TSTP Solution File: GRP054-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP054-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 00:14:33 EDT 2023
% Result : Unsatisfiable 2.83s 2.88s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
inverse: $i > $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
a1: $i ).
tff(decl_25,type,
b1: $i ).
tff(decl_26,type,
b2: $i ).
tff(decl_27,type,
a2: $i ).
tff(decl_28,type,
a3: $i ).
tff(decl_29,type,
b3: $i ).
tff(decl_30,type,
c3: $i ).
cnf(single_axiom,axiom,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3))) = X2,
single_axiom ).
cnf(c_0_3,plain,
inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X4,X5)),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(inverse(X1)),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)) = X1,
inference(rw,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X4,X5)),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X1,X3),inverse(multiply(inverse(multiply(X1,X3)),multiply(X1,X3))))))))),X2) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_6]),c_0_3]) ).
cnf(c_0_8,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),inverse(multiply(inverse(X2),inverse(multiply(multiply(X4,X5),inverse(multiply(inverse(multiply(X4,X5)),multiply(X4,X5)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_3]),c_0_6]),c_0_6]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(a1,X1)),multiply(a1,X2)) = multiply(inverse(multiply(X3,X1)),multiply(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_8]),c_0_8]),c_0_6]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(inverse(multiply(a1,X1)),multiply(a1,X2))),multiply(inverse(multiply(X3,X1)),X4)) = multiply(inverse(multiply(a1,multiply(X3,X2))),multiply(a1,X4)),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(inverse(multiply(X4,X2)),X5)) = multiply(inverse(multiply(a1,multiply(X4,X3))),multiply(a1,X5)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(inverse(X4),inverse(multiply(multiply(X1,X3),inverse(multiply(inverse(multiply(X1,X3)),multiply(X1,X3))))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X2),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_3]),c_0_3]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),inverse(multiply(multiply(a1,a1),inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,a1))))))))),X3)) = multiply(inverse(multiply(a1,multiply(X2,multiply(a1,a1)))),multiply(a1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_3]),c_0_4]) ).
cnf(c_0_15,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(a1,multiply(X2,multiply(a1,a1)))),multiply(a1,multiply(X2,multiply(a1,a1)))),
inference(spm,[status(thm)],[c_0_14,c_0_6]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),X1) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_15]),c_0_15]) ).
cnf(c_0_17,plain,
multiply(inverse(inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_8]),c_0_6]) ).
cnf(c_0_18,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
cnf(c_0_19,plain,
multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(inverse(X2),inverse(multiply(inverse(a1),a1))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).
cnf(c_0_20,plain,
multiply(inverse(X1),X1) = inverse(multiply(inverse(a1),a1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = multiply(inverse(multiply(X4,inverse(multiply(X2,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X4,X5)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_3]),c_0_3]),c_0_4]) ).
cnf(c_0_22,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_8]),c_0_6]),c_0_6]) ).
cnf(c_0_23,plain,
multiply(inverse(X1),X1) = inverse(multiply(inverse(X2),X2)),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X1,X3)) = multiply(inverse(multiply(inverse(multiply(X4,inverse(multiply(X5,inverse(multiply(X6,inverse(multiply(inverse(X6),X6)))))))),inverse(multiply(X2,inverse(multiply(multiply(X4,X6),multiply(inverse(a1),a1))))))),multiply(inverse(multiply(X7,inverse(multiply(X5,inverse(multiply(X8,inverse(multiply(inverse(X8),X8)))))))),multiply(X7,X8))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_21]),c_0_18]),c_0_20]) ).
cnf(c_0_25,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(X1,multiply(inverse(a1),a1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_26,plain,
multiply(inverse(multiply(X1,multiply(inverse(a1),a1))),multiply(X1,X2)) = multiply(X2,multiply(inverse(a1),a1)),
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_24,c_0_23]),c_0_23]),c_0_23]),c_0_24]),c_0_6]),c_0_23]) ).
cnf(c_0_27,plain,
multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(X1),multiply(inverse(X2),X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_28,plain,
inverse(multiply(inverse(a1),multiply(inverse(a1),a1))) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
cnf(c_0_29,plain,
multiply(multiply(inverse(a1),a1),a1) = a1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,plain,
multiply(multiply(inverse(a1),a1),multiply(inverse(X1),X1)) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_31,plain,
multiply(a1,multiply(inverse(a1),a1)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_29]),c_0_30]),c_0_23]),c_0_29]) ).
