%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.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 01:30:25 PM UTC 2026
% Result : Unsatisfiable 21.20s 4.73s
% Output : CNFRefutation 21.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 13
% Syntax : Number of formulae : 237 ( 230 unt; 11 def)
% Number of atoms : 897 ( 248 equ)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 32 ( 20 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 12 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 152 ( 0 sgn 152 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
file('/export/starexec/sandbox/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/sandbox/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,X3: $i] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(X3,inverse(X3)))) = X2,
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_69,definition,
iPr_def_10 = inverse(b2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_70,definition,
iPr_def_11 = multiply(iPr_def_10,b2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_71,definition,
iPr_def_12 = multiply(iPr_def_11,a2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_72,definition,
iPr_def_13 = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_73,definition,
iPr_def_14 = multiply(iPr_def_13,c3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_74,definition,
iPr_def_15 = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_75,definition,
iPr_def_16 = multiply(a3,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_76,definition,
iPr_def_17 = inverse(a1),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_77,definition,
iPr_def_18 = multiply(iPr_def_17,a1),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_78,definition,
iPr_def_19 = inverse(b1),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_79,definition,
iPr_def_20 = multiply(iPr_def_19,b1),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_80,negated_conjecture,
( ( iPr_def_18 != iPr_def_20 )
| ( iPr_def_14 != iPr_def_16 )
| ( iPr_def_12 != a2 ) ),
inference(demodulation,[status(thm)],[c_52,c_78,c_79,c_76,c_77,c_74,c_75,c_72,c_73,c_69,c_70,c_71]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_13,X0)),a3),b3),multiply(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_72,c_51]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_15,X0)),b3),c3),multiply(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_74,c_51]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_11,X0)),iPr_def_10),b2),multiply(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_70,c_51]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_18,X0)),iPr_def_17),a1),multiply(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_77,c_51]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_20,X0)),iPr_def_19),b1),multiply(X1,inverse(X1)))) = X0,
inference(superposition,[status(thm)],[c_79,c_51]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(a1,iPr_def_17))) = X2,
inference(superposition,[status(thm)],[c_76,c_51]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3)))) = multiply(X4,inverse(X4)),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_167,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),multiply(X0,inverse(X0)))) = c3,
inference(superposition,[status(thm)],[c_73,c_140]) ).
tcf(c_169,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_13,X0)),a3),b3),multiply(a1,iPr_def_17))) = X0,
inference(superposition,[status(thm)],[c_76,c_140]) ).
tcf(c_193,plain,
inverse(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),multiply(a1,iPr_def_17))) = c3,
inference(superposition,[status(thm)],[c_76,c_167]) ).
tcf(c_194,plain,
inverse(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),multiply(b1,iPr_def_19))) = c3,
inference(superposition,[status(thm)],[c_78,c_167]) ).
tcf(c_195,plain,
inverse(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),multiply(b2,iPr_def_10))) = c3,
inference(superposition,[status(thm)],[c_69,c_167]) ).
tcf(c_228,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(c3,multiply(inverse(iPr_def_14),a3)),b3),multiply(X0,inverse(X0)))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_193,c_51]) ).
tcf(c_249,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(c3,multiply(inverse(iPr_def_14),a3)),b3),multiply(X0,inverse(X0)))) = multiply(b1,iPr_def_19),
inference(superposition,[status(thm)],[c_194,c_51]) ).
tcf(c_253,plain,
multiply(a1,iPr_def_17) = multiply(b1,iPr_def_19),
inference(light_normalisation,[status(thm)],[c_249,c_228]) ).
tcf(c_259,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(c3,multiply(inverse(iPr_def_14),a3)),b3),multiply(X0,inverse(X0)))) = multiply(b2,iPr_def_10),
inference(superposition,[status(thm)],[c_195,c_51]) ).
tcf(c_263,plain,
multiply(a1,iPr_def_17) = multiply(b2,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_259,c_228]) ).
tcf(c_314,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_15,X0)),b3),c3),multiply(b2,iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_69,c_141]) ).
tcf(c_325,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_15,X0)),b3),c3),multiply(a1,iPr_def_17))) = X0,
inference(light_normalisation,[status(thm)],[c_314,c_263]) ).
tcf(c_375,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_11,X0)),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(multiply(iPr_def_13,X1)),a3),b3),multiply(a1,iPr_def_17)),X1))) = X0,
inference(superposition,[status(thm)],[c_169,c_142]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_11,X0)),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(multiply(iPr_def_15,X1)),b3),c3),multiply(a1,iPr_def_17)),X1))) = X0,
inference(superposition,[status(thm)],[c_325,c_142]) ).
tcf(c_1066,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_18,X0)),iPr_def_17),a1),multiply(b2,iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_69,c_146]) ).
tcf(c_1095,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_18,X0)),iPr_def_17),a1),multiply(a1,iPr_def_17))) = X0,
inference(light_normalisation,[status(thm)],[c_1066,c_263]) ).
tcf(c_1293,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_20,X0)),iPr_def_19),b1),multiply(b2,iPr_def_10))) = X0,
inference(superposition,[status(thm)],[c_69,c_147]) ).
tcf(c_1325,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(iPr_def_20,X0)),iPr_def_19),b1),multiply(a1,iPr_def_17))) = X0,
inference(light_normalisation,[status(thm)],[c_1293,c_263]) ).
tcf(c_1577,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(a1,iPr_def_17),X0)),b1),iPr_def_19),multiply(a1,iPr_def_17))) = X0,
inference(superposition,[status(thm)],[c_253,c_149]) ).
tcf(c_1579,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_149,c_149]) ).
tcf(c_1580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(multiply(multiply(X0,multiply(inverse(multiply(multiply(X1,X2),X0)),X1)),X2),multiply(X3,inverse(X3)))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_149,c_51]) ).
