%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP420-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:33:52 PM UTC 2026
% Result : Unsatisfiable 16.09s 3.22s
% Output : CNFRefutation 16.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 2
% Syntax : Number of formulae : 148 ( 148 unt; 0 def)
% Number of atoms : 691 ( 147 equ)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 21 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 398 ( 0 sgn 398 !; 0 ?; 395 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f2,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_52,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)),inverse(multiply(X3,multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4)))))))))),multiply(X0,multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X2,X4))))) = X1,
inference(superposition,[status(thm)],[c_51,c_51]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2))) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_60]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_60]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)))) = X1,
inference(demodulation,[status(thm)],[c_61,c_63]) ).
tcf(c_65,plain,
! [X0: $i] : iPr_def_10(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_51,c_62]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),multiply(X0,X2)) = iPr_def_10(iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_62,c_65]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(X1)) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_63,c_63]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(X1))) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_63,c_62]) ).
tcf(c_85,plain,
! [X0: $i] : inverse(iPr_def_10(X0)) = iPr_def_10(inverse(X0)),
inference(superposition,[status(thm)],[c_63,c_62]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_64,c_65]) ).
tcf(c_96,plain,
! [X0: $i] : inverse(iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_85,c_65]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(iPr_def_10(X1))) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_79,c_79]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,iPr_def_10(X2)),inverse(multiply(inverse(multiply(X0,iPr_def_10(X2))),multiply(X0,iPr_def_10(X2)))))))))),iPr_def_10(X1)) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_95,c_79]) ).
tcf(c_165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_65,c_82]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),inverse(multiply(X4,inverse(multiply(iPr_def_10(X1),inverse(multiply(inverse(iPr_def_10(X1)),iPr_def_10(X1))))))))),iPr_def_10(X3)) = iPr_def_10(iPr_def_10(X4)),
inference(superposition,[status(thm)],[c_82,c_79]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1)) = iPr_def_10(X3),
inference(superposition,[status(thm)],[c_65,c_84]) ).
tcf(c_195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(X1)) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_84,c_65]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),inverse(multiply(X4,inverse(multiply(iPr_def_10(X1),inverse(multiply(X1,iPr_def_10(X1))))))))),iPr_def_10(X3)) = iPr_def_10(iPr_def_10(X4)),
inference(demodulation,[status(thm)],[c_167,c_96]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : iPr_def_10(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3))))))))) = multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X4)))),X5),
inference(superposition,[status(thm)],[c_165,c_165]) ).
tcf(c_385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : iPr_def_10(iPr_def_10(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3))))))))))) = multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(X5,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X4)))),iPr_def_10(iPr_def_10(X5))),
inference(superposition,[status(thm)],[c_165,c_135]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : iPr_def_10(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),iPr_def_10(X4))),X5)),
inference(superposition,[status(thm)],[c_188,c_188]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(iPr_def_10(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),iPr_def_10(multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X6,inverse(multiply(inverse(X6),X6)))))))),inverse(multiply(X1,inverse(multiply(multiply(X4,X6),inverse(multiply(inverse(multiply(X4,X6)),multiply(X4,X6))))))))),X5))) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_188,c_195]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : iPr_def_10(iPr_def_10(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3))))))))))) = multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X5),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X4)))),iPr_def_10(X5)),
inference(superposition,[status(thm)],[c_165,c_195]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))))),X1) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_65,c_195]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),inverse(multiply(X3,inverse(multiply(multiply(X0,iPr_def_10(X2)),inverse(multiply(inverse(multiply(X0,iPr_def_10(X2))),multiply(X0,iPr_def_10(X2)))))))))),iPr_def_10(iPr_def_10(X1))) = iPr_def_10(iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_96,c_141]) ).