cnf(c_0_32,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(a1))) = a1,
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_33,plain,
multiply(a1,multiply(multiply(inverse(a1),a1),inverse(a1))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_32]),c_0_23]) ).
cnf(c_0_34,plain,
multiply(a1,multiply(inverse(X1),X1)) = a1,
inference(spm,[status(thm)],[c_0_31,c_0_18]) ).
cnf(c_0_35,plain,
multiply(multiply(multiply(inverse(a1),a1),inverse(a1)),multiply(inverse(a1),a1)) = multiply(inverse(a1),multiply(inverse(a1),a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_34]) ).
cnf(c_0_36,plain,
inverse(multiply(inverse(a1),multiply(inverse(X1),X1))) = a1,
inference(spm,[status(thm)],[c_0_28,c_0_18]) ).
cnf(c_0_37,plain,
multiply(multiply(inverse(X1),X1),a1) = a1,
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_38,plain,
inverse(multiply(multiply(inverse(X1),X1),inverse(a1))) = a1,
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_39,plain,
multiply(multiply(inverse(a1),a1),inverse(a1)) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_35]),c_0_36]),c_0_37]) ).
cnf(c_0_40,plain,
inverse(inverse(a1)) = a1,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_42,plain,
inverse(multiply(inverse(a1),multiply(a1,inverse(a1)))) = a1,
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_43,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_44,plain,
multiply(a1,multiply(a1,inverse(a1))) = a1,
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_45,plain,
multiply(inverse(multiply(X1,multiply(a1,inverse(a1)))),multiply(X1,X2)) = multiply(X2,multiply(a1,inverse(a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_41]),c_0_41]) ).
cnf(c_0_46,plain,
multiply(inverse(multiply(a1,inverse(a1))),inverse(a1)) = multiply(inverse(a1),multiply(a1,inverse(a1))),
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_19,c_0_42]),c_0_23]),c_0_43]),c_0_23]),c_0_43]),c_0_44]) ).
cnf(c_0_47,plain,
inverse(multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_45]),c_0_23]),c_0_43]),c_0_43]) ).
cnf(c_0_48,plain,
multiply(multiply(a1,inverse(a1)),inverse(a1)) = inverse(a1),
inference(rw,[status(thm)],[c_0_39,c_0_41]) ).
cnf(c_0_49,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(X1),multiply(a1,inverse(a1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_41]),c_0_43]) ).
cnf(c_0_50,plain,
multiply(inverse(a1),multiply(a1,inverse(a1))) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_51,plain,
multiply(a1,inverse(multiply(inverse(inverse(X1)),a1))) = multiply(multiply(a1,inverse(a1)),inverse(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_49,c_0_6]),c_0_18]),c_0_43]),c_0_47]),c_0_50]),c_0_40]) ).
cnf(c_0_52,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X1,X3),inverse(multiply(inverse(multiply(X1,X3)),multiply(X1,X3))))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X2),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)))) = multiply(inverse(multiply(X5,inverse(multiply(inverse(X4),inverse(multiply(X6,inverse(multiply(inverse(X6),X6)))))))),multiply(X5,X6)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_3]) ).
cnf(c_0_53,plain,
multiply(a1,multiply(inverse(a1),X1)) = multiply(X1,multiply(a1,inverse(a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_45]),c_0_42]),c_0_44]) ).
cnf(c_0_54,plain,
multiply(a1,inverse(multiply(a1,a1))) = inverse(a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_40]),c_0_48]) ).