tcf(c_1696,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_152,c_1580]) ).
tcf(c_1710,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(a1,iPr_def_17)),X2) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_149,c_1696]) ).
tcf(c_1721,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(multiply(a1,iPr_def_17),X0)),X1),inverse(X1)),multiply(a1,iPr_def_17))) = X0,
inference(superposition,[status(thm)],[c_1696,c_149]) ).
tcf(c_1722,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),X0),X1),multiply(a1,iPr_def_17))) = inverse(multiply(X0,X1)),
inference(superposition,[status(thm)],[c_1696,c_149]) ).
tcf(c_1986,plain,
! [X0: $i,X1: $i] : multiply(multiply(multiply(multiply(inverse(multiply(multiply(a1,iPr_def_17),X0)),X1),inverse(X1)),multiply(a1,iPr_def_17)),X0) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_1721,c_1696]) ).
tcf(c_2010,plain,
! [X0: $i] : inverse(multiply(X0,inverse(multiply(inverse(multiply(a1,iPr_def_17)),X0)))) = inverse(multiply(multiply(a1,iPr_def_17),multiply(a1,iPr_def_17))),
inference(superposition,[status(thm)],[c_1696,c_1722]) ).
tcf(c_2011,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(a1,iPr_def_17),X0),multiply(a1,iPr_def_17))) = inverse(multiply(inverse(inverse(multiply(a1,iPr_def_17))),X0)),
inference(superposition,[status(thm)],[c_1696,c_1722]) ).
tcf(c_2397,plain,
inverse(multiply(inverse(inverse(multiply(a1,iPr_def_17))),inverse(multiply(a1,iPr_def_17)))) = inverse(multiply(multiply(a1,iPr_def_17),multiply(a1,iPr_def_17))),
inference(superposition,[status(thm)],[c_1696,c_2010]) ).
tcf(c_3558,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(inverse(multiply(multiply(X0,X1),inverse(multiply(a1,iPr_def_17)))),X0),X1)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_1579,c_1722]) ).
tcf(c_4356,plain,
inverse(multiply(multiply(inverse(multiply(a1,iPr_def_17)),a1),iPr_def_17)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_1696,c_3558]) ).
tcf(c_4377,plain,
inverse(multiply(multiply(inverse(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17)))),b1),iPr_def_19)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_253,c_3558]) ).
tcf(c_4378,plain,
inverse(multiply(multiply(inverse(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17)))),b2),iPr_def_10)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_263,c_3558]) ).
tcf(c_4379,plain,
! [X0: $i] : inverse(multiply(multiply(inverse(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17)))),X0),inverse(X0))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_1696,c_3558]) ).
tcf(c_4413,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(multiply(X0,X1),inverse(multiply(a1,iPr_def_17))))),X0),multiply(a1,iPr_def_17))) = X1,
inference(superposition,[status(thm)],[c_3558,c_149]) ).
tcf(c_4578,plain,
multiply(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),a1),multiply(a1,iPr_def_17)),iPr_def_17) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_4356,c_1710]) ).
tcf(c_4579,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),a1),multiply(a1,iPr_def_17))) = iPr_def_17,
inference(superposition,[status(thm)],[c_4356,c_149]) ).
tcf(c_4580,plain,
multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),a1),iPr_def_17),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_4356,c_1696]) ).
tcf(c_4624,plain,
inverse(multiply(inverse(inverse(multiply(a1,iPr_def_17))),a1)) = iPr_def_17,
inference(demodulation,[status(thm)],[c_4579,c_1696,c_2011]) ).
tcf(c_4658,plain,
inverse(multiply(multiply(inverse(multiply(a1,iPr_def_17)),b1),iPr_def_19)) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4377,c_1696]) ).
tcf(c_4659,plain,
multiply(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),b1),multiply(a1,iPr_def_17)),iPr_def_19) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_4658,c_1710]) ).
tcf(c_4660,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),b1),multiply(a1,iPr_def_17))) = iPr_def_19,
inference(superposition,[status(thm)],[c_4658,c_149]) ).
tcf(c_4714,plain,
inverse(multiply(inverse(inverse(multiply(a1,iPr_def_17))),b1)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4660,c_1696,c_2011]) ).
tcf(c_4740,plain,
inverse(multiply(multiply(inverse(multiply(a1,iPr_def_17)),b2),iPr_def_10)) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4378,c_1696]) ).
tcf(c_4741,plain,
multiply(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),b2),multiply(a1,iPr_def_17)),iPr_def_10) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_4740,c_1710]) ).
tcf(c_4742,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),b2),multiply(a1,iPr_def_17))) = iPr_def_10,
inference(superposition,[status(thm)],[c_4740,c_149]) ).
tcf(c_4864,plain,
inverse(multiply(inverse(inverse(multiply(a1,iPr_def_17))),b2)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4742,c_1696,c_2011]) ).
tcf(c_4877,plain,
! [X0: $i] : inverse(multiply(multiply(inverse(multiply(a1,iPr_def_17)),X0),inverse(X0))) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4379,c_1696]) ).
tcf(c_4944,plain,
! [X0: $i] : multiply(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),X0),multiply(a1,iPr_def_17)),inverse(X0)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_4877,c_1710]) ).
tcf(c_4945,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),X0),multiply(a1,iPr_def_17))) = inverse(X0),
inference(superposition,[status(thm)],[c_4877,c_149]) ).
tcf(c_4947,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),X0),inverse(X0)),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_4877,c_1696]) ).
tcf(c_4950,plain,
inverse(multiply(multiply(multiply(a1,iPr_def_17),inverse(multiply(a1,iPr_def_17))),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_4877,c_3558]) ).
tcf(c_5623,plain,
inverse(multiply(multiply(a1,iPr_def_17),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4950,c_2011,c_2397]) ).