tcf(c_509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X3)))),inverse(multiply(X4,inverse(multiply(iPr_def_10(X1),inverse(multiply(X1,iPr_def_10(X1))))))))),iPr_def_10(multiply(inverse(multiply(X5,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X0,X2),inverse(multiply(inverse(multiply(X0,X2)),multiply(X0,X2))))))),inverse(multiply(X6,inverse(multiply(inverse(X6),X6)))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(X5,X6),inverse(multiply(inverse(multiply(X5,X6)),multiply(X5,X6)))))))))) = iPr_def_10(iPr_def_10(X4)),
inference(superposition,[status(thm)],[c_165,c_199]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3)))))))) = inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X5)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),iPr_def_10(X4))),X5)),
inference(demodulation,[status(thm)],[c_427,c_65]) ).
tcf(c_636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(inverse(multiply(multiply(X1,X2),inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X2))))))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X0,X3),inverse(multiply(inverse(multiply(X0,X3)),multiply(X0,X3)))))))) = iPr_def_11(X1,X2,X4),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_634]) ).
tcf(c_639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X3)))),X1) = iPr_def_10(iPr_def_11(X0,X2,inverse(X3))),
inference(demodulation,[status(thm)],[c_384,c_636]) ).
tcf(c_640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(inverse(X1)),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),X1) = iPr_def_10(iPr_def_11(X0,X2,inverse(X3))),
inference(demodulation,[status(thm)],[c_639,c_96]) ).
tcf(c_652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X3)))),iPr_def_10(X1)) = iPr_def_10(iPr_def_10(inverse(iPr_def_11(X0,X2,inverse(X3))))),
inference(demodulation,[status(thm)],[c_442,c_636]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),iPr_def_10(X1)) = iPr_def_10(iPr_def_11(X0,X2,inverse(X3))),
inference(demodulation,[status(thm)],[c_652,c_65,c_96]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X3)))),iPr_def_10(iPr_def_10(X1))) = iPr_def_10(iPr_def_10(inverse(iPr_def_11(X0,X2,inverse(X3))))),
inference(demodulation,[status(thm)],[c_385,c_636]) ).
tcf(c_656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),iPr_def_10(iPr_def_10(X1))) = iPr_def_10(iPr_def_11(X0,X2,inverse(X3))),
inference(demodulation,[status(thm)],[c_655,c_65,c_96]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(inverse(multiply(X2,inverse(multiply(multiply(X0,X1),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1)))))))))) = iPr_def_10(iPr_def_10(X2)),
inference(demodulation,[status(thm)],[c_438,c_459,c_656]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),inverse(iPr_def_10(X3)))),inverse(multiply(X4,inverse(multiply(iPr_def_10(X1),inverse(multiply(X1,iPr_def_10(X1))))))))),iPr_def_10(iPr_def_11(X0,X2,inverse(X3)))) = iPr_def_10(iPr_def_10(X4)),
inference(demodulation,[status(thm)],[c_509,c_636]) ).
tcf(c_732,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(inverse(multiply(X0,inverse(multiply(inverse(X1),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))))),X3)),inverse(multiply(X4,inverse(multiply(iPr_def_10(X1),inverse(multiply(X1,iPr_def_10(X1))))))))),iPr_def_10(iPr_def_11(X0,X2,inverse(X3)))) = iPr_def_10(iPr_def_10(X4)),
inference(demodulation,[status(thm)],[c_731,c_96]) ).
tcf(c_1637,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,inverse(multiply(multiply(X0,X1),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1))))))))) = inverse(iPr_def_10(iPr_def_10(X2))),
inference(superposition,[status(thm)],[c_680,c_96]) ).
tcf(c_1638,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(multiply(X0,X1)))) = multiply(inverse(iPr_def_10(iPr_def_10(inverse(inverse(X2))))),X2),
inference(superposition,[status(thm)],[c_79,c_640]) ).
tcf(c_1653,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(multiply(X0,X1)))) = multiply(inverse(iPr_def_10(iPr_def_10(inverse(X2)))),iPr_def_10(X2)),
inference(superposition,[status(thm)],[c_79,c_653]) ).
tcf(c_1752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(inverse(iPr_def_10(iPr_def_10(inverse(X0)))),inverse(multiply(X1,inverse(multiply(iPr_def_10(X0),inverse(multiply(X0,iPr_def_10(X0))))))))),iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3))))) = iPr_def_10(iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_79,c_732]) ).