cnf(c_0_55,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(a1),a1))))))),inverse(multiply(X6,inverse(multiply(multiply(X3,X5),multiply(inverse(a1),a1))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1))),inverse(multiply(multiply(inverse(multiply(X7,inverse(multiply(inverse(X6),inverse(multiply(X8,multiply(inverse(a1),a1))))))),multiply(X7,X8)),multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(a1),a1))))))),inverse(multiply(X6,inverse(multiply(multiply(X3,X5),multiply(inverse(a1),a1))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1))))))))))),multiply(X1,multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(a1),a1))))))),inverse(multiply(X6,inverse(multiply(multiply(X3,X5),multiply(inverse(a1),a1))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1))))) = multiply(inverse(multiply(X9,inverse(multiply(X2,inverse(multiply(X10,multiply(inverse(a1),a1))))))),multiply(X9,X10)),
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(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_21,c_0_52]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_31]),c_0_23]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_31]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_31]),c_0_23]) ).
cnf(c_0_56,plain,
inverse(multiply(multiply(a1,inverse(a1)),inverse(multiply(X1,multiply(a1,inverse(a1)))))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_43]) ).
cnf(c_0_57,plain,
multiply(a1,multiply(inverse(a1),inverse(a1))) = inverse(a1),
inference(rw,[status(thm)],[c_0_50,c_0_53]) ).
cnf(c_0_58,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,multiply(inverse(a1),inverse(X1))))) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_53]) ).
cnf(c_0_59,plain,
multiply(a1,multiply(inverse(a1),inverse(multiply(a1,a1)))) = multiply(inverse(a1),inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_54]),c_0_44]),c_0_53]) ).
cnf(c_0_60,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,multiply(inverse(a1),a1))))))),multiply(X1,X3)) = multiply(inverse(multiply(a1,inverse(multiply(X2,inverse(a1))))),multiply(a1,a1)),
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(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_21,c_0_52]),c_0_23]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_34]),c_0_23]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_34]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_34]),c_0_55]),c_0_34]) ).
cnf(c_0_61,plain,
inverse(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,multiply(inverse(a1),X1))))) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_53]) ).
cnf(c_0_62,plain,
multiply(a1,multiply(inverse(a1),multiply(inverse(a1),inverse(a1)))) = multiply(inverse(a1),inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_57]),c_0_44]),c_0_53]) ).
cnf(c_0_63,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(a1),inverse(a1)))) = multiply(a1,a1),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(a1),inverse(a1))))),multiply(a1,a1)) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_40]),c_0_23]),c_0_60]) ).
cnf(c_0_65,plain,
multiply(inverse(a1),inverse(a1)) = inverse(multiply(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_66,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(a1),a1))))))),inverse(multiply(X6,inverse(multiply(multiply(X3,X5),multiply(inverse(a1),a1))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1))),inverse(multiply(multiply(inverse(multiply(X7,inverse(multiply(inverse(X6),inverse(multiply(X8,multiply(inverse(a1),a1))))))),multiply(X7,X8)),multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(a1),a1))))))),inverse(multiply(X6,inverse(multiply(multiply(X3,X5),multiply(inverse(a1),a1))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1))))))))))),multiply(X1,multiply(inverse(multiply(inverse(multiply(X3,inverse(multiply(inverse(X4),inverse(multiply(X5,multiply(inverse(a1),a1))))))),inverse(multiply(X6,inverse(multiply(multiply(X3,X5),multiply(inverse(a1),a1))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1))))) = 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(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_6,c_0_52]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_31]),c_0_23]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_31]),c_0_23]),c_0_18]),c_0_23]),c_0_23]),c_0_31]) ).
cnf(c_0_67,plain,
multiply(inverse(multiply(a1,inverse(inverse(multiply(a1,a1))))),multiply(a1,a1)) = inverse(a1),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_68,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(inverse(X1)),inverse(a1))))),multiply(a1,a1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_55]),c_0_31]) ).
cnf(c_0_69,plain,
multiply(inverse(multiply(X1,inverse(inverse(multiply(a1,a1))))),multiply(X1,a1)) = inverse(a1),
inference(spm,[status(thm)],[c_0_11,c_0_67]) ).
cnf(c_0_70,plain,
multiply(multiply(a1,inverse(a1)),a1) = a1,
inference(spm,[status(thm)],[c_0_37,c_0_40]) ).
cnf(c_0_71,plain,
multiply(multiply(a1,inverse(a1)),inverse(inverse(multiply(a1,a1)))) = multiply(a1,a1),
inference(spm,[status(thm)],[c_0_63,c_0_65]) ).