tcf(c_5625,plain,
! [X0: $i] : inverse(multiply(X0,inverse(multiply(inverse(multiply(a1,iPr_def_17)),X0)))) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_2010,c_5623]) ).
tcf(c_5640,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),b1),iPr_def_19),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_5623,c_1577]) ).
tcf(c_5646,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),X0),X1),multiply(a1,iPr_def_17))) = inverse(multiply(inverse(multiply(a1,iPr_def_17)),multiply(X0,X1))),
inference(superposition,[status(thm)],[c_5625,c_149]) ).
tcf(c_5682,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),b1),iPr_def_19),multiply(a1,iPr_def_17))) = inverse(multiply(inverse(multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))),
inference(superposition,[status(thm)],[c_5625,c_1577]) ).
tcf(c_5684,plain,
inverse(multiply(inverse(multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_5682,c_5640]) ).
tcf(c_5725,plain,
multiply(multiply(inverse(multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_5684,c_1696]) ).
tcf(c_6080,plain,
! [X0: $i] : inverse(multiply(inverse(multiply(a1,iPr_def_17)),multiply(inverse(multiply(a1,iPr_def_17)),X0))) = inverse(X0),
inference(demodulation,[status(thm)],[c_4945,c_5646]) ).
tcf(c_6081,plain,
inverse(multiply(inverse(multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = inverse(inverse(inverse(multiply(a1,iPr_def_17)))),
inference(superposition,[status(thm)],[c_1696,c_6080]) ).
tcf(c_6088,plain,
inverse(inverse(inverse(multiply(a1,iPr_def_17)))) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_6081,c_5684]) ).
tcf(c_7212,plain,
multiply(multiply(multiply(multiply(a1,iPr_def_17),a1),multiply(a1,iPr_def_17)),iPr_def_17) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4578,c_1696]) ).
tcf(c_7232,plain,
multiply(multiply(multiply(multiply(a1,iPr_def_17),b1),multiply(a1,iPr_def_17)),iPr_def_19) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4659,c_1696]) ).
tcf(c_7296,plain,
multiply(multiply(multiply(multiply(a1,iPr_def_17),b2),multiply(a1,iPr_def_17)),iPr_def_10) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4741,c_1696]) ).
tcf(c_8075,plain,
! [X0: $i] : multiply(multiply(multiply(multiply(multiply(a1,iPr_def_17),X0),inverse(X0)),multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_5623,c_1986]) ).
tcf(c_10733,plain,
! [X0: $i] : multiply(multiply(multiply(multiply(a1,iPr_def_17),X0),multiply(a1,iPr_def_17)),inverse(X0)) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4944,c_1696]) ).
tcf(c_10736,plain,
multiply(multiply(multiply(a1,iPr_def_17),multiply(a1,iPr_def_17)),inverse(inverse(multiply(a1,iPr_def_17)))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_1696,c_10733]) ).
tcf(c_11216,plain,
inverse(multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = inverse(inverse(multiply(a1,iPr_def_17))),
inference(superposition,[status(thm)],[c_10736,c_149]) ).
tcf(c_11219,plain,
inverse(inverse(multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_11216,c_5623,c_5725]) ).
tcf(c_11228,plain,
inverse(multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_6088,c_11219]) ).
tcf(c_11232,plain,
inverse(multiply(multiply(a1,iPr_def_17),b2)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_4864,c_11219]) ).
tcf(c_11234,plain,
inverse(multiply(multiply(a1,iPr_def_17),b1)) = iPr_def_19,
inference(demodulation,[status(thm)],[c_4714,c_11219]) ).
tcf(c_11236,plain,
inverse(multiply(multiply(a1,iPr_def_17),a1)) = iPr_def_17,
inference(demodulation,[status(thm)],[c_4624,c_11219]) ).
tcf(c_11238,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(a1,iPr_def_17),X0),multiply(a1,iPr_def_17))) = inverse(multiply(multiply(a1,iPr_def_17),X0)),
inference(demodulation,[status(thm)],[c_2011,c_11219]) ).
tcf(c_11273,plain,
! [X0: $i] : inverse(multiply(multiply(a1,iPr_def_17),multiply(multiply(a1,iPr_def_17),X0))) = inverse(X0),
inference(demodulation,[status(thm)],[c_6080,c_11228]) ).
tcf(c_11285,plain,
! [X0: $i] : inverse(multiply(X0,inverse(multiply(multiply(a1,iPr_def_17),X0)))) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_5625,c_11228]) ).
tcf(c_11286,plain,
! [X0: $i] : multiply(multiply(multiply(multiply(a1,iPr_def_17),X0),inverse(X0)),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4947,c_11228]) ).
tcf(c_11287,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(a1,iPr_def_17),X0),inverse(X0))) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4877,c_11228]) ).
tcf(c_11292,plain,
multiply(multiply(multiply(multiply(a1,iPr_def_17),a1),iPr_def_17),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_4580,c_11228]) ).
tcf(c_11328,plain,
multiply(multiply(a1,iPr_def_17),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_8075,c_11286]) ).
tcf(c_11355,plain,
inverse(multiply(multiply(multiply(iPr_def_10,a1),iPr_def_17),multiply(a1,iPr_def_17))) = b2,
inference(superposition,[status(thm)],[c_11232,c_149]) ).
tcf(c_11449,plain,
inverse(multiply(multiply(multiply(iPr_def_19,a1),iPr_def_17),multiply(a1,iPr_def_17))) = b1,
inference(superposition,[status(thm)],[c_11234,c_149]) ).
tcf(c_11498,plain,
inverse(multiply(multiply(multiply(iPr_def_17,a1),iPr_def_17),multiply(a1,iPr_def_17))) = a1,
inference(superposition,[status(thm)],[c_11236,c_149]) ).