tcf(c_1974,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),inverse(iPr_def_10(iPr_def_10(X1))))) = multiply(inverse(iPr_def_10(iPr_def_10(inverse(inverse(X3))))),X3),
inference(superposition,[status(thm)],[c_470,c_640]) ).
tcf(c_1976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),inverse(iPr_def_10(iPr_def_10(X1))))) = multiply(inverse(iPr_def_10(iPr_def_10(inverse(X3)))),iPr_def_10(X3)),
inference(superposition,[status(thm)],[c_470,c_653]) ).
tcf(c_1981,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(multiply(X0,X1)))) = multiply(X2,iPr_def_10(X2)),
inference(demodulation,[status(thm)],[c_1653,c_65,c_96]) ).
tcf(c_1982,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(multiply(X0,X1)))) = multiply(inverse(X2),X2),
inference(demodulation,[status(thm)],[c_1638,c_65,c_96]) ).
tcf(c_1984,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,inverse(multiply(multiply(X0,X1),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1))))))))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_1637,c_96]) ).
tcf(c_1985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X0),inverse(multiply(X0,iPr_def_10(X0))))))))),iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3))))) = iPr_def_10(iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_1752,c_65,c_96]) ).
tcf(c_1987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),iPr_def_10(X1))) = multiply(X3,iPr_def_10(X3)),
inference(demodulation,[status(thm)],[c_1976,c_65,c_96]) ).
tcf(c_1988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(iPr_def_11(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X2),inverse(multiply(X2,iPr_def_10(X2))))))))),multiply(X0,iPr_def_10(X2)),iPr_def_10(X1))) = multiply(inverse(X3),X3),
inference(demodulation,[status(thm)],[c_1974,c_65,c_96]) ).
tcf(c_2814,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(multiply(X0,X1))) = inverse(multiply(inverse(X2),X2)),
inference(superposition,[status(thm)],[c_1982,c_96]) ).
tcf(c_2825,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(iPr_def_10(iPr_def_11(X3,X4,inverse(multiply(X3,X4))))))))))),multiply(X0,X2)) = iPr_def_10(iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_1982,c_79]) ).
tcf(c_2834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(iPr_def_11(X1,X2,inverse(multiply(X1,X2))))))),multiply(X0,X3)) = iPr_def_10(iPr_def_10(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))))),
inference(superposition,[status(thm)],[c_1982,c_79]) ).
tcf(c_2836,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : multiply(inverse(iPr_def_10(iPr_def_11(X0,X1,inverse(multiply(X0,X1))))),multiply(inverse(inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))))),X3)) = iPr_def_10(iPr_def_10(X2)),
inference(superposition,[status(thm)],[c_1982,c_79]) ).
tcf(c_2842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(iPr_def_10(iPr_def_11(X1,X2,inverse(multiply(X1,X2))))))),X3)),multiply(X4,inverse(multiply(inverse(X4),X4)))) = iPr_def_10(iPr_def_11(X0,X4,inverse(X3))),
inference(superposition,[status(thm)],[c_1982,c_640]) ).
tcf(c_2853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_10(inverse(inverse(multiply(multiply(X0,X1),inverse(multiply(inverse(multiply(X0,X1)),multiply(X0,X1))))))) = iPr_def_11(X0,X1,inverse(inverse(iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3))))))),
inference(superposition,[status(thm)],[c_1982,c_1984]) ).
tcf(c_2865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,inverse(multiply(multiply(X0,X1),inverse(iPr_def_10(iPr_def_11(X3,X4,inverse(multiply(X3,X4))))))))))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_1982,c_1984]) ).
tcf(c_2876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_11(inverse(X0),X0,inverse(inverse(multiply(X1,inverse(multiply(iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3)))),inverse(multiply(inverse(iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3))))),iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3)))))))))))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_1982,c_1984]) ).
