818]) ).
tcf(c_4831,plain,
iPr_def_16(iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4588,c_4829]) ).
tcf(c_4833,plain,
inverse(iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4580,c_4831]) ).
tcf(c_5019,plain,
! [X0: $i] : inverse(iPr_def_10(iPr_def_19,X0)) = inverse(inverse(inverse(iPr_def_19))),
inference(demodulation,[status(thm)],[c_1802,c_1935,c_1999,c_2281,c_3207]) ).
tcf(c_5031,plain,
! [X0: $i,X1: $i] : inverse(iPr_def_10(iPr_def_19,X0)) = inverse(iPr_def_10(iPr_def_19,X1)),
inference(superposition,[status(thm)],[c_5019,c_5019]) ).
tcf(c_5032,plain,
! [X0: $i] : inverse(iPr_def_10(iPr_def_19,X0)) = iPr_def_21,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_21])],[c_5031]) ).
tcf(c_5035,plain,
inverse(inverse(inverse(iPr_def_19))) = iPr_def_21,
inference(demodulation,[status(thm)],[c_5019,c_5032]) ).
tcf(c_5041,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(iPr_def_10(inverse(iPr_def_19),X0),inverse(multiply(X1,multiply(inverse(X0),X0))))) = iPr_def_10(iPr_def_10(X1,multiply(inverse(X0),X0)),X2),
inference(light_normalisation,[status(thm)],[c_336,c_3207]) ).
tcf(c_5042,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(iPr_def_10(inverse(iPr_def_19),X0),inverse(multiply(X1,iPr_def_19)))) = iPr_def_10(iPr_def_10(X1,iPr_def_19),X2),
inference(light_normalisation,[status(thm)],[c_5041,c_3207]) ).
tcf(c_5043,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_10(X0,iPr_def_19),X1) = iPr_def_16(iPr_def_13(X0,iPr_def_19,iPr_def_19)),
inference(demodulation,[status(thm)],[c_5042,c_1126,c_4818,c_4833]) ).
tcf(c_5049,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(X0,X1),X2) = iPr_def_16(iPr_def_13(X0,iPr_def_19,iPr_def_19)),
inference(superposition,[status(thm)],[c_1128,c_5043]) ).
tcf(c_5089,plain,
! [X0: $i] : iPr_def_11(iPr_def_19,X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_4831,c_1269]) ).
tcf(c_5227,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(iPr_def_16(X0)),X1) = iPr_def_13(iPr_def_19,iPr_def_19,X0),
inference(superposition,[status(thm)],[c_4833,c_1218]) ).
tcf(c_5228,plain,
! [X0: $i,X1: $i] : iPr_def_13(inverse(X0),X0,X1) = iPr_def_13(iPr_def_19,iPr_def_19,X1),
inference(demodulation,[status(thm)],[c_1218,c_5227]) ).
tcf(c_5935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_11(X1,X2)))),multiply(X0,inverse(multiply(X3,iPr_def_19)))) = iPr_def_10(inverse(multiply(X3,inverse(X1))),X4),
inference(demodulation,[status(thm)],[c_2826,c_3207,c_4833]) ).
tcf(c_5965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_11(X1,X2)))),multiply(X0,inverse(multiply(X3,iPr_def_19)))) = multiply(inverse(multiply(X4,inverse(iPr_def_11(X1,X5)))),multiply(X4,inverse(multiply(X3,iPr_def_19)))),
inference(superposition,[status(thm)],[c_5935,c_5935]) ).
tcf(c_5972,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_11(X1,X2)))),multiply(X0,inverse(multiply(X3,iPr_def_19)))) = iPr_def_23(X1,X3),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_23])],[c_5965]) ).
tcf(c_5975,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(inverse(multiply(X0,inverse(X1))),X2) = iPr_def_23(X1,X0),
inference(demodulation,[status(thm)],[c_5935,c_5972]) ).
tcf(c_6267,plain,
! [X0: $i] : multiply(X0,iPr_def_19) = iPr_def_16(X0),
inference(light_normalisation,[status(thm)],[c_4589,c_4831]) ).
tcf(c_6277,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(iPr_def_10(X0,iPr_def_19),inverse(iPr_def_10(iPr_def_10(X1,X2),iPr_def_19)))),X0) = iPr_def_10(inverse(multiply(iPr_def_19,inverse(X1))),multiply(iPr_def_19,iPr_def_19)),
inference(light_normalisation,[status(thm)],[c_170,c_3207,c_4833]) ).
tcf(c_6278,plain,
! [X0: $i,X1: $i] : iPr_def_13(iPr_def_10(X0,X1),iPr_def_19,iPr_def_19) = iPr_def_23(X0,iPr_def_19),
inference(demodulation,[status(thm)],[c_6277,c_1168,c_4833,c_5975]) ).
tcf(c_6283,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_19,iPr_def_19) = iPr_def_23(iPr_def_16(X0),iPr_def_19),
inference(superposition,[status(thm)],[c_1078,c_6278]) ).
