TSTP Solution File: GRP405-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP405-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:19:01 EDT 2023
% Result : Unsatisfiable 2.36s 2.45s
% Output : CNFRefutation 2.36s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
multiply: ( $i * $i ) > $i ).
tff(decl_23,type,
inverse: $i > $i ).
tff(decl_24,type,
a3: $i ).
tff(decl_25,type,
b3: $i ).
tff(decl_26,type,
c3: $i ).
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(X2,multiply(inverse(X2),X2)))))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_3,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(X2,multiply(inverse(X2),X2)))))) = X3,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(inverse(X3),X3)))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X3)),X4)),X2)),inverse(multiply(X4,multiply(inverse(X4),X4))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(X3),inverse(multiply(X2,multiply(inverse(X2),X2))))))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(X5),X5)))))))) = multiply(inverse(multiply(inverse(multiply(X3,X5)),X2)),X4),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(inverse(multiply(X4,X5)),X2)),multiply(inverse(multiply(X4,X5)),X3)),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_2]) ).
cnf(c_0_9,plain,
multiply(X1,multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X1))),X4)) = multiply(inverse(multiply(X5,inverse(multiply(X3,multiply(inverse(X3),X3))))),multiply(X5,X4)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(X1,X2)),inverse(multiply(X3,inverse(multiply(multiply(X1,X3),multiply(inverse(multiply(X1,X3)),multiply(X1,X3))))))) = inverse(multiply(X2,multiply(inverse(X2),X2))),
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(inverse(multiply(inverse(multiply(X2,X3)),multiply(X2,X1))),X4)) = multiply(X5,multiply(inverse(multiply(inverse(multiply(X6,X3)),multiply(X6,X5))),X4)),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(X3)))),inverse(multiply(X2,multiply(inverse(X2),X2)))) = X3,
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_13,plain,
multiply(inverse(X1),X1) = multiply(X2,multiply(inverse(multiply(inverse(multiply(X3,X4)),multiply(X3,X2))),inverse(multiply(X4,multiply(inverse(X4),X4))))),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_15,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X4)),inverse(multiply(X3,multiply(inverse(X3),X3))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X5)),X4)),inverse(multiply(X5,multiply(inverse(X5),X5))))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),multiply(inverse(a3),a3)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_14]),c_0_14]) ).
cnf(c_0_17,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_13]),c_0_12]),c_0_8]) ).
cnf(c_0_18,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),inverse(multiply(multiply(X1,inverse(multiply(inverse(X4),inverse(multiply(X2,multiply(inverse(X2),X2)))))),inverse(multiply(X4,multiply(inverse(X4),X4)))))) = inverse(multiply(X3,multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_19,plain,
multiply(inverse(multiply(X1,X2)),inverse(multiply(inverse(inverse(multiply(X3,multiply(inverse(X3),X3)))),inverse(multiply(X3,multiply(inverse(X3),X3)))))) = inverse(multiply(multiply(X1,inverse(multiply(inverse(X4),inverse(multiply(X2,multiply(inverse(X2),X2)))))),inverse(multiply(X4,multiply(inverse(X4),X4))))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_20,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X1,multiply(X2,X3))),X4)),inverse(multiply(multiply(X2,X3),multiply(inverse(multiply(X5,X3)),multiply(X5,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(X2),X2))) = multiply(inverse(a3),a3),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_22,plain,
inverse(multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(X2,multiply(inverse(X3),X3))))) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_23,plain,
multiply(inverse(multiply(a3,X1)),multiply(a3,inverse(multiply(inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))),inverse(multiply(a3,multiply(inverse(a3),a3))))))) = inverse(multiply(X1,multiply(inverse(X1),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_7]) ).
cnf(c_0_24,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_14]) ).
cnf(c_0_25,plain,
multiply(X1,inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X3)),X4)),inverse(multiply(X3,multiply(inverse(X3),X3)))))),X5)),multiply(inverse(multiply(a3,inverse(multiply(inverse(X4),inverse(multiply(X2,multiply(inverse(X2),X2))))))),multiply(a3,inverse(multiply(inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))),inverse(multiply(a3,multiply(inverse(a3),a3)))))))))) = X5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_3]),c_0_23]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(multiply(a3,inverse(multiply(inverse(X3),inverse(multiply(X4,multiply(inverse(X4),X4))))))),multiply(a3,inverse(multiply(inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))),inverse(multiply(a3,multiply(inverse(a3),a3)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X4)),X5)),X3)),inverse(multiply(X5,multiply(inverse(X5),X5)))))),X6)),X2)),inverse(multiply(X6,multiply(inverse(X6),X6))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_23]) ).