tcf(c_11512,plain,
inverse(multiply(multiply(iPr_def_18,iPr_def_17),multiply(a1,iPr_def_17))) = a1,
inference(light_normalisation,[status(thm)],[c_11498,c_77]) ).
tcf(c_11850,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(X0),a1),iPr_def_17),multiply(a1,iPr_def_17))) = multiply(multiply(a1,iPr_def_17),X0),
inference(superposition,[status(thm)],[c_11273,c_149]) ).
tcf(c_11861,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(X0),X1),inverse(X1)),multiply(a1,iPr_def_17))) = multiply(multiply(a1,iPr_def_17),X0),
inference(superposition,[status(thm)],[c_11273,c_1721]) ).
tcf(c_11865,plain,
! [X0: $i] : multiply(multiply(a1,iPr_def_17),multiply(multiply(a1,iPr_def_17),X0)) = X0,
inference(demodulation,[status(thm)],[c_1721,c_11861]) ).
tcf(c_11886,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(X0,X1)),multiply(a1,iPr_def_17)),multiply(multiply(a1,iPr_def_17),X0)),multiply(a1,iPr_def_17))) = X1,
inference(superposition,[status(thm)],[c_11865,c_149]) ).
tcf(c_11924,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),b3),c3),multiply(a1,iPr_def_17))) = inverse(multiply(multiply(a1,iPr_def_17),iPr_def_15)),
inference(superposition,[status(thm)],[c_11285,c_325]) ).
tcf(c_11939,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),iPr_def_17),a1),multiply(a1,iPr_def_17))) = inverse(multiply(multiply(a1,iPr_def_17),iPr_def_18)),
inference(superposition,[status(thm)],[c_11285,c_1095]) ).
tcf(c_11942,plain,
inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),iPr_def_19),b1),multiply(a1,iPr_def_17))) = inverse(multiply(multiply(a1,iPr_def_17),iPr_def_20)),
inference(superposition,[status(thm)],[c_11285,c_1325]) ).
tcf(c_12391,plain,
inverse(multiply(multiply(multiply(iPr_def_17,a1),iPr_def_17),multiply(a1,iPr_def_17))) = multiply(multiply(a1,iPr_def_17),a1),
inference(superposition,[status(thm)],[c_76,c_11850]) ).
tcf(c_12392,plain,
inverse(multiply(multiply(multiply(iPr_def_19,a1),iPr_def_17),multiply(a1,iPr_def_17))) = multiply(multiply(a1,iPr_def_17),b1),
inference(superposition,[status(thm)],[c_78,c_11850]) ).
tcf(c_12393,plain,
inverse(multiply(multiply(multiply(iPr_def_10,a1),iPr_def_17),multiply(a1,iPr_def_17))) = multiply(multiply(a1,iPr_def_17),b2),
inference(superposition,[status(thm)],[c_69,c_11850]) ).
tcf(c_12444,plain,
multiply(multiply(a1,iPr_def_17),b2) = b2,
inference(light_normalisation,[status(thm)],[c_12393,c_11355]) ).
tcf(c_12445,plain,
multiply(multiply(a1,iPr_def_17),b1) = b1,
inference(light_normalisation,[status(thm)],[c_12392,c_11449]) ).
tcf(c_12446,plain,
multiply(multiply(a1,iPr_def_17),a1) = a1,
inference(light_normalisation,[status(thm)],[c_12391,c_77,c_11512]) ).
tcf(c_12470,plain,
multiply(multiply(b2,multiply(a1,iPr_def_17)),iPr_def_10) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_7296,c_12444]) ).
tcf(c_12473,plain,
multiply(multiply(b1,multiply(a1,iPr_def_17)),iPr_def_19) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_7232,c_12445]) ).
tcf(c_12476,plain,
multiply(multiply(a1,multiply(a1,iPr_def_17)),iPr_def_17) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_7212,c_12446]) ).
tcf(c_12845,plain,
inverse(multiply(multiply(multiply(iPr_def_10,multiply(inverse(multiply(a1,iPr_def_17)),b2)),multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_12470,c_1579]) ).
tcf(c_12848,plain,
inverse(multiply(multiply(iPr_def_11,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_12845,c_70,c_11228,c_12444]) ).
tcf(c_12861,plain,
inverse(multiply(multiply(multiply(iPr_def_19,multiply(inverse(multiply(a1,iPr_def_17)),b1)),multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_12473,c_1579]) ).
tcf(c_12864,plain,
inverse(multiply(multiply(iPr_def_20,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_12861,c_79,c_11228,c_12445]) ).
tcf(c_12877,plain,
inverse(multiply(multiply(multiply(iPr_def_17,multiply(inverse(multiply(a1,iPr_def_17)),a1)),multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_12476,c_1579]) ).
tcf(c_12880,plain,
inverse(multiply(multiply(iPr_def_18,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_12877,c_77,c_11228,c_12446]) ).
tcf(c_13096,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(multiply(a1,iPr_def_17),multiply(a1,iPr_def_17)),X0),multiply(a1,iPr_def_17))) = inverse(X0),
inference(superposition,[status(thm)],[c_11287,c_149]) ).
tcf(c_13105,plain,
! [X0: $i] : inverse(multiply(multiply(a1,iPr_def_17),X0)) = inverse(X0),
inference(light_normalisation,[status(thm)],[c_13096,c_11328,c_11238]) ).
tcf(c_13219,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(X0),a1),iPr_def_17),multiply(a1,iPr_def_17))) = X0,
inference(superposition,[status(thm)],[c_13105,c_149]) ).
tcf(c_13221,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(X0),a1),iPr_def_17),multiply(a1,iPr_def_17))) = multiply(multiply(a1,iPr_def_17),multiply(multiply(a1,iPr_def_17),X0)),
inference(superposition,[status(thm)],[c_13105,c_11850]) ).