tcf(c_6372,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(inverse(multiply(iPr_def_10(iPr_def_19,X0),inverse(multiply(X1,multiply(inverse(X0),X0))))),iPr_def_19) = iPr_def_11(iPr_def_10(X1,multiply(inverse(X0),X0)),X2),
inference(light_normalisation,[status(thm)],[c_332,c_3207,c_4833]) ).
tcf(c_6373,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(multiply(iPr_def_19,inverse(multiply(X0,iPr_def_19)))),iPr_def_19) = iPr_def_11(iPr_def_10(X0,iPr_def_19),X1),
inference(light_normalisation,[status(thm)],[c_6372,c_3207,c_4818]) ).
tcf(c_6374,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(multiply(iPr_def_19,inverse(iPr_def_16(X0)))),iPr_def_19) = iPr_def_11(iPr_def_10(X0,iPr_def_19),X1),
inference(light_normalisation,[status(thm)],[c_6373,c_6267]) ).
tcf(c_6375,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_10(X0,iPr_def_19),X1) = iPr_def_13(X0,iPr_def_19,iPr_def_19),
inference(demodulation,[status(thm)],[c_6374,c_5975,c_6283]) ).
tcf(c_6381,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_10(X0,X1),X2) = iPr_def_13(X0,iPr_def_19,iPr_def_19),
inference(superposition,[status(thm)],[c_1128,c_6375]) ).
tcf(c_6398,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_13(X0,iPr_def_19,iPr_def_19)) = iPr_def_11(X0,X1),
inference(demodulation,[status(thm)],[c_1517,c_6381]) ).
tcf(c_6416,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_10(X0,X1),X2) = iPr_def_16(iPr_def_23(X0,iPr_def_19)),
inference(superposition,[status(thm)],[c_6278,c_6398]) ).
tcf(c_6442,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_16(iPr_def_13(iPr_def_16(X0),iPr_def_19,iPr_def_19)),X1) = iPr_def_11(X0,X2),
inference(superposition,[status(thm)],[c_6398,c_1463]) ).
tcf(c_6446,plain,
! [X0: $i] : iPr_def_16(iPr_def_13(iPr_def_16(iPr_def_16(X0)),iPr_def_19,iPr_def_19)) = X0,
inference(superposition,[status(thm)],[c_6398,c_1269]) ).
tcf(c_6452,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_19,iPr_def_19) = iPr_def_16(iPr_def_23(X0,iPr_def_19)),
inference(demodulation,[status(thm)],[c_6416,c_6381]) ).
tcf(c_6453,plain,
! [X0: $i,X1: $i] : iPr_def_13(iPr_def_16(X0),iPr_def_19,iPr_def_19) = iPr_def_11(X0,X1),
inference(demodulation,[status(thm)],[c_6442,c_1078]) ).
tcf(c_6724,plain,
! [X0: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_19))),iPr_def_15(X0)) = iPr_def_10(inverse(iPr_def_19),iPr_def_19),
inference(superposition,[status(thm)],[c_3207,c_3405]) ).
tcf(c_6742,plain,
iPr_def_10(inverse(iPr_def_19),iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_6724,c_3207,c_3215]) ).
tcf(c_6773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_13(iPr_def_16(iPr_def_13(X0,iPr_def_19,iPr_def_10(X1,X2))),X1,X3) = iPr_def_23(iPr_def_10(X0,iPr_def_19),X3),
inference(demodulation,[status(thm)],[c_881,c_1126,c_3207,c_5975]) ).
tcf(c_6936,plain,
! [X0: $i] : iPr_def_13(iPr_def_16(iPr_def_16(X0)),iPr_def_19,iPr_def_19) = iPr_def_16(iPr_def_13(iPr_def_16(X0),iPr_def_19,iPr_def_19)),
inference(superposition,[status(thm)],[c_6446,c_6446]) ).
tcf(c_6943,plain,
! [X0: $i,X1: $i] : iPr_def_13(iPr_def_16(iPr_def_16(X0)),iPr_def_19,iPr_def_19) = iPr_def_10(X0,X1),
inference(superposition,[status(thm)],[c_6446,c_1078]) ).
tcf(c_6953,plain,
! [X0: $i] : iPr_def_13(iPr_def_16(iPr_def_16(iPr_def_16(X0))),iPr_def_19,iPr_def_19) = X0,
inference(demodulation,[status(thm)],[c_6446,c_6936]) ).
tcf(c_6981,plain,
! [X0: $i] : iPr_def_10(inverse(iPr_def_19),X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_6742,c_2089]) ).
tcf(c_6999,plain,
inverse(iPr_def_19) = iPr_def_15(iPr_def_19),
inference(superposition,[status(thm)],[c_6981,c_2078]) ).
tcf(c_7016,plain,
inverse(inverse(iPr_def_15(iPr_def_19))) = iPr_def_21,
inference(demodulation,[status(thm)],[c_5035,c_6999]) ).
tcf(c_7024,plain,
! [X0: $i] : iPr_def_10(iPr_def_19,X0) = inverse(iPr_def_15(iPr_def_19)),
inference(demodulation,[status(thm)],[c_3412,c_6999]) ).