tcf(c_2878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(multiply(X1,inverse(multiply(iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3)))),inverse(multiply(inverse(iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3))))),iPr_def_10(iPr_def_11(X2,X3,inverse(multiply(X2,X3)))))))))))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_1981,c_1984]) ).
tcf(c_2891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(iPr_def_11(X1,X2,inverse(multiply(X1,X2))))))),iPr_def_10(iPr_def_11(X3,X4,inverse(multiply(X3,X4))))) = iPr_def_10(iPr_def_10(inverse(inverse(multiply(iPr_def_10(X0),inverse(multiply(X0,iPr_def_10(X0)))))))),
inference(superposition,[status(thm)],[c_1982,c_1985]) ).
tcf(c_2901,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X0),inverse(multiply(X0,iPr_def_10(X0))))))))),multiply(X2,iPr_def_10(X2))) = iPr_def_10(iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_1981,c_1985]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),X0) = multiply(X1,iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_1988,c_1987]) ).
tcf(c_3108,plain,
! [X0: $i] : multiply(inverse(X0),X0) = iPr_def_12,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_12])],[c_3061]) ).
tcf(c_3109,plain,
! [X0: $i] : multiply(X0,iPr_def_10(X0)) = iPr_def_12,
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_3061]) ).
tcf(c_3110,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,X1,inverse(multiply(X0,X1))) = inverse(iPr_def_12),
inference(demodulation,[status(thm)],[c_2814,c_3108]) ).
tcf(c_3128,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X0),inverse(iPr_def_12))))))),iPr_def_12) = iPr_def_10(iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_2901,c_3109]) ).
tcf(c_3129,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,inverse(multiply(multiply(X0,X1),inverse(iPr_def_10(inverse(iPr_def_12))))))))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_2865,c_3110]) ).
tcf(c_3130,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,inverse(multiply(multiply(X0,X1),inverse(iPr_def_12))))))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_3129,c_96]) ).
tcf(c_3132,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(iPr_def_10(inverse(iPr_def_12))))))))),multiply(X0,X2)) = iPr_def_10(iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_2825,c_3110]) ).
tcf(c_3133,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(X2,inverse(iPr_def_12))))))),multiply(X0,X2)) = iPr_def_10(iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_3132,c_96]) ).
tcf(c_3140,plain,
! [X0: $i,X1: $i] : multiply(inverse(iPr_def_10(inverse(iPr_def_12))),multiply(inverse(inverse(multiply(X0,inverse(multiply(X1,inverse(iPr_def_12)))))),X1)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_2836,c_3108,c_3110]) ).
tcf(c_3141,plain,
! [X0: $i,X1: $i] : multiply(inverse(iPr_def_12),multiply(inverse(inverse(multiply(X0,inverse(multiply(X1,inverse(iPr_def_12)))))),X1)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_3140,c_96]) ).
tcf(c_3142,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(iPr_def_12))))),multiply(X0,X1)) = iPr_def_10(iPr_def_10(inverse(inverse(multiply(X1,inverse(iPr_def_12)))))),
inference(demodulation,[status(thm)],[c_2834,c_3108,c_3110]) ).
tcf(c_3143,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_12))),multiply(X0,X1)) = multiply(X1,inverse(iPr_def_12)),
inference(demodulation,[status(thm)],[c_3142,c_65,c_96]) ).
tcf(c_3150,plain,
! [X0: $i,X1: $i] : iPr_def_10(inverse(inverse(multiply(multiply(X0,X1),inverse(iPr_def_12))))) = iPr_def_11(X0,X1,inverse(inverse(iPr_def_10(inverse(iPr_def_12))))),
inference(demodulation,[status(thm)],[c_2853,c_3108,c_3110]) ).
tcf(c_3151,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(X0,X1),inverse(iPr_def_12))) = iPr_def_11(X0,X1,inverse(inverse(iPr_def_12))),
inference(demodulation,[status(thm)],[c_3150,c_65,c_96]) ).
tcf(c_3152,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(iPr_def_12))))),X1)),multiply(X2,inverse(iPr_def_12))) = iPr_def_10(iPr_def_11(X0,X2,inverse(X1))),
inference(demodulation,[status(thm)],[c_2842,c_3108,c_3110]) ).