cnf(c_0_27,plain,
multiply(inverse(multiply(X1,X2)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X4))),X5)),inverse(multiply(multiply(X1,X4),multiply(inverse(a3),a3)))))) = X5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_7]),c_0_14]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(inverse(multiply(a3,X1)),X2)),inverse(multiply(X1,multiply(inverse(X1),X1)))) = multiply(inverse(multiply(inverse(multiply(a3,a3)),X2)),inverse(multiply(a3,multiply(inverse(a3),a3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_5]) ).
cnf(c_0_29,plain,
multiply(multiply(inverse(a3),a3),multiply(inverse(a3),a3)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_24]),c_0_24]) ).
cnf(c_0_30,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(inverse(X3),inverse(multiply(X4,multiply(inverse(X4),X4)))))))),multiply(X1,X5)) = multiply(inverse(X3),multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_31,plain,
inverse(multiply(multiply(inverse(a3),a3),inverse(multiply(X1,multiply(inverse(X1),X1))))) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_24]) ).
cnf(c_0_32,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),a3)),X3)),inverse(multiply(a3,multiply(inverse(a3),a3)))))),a3)),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),X4)),X3)),inverse(multiply(X4,multiply(inverse(X4),X4)))))),X5))),inverse(multiply(a3,multiply(inverse(a3),a3))))) = X5,
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
multiply(inverse(multiply(X1,a3)),inverse(multiply(X2,inverse(multiply(multiply(X1,X2),multiply(inverse(a3),a3)))))) = inverse(multiply(a3,multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_8]) ).
cnf(c_0_34,plain,
multiply(multiply(inverse(X1),X1),multiply(inverse(X1),X1)) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_29,c_0_14]) ).
cnf(c_0_35,plain,
multiply(inverse(multiply(X1,multiply(X2,inverse(multiply(X3,inverse(multiply(X4,multiply(inverse(X4),X4)))))))),multiply(X1,X5)) = multiply(X3,multiply(inverse(multiply(X2,X4)),X5)),
inference(spm,[status(thm)],[c_0_30,c_0_8]) ).
cnf(c_0_36,plain,
inverse(multiply(multiply(inverse(X1),X1),inverse(multiply(X2,multiply(inverse(X2),X2))))) = X2,
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_37,plain,
inverse(multiply(multiply(inverse(a3),a3),inverse(multiply(a3,multiply(inverse(a3),a3))))) = a3,
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_38,plain,
multiply(multiply(inverse(a3),a3),inverse(multiply(a3,multiply(inverse(a3),a3)))) = inverse(multiply(a3,multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24]),c_0_24]) ).
cnf(c_0_39,plain,
multiply(inverse(inverse(multiply(X1,multiply(inverse(X1),X1)))),multiply(inverse(multiply(a3,X1)),X2)) = multiply(inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))),multiply(inverse(multiply(a3,a3)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_35]) ).
cnf(c_0_40,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),X5)),inverse(multiply(X4,multiply(inverse(X4),X4))))))) = multiply(inverse(multiply(X3,X2)),X5),
inference(spm,[status(thm)],[c_0_7,c_0_2]) ).
cnf(c_0_41,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(multiply(X2,X3)),X4)),inverse(multiply(X3,multiply(inverse(X3),X3))))))),multiply(X1,X5)) = multiply(inverse(X4),multiply(X2,X5)),
inference(spm,[status(thm)],[c_0_7,c_0_2]) ).
cnf(c_0_42,plain,
inverse(multiply(multiply(inverse(X1),X1),inverse(multiply(X2,multiply(inverse(X3),X3))))) = X2,
inference(spm,[status(thm)],[c_0_36,c_0_14]) ).
cnf(c_0_43,plain,
inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))) = a3,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
multiply(inverse(inverse(multiply(X1,multiply(inverse(X1),X1)))),multiply(inverse(multiply(X2,X1)),X3)) = multiply(inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))),multiply(inverse(multiply(X2,a3)),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_40]) ).