tcf(c_7025,plain,
iPr_def_15(inverse(iPr_def_15(iPr_def_19))) = iPr_def_19,
inference(demodulation,[status(thm)],[c_3406,c_6999]) ).
tcf(c_7026,plain,
! [X0: $i] : multiply(X0,iPr_def_15(iPr_def_19)) = iPr_def_15(X0),
inference(demodulation,[status(thm)],[c_3215,c_6999]) ).
tcf(c_7081,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_13(iPr_def_10(X0,X1),iPr_def_19,iPr_def_19) = iPr_def_11(iPr_def_11(X0,X2),X3),
inference(superposition,[status(thm)],[c_1450,c_6453]) ).
tcf(c_7113,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(iPr_def_11(X0,X1),X2) = iPr_def_23(X0,iPr_def_19),
inference(demodulation,[status(thm)],[c_7081,c_6278]) ).
tcf(c_7240,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_15(X1)))),multiply(X0,inverse(iPr_def_15(iPr_def_19)))) = iPr_def_10(X1,iPr_def_15(iPr_def_19)),
inference(light_normalisation,[status(thm)],[c_3404,c_6999]) ).
tcf(c_7258,plain,
iPr_def_10(iPr_def_19,iPr_def_15(iPr_def_19)) = iPr_def_19,
inference(superposition,[status(thm)],[c_7240,c_3207]) ).
tcf(c_7259,plain,
inverse(iPr_def_15(iPr_def_19)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_7258,c_7024]) ).
tcf(c_7265,plain,
iPr_def_15(iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_7025,c_7259]) ).
tcf(c_7266,plain,
inverse(iPr_def_19) = iPr_def_21,
inference(demodulation,[status(thm)],[c_7016,c_7259]) ).
tcf(c_7267,plain,
iPr_def_15(iPr_def_19) = iPr_def_21,
inference(demodulation,[status(thm)],[c_6999,c_7266]) ).
tcf(c_7274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(X1))),multiply(X0,inverse(multiply(X2,inverse(X3))))) = iPr_def_23(multiply(iPr_def_16(X1),X3),X2),
inference(demodulation,[status(thm)],[c_502,c_3207,c_4833,c_5975,c_6267]) ).
tcf(c_7281,plain,
! [X0: $i,X1: $i] : iPr_def_23(multiply(iPr_def_16(multiply(X0,inverse(X1))),X1),X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_7274,c_3207]) ).
tcf(c_7355,plain,
! [X0: $i] : iPr_def_16(iPr_def_13(iPr_def_19,iPr_def_19,X0)) = inverse(iPr_def_16(X0)),
inference(light_normalisation,[status(thm)],[c_4594,c_4831]) ).
tcf(c_7369,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(inverse(iPr_def_16(iPr_def_10(X0,X1))),X0,X2) = iPr_def_23(iPr_def_10(iPr_def_19,iPr_def_19),X2),
inference(superposition,[status(thm)],[c_7355,c_6773]) ).
tcf(c_7371,plain,
! [X0: $i] : iPr_def_13(iPr_def_19,iPr_def_19,X0) = iPr_def_23(iPr_def_19,X0),
inference(demodulation,[status(thm)],[c_7369,c_1080,c_4818,c_5228]) ).
tcf(c_7372,plain,
! [X0: $i] : iPr_def_16(iPr_def_23(iPr_def_19,X0)) = inverse(iPr_def_16(X0)),
inference(demodulation,[status(thm)],[c_7355,c_7371]) ).
tcf(c_7378,plain,
! [X0: $i] : iPr_def_11(iPr_def_19,X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_7265,c_2338]) ).
tcf(c_7381,plain,
! [X0: $i] : iPr_def_10(iPr_def_19,X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_7265,c_2083]) ).
tcf(c_7388,plain,
! [X0: $i,X1: $i] : iPr_def_12(X0,X1) = iPr_def_19,
inference(demodulation,[status(thm)],[c_3218,c_7378]) ).
tcf(c_7451,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(iPr_def_16(X0)),X1) = iPr_def_23(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_7372,c_1078]) ).
tcf(c_7455,plain,
iPr_def_19 = iPr_def_21,
inference(light_normalisation,[status(thm)],[c_7267,c_7265]) ).
tcf(c_7456,plain,
inverse(iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_7266,c_7455]) ).
tcf(c_7606,plain,
! [X0: $i] : multiply(X0,iPr_def_19) = iPr_def_15(X0),
inference(light_normalisation,[status(thm)],[c_7026,c_7265]) ).
tcf(c_7629,plain,
! [X0: $i,X1: $i] : multiply(inverse(iPr_def_10(X0,X1)),iPr_def_15(iPr_def_11(X0,X1))) = iPr_def_19,
inference(demodulation,[status(thm)],[c_1785,c_3207,c_7456,c_7388,c_7606]) ).