tcf(c_3153,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,inverse(iPr_def_12))),X1)),multiply(X2,inverse(iPr_def_12))) = iPr_def_10(iPr_def_11(X0,X2,inverse(X1))),
inference(demodulation,[status(thm)],[c_3152,c_96]) ).
tcf(c_3216,plain,
! [X0: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_10(inverse(iPr_def_12))))),iPr_def_10(inverse(iPr_def_12))) = iPr_def_10(iPr_def_10(inverse(inverse(multiply(iPr_def_10(X0),inverse(iPr_def_12)))))),
inference(demodulation,[status(thm)],[c_2891,c_3109,c_3110]) ).
tcf(c_3217,plain,
! [X0: $i] : multiply(inverse(multiply(X0,inverse(iPr_def_12))),iPr_def_12) = multiply(iPr_def_10(X0),inverse(iPr_def_12)),
inference(demodulation,[status(thm)],[c_3216,c_65,c_96]) ).
tcf(c_3266,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(multiply(X1,inverse(multiply(iPr_def_10(inverse(iPr_def_12)),inverse(iPr_def_12))))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_2878,c_3108,c_3110]) ).
tcf(c_3267,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(multiply(X1,inverse(multiply(iPr_def_12,inverse(iPr_def_12))))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_3266,c_65]) ).
tcf(c_3268,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X0,inverse(inverse(multiply(X1,inverse(multiply(iPr_def_10(inverse(iPr_def_12)),inverse(iPr_def_12))))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_2876,c_3108,c_3110]) ).
tcf(c_3269,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X0,inverse(inverse(multiply(X1,inverse(multiply(iPr_def_12,inverse(iPr_def_12))))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_3268,c_65]) ).
tcf(c_4470,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),multiply(inverse(inverse(iPr_def_12)),X0)) = multiply(X0,inverse(iPr_def_12)),
inference(superposition,[status(thm)],[c_3108,c_3143]) ).
tcf(c_4475,plain,
multiply(inverse(iPr_def_12),inverse(iPr_def_12)) = iPr_def_12,
inference(superposition,[status(thm)],[c_3143,c_3108]) ).
tcf(c_4484,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(inverse(iPr_def_12)))) = multiply(multiply(X0,X1),inverse(iPr_def_12)),
inference(superposition,[status(thm)],[c_3151,c_65]) ).
tcf(c_4520,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),multiply(inverse(inverse(multiply(X0,inverse(iPr_def_12)))),inverse(inverse(iPr_def_12)))) = iPr_def_10(iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_3108,c_3141]) ).
tcf(c_4620,plain,
! [X0: $i] : iPr_def_10(iPr_def_11(X0,inverse(multiply(X0,inverse(iPr_def_12))),inverse(inverse(iPr_def_12)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_3153,c_3108]) ).
tcf(c_4941,plain,
! [X0: $i] : multiply(inverse(multiply(inverse(iPr_def_12),inverse(multiply(X0,inverse(iPr_def_12))))),iPr_def_12) = iPr_def_10(iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_4475,c_3133]) ).
tcf(c_4950,plain,
! [X0: $i] : multiply(inverse(iPr_def_12),multiply(inverse(iPr_def_12),X0)) = multiply(X0,inverse(iPr_def_12)),
inference(superposition,[status(thm)],[c_4475,c_3143]) ).
tcf(c_4968,plain,
iPr_def_10(iPr_def_11(inverse(iPr_def_12),inverse(iPr_def_12),inverse(inverse(iPr_def_12)))) = iPr_def_12,
inference(superposition,[status(thm)],[c_4475,c_4620]) ).
tcf(c_4990,plain,
multiply(inverse(iPr_def_12),multiply(inverse(inverse(iPr_def_12)),inverse(inverse(iPr_def_12)))) = iPr_def_10(iPr_def_10(inverse(iPr_def_12))),
inference(superposition,[status(thm)],[c_4475,c_4520]) ).