cnf(c_0_45,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(X3),multiply(X1,inverse(multiply(inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))),inverse(multiply(a3,multiply(inverse(a3),a3)))))))))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(X3),X4)),X2)),inverse(multiply(X4,multiply(inverse(X4),X4))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_2]),c_0_23]),c_0_41]) ).
cnf(c_0_46,plain,
multiply(inverse(multiply(X1,a3)),multiply(X1,multiply(inverse(X2),X2))) = inverse(multiply(a3,multiply(inverse(a3),a3))),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_47,plain,
inverse(inverse(multiply(a3,multiply(inverse(X1),X1)))) = a3,
inference(spm,[status(thm)],[c_0_43,c_0_14]) ).
cnf(c_0_48,plain,
multiply(inverse(inverse(multiply(X1,multiply(inverse(X1),X1)))),multiply(inverse(multiply(X2,X1)),X3)) = multiply(a3,multiply(inverse(multiply(X2,a3)),X3)),
inference(rw,[status(thm)],[c_0_44,c_0_43]) ).
cnf(c_0_49,plain,
multiply(multiply(inverse(a3),a3),a3) = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_14]),c_0_24]),c_0_24]),c_0_47]),c_0_8]) ).
cnf(c_0_50,plain,
multiply(a3,inverse(multiply(a3,multiply(inverse(a3),a3)))) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_14]),c_0_33]) ).
cnf(c_0_51,plain,
multiply(multiply(inverse(X1),X1),a3) = a3,
inference(spm,[status(thm)],[c_0_49,c_0_14]) ).
cnf(c_0_52,plain,
multiply(a3,inverse(multiply(a3,multiply(inverse(X1),X1)))) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_50,c_0_14]) ).
cnf(c_0_53,plain,
multiply(inverse(multiply(X1,a3)),multiply(X1,inverse(multiply(inverse(X2),X2)))) = inverse(multiply(a3,multiply(inverse(a3),a3))),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_54,plain,
inverse(multiply(a3,multiply(inverse(a3),a3))) = multiply(inverse(a3),multiply(inverse(a3),a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_51]),c_0_51]),c_0_52]),c_0_24]) ).
cnf(c_0_55,plain,
multiply(multiply(inverse(a3),a3),multiply(inverse(a3),multiply(inverse(a3),a3))) = inverse(multiply(a3,multiply(inverse(a3),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_24]),c_0_24]) ).
cnf(c_0_56,plain,
inverse(multiply(inverse(a3),multiply(inverse(a3),a3))) = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_54]),c_0_24]),c_0_55]),c_0_54]) ).
cnf(c_0_57,plain,
multiply(multiply(inverse(a3),a3),inverse(multiply(inverse(X1),multiply(inverse(a3),a3)))) = X1,
inference(rw,[status(thm)],[c_0_16,c_0_24]) ).
cnf(c_0_58,plain,
inverse(multiply(multiply(inverse(a3),a3),multiply(inverse(X1),X1))) = multiply(inverse(a3),a3),
inference(spm,[status(thm)],[c_0_24,c_0_24]) ).
cnf(c_0_59,plain,
inverse(multiply(inverse(a3),multiply(inverse(X1),X1))) = a3,
inference(spm,[status(thm)],[c_0_56,c_0_14]) ).
cnf(c_0_60,plain,
multiply(multiply(inverse(a3),a3),multiply(inverse(X1),X1)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_34]),c_0_24]),c_0_34]) ).
cnf(c_0_61,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),multiply(X1,X3)) = multiply(a3,multiply(inverse(a3),X3)),
inference(spm,[status(thm)],[c_0_7,c_0_59]) ).
cnf(c_0_62,plain,
multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2)) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_60,c_0_14]) ).
cnf(c_0_63,plain,
inverse(multiply(a3,multiply(inverse(X1),X1))) = multiply(inverse(a3),multiply(inverse(X1),X1)),
inference(spm,[status(thm)],[c_0_54,c_0_14]) ).
cnf(c_0_64,plain,
multiply(a3,multiply(inverse(a3),a3)) = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_51]),c_0_62]),c_0_24]),c_0_51]) ).
cnf(c_0_65,plain,
multiply(inverse(a3),multiply(inverse(a3),a3)) = inverse(a3),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_66,plain,
multiply(a3,multiply(inverse(a3),multiply(inverse(X1),X1))) = multiply(inverse(X1),X1),
inference(rw,[status(thm)],[c_0_52,c_0_63]) ).