tcf(c_7655,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(iPr_def_10(X0,X1)),iPr_def_15(iPr_def_11(X0,X2))) = iPr_def_19,
inference(superposition,[status(thm)],[c_2236,c_7629]) ).
tcf(c_7939,plain,
! [X0: $i,X1: $i] : iPr_def_15(multiply(inverse(iPr_def_15(X0)),multiply(X0,inverse(X1)))) = inverse(X1),
inference(demodulation,[status(thm)],[c_1988,c_2078,c_3207,c_7381,c_7456,c_7606]) ).
tcf(c_7949,plain,
! [X0: $i] : iPr_def_15(multiply(inverse(iPr_def_19),multiply(iPr_def_19,inverse(X0)))) = inverse(X0),
inference(superposition,[status(thm)],[c_7265,c_7939]) ).
tcf(c_7951,plain,
! [X0: $i] : iPr_def_15(multiply(inverse(iPr_def_15(inverse(inverse(X0)))),iPr_def_19)) = inverse(X0),
inference(superposition,[status(thm)],[c_3207,c_7939]) ).
tcf(c_7961,plain,
! [X0: $i] : iPr_def_15(iPr_def_15(inverse(iPr_def_15(inverse(inverse(X0)))))) = inverse(X0),
inference(demodulation,[status(thm)],[c_7951,c_7606]) ).
tcf(c_7962,plain,
! [X0: $i] : iPr_def_15(multiply(iPr_def_19,multiply(iPr_def_19,inverse(X0)))) = inverse(X0),
inference(demodulation,[status(thm)],[c_7949,c_7456]) ).
tcf(c_8016,plain,
! [X0: $i,X1: $i] : iPr_def_15(inverse(iPr_def_15(inverse(inverse(X0))))) = iPr_def_10(inverse(X0),X1),
inference(superposition,[status(thm)],[c_7961,c_2083]) ).
tcf(c_8028,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_19,multiply(iPr_def_19,inverse(X0))) = iPr_def_10(inverse(X0),X1),
inference(superposition,[status(thm)],[c_7962,c_2083]) ).
tcf(c_8100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_19))),multiply(X0,inverse(iPr_def_15(iPr_def_11(X1,X2))))) = iPr_def_10(inverse(iPr_def_10(X1,X3)),iPr_def_15(iPr_def_11(X1,X2))),
inference(superposition,[status(thm)],[c_7655,c_1734]) ).
tcf(c_8106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(iPr_def_15(X0)),multiply(X0,inverse(iPr_def_15(iPr_def_11(X1,X2))))) = multiply(iPr_def_19,multiply(iPr_def_19,inverse(iPr_def_10(X1,X3)))),
inference(demodulation,[status(thm)],[c_8100,c_7456,c_7606,c_8028]) ).
tcf(c_8107,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_19,multiply(iPr_def_19,inverse(iPr_def_10(X0,X1)))) = iPr_def_25(X0),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_25])],[c_8106]) ).
tcf(c_8134,plain,
! [X0: $i,X1: $i] : iPr_def_13(iPr_def_13(iPr_def_16(iPr_def_16(X0)),iPr_def_19,iPr_def_19),iPr_def_19,X1) = iPr_def_23(X0,X1),
inference(demodulation,[status(thm)],[c_884,c_3207,c_4833,c_5089,c_5975,c_6943]) ).
tcf(c_8136,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,iPr_def_19,X1) = iPr_def_23(iPr_def_16(X0),X1),
inference(superposition,[status(thm)],[c_6953,c_8134]) ).
tcf(c_8642,plain,
! [X0: $i] : multiply(iPr_def_19,multiply(iPr_def_19,inverse(X0))) = iPr_def_15(inverse(iPr_def_15(inverse(inverse(X0))))),
inference(superposition,[status(thm)],[c_8028,c_8016]) ).
tcf(c_8887,plain,
! [X0: $i,X1: $i] : iPr_def_15(inverse(iPr_def_15(inverse(inverse(iPr_def_10(X0,X1)))))) = iPr_def_25(X0),
inference(demodulation,[status(thm)],[c_8107,c_8642]) ).
tcf(c_8901,plain,
! [X0: $i] : iPr_def_15(inverse(iPr_def_15(inverse(inverse(X0))))) = iPr_def_25(iPr_def_15(X0)),
inference(superposition,[status(thm)],[c_2083,c_8887]) ).
tcf(c_8921,plain,
! [X0: $i] : iPr_def_15(iPr_def_25(iPr_def_15(X0))) = inverse(X0),
inference(demodulation,[status(thm)],[c_7961,c_8901]) ).
tcf(c_9309,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(X1))) = iPr_def_16(iPr_def_23(X1,X0)),
inference(superposition,[status(thm)],[c_5975,c_1080]) ).
tcf(c_9343,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_15(iPr_def_25(iPr_def_15(iPr_def_11(X0,X1)))) = inverse(iPr_def_11(X0,X2)),
inference(superposition,[status(thm)],[c_2479,c_8921]) ).