tcf(c_13222,plain,
! [X0: $i] : multiply(multiply(multiply(multiply(a1,iPr_def_17),multiply(multiply(a1,iPr_def_17),X0)),multiply(a1,iPr_def_17)),inverse(X0)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_13105,c_10733]) ).
tcf(c_13227,plain,
! [X0: $i] : multiply(multiply(X0,multiply(a1,iPr_def_17)),inverse(X0)) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_13222,c_11865]) ).
tcf(c_13228,plain,
! [X0: $i] : multiply(multiply(a1,iPr_def_17),X0) = X0,
inference(light_normalisation,[status(thm)],[c_13221,c_11850,c_11865]) ).
tcf(c_13276,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),multiply(a1,iPr_def_17)) = inverse(multiply(multiply(multiply(X2,a1),iPr_def_17),multiply(a1,iPr_def_17))),
inference(superposition,[status(thm)],[c_149,c_13219]) ).
tcf(c_13285,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(multiply(iPr_def_18,X0)),iPr_def_17),a1),multiply(a1,iPr_def_17)) = inverse(multiply(multiply(multiply(X0,a1),iPr_def_17),multiply(a1,iPr_def_17))),
inference(superposition,[status(thm)],[c_1095,c_13219]) ).
tcf(c_13316,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(X0),a1),iPr_def_17),multiply(a1,iPr_def_17)) = inverse(multiply(multiply(multiply(X0,a1),iPr_def_17),multiply(a1,iPr_def_17))),
inference(superposition,[status(thm)],[c_13219,c_13219]) ).
tcf(c_13354,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(inverse(X0)),a1),iPr_def_17),multiply(a1,iPr_def_17)) = X0,
inference(demodulation,[status(thm)],[c_13219,c_13316]) ).
tcf(c_14306,plain,
multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),a1),iPr_def_17),multiply(a1,iPr_def_17)) = multiply(multiply(iPr_def_11,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)),
inference(superposition,[status(thm)],[c_12848,c_13354]) ).
tcf(c_14310,plain,
multiply(multiply(iPr_def_11,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_14306,c_11228,c_11292]) ).
tcf(c_14312,plain,
multiply(multiply(a1,iPr_def_17),inverse(multiply(iPr_def_11,multiply(a1,iPr_def_17)))) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_14310,c_13227]) ).
tcf(c_14313,plain,
multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),a1),iPr_def_17),multiply(a1,iPr_def_17)) = multiply(multiply(iPr_def_20,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)),
inference(superposition,[status(thm)],[c_12864,c_13354]) ).
tcf(c_14317,plain,
multiply(multiply(iPr_def_20,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_14313,c_11228,c_11292]) ).
tcf(c_14320,plain,
multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),a1),iPr_def_17),multiply(a1,iPr_def_17)) = multiply(multiply(iPr_def_18,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)),
inference(superposition,[status(thm)],[c_12880,c_13354]) ).
tcf(c_14324,plain,
multiply(multiply(iPr_def_18,multiply(a1,iPr_def_17)),multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_14320,c_11228,c_11292]) ).
tcf(c_14487,plain,
inverse(multiply(iPr_def_11,multiply(a1,iPr_def_17))) = multiply(a1,iPr_def_17),
inference(demodulation,[status(thm)],[c_14312,c_13228]) ).
tcf(c_14489,plain,
multiply(multiply(multiply(inverse(multiply(a1,iPr_def_17)),a1),iPr_def_17),multiply(a1,iPr_def_17)) = multiply(iPr_def_11,multiply(a1,iPr_def_17)),
inference(superposition,[status(thm)],[c_14487,c_13354]) ).
tcf(c_14492,plain,
multiply(iPr_def_11,multiply(a1,iPr_def_17)) = multiply(a1,iPr_def_17),
inference(light_normalisation,[status(thm)],[c_14489,c_11228,c_11292]) ).
tcf(c_14496,plain,
multiply(multiply(a1,iPr_def_17),inverse(iPr_def_11)) = multiply(a1,iPr_def_17),
inference(superposition,[status(thm)],[c_14492,c_13227]) ).
tcf(c_14497,plain,
multiply(a1,iPr_def_17) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_14496,c_13228]) ).
tcf(c_14505,plain,
multiply(multiply(iPr_def_18,inverse(iPr_def_11)),inverse(iPr_def_11)) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_14324,c_14497]) ).
tcf(c_14506,plain,
multiply(multiply(iPr_def_20,inverse(iPr_def_11)),inverse(iPr_def_11)) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_14317,c_14497]) ).
tcf(c_14526,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(inverse(X0)),a1),iPr_def_17),inverse(iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_13354,c_14497]) ).
tcf(c_14536,plain,
! [X0: $i] : multiply(multiply(X0,inverse(iPr_def_11)),inverse(X0)) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_13227,c_14497]) ).
tcf(c_14540,plain,
! [X0: $i] : multiply(inverse(iPr_def_11),X0) = X0,
inference(demodulation,[status(thm)],[c_13228,c_14497]) ).
tcf(c_14546,plain,
inverse(inverse(iPr_def_11)) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_11228,c_14497]) ).
tcf(c_14549,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_1696,c_14497]) ).
tcf(c_14605,plain,
multiply(inverse(iPr_def_11),inverse(multiply(iPr_def_18,inverse(iPr_def_11)))) = inverse(iPr_def_11),
inference(superposition,[status(thm)],[c_14505,c_14536]) ).
tcf(c_14606,plain,
multiply(inverse(iPr_def_11),inverse(multiply(iPr_def_20,inverse(iPr_def_11)))) = inverse(iPr_def_11),
inference(superposition,[status(thm)],[c_14506,c_14536]) ).
tcf(c_14803,plain,
inverse(multiply(iPr_def_18,inverse(iPr_def_11))) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_14605,c_14540]) ).