cnf(c_0_67,plain,
multiply(inverse(multiply(multiply(inverse(a3),a3),a3)),multiply(inverse(a3),a3)) = inverse(multiply(a3,multiply(inverse(a3),a3))),
inference(spm,[status(thm)],[c_0_53,c_0_57]) ).
cnf(c_0_68,plain,
multiply(inverse(a3),a3) = multiply(a3,inverse(a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_65]),c_0_59]),c_0_66]) ).
cnf(c_0_69,plain,
multiply(a3,multiply(inverse(multiply(inverse(multiply(multiply(inverse(a3),a3),a3)),a3)),X1)) = multiply(multiply(inverse(a3),a3),multiply(a3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_67]),c_0_24]),c_0_34]),c_0_34]),c_0_24]),c_0_24]),c_0_43]) ).
cnf(c_0_70,plain,
multiply(inverse(X1),X1) = multiply(a3,inverse(a3)),
inference(spm,[status(thm)],[c_0_14,c_0_68]) ).
cnf(c_0_71,plain,
multiply(inverse(a3),multiply(a3,inverse(a3))) = inverse(a3),
inference(rw,[status(thm)],[c_0_65,c_0_68]) ).
cnf(c_0_72,plain,
multiply(multiply(a3,inverse(a3)),multiply(inverse(a3),multiply(a3,inverse(a3)))) = multiply(inverse(a3),multiply(a3,inverse(a3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_54]),c_0_68]),c_0_68]),c_0_68]) ).
cnf(c_0_73,plain,
inverse(inverse(multiply(multiply(inverse(a3),a3),multiply(a3,multiply(inverse(multiply(multiply(inverse(a3),a3),a3)),a3))))) = a3,
inference(spm,[status(thm)],[c_0_47,c_0_69]) ).
cnf(c_0_74,plain,
multiply(multiply(a3,inverse(a3)),a3) = a3,
inference(spm,[status(thm)],[c_0_51,c_0_68]) ).
cnf(c_0_75,plain,
multiply(a3,multiply(a3,inverse(a3))) = a3,
inference(rw,[status(thm)],[c_0_64,c_0_68]) ).
cnf(c_0_76,plain,
multiply(inverse(multiply(X1,a3)),inverse(multiply(X2,inverse(multiply(multiply(X1,X2),multiply(a3,inverse(a3))))))) = inverse(a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_54]),c_0_70]),c_0_70]),c_0_71]) ).
cnf(c_0_77,plain,
multiply(multiply(a3,inverse(a3)),inverse(a3)) = inverse(a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_71]),c_0_71]) ).
cnf(c_0_78,plain,
inverse(inverse(a3)) = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_70]),c_0_74]),c_0_70]),c_0_75]),c_0_74]) ).
cnf(c_0_79,plain,
multiply(inverse(multiply(X1,a3)),multiply(X1,multiply(inverse(X2),X2))) = multiply(inverse(a3),multiply(inverse(a3),a3)),
inference(rw,[status(thm)],[c_0_46,c_0_54]) ).
cnf(c_0_80,plain,
multiply(inverse(multiply(a3,a3)),a3) = inverse(a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_75]),c_0_77]),c_0_78]) ).
cnf(c_0_81,plain,
multiply(inverse(multiply(X1,a3)),multiply(X1,multiply(a3,inverse(a3)))) = inverse(a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_65]),c_0_70]) ).
cnf(c_0_82,plain,
multiply(inverse(multiply(X1,a3)),multiply(X1,X2)) = multiply(a3,multiply(inverse(multiply(a3,a3)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_80]),c_0_78]) ).
cnf(c_0_83,plain,
multiply(a3,inverse(multiply(a3,a3))) = inverse(a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_80]),c_0_80]),c_0_78]),c_0_71]),c_0_78]) ).
cnf(c_0_84,plain,
multiply(a3,multiply(a3,multiply(inverse(multiply(a3,a3)),inverse(a3)))) = inverse(a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_82]) ).
cnf(c_0_85,plain,
inverse(multiply(X1,multiply(a3,inverse(a3)))) = multiply(inverse(multiply(a3,X1)),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_83]),c_0_59]),c_0_80]),c_0_78]),c_0_70]) ).