tcf(c_9360,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(iPr_def_11(X0,X1)) = inverse(iPr_def_11(X0,X2)),
inference(demodulation,[status(thm)],[c_9343,c_8921]) ).
tcf(c_9361,plain,
! [X0: $i,X1: $i] : inverse(iPr_def_11(X0,X1)) = iPr_def_27(X0),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_27])],[c_9360]) ).
tcf(c_15359,plain,
! [X0: $i] : iPr_def_23(multiply(iPr_def_16(multiply(X0,iPr_def_19)),iPr_def_19),X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_4833,c_7281]) ).
tcf(c_15363,plain,
! [X0: $i] : iPr_def_13(iPr_def_16(iPr_def_16(X0)),iPr_def_19,X0) = iPr_def_19,
inference(demodulation,[status(thm)],[c_15359,c_6267,c_8136]) ).
tcf(c_15532,plain,
! [X0: $i] : multiply(iPr_def_16(iPr_def_19),iPr_def_16(X0)) = iPr_def_10(iPr_def_16(iPr_def_16(X0)),iPr_def_19),
inference(superposition,[status(thm)],[c_15363,c_4100]) ).
tcf(c_15548,plain,
! [X0: $i] : multiply(iPr_def_19,iPr_def_16(X0)) = iPr_def_16(X0),
inference(demodulation,[status(thm)],[c_15532,c_1078,c_4831]) ).
tcf(c_15587,plain,
! [X0: $i] : multiply(iPr_def_19,X0) = X0,
inference(superposition,[status(thm)],[c_1523,c_15548]) ).
tcf(c_15601,plain,
( ( a2 != a2 )
| ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
inference(demodulation,[status(thm)],[c_3423,c_15587]) ).
tcf(c_15603,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(equality_resolution_simp,[status(thm)],[c_15601]) ).
tcf(c_15606,plain,
! [X0: $i] : iPr_def_16(iPr_def_23(X0,iPr_def_19)) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_15587,c_9309]) ).
tcf(c_15612,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_19,iPr_def_19) = inverse(inverse(X0)),
inference(demodulation,[status(thm)],[c_6452,c_15606]) ).
tcf(c_15617,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(X0,X1),X2) = iPr_def_16(inverse(inverse(X0))),
inference(demodulation,[status(thm)],[c_5049,c_15612]) ).
tcf(c_15701,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(iPr_def_16(X0))),multiply(iPr_def_23(iPr_def_19,X0),inverse(X1))) = iPr_def_10(inverse(X1),X2),
inference(superposition,[status(thm)],[c_7372,c_4024]) ).
tcf(c_15703,plain,
! [X0: $i,X1: $i] : multiply(inverse(iPr_def_16(iPr_def_19)),inverse(X0)) = iPr_def_10(inverse(X0),X1),
inference(superposition,[status(thm)],[c_15587,c_4024]) ).
tcf(c_15713,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(iPr_def_16(X0)),multiply(X0,iPr_def_16(iPr_def_23(X1,X2)))) = iPr_def_10(iPr_def_16(iPr_def_23(X1,X2)),X3),
inference(superposition,[status(thm)],[c_9309,c_4024]) ).
tcf(c_15731,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(X0),X1) = inverse(X0),
inference(demodulation,[status(thm)],[c_15703,c_4831,c_4833,c_15587]) ).
tcf(c_15737,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(iPr_def_16(X0)),multiply(X0,iPr_def_16(iPr_def_23(X1,X2)))) = iPr_def_23(X1,X2),
inference(demodulation,[status(thm)],[c_15713,c_1078]) ).
tcf(c_15743,plain,
! [X0: $i] : inverse(iPr_def_16(X0)) = iPr_def_23(iPr_def_19,X0),
inference(demodulation,[status(thm)],[c_7451,c_15731]) ).
tcf(c_16723,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_16(iPr_def_23(X0,X1)),X2) = iPr_def_16(iPr_def_23(X0,X1)),
inference(superposition,[status(thm)],[c_9309,c_15731]) ).
tcf(c_16728,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(inverse(X0),X1) = iPr_def_11(inverse(X0),X2),
inference(superposition,[status(thm)],[c_15731,c_1461]) ).
tcf(c_16730,plain,
! [X0: $i] : iPr_def_16(inverse(X0)) = inverse(X0),
inference(superposition,[status(thm)],[c_15731,c_1080]) ).
tcf(c_16734,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X1) = inverse(X0),
inference(demodulation,[status(thm)],[c_16728,c_15731]) ).
tcf(c_16735,plain,
! [X0: $i,X1: $i] : iPr_def_16(iPr_def_23(X0,X1)) = iPr_def_23(X0,X1),
inference(demodulation,[status(thm)],[c_16723,c_1078]) ).
tcf(c_16736,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(X1))) = iPr_def_23(X1,X0),
inference(demodulation,[status(thm)],[c_9309,c_16735]) ).
tcf(c_16898,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_10(inverse(X0),X1),X2) = inverse(X0),
inference(superposition,[status(thm)],[c_16734,c_1461]) ).