tcf(c_14807,plain,
inverse(multiply(iPr_def_20,inverse(iPr_def_11))) = inverse(iPr_def_11),
inference(demodulation,[status(thm)],[c_14606,c_14540]) ).
tcf(c_14839,plain,
multiply(multiply(multiply(inverse(iPr_def_11),a1),iPr_def_17),inverse(iPr_def_11)) = iPr_def_11,
inference(superposition,[status(thm)],[c_14546,c_14526]) ).
tcf(c_14894,plain,
inverse(multiply(multiply(multiply(inverse(iPr_def_11),b3),c3),inverse(iPr_def_11))) = inverse(multiply(inverse(iPr_def_11),iPr_def_15)),
inference(light_normalisation,[status(thm)],[c_11924,c_14497]) ).
tcf(c_14895,plain,
inverse(multiply(iPr_def_15,inverse(iPr_def_11))) = inverse(iPr_def_15),
inference(demodulation,[status(thm)],[c_14894,c_74,c_14540]) ).
tcf(c_14902,plain,
inverse(iPr_def_11) = iPr_def_11,
inference(demodulation,[status(thm)],[c_14839,c_14497,c_14540]) ).
tcf(c_14905,plain,
inverse(multiply(iPr_def_15,iPr_def_11)) = inverse(iPr_def_15),
inference(demodulation,[status(thm)],[c_14895,c_14902]) ).
tcf(c_14907,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(inverse(X0)),a1),iPr_def_17),iPr_def_11) = X0,
inference(demodulation,[status(thm)],[c_14526,c_14902]) ).
tcf(c_14917,plain,
inverse(multiply(iPr_def_20,iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_14807,c_14902]) ).
tcf(c_14918,plain,
inverse(multiply(iPr_def_18,iPr_def_11)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_14803,c_14902]) ).
tcf(c_14949,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = iPr_def_11,
inference(demodulation,[status(thm)],[c_14549,c_14902]) ).
tcf(c_14953,plain,
! [X0: $i] : multiply(iPr_def_11,X0) = X0,
inference(demodulation,[status(thm)],[c_14540,c_14902]) ).
tcf(c_14955,plain,
multiply(a1,iPr_def_17) = iPr_def_11,
inference(demodulation,[status(thm)],[c_14497,c_14902]) ).
tcf(c_14956,plain,
a2 = iPr_def_12,
inference(demodulation,[status(thm)],[c_71,c_14953]) ).
tcf(c_14957,plain,
( ( iPr_def_18 != iPr_def_20 )
| ( iPr_def_14 != iPr_def_16 )
| ( iPr_def_12 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_80,c_14956]) ).
tcf(c_14958,plain,
( ( iPr_def_18 != iPr_def_20 )
| ( iPr_def_14 != iPr_def_16 ) ),
inference(equality_resolution_simp,[status(thm)],[c_14957]) ).
tcf(c_14967,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(multiply(iPr_def_13,X1)),a3),b3),iPr_def_11),X1))) = X0,
inference(light_normalisation,[status(thm)],[c_375,c_14953,c_14955]) ).
tcf(c_14981,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),iPr_def_11),c3))) = X0,
inference(superposition,[status(thm)],[c_73,c_14967]) ).
tcf(c_15025,plain,
inverse(multiply(multiply(multiply(iPr_def_11,iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),iPr_def_11),c3))) = iPr_def_11,
inference(superposition,[status(thm)],[c_14902,c_14981]) ).
tcf(c_15032,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),iPr_def_11),c3)) = inverse(multiply(multiply(multiply(X0,iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),iPr_def_11),c3))),
inference(superposition,[status(thm)],[c_14981,c_14981]) ).
tcf(c_15037,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(inverse(X0)),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),iPr_def_11),c3)) = X0,
inference(demodulation,[status(thm)],[c_14981,c_15032]) ).
tcf(c_15138,plain,
inverse(multiply(multiply(multiply(iPr_def_11,iPr_def_17),a1),iPr_def_11)) = inverse(multiply(iPr_def_11,iPr_def_18)),
inference(light_normalisation,[status(thm)],[c_11939,c_14955]) ).
tcf(c_15139,plain,
inverse(iPr_def_18) = iPr_def_11,
inference(demodulation,[status(thm)],[c_15138,c_77,c_14918,c_14953]) ).
tcf(c_15143,plain,
inverse(multiply(multiply(multiply(iPr_def_11,iPr_def_19),b1),iPr_def_11)) = inverse(multiply(iPr_def_11,iPr_def_20)),
inference(light_normalisation,[status(thm)],[c_11942,c_14955]) ).
tcf(c_15144,plain,
inverse(iPr_def_20) = iPr_def_11,
inference(demodulation,[status(thm)],[c_15143,c_79,c_14917,c_14953]) ).
tcf(c_15177,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(multiply(iPr_def_15,X1)),b3),c3),iPr_def_11),X1))) = X0,
inference(light_normalisation,[status(thm)],[c_377,c_14953,c_14955]) ).
tcf(c_15265,plain,
multiply(multiply(multiply(multiply(inverse(iPr_def_14),a3),b3),iPr_def_11),c3) = iPr_def_11,
inference(demodulation,[status(thm)],[c_15025,c_70,c_14902,c_14953,c_15032]) ).
tcf(c_15422,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(inverse(X0)),iPr_def_10),b2),iPr_def_11) = X0,
inference(light_normalisation,[status(thm)],[c_15037,c_15265]) ).
tcf(c_15433,plain,
multiply(multiply(multiply(inverse(iPr_def_11),iPr_def_10),b2),iPr_def_11) = iPr_def_18,
inference(superposition,[status(thm)],[c_15139,c_15422]) ).
tcf(c_15434,plain,
multiply(multiply(multiply(inverse(iPr_def_11),iPr_def_10),b2),iPr_def_11) = iPr_def_20,
inference(superposition,[status(thm)],[c_15144,c_15422]) ).