cnf(c_0_86,plain,
multiply(a3,inverse(multiply(inverse(multiply(a3,X1)),multiply(a3,a3)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_84]),c_0_78]),c_0_70]),c_0_85]),c_0_84]),c_0_78]) ).
cnf(c_0_87,plain,
multiply(inverse(a3),multiply(a3,X1)) = multiply(a3,multiply(inverse(a3),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_77]),c_0_59]),c_0_78]),c_0_74]) ).
cnf(c_0_88,plain,
multiply(multiply(inverse(a3),a3),multiply(a3,X1)) = multiply(a3,multiply(multiply(inverse(a3),a3),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_51]),c_0_24]) ).
cnf(c_0_89,plain,
multiply(a3,inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,a3)))) = X2,
inference(spm,[status(thm)],[c_0_86,c_0_7]) ).
cnf(c_0_90,plain,
multiply(a3,multiply(inverse(a3),inverse(a3))) = inverse(a3),
inference(rw,[status(thm)],[c_0_71,c_0_87]) ).
cnf(c_0_91,plain,
multiply(a3,inverse(multiply(a3,multiply(a3,a3)))) = inverse(multiply(a3,a3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_83]),c_0_78]) ).
cnf(c_0_92,plain,
inverse(multiply(X1,multiply(inverse(X1),X1))) = multiply(inverse(multiply(X2,X1)),multiply(X2,inverse(multiply(inverse(inverse(multiply(a3,multiply(inverse(a3),a3)))),inverse(multiply(a3,multiply(inverse(a3),a3))))))),
inference(spm,[status(thm)],[c_0_7,c_0_23]) ).
cnf(c_0_93,plain,
inverse(multiply(a3,inverse(a3))) = multiply(a3,inverse(a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_68]),c_0_70]) ).
cnf(c_0_94,plain,
multiply(multiply(inverse(X1),X1),multiply(a3,X2)) = multiply(a3,multiply(multiply(inverse(X1),X1),X2)),
inference(spm,[status(thm)],[c_0_88,c_0_14]) ).
cnf(c_0_95,plain,
multiply(inverse(a3),inverse(a3)) = inverse(multiply(a3,a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_78]),c_0_91]) ).
cnf(c_0_96,plain,
inverse(multiply(a3,multiply(inverse(multiply(a3,a3)),inverse(a3)))) = multiply(a3,a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_83]),c_0_70]),c_0_78]),c_0_14]),c_0_70]),c_0_93]),c_0_75]),c_0_82]) ).
cnf(c_0_97,plain,
multiply(a3,multiply(inverse(multiply(a3,a3)),inverse(a3))) = inverse(multiply(a3,a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_84]),c_0_78]),c_0_91]) ).
cnf(c_0_98,plain,
multiply(multiply(a3,inverse(a3)),multiply(a3,X1)) = multiply(a3,multiply(multiply(a3,inverse(a3)),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_70]),c_0_70]) ).
cnf(c_0_99,plain,
multiply(inverse(inverse(multiply(a3,a3))),inverse(a3)) = a3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_95]),c_0_59]),c_0_14]),c_0_70]),c_0_93]),c_0_87]),c_0_95]),c_0_83]) ).
cnf(c_0_100,plain,
inverse(inverse(multiply(a3,a3))) = multiply(a3,a3),
inference(rw,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,plain,
multiply(inverse(multiply(a3,X1)),a3) = multiply(a3,inverse(multiply(X1,a3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_22]),c_0_70]),c_0_93]),c_0_74]),c_0_70]),c_0_85]) ).
cnf(c_0_102,plain,
multiply(inverse(multiply(X1,inverse(a3))),multiply(X1,X2)) = multiply(a3,multiply(multiply(a3,inverse(a3)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_93]),c_0_98]) ).
cnf(c_0_103,plain,
multiply(multiply(a3,a3),inverse(a3)) = a3,
inference(rw,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_104,plain,
multiply(multiply(a3,inverse(a3)),inverse(multiply(a3,inverse(multiply(X1,a3))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_77]),c_0_78]),c_0_59]),c_0_101]) ).
cnf(c_0_105,plain,
multiply(a3,multiply(a3,inverse(multiply(inverse(multiply(inverse(a3),X1)),a3)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_70]),c_0_85]),c_0_101]) ).