tcf(c_16903,plain,
! [X0: $i] : inverse(inverse(inverse(X0))) = inverse(X0),
inference(demodulation,[status(thm)],[c_16898,c_15617,c_16730]) ).
tcf(c_16980,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_16(iPr_def_13(X0,X1,X2)) = iPr_def_23(multiply(X0,X1),X2),
inference(demodulation,[status(thm)],[c_1126,c_16736]) ).
tcf(c_17012,plain,
! [X0: $i] : inverse(inverse(X0)) = iPr_def_23(X0,iPr_def_19),
inference(demodulation,[status(thm)],[c_15606,c_16735]) ).
tcf(c_17013,plain,
! [X0: $i] : inverse(iPr_def_23(X0,iPr_def_19)) = inverse(X0),
inference(demodulation,[status(thm)],[c_16903,c_17012]) ).
tcf(c_17113,plain,
! [X0: $i] : inverse(iPr_def_13(X0,iPr_def_19,iPr_def_19)) = inverse(iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_8136,c_17013]) ).
tcf(c_17125,plain,
! [X0: $i] : iPr_def_23(iPr_def_19,X0) = inverse(X0),
inference(demodulation,[status(thm)],[c_17113,c_15612,c_15743,c_17012,c_17013]) ).
tcf(c_17128,plain,
! [X0: $i] : inverse(iPr_def_16(X0)) = inverse(X0),
inference(demodulation,[status(thm)],[c_15743,c_17125]) ).
tcf(c_17258,plain,
! [X0: $i,X1: $i] : inverse(iPr_def_16(iPr_def_11(X0,X1))) = iPr_def_27(iPr_def_16(X0)),
inference(superposition,[status(thm)],[c_1452,c_9361]) ).
tcf(c_17262,plain,
! [X0: $i,X1: $i] : iPr_def_27(iPr_def_11(X0,X1)) = inverse(iPr_def_23(X0,iPr_def_19)),
inference(superposition,[status(thm)],[c_7113,c_9361]) ).
tcf(c_17263,plain,
inverse(iPr_def_19) = iPr_def_27(iPr_def_19),
inference(superposition,[status(thm)],[c_5089,c_9361]) ).
tcf(c_17264,plain,
! [X0: $i] : inverse(inverse(X0)) = iPr_def_27(inverse(X0)),
inference(superposition,[status(thm)],[c_16734,c_9361]) ).
tcf(c_17271,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_27(X0),X1) = iPr_def_27(X0),
inference(superposition,[status(thm)],[c_9361,c_15731]) ).
tcf(c_17274,plain,
iPr_def_27(iPr_def_19) = iPr_def_19,
inference(demodulation,[status(thm)],[c_17263,c_4833]) ).
tcf(c_17275,plain,
! [X0: $i] : iPr_def_23(X0,iPr_def_19) = iPr_def_27(inverse(X0)),
inference(demodulation,[status(thm)],[c_17264,c_17012]) ).
tcf(c_17278,plain,
! [X0: $i,X1: $i] : iPr_def_27(iPr_def_11(X0,X1)) = inverse(X0),
inference(demodulation,[status(thm)],[c_17262,c_17013]) ).
tcf(c_17279,plain,
! [X0: $i] : iPr_def_27(iPr_def_16(X0)) = iPr_def_27(X0),
inference(demodulation,[status(thm)],[c_17258,c_9361,c_17128]) ).
tcf(c_17336,plain,
! [X0: $i,X1: $i] : iPr_def_27(iPr_def_16(iPr_def_11(X0,X1))) = iPr_def_27(X0),
inference(superposition,[status(thm)],[c_1523,c_17279]) ).
tcf(c_17338,plain,
! [X0: $i] : inverse(X0) = iPr_def_27(X0),
inference(demodulation,[status(thm)],[c_17336,c_17278,c_17279]) ).
tcf(c_17343,plain,
! [X0: $i] : iPr_def_23(iPr_def_19,X0) = iPr_def_27(X0),
inference(demodulation,[status(thm)],[c_17125,c_17338]) ).
tcf(c_17351,plain,
! [X0: $i] : multiply(iPr_def_27(X0),X0) = iPr_def_19,
inference(demodulation,[status(thm)],[c_3207,c_17338]) ).
tcf(c_17360,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_16(iPr_def_13(X0,X1,X2)),multiply(X2,iPr_def_27(X1))) = iPr_def_10(X0,X1),
inference(demodulation,[status(thm)],[c_1130,c_17338]) ).
tcf(c_17397,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_27(X0),multiply(X0,iPr_def_23(X1,X2))) = iPr_def_23(X1,X2),
inference(demodulation,[status(thm)],[c_15737,c_16735,c_17279,c_17338]) ).
tcf(c_17487,plain,
! [X0: $i] : iPr_def_23(X0,iPr_def_19) = iPr_def_27(iPr_def_27(X0)),
inference(light_normalisation,[status(thm)],[c_17275,c_17338]) ).
tcf(c_17788,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_19,iPr_def_19) = inverse(iPr_def_27(X0)),
inference(light_normalisation,[status(thm)],[c_15612,c_17338]) ).