tcf(c_15443,plain,
! [X0: $i,X1: $i] : multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),multiply(multiply(multiply(multiply(inverse(multiply(iPr_def_15,X1)),b3),c3),iPr_def_11),X1)) = multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),iPr_def_11),
inference(superposition,[status(thm)],[c_15177,c_15422]) ).
tcf(c_15448,plain,
multiply(multiply(multiply(iPr_def_11,iPr_def_10),b2),iPr_def_11) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_15434,c_14902]) ).
tcf(c_15449,plain,
multiply(multiply(multiply(iPr_def_11,iPr_def_10),b2),iPr_def_11) = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_15433,c_14902]) ).
tcf(c_15454,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),iPr_def_11)) = X0,
inference(demodulation,[status(thm)],[c_15177,c_15443]) ).
tcf(c_15485,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(inverse(multiply(X0,X1)),iPr_def_11),X0),iPr_def_11)) = X1,
inference(light_normalisation,[status(thm)],[c_11886,c_14953,c_14955]) ).
tcf(c_15497,plain,
inverse(multiply(multiply(multiply(inverse(iPr_def_16),iPr_def_11),a3),iPr_def_11)) = iPr_def_15,
inference(superposition,[status(thm)],[c_75,c_15485]) ).
tcf(c_15504,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(inverse(iPr_def_11),iPr_def_11),X0),iPr_def_11)) = inverse(X0),
inference(superposition,[status(thm)],[c_14949,c_15485]) ).
tcf(c_15544,plain,
! [X0: $i] : inverse(multiply(multiply(multiply(iPr_def_11,iPr_def_11),X0),iPr_def_11)) = inverse(X0),
inference(light_normalisation,[status(thm)],[c_15504,c_14902]) ).
tcf(c_15723,plain,
iPr_def_18 = iPr_def_20,
inference(demodulation,[status(thm)],[c_15448,c_15449]) ).
tcf(c_15728,plain,
( ( iPr_def_18 != iPr_def_18 )
| ( iPr_def_14 != iPr_def_16 ) ),
inference(demodulation,[status(thm)],[c_14958,c_15723]) ).
tcf(c_15730,plain,
iPr_def_14 != iPr_def_16,
inference(equality_resolution_simp,[status(thm)],[c_15728]) ).
tcf(c_15989,plain,
multiply(multiply(multiply(inverse(iPr_def_15),iPr_def_10),b2),iPr_def_11) = multiply(multiply(multiply(inverse(iPr_def_16),iPr_def_11),a3),iPr_def_11),
inference(superposition,[status(thm)],[c_15497,c_15422]) ).
tcf(c_15993,plain,
iPr_def_11 = iPr_def_18,
inference(demodulation,[status(thm)],[c_15449,c_70,c_14953]) ).
tcf(c_16668,plain,
inverse(multiply(multiply(multiply(inverse(iPr_def_15),iPr_def_10),b2),iPr_def_11)) = multiply(iPr_def_15,iPr_def_11),
inference(superposition,[status(thm)],[c_14905,c_15454]) ).
tcf(c_16680,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(X0),a1),iPr_def_17),iPr_def_11) = multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),iPr_def_11),
inference(superposition,[status(thm)],[c_15454,c_14907]) ).
tcf(c_16824,plain,
! [X0: $i] : inverse(multiply(X0,iPr_def_11)) = inverse(X0),
inference(demodulation,[status(thm)],[c_15544,c_14953]) ).
tcf(c_16848,plain,
inverse(multiply(multiply(multiply(inverse(iPr_def_15),iPr_def_10),b2),iPr_def_11)) = inverse(multiply(multiply(inverse(iPr_def_16),iPr_def_11),a3)),
inference(superposition,[status(thm)],[c_15989,c_16824]) ).
tcf(c_16850,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(inverse(X0)),iPr_def_10),b2),iPr_def_11) = multiply(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_16824,c_15422]) ).
tcf(c_16863,plain,
! [X0: $i] : multiply(X0,iPr_def_11) = X0,
inference(light_normalisation,[status(thm)],[c_16850,c_15422]) ).
tcf(c_16864,plain,
inverse(multiply(multiply(inverse(iPr_def_16),iPr_def_11),a3)) = multiply(iPr_def_15,iPr_def_11),
inference(light_normalisation,[status(thm)],[c_16848,c_16668]) ).
tcf(c_16895,plain,
! [X0: $i] : multiply(multiply(inverse(inverse(X0)),iPr_def_10),b2) = X0,
inference(demodulation,[status(thm)],[c_15422,c_16863]) ).
tcf(c_17720,plain,
inverse(multiply(inverse(iPr_def_16),a3)) = iPr_def_15,
inference(demodulation,[status(thm)],[c_16864,c_16863]) ).
tcf(c_17735,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(multiply(iPr_def_11,inverse(multiply(multiply(X0,X1),iPr_def_11))),X0),iPr_def_11)) = X1,
inference(light_normalisation,[status(thm)],[c_4413,c_14902,c_14955]) ).
tcf(c_17736,plain,
! [X0: $i,X1: $i] : inverse(multiply(inverse(multiply(X0,X1)),X0)) = X1,
inference(demodulation,[status(thm)],[c_17735,c_14953,c_16863]) ).
tcf(c_17737,plain,
! [X0: $i] : inverse(inverse(multiply(iPr_def_11,X0))) = X0,
inference(superposition,[status(thm)],[c_16863,c_17736]) ).
tcf(c_17740,plain,
inverse(multiply(iPr_def_15,inverse(iPr_def_16))) = a3,
inference(superposition,[status(thm)],[c_17720,c_17736]) ).