cnf(c_0_72,plain,
multiply(inverse(a1),multiply(a1,a1)) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_18]),c_0_23]),c_0_31]) ).
cnf(c_0_73,plain,
multiply(a1,multiply(inverse(a1),inverse(multiply(inverse(a1),inverse(a1))))) = multiply(multiply(a1,inverse(a1)),multiply(a1,a1)),
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_63]),c_0_53]),c_0_53]),c_0_57]),c_0_47]),c_0_53]) ).
cnf(c_0_74,plain,
multiply(a1,inverse(multiply(inverse(X1),a1))) = multiply(multiply(a1,inverse(a1)),X1),
inference(spm,[status(thm)],[c_0_51,c_0_25]) ).
cnf(c_0_75,plain,
multiply(inverse(multiply(a1,a1)),a1) = inverse(a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_76,plain,
multiply(multiply(a1,a1),multiply(inverse(a1),a1)) = multiply(a1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_72]),c_0_28]) ).
cnf(c_0_77,plain,
multiply(a1,multiply(inverse(a1),inverse(inverse(multiply(a1,a1))))) = multiply(multiply(a1,inverse(a1)),multiply(a1,a1)),
inference(spm,[status(thm)],[c_0_73,c_0_65]) ).
cnf(c_0_78,plain,
multiply(multiply(a1,inverse(a1)),multiply(a1,a1)) = multiply(a1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_40]) ).
cnf(c_0_79,plain,
inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(a1,a1)))) = multiply(a1,a1),
inference(spm,[status(thm)],[c_0_25,c_0_76]) ).
cnf(c_0_80,plain,
multiply(a1,multiply(inverse(a1),inverse(inverse(multiply(a1,a1))))) = multiply(a1,a1),
inference(rw,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,plain,
inverse(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,a1)))) = multiply(a1,a1),
inference(spm,[status(thm)],[c_0_79,c_0_43]) ).
cnf(c_0_82,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(multiply(a1,inverse(a1)),multiply(a1,a1)))) = multiply(inverse(a1),inverse(a1)),
inference(spm,[status(thm)],[c_0_58,c_0_73]) ).
cnf(c_0_83,plain,
multiply(inverse(inverse(multiply(a1,a1))),inverse(a1)) = a1,
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_75]),c_0_53]),c_0_59]),c_0_65]),c_0_44]) ).
cnf(c_0_84,plain,
inverse(inverse(multiply(a1,a1))) = multiply(a1,a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_80]),c_0_81]) ).
cnf(c_0_85,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(multiply(a1,inverse(a1)),multiply(a1,a1)))) = inverse(multiply(a1,a1)),
inference(rw,[status(thm)],[c_0_82,c_0_65]) ).
cnf(c_0_86,plain,
multiply(multiply(a1,a1),inverse(a1)) = a1,
inference(rw,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_87,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),inverse(multiply(X4,inverse(multiply(multiply(X1,X3),inverse(multiply(inverse(a1),a1)))))))),multiply(inverse(multiply(X5,inverse(multiply(X2,inverse(multiply(X6,inverse(multiply(inverse(X6),X6)))))))),multiply(X5,X6))) = multiply(inverse(multiply(X7,inverse(multiply(X4,inverse(multiply(X8,inverse(multiply(inverse(X8),X8)))))))),multiply(X7,X8)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_21]),c_0_16]) ).
cnf(c_0_88,plain,
multiply(inverse(multiply(X1,inverse(multiply(a1,a1)))),multiply(X1,X2)) = multiply(a1,multiply(a1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_54]),c_0_40]) ).
cnf(c_0_89,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,a1))) = inverse(multiply(a1,a1)),
inference(spm,[status(thm)],[c_0_85,c_0_78]) ).
cnf(c_0_90,plain,
inverse(multiply(inverse(inverse(multiply(inverse(multiply(multiply(a1,a1),X1)),a1))),a1)) = 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(spm,[status(thm)],[c_0_22,c_0_86]),c_0_18]),c_0_43]),c_0_47]),c_0_53]),c_0_65]),c_0_54]),c_0_40]) ).
cnf(c_0_91,plain,
multiply(multiply(a1,a1),inverse(multiply(a1,a1))) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_43,c_0_84]) ).