tcf(c_17789,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_19,iPr_def_19) = iPr_def_23(X0,iPr_def_19),
inference(demodulation,[status(thm)],[c_17788,c_17338,c_17487]) ).
tcf(c_17793,plain,
! [X0: $i] : multiply(iPr_def_16(iPr_def_23(X0,iPr_def_19)),multiply(iPr_def_19,iPr_def_27(iPr_def_19))) = iPr_def_10(X0,iPr_def_19),
inference(superposition,[status(thm)],[c_17789,c_17360]) ).
tcf(c_17797,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_19) = iPr_def_23(X0,iPr_def_19),
inference(demodulation,[status(thm)],[c_17793,c_6267,c_17274,c_15587,c_16735]) ).
tcf(c_17798,plain,
! [X0: $i] : iPr_def_13(X0,iPr_def_19,iPr_def_19) = iPr_def_10(X0,iPr_def_19),
inference(demodulation,[status(thm)],[c_17789,c_17797]) ).
tcf(c_17800,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_19) = iPr_def_27(iPr_def_27(X0)),
inference(demodulation,[status(thm)],[c_17487,c_17797]) ).
tcf(c_17859,plain,
! [X0: $i] : iPr_def_10(iPr_def_16(X0),iPr_def_19) = iPr_def_13(X0,iPr_def_19,iPr_def_19),
inference(superposition,[status(thm)],[c_17797,c_8136]) ).
tcf(c_17861,plain,
! [X0: $i] : iPr_def_10(X0,iPr_def_19) = X0,
inference(demodulation,[status(thm)],[c_17859,c_1078,c_17798]) ).
tcf(c_17862,plain,
! [X0: $i] : iPr_def_23(X0,iPr_def_19) = X0,
inference(demodulation,[status(thm)],[c_17797,c_17861]) ).
tcf(c_18070,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(inverse(iPr_def_16(X0))),multiply(iPr_def_27(X0),inverse(X1))) = iPr_def_10(inverse(X1),X2),
inference(light_normalisation,[status(thm)],[c_15701,c_17343]) ).
tcf(c_18071,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(iPr_def_27(X0),iPr_def_27(X1))) = iPr_def_27(X1),
inference(demodulation,[status(thm)],[c_18070,c_17271,c_17279,c_17338,c_17800,c_17861]) ).
tcf(c_18110,plain,
! [X0: $i,X1: $i] : iPr_def_10(X0,X1) = X0,
inference(superposition,[status(thm)],[c_17861,c_1128]) ).
tcf(c_18122,plain,
! [X0: $i] : iPr_def_16(X0) = X0,
inference(demodulation,[status(thm)],[c_1078,c_18110]) ).
tcf(c_18129,plain,
! [X0: $i,X1: $i] : iPr_def_13(X0,iPr_def_19,X1) = iPr_def_23(X0,X1),
inference(demodulation,[status(thm)],[c_8136,c_18122]) ).
tcf(c_18130,plain,
! [X0: $i] : multiply(X0,iPr_def_19) = X0,
inference(demodulation,[status(thm)],[c_6267,c_18122]) ).
tcf(c_18132,plain,
! [X0: $i,X1: $i] : iPr_def_11(iPr_def_16(X0),X1) = X0,
inference(demodulation,[status(thm)],[c_1269,c_18122]) ).
tcf(c_18136,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_23(multiply(X0,X1),X2) = iPr_def_13(X0,X1,X2),
inference(demodulation,[status(thm)],[c_16980,c_18122]) ).
tcf(c_18150,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_27(X0),multiply(X0,X1)) = X1,
inference(superposition,[status(thm)],[c_17862,c_17397]) ).
tcf(c_18160,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,X1) = X0,
inference(light_normalisation,[status(thm)],[c_18132,c_18122]) ).
tcf(c_18180,plain,
! [X0: $i] : iPr_def_27(iPr_def_27(X0)) = X0,
inference(demodulation,[status(thm)],[c_17800,c_18110]) ).
tcf(c_18187,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(iPr_def_27(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_18180,c_18071]) ).
tcf(c_18209,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_23(X0,X1),X1) = X0,
inference(demodulation,[status(thm)],[c_1131,c_17338,c_17351,c_18110,c_18122,c_18129]) ).
tcf(c_18310,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_27(X0),iPr_def_23(X0,iPr_def_27(X1))) = X1,
inference(demodulation,[status(thm)],[c_1355,c_17274,c_17338,c_17351,c_18110,c_18122,c_18129,c_18130,c_18160]) ).
tcf(c_18318,plain,
! [X0: $i,X1: $i] : iPr_def_23(X0,iPr_def_27(X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_18310,c_18187]) ).
tcf(c_18324,plain,
! [X0: $i,X1: $i] : multiply(X0,iPr_def_27(X1)) = iPr_def_23(X0,X1),
inference(superposition,[status(thm)],[c_18180,c_18318]) ).