tcf(c_17782,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(multiply(X1,X0)))) = X1,
inference(superposition,[status(thm)],[c_17736,c_17736]) ).
tcf(c_17789,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_17737,c_14953]) ).
tcf(c_17813,plain,
! [X0: $i] : multiply(multiply(X0,iPr_def_10),b2) = X0,
inference(demodulation,[status(thm)],[c_16895,c_17789]) ).
tcf(c_17863,plain,
multiply(iPr_def_15,inverse(iPr_def_16)) = inverse(a3),
inference(superposition,[status(thm)],[c_17740,c_17789]) ).
tcf(c_17984,plain,
! [X0: $i,X1: $i] : multiply(X0,inverse(multiply(X1,X0))) = inverse(X1),
inference(superposition,[status(thm)],[c_17782,c_17789]) ).
tcf(c_19552,plain,
! [X0: $i] : multiply(multiply(multiply(inverse(X0),iPr_def_10),b2),iPr_def_11) = multiply(multiply(multiply(inverse(X0),iPr_def_17),a1),iPr_def_11),
inference(light_normalisation,[status(thm)],[c_13285,c_13316,c_14953,c_14955,c_15993,c_16680]) ).
tcf(c_19553,plain,
! [X0: $i] : multiply(multiply(inverse(X0),iPr_def_17),a1) = inverse(X0),
inference(demodulation,[status(thm)],[c_19552,c_16863,c_17813]) ).
tcf(c_19564,plain,
! [X0: $i] : multiply(multiply(X0,iPr_def_17),a1) = X0,
inference(superposition,[status(thm)],[c_17789,c_19553]) ).
tcf(c_19623,plain,
! [X0: $i] : multiply(a1,inverse(X0)) = inverse(multiply(X0,iPr_def_17)),
inference(superposition,[status(thm)],[c_19564,c_17984]) ).
tcf(c_19661,plain,
! [X0: $i] : inverse(multiply(a1,inverse(X0))) = multiply(X0,iPr_def_17),
inference(superposition,[status(thm)],[c_19623,c_17789]) ).
tcf(c_19748,plain,
! [X0: $i] : multiply(multiply(X0,a1),iPr_def_17) = inverse(inverse(X0)),
inference(superposition,[status(thm)],[c_17984,c_19661]) ).
tcf(c_19791,plain,
! [X0: $i] : multiply(multiply(X0,a1),iPr_def_17) = X0,
inference(light_normalisation,[status(thm)],[c_19748,c_17789]) ).
tcf(c_27311,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1),iPr_def_11) = inverse(multiply(multiply(multiply(X2,a1),iPr_def_17),iPr_def_11)),
inference(light_normalisation,[status(thm)],[c_13276,c_14955]) ).
tcf(c_27312,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(inverse(multiply(multiply(X0,X1),X2)),X0),X1) = inverse(X2),
inference(demodulation,[status(thm)],[c_27311,c_16863,c_19791]) ).
tcf(c_27426,plain,
! [X0: $i] : multiply(multiply(inverse(multiply(iPr_def_15,X0)),b3),c3) = inverse(X0),
inference(superposition,[status(thm)],[c_74,c_27312]) ).
tcf(c_29273,plain,
multiply(multiply(inverse(inverse(a3)),b3),c3) = inverse(inverse(iPr_def_16)),
inference(superposition,[status(thm)],[c_17863,c_27426]) ).
tcf(c_29749,plain,
iPr_def_14 = iPr_def_16,
inference(demodulation,[status(thm)],[c_29273,c_72,c_73,c_17789]) ).
tcf(c_29750,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29749,c_15730]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP059-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n006.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Wed Sep 23 13:25:11 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 21.20/4.73 % SZS status Started for theBenchmark.p
% 21.20/4.73 % SZS status Unsatisfiable for theBenchmark.p
% 21.20/4.73
% 21.20/4.73 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.20/4.73
% 21.20/4.73 % ------ iProver source info
% 21.20/4.73
% 21.20/4.73 % git: date: 2026-07-19 20:42:38 +0200
% 21.20/4.73 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.20/4.73 % git: non_committed_changes: false
% 21.20/4.73
% 21.20/4.73 % ------ Parsing...% successful
% 21.20/4.73
% 21.20/4.73
% 21.20/4.73 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.20/4.73
% 21.20/4.73 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 21.20/4.73
% 21.20/4.73 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.20/4.73
% 21.20/4.73 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 21.20/4.73 % ------ Proving...
% 21.20/4.73 % ------ Problem Properties
% 21.20/4.73
% 21.20/4.73 %
% 21.20/4.73 % clauses 13
% 21.20/4.73 % conjectures 1
% 21.20/4.73 % EPR 1
% 21.20/4.73 % Horn 13
% 21.20/4.73 % unary 12
% 21.20/4.73 % binary 0
% 21.20/4.73 % lits 15
% 21.20/4.73 % lits eq 15
% 21.20/4.73 % fd_pure 0
% 21.20/4.73 % fd_pseudo 0
% 21.20/4.73 % fd_cond 0
% 21.20/4.73 % fd_pseudo_cond 0
% 21.20/4.73 % AC symbols 0
% 21.20/4.73
% 21.20/4.73 % ------ Schedule dynamic 5 is on
% 21.20/4.73
% 21.20/4.73 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.20/4.73
% 21.20/4.73
% 21.20/4.73 % ------
% 21.20/4.73 % Current options:
% 21.20/4.73 % ------
% 21.20/4.73
% 21.20/4.73
% 21.20/4.73 %
% 21.20/4.73
% 21.20/4.73 % ------ Proving...
% 21.20/4.73 %
% 21.20/4.73
% 21.20/4.73 % SZS status Unsatisfiable for theBenchmark.p
% 21.20/4.73
% 21.20/4.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.20/4.74
% 21.20/4.74
%------------------------------------------------------------------------------