tcf(c_4998,plain,
multiply(multiply(inverse(iPr_def_12),inverse(iPr_def_12)),inverse(iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_4968,c_4484]) ).
tcf(c_4999,plain,
multiply(iPr_def_12,inverse(iPr_def_12)) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_4998,c_4475]) ).
tcf(c_5004,plain,
iPr_def_10(iPr_def_12) = iPr_def_12,
inference(demodulation,[status(thm)],[c_4990,c_65,c_3108,c_4470]) ).
tcf(c_5024,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X0,inverse(inverse(multiply(X1,inverse(iPr_def_12))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_3269,c_4999]) ).
tcf(c_5025,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(multiply(X1,inverse(iPr_def_12))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_3267,c_4999]) ).
tcf(c_5070,plain,
inverse(iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_5004,c_96]) ).
tcf(c_5516,plain,
! [X0: $i] : multiply(inverse(multiply(iPr_def_12,inverse(multiply(X0,iPr_def_12)))),iPr_def_12) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_4941,c_5070]) ).
tcf(c_5519,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(multiply(X1,iPr_def_12)))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_5025,c_5070]) ).
tcf(c_5520,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X0,inverse(inverse(multiply(X1,iPr_def_12)))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_5024,c_5070]) ).
tcf(c_5524,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(iPr_def_12,X0)) = multiply(X0,iPr_def_12),
inference(demodulation,[status(thm)],[c_4950,c_5070]) ).
tcf(c_5529,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(iPr_def_12))) = multiply(multiply(X0,X1),iPr_def_12),
inference(demodulation,[status(thm)],[c_4484,c_5070]) ).
tcf(c_5537,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(inverse(multiply(inverse(multiply(X0,iPr_def_12)),X1)),multiply(X2,iPr_def_12)) = iPr_def_10(iPr_def_11(X0,X2,inverse(X1))),
inference(demodulation,[status(thm)],[c_3153,c_5070]) ).
tcf(c_5539,plain,
! [X0: $i,X1: $i] : multiply(iPr_def_12,multiply(inverse(inverse(multiply(X0,inverse(multiply(X1,iPr_def_12))))),X1)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_3141,c_5070]) ).
tcf(c_5541,plain,
! [X0: $i,X1: $i] : multiply(inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X0),iPr_def_12)))))),iPr_def_12) = iPr_def_10(iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_3128,c_5070]) ).
tcf(c_5542,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,inverse(multiply(multiply(X0,X1),iPr_def_12)))))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_3130,c_5070]) ).
tcf(c_5543,plain,
! [X0: $i,X1: $i] : inverse(multiply(multiply(X0,X1),iPr_def_12)) = iPr_def_11(X0,X1,inverse(iPr_def_12)),
inference(demodulation,[status(thm)],[c_3151,c_5070]) ).
tcf(c_5545,plain,
! [X0: $i] : multiply(inverse(multiply(X0,iPr_def_12)),iPr_def_12) = multiply(iPr_def_10(X0),iPr_def_12),
inference(demodulation,[status(thm)],[c_3217,c_5070]) ).
tcf(c_5547,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,iPr_def_11(X0,X1,inverse(iPr_def_12)))))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_5542,c_5543]) ).
tcf(c_7867,plain,
! [X0: $i,X1: $i] : iPr_def_11(inverse(X0),X0,inverse(inverse(multiply(iPr_def_10(X1),iPr_def_12)))) = iPr_def_10(inverse(multiply(X1,iPr_def_12))),
inference(superposition,[status(thm)],[c_5545,c_5520]) ).
tcf(c_7873,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),iPr_def_12) = iPr_def_10(iPr_def_11(X0,X1,iPr_def_12)),
inference(superposition,[status(thm)],[c_5070,c_5529]) ).
tcf(c_8021,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(iPr_def_10(iPr_def_10(X1))))) = iPr_def_10(inverse(multiply(iPr_def_12,inverse(multiply(X1,iPr_def_12))))),
inference(superposition,[status(thm)],[c_5516,c_5519]) ).