tcf(c_18352,plain,
! [X0: $i,X1: $i] : iPr_def_27(iPr_def_23(X0,X1)) = iPr_def_23(X1,X0),
inference(demodulation,[status(thm)],[c_16736,c_17338,c_18324]) ).
tcf(c_18357,plain,
! [X0: $i,X1: $i] : iPr_def_23(iPr_def_27(X0),X1) = iPr_def_27(multiply(X1,X0)),
inference(superposition,[status(thm)],[c_18318,c_18352]) ).
tcf(c_18364,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,iPr_def_23(X1,X2)) = iPr_def_23(X0,iPr_def_23(X2,X1)),
inference(superposition,[status(thm)],[c_18352,c_18324]) ).
tcf(c_18479,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_23(iPr_def_23(X0,X1),iPr_def_23(X2,X1)) = iPr_def_23(X0,X2),
inference(demodulation,[status(thm)],[c_1307,c_17338,c_17351,c_18110,c_18129,c_18180,c_18324,c_18357,c_18364]) ).
tcf(c_18491,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_23(iPr_def_23(X0,iPr_def_27(X1)),multiply(X2,X1)) = iPr_def_23(X0,X2),
inference(superposition,[status(thm)],[c_18318,c_18479]) ).
tcf(c_18503,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,X1,multiply(X2,X1)) = iPr_def_23(X0,X2),
inference(demodulation,[status(thm)],[c_18491,c_18136,c_18318]) ).
tcf(c_18569,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(iPr_def_13(X0,X1,X2),X2) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_18136,c_18209]) ).
tcf(c_18571,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = iPr_def_13(X0,X1,iPr_def_27(X2)),
inference(superposition,[status(thm)],[c_18136,c_18318]) ).
tcf(c_18576,plain,
multiply(a3,multiply(b3,c3)) != iPr_def_13(a3,b3,iPr_def_27(c3)),
inference(demodulation,[status(thm)],[c_15603,c_18571]) ).
tcf(c_18610,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,multiply(X1,X2),X2) = iPr_def_23(X0,iPr_def_27(X1)),
inference(superposition,[status(thm)],[c_18150,c_18503]) ).
tcf(c_18620,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_13(X0,multiply(X1,X2),X2) = multiply(X0,X1),
inference(demodulation,[status(thm)],[c_18610,c_18318]) ).
tcf(c_18698,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(superposition,[status(thm)],[c_18620,c_18569]) ).
tcf(c_18703,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,X2)) = iPr_def_13(X0,X1,iPr_def_27(X2)),
inference(demodulation,[status(thm)],[c_18698,c_18571]) ).
tcf(c_18705,plain,
iPr_def_13(a3,b3,iPr_def_27(c3)) != iPr_def_13(a3,b3,iPr_def_27(c3)),
inference(demodulation,[status(thm)],[c_18576,c_18703]) ).
tcf(c_18707,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_18705]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP051-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 13:24:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 189.72/27.43 % SZS status Started for theBenchmark.p
% 189.72/27.43 % SZS status Unsatisfiable for theBenchmark.p
% 189.72/27.43
% 189.72/27.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 189.72/27.43
% 189.72/27.43 % ------ iProver source info
% 189.72/27.43
% 189.72/27.43 % git: date: 2026-07-19 20:42:38 +0200
% 189.72/27.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 189.72/27.43 % git: non_committed_changes: false
% 189.72/27.43
% 189.72/27.43 % ------ Parsing...% successful
% 189.72/27.43
% 189.72/27.43
% 189.72/27.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 189.72/27.43
% 189.72/27.43 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 189.72/27.43
% 189.72/27.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 189.72/27.43
% 189.72/27.43 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 189.72/27.43 % ------ Proving...
% 189.72/27.43 % ------ Problem Properties
% 189.72/27.43
% 189.72/27.43 %
% 189.72/27.43 % clauses 2
% 189.72/27.43 % conjectures 1
% 189.72/27.43 % EPR 0
% 189.72/27.43 % Horn 2
% 189.72/27.43 % unary 1
% 189.72/27.43 % binary 0
% 189.72/27.43 % lits 4
% 189.72/27.43 % lits eq 4
% 189.72/27.43 % fd_pure 0
% 189.72/27.43 % fd_pseudo 0
% 189.72/27.43 % fd_cond 0
% 189.72/27.43 % fd_pseudo_cond 0
% 189.72/27.43 % AC symbols 0
% 189.72/27.43
% 189.72/27.43 % ------ Input Options Time Limit: Unbounded
% 189.72/27.43
% 189.72/27.43
% 189.72/27.43 % ------
% 189.72/27.43 % Current options:
% 189.72/27.43 % ------
% 189.72/27.43
% 189.72/27.43
% 189.72/27.43 %
% 189.72/27.43
% 189.72/27.43 % ------ Proving...
% 189.72/27.43 %
% 189.72/27.43
% 189.72/27.43 % SZS status Unsatisfiable for theBenchmark.p
% 189.72/27.43
% 189.72/27.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 189.72/27.44
% 189.72/27.44
%------------------------------------------------------------------------------