cnf(c_0_106,plain,
multiply(inverse(a3),multiply(multiply(a3,a3),X1)) = multiply(a3,multiply(multiply(a3,inverse(a3)),X1)),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,plain,
inverse(multiply(a3,inverse(multiply(X1,a3)))) = multiply(a3,inverse(multiply(inverse(X1),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_104]),c_0_74]) ).
cnf(c_0_108,plain,
multiply(a3,inverse(multiply(inverse(multiply(multiply(a3,inverse(a3)),X1)),a3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_93]),c_0_59]) ).
cnf(c_0_109,plain,
inverse(multiply(X1,multiply(a3,inverse(a3)))) = multiply(a3,inverse(multiply(X1,a3))),
inference(rw,[status(thm)],[c_0_85,c_0_101]) ).
cnf(c_0_110,plain,
multiply(inverse(multiply(X1,multiply(X2,multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(X5),X5))))))))),multiply(X1,inverse(multiply(inverse(X6),inverse(multiply(multiply(X2,multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(X5),X5))))))),multiply(inverse(X4),X4))))))) = X6,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_4]) ).
cnf(c_0_111,plain,
multiply(multiply(a3,a3),X1) = multiply(a3,multiply(a3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_101]),c_0_107]),c_0_108]) ).
cnf(c_0_112,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X3,inverse(multiply(inverse(X4),multiply(a3,inverse(multiply(multiply(X5,X6),a3)))))))) = multiply(inverse(multiply(inverse(multiply(X3,multiply(X5,X6))),X2)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_70]),c_0_109]) ).
cnf(c_0_113,plain,
multiply(multiply(a3,inverse(multiply(X1,a3))),multiply(X1,X2)) = multiply(a3,multiply(inverse(a3),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_82]),c_0_80]),c_0_85]),c_0_101]) ).
cnf(c_0_114,plain,
multiply(multiply(a3,inverse(a3)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_70]),c_0_85]),c_0_101]),c_0_111]),c_0_70]),c_0_85]),c_0_101]),c_0_70]),c_0_109]),c_0_112]),c_0_70]),c_0_93]) ).
cnf(c_0_115,plain,
multiply(a3,multiply(inverse(a3),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_114]),c_0_114]) ).
cnf(c_0_116,plain,
multiply(inverse(a3),multiply(a3,X1)) = X1,
inference(rw,[status(thm)],[c_0_87,c_0_115]) ).
cnf(c_0_117,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_114]),c_0_114]) ).
cnf(c_0_118,plain,
inverse(multiply(inverse(X1),a3)) = multiply(inverse(a3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_108]),c_0_114]) ).
cnf(c_0_119,plain,
multiply(a3,multiply(a3,multiply(inverse(multiply(a3,a3)),X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_116]),c_0_24]),c_0_70]),c_0_114]),c_0_82]) ).
cnf(c_0_120,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_117]),c_0_70]),c_0_85]),c_0_101]),c_0_107]),c_0_118]),c_0_115]),c_0_82]),c_0_119]) ).
cnf(c_0_121,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_120]),c_0_70]),c_0_93]),c_0_114]) ).
cnf(c_0_122,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_121]),c_0_70]),c_0_93]),c_0_114]),c_0_121]) ).
cnf(c_0_123,plain,
multiply(X1,multiply(inverse(multiply(inverse(X2),X1)),X3)) = multiply(X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_117]),c_0_117]),c_0_70]),c_0_85]),c_0_101]),c_0_107]),c_0_118]),c_0_115]) ).
cnf(c_0_124,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_122]),c_0_122]) ).
cnf(c_0_125,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
prove_these_axioms_3 ).
cnf(c_0_126,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_121]) ).
cnf(c_0_127,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_125,c_0_126])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP405-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n028.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Aug 29 01:27:10 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 2.36/2.45 % Version : CSE_E---1.5
% 2.36/2.45 % Problem : theBenchmark.p
% 2.36/2.45 % Proof found
% 2.36/2.45 % SZS status Theorem for theBenchmark.p
% 2.36/2.45 % SZS output start Proof
% See solution above
% 2.36/2.46 % Total time : 1.889000 s
% 2.36/2.46 % SZS output end Proof
% 2.36/2.46 % Total time : 1.892000 s
%------------------------------------------------------------------------------