tcf(c_8234,plain,
! [X0: $i] : multiply(X0,iPr_def_12) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_7867,c_65,c_5520]) ).
tcf(c_8282,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(iPr_def_10(iPr_def_10(X1))))) = iPr_def_10(inverse(multiply(iPr_def_12,inverse(iPr_def_10(iPr_def_10(X1)))))),
inference(demodulation,[status(thm)],[c_8021,c_8234]) ).
tcf(c_8283,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),X1) = multiply(iPr_def_12,iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_8282,c_65,c_96]) ).
tcf(c_8399,plain,
! [X0: $i,X1: $i] : iPr_def_11(X0,iPr_def_10(X0),inverse(inverse(iPr_def_10(iPr_def_10(X1))))) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_5519,c_8234]) ).
tcf(c_8406,plain,
! [X0: $i] : multiply(iPr_def_12,multiply(iPr_def_12,X0)) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_5524,c_8234]) ).
tcf(c_8427,plain,
! [X0: $i] : multiply(iPr_def_12,iPr_def_10(inverse(inverse(iPr_def_10(iPr_def_10(X0)))))) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_8399,c_8283]) ).
tcf(c_8428,plain,
! [X0: $i] : multiply(iPr_def_12,iPr_def_10(X0)) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_8427,c_65,c_96]) ).
tcf(c_8539,plain,
! [X0: $i] : multiply(iPr_def_12,X0) = X0,
inference(superposition,[status(thm)],[c_65,c_8428]) ).
tcf(c_8638,plain,
! [X0: $i] : multiply(iPr_def_12,X0) = iPr_def_10(iPr_def_10(X0)),
inference(demodulation,[status(thm)],[c_8406,c_8539]) ).
tcf(c_8645,plain,
! [X0: $i] : iPr_def_10(iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_8638,c_8539]) ).
tcf(c_8647,plain,
! [X0: $i] : multiply(X0,iPr_def_12) = X0,
inference(demodulation,[status(thm)],[c_8234,c_8645]) ).
tcf(c_8695,plain,
! [X0: $i] : inverse(X0) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_8645,c_96]) ).
tcf(c_8932,plain,
! [X0: $i,X1: $i] : iPr_def_10(iPr_def_11(X0,X1,iPr_def_12)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_7873,c_8647]) ).
tcf(c_11033,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(X0,X1)) = iPr_def_11(X0,X1,iPr_def_12),
inference(superposition,[status(thm)],[c_8932,c_8645]) ).
tcf(c_11502,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,inverse(inverse(multiply(X2,iPr_def_11(X0,X1,iPr_def_10(iPr_def_12)))))) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_8695,c_5547]) ).
tcf(c_11535,plain,
! [X0: $i,X1: $i] : multiply(inverse(inverse(multiply(X0,inverse(multiply(X1,iPr_def_12))))),X1) = iPr_def_10(iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_5539,c_8539]) ).
tcf(c_11650,plain,
! [X0: $i,X1: $i] : inverse(multiply(X0,inverse(multiply(X1,inverse(multiply(iPr_def_10(X0),iPr_def_12)))))) = iPr_def_10(iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_5541,c_8647]) ).
tcf(c_11722,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,iPr_def_10(X1)),X1) = X0,
inference(demodulation,[status(thm)],[c_11535,c_8645,c_8647,c_8695]) ).
tcf(c_11738,plain,
! [X0: $i,X1: $i] : iPr_def_10(multiply(X0,iPr_def_10(multiply(X1,X0)))) = X1,
inference(demodulation,[status(thm)],[c_11650,c_8645,c_8647,c_8695]) ).
tcf(c_11773,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,multiply(X2,iPr_def_11(X0,X1,iPr_def_10(iPr_def_12)))) = iPr_def_10(X2),
inference(demodulation,[status(thm)],[c_11502,c_8645,c_8695]) ).
tcf(c_11774,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_11(X0,X1,multiply(X2,iPr_def_10(multiply(X0,X1)))) = iPr_def_10(X2),
inference(light_normalisation,[status(thm)],[c_11773,c_5004,c_11033]) ).
tcf(c_12166,plain,
! [X0: $i,X1: $i] : multiply(multiply(X0,X1),iPr_def_10(X1)) = X0,
inference(superposition,[status(thm)],[c_8645,c_11722]) ).
tcf(c_12292,plain,
! [X0: $i,X1: $i] : multiply(X0,iPr_def_10(multiply(X1,X0))) = iPr_def_10(X1),
inference(superposition,[status(thm)],[c_11738,c_8645]) ).
tcf(c_12865,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_11(X0,X1,inverse(iPr_def_10(multiply(X2,inverse(multiply(X0,iPr_def_12))))))) = multiply(inverse(iPr_def_10(X2)),multiply(X1,iPr_def_12)),
inference(superposition,[status(thm)],[c_12292,c_5537]) ).
tcf(c_13144,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(iPr_def_11(X0,X1,multiply(X2,iPr_def_10(X0)))) = multiply(X2,X1),
inference(demodulation,[status(thm)],[c_12865,c_8645,c_8647,c_8695]) ).
tcf(c_13681,plain,
! [X0: $i,X1: $i,X2: $i] : iPr_def_10(multiply(X0,multiply(X1,X2))) = iPr_def_11(X1,X2,X0),
inference(superposition,[status(thm)],[c_12166,c_11774]) ).
tcf(c_14082,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(X0,multiply(X1,X2)) = iPr_def_10(iPr_def_11(X1,X2,X0)),
inference(superposition,[status(thm)],[c_13681,c_8645]) ).
tcf(c_14239,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = iPr_def_10(iPr_def_11(X1,X2,X0)),
inference(superposition,[status(thm)],[c_12166,c_13144]) ).
tcf(c_14561,plain,
multiply(multiply(a3,b3),c3) != iPr_def_10(iPr_def_11(b3,c3,a3)),
inference(demodulation,[status(thm)],[c_52,c_14082]) ).
tcf(c_14580,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_14561,c_14239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP420-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:42:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running UEQ theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 16.09/3.22 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 16.09/3.22 % SZS status Started for theBenchmark.p
% 16.09/3.22 % SZS status Unsatisfiable for theBenchmark.p
% 16.09/3.22
% 16.09/3.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.09/3.22
% 16.09/3.22 % ------ iProver source info
% 16.09/3.22
% 16.09/3.22 % git: date: 2026-07-19 20:42:38 +0200
% 16.09/3.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.09/3.22 % git: non_committed_changes: false
% 16.09/3.22
% 16.09/3.22 % ------ Parsing...% successful
% 16.09/3.22
% 16.09/3.22
% 16.09/3.22 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 16.09/3.22 % ------ Proving...
% 16.09/3.22 % ------ Problem Properties
% 16.09/3.22
% 16.09/3.22 %
% 16.09/3.22 % clauses 2
% 16.09/3.22 % conjectures 1
% 16.09/3.22 % EPR 0
% 16.09/3.22 % Horn 2
% 16.09/3.22 % unary 2
% 16.09/3.22 % binary 0
% 16.09/3.22 % lits 2
% 16.09/3.22 % lits eq 2
% 16.09/3.22 % fd_pure 0
% 16.09/3.22 % fd_pseudo 0
% 16.09/3.22 % fd_cond 0
% 16.09/3.22 % fd_pseudo_cond 0
% 16.09/3.22 % AC symbols 0
% 16.09/3.22
% 16.09/3.22 % ------ Input Options Time Limit: Unbounded
% 16.09/3.22
% 16.09/3.22
% 16.09/3.22 % ------
% 16.09/3.22 % Current options:
% 16.09/3.22 % ------
% 16.09/3.22
% 16.09/3.22
% 16.09/3.22 %
% 16.09/3.22
% 16.09/3.22 % ------ Proving...
% 16.09/3.22 %
% 16.09/3.22
% 16.09/3.22 % SZS status Unsatisfiable for theBenchmark.p
% 16.09/3.22
% 16.09/3.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.09/3.23
% 16.09/3.23
%------------------------------------------------------------------------------