cnf(c_0_92,plain,
multiply(X1,multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_87]),c_0_87]),c_0_16]) ).
cnf(c_0_93,plain,
multiply(multiply(a1,a1),multiply(multiply(a1,inverse(a1)),X1)) = multiply(a1,multiply(a1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_84]) ).
cnf(c_0_94,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(multiply(a1,a1),X1)),a1))) = multiply(a1,X1),
inference(spm,[status(thm)],[c_0_74,c_0_90]) ).
cnf(c_0_95,plain,
multiply(multiply(a1,inverse(a1)),multiply(multiply(a1,a1),X1)) = multiply(a1,multiply(a1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_91]),c_0_47]) ).
cnf(c_0_96,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(X4),inverse(multiply(a1,multiply(inverse(a1),multiply(X1,X3)))))))),inverse(multiply(X5,inverse(multiply(a1,multiply(inverse(a1),multiply(inverse(multiply(a1,inverse(multiply(inverse(X2),inverse(a1))))),multiply(a1,a1))))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1))) = multiply(inverse(multiply(X6,inverse(multiply(X5,inverse(multiply(X7,multiply(a1,inverse(a1)))))))),multiply(X6,X7)),
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(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_21,c_0_13]),c_0_3]),c_0_4]),c_0_23]),c_0_43]),c_0_16]),c_0_43]),c_0_47]),c_0_53]),c_0_23]),c_0_43]),c_0_44]),c_0_92]),c_0_43]),c_0_47]),c_0_53]),c_0_23]),c_0_43]),c_0_44]),c_0_23]),c_0_43]) ).
cnf(c_0_97,plain,
multiply(multiply(a1,a1),multiply(a1,X1)) = multiply(a1,multiply(a1,multiply(a1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_74]),c_0_95]) ).
cnf(c_0_98,plain,
multiply(inverse(multiply(X1,inverse(multiply(X2,inverse(multiply(X3,multiply(a1,inverse(a1)))))))),multiply(X1,X3)) = multiply(inverse(multiply(a1,inverse(multiply(X2,inverse(a1))))),multiply(a1,a1)),
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(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_21,c_0_13]),c_0_3]),c_0_6]),c_0_23]),c_0_43]),c_0_23]),c_0_43]),c_0_18]),c_0_43]),c_0_47]),c_0_53]),c_0_23]),c_0_43]),c_0_44]),c_0_92]),c_0_43]),c_0_47]),c_0_53]),c_0_23]),c_0_43]),c_0_44]),c_0_96]),c_0_44]) ).
cnf(c_0_99,plain,
multiply(a1,multiply(a1,multiply(multiply(a1,inverse(a1)),X1))) = multiply(a1,multiply(a1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_74]),c_0_93]) ).
cnf(c_0_100,plain,
multiply(a1,multiply(a1,inverse(multiply(a1,multiply(inverse(a1),inverse(X1)))))) = multiply(multiply(a1,a1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_49]),c_0_89]),c_0_84]),c_0_53]) ).
cnf(c_0_101,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(X4),inverse(multiply(a1,multiply(inverse(a1),multiply(X1,X3)))))))),multiply(inverse(multiply(a1,inverse(multiply(inverse(X2),inverse(a1))))),multiply(a1,a1))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X4),inverse(a1))))),multiply(a1,a1)),
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_13,c_0_21]),c_0_23]),c_0_43]),c_0_16]),c_0_43]),c_0_47]),c_0_53]),c_0_23]),c_0_43]),c_0_98]),c_0_23]),c_0_43]),c_0_44]) ).
cnf(c_0_102,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(X3,multiply(a1,inverse(a1)))))))),X4)),multiply(inverse(multiply(a1,inverse(multiply(inverse(X2),inverse(a1))))),multiply(a1,a1))) = multiply(inverse(multiply(a1,X4)),multiply(a1,multiply(X1,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_7]),c_0_3]),c_0_6]),c_0_23]),c_0_43]),c_0_23]),c_0_43]),c_0_44]),c_0_8]),c_0_23]),c_0_43]),c_0_44]),c_0_68]) ).
cnf(c_0_103,plain,
multiply(inverse(multiply(multiply(a1,a1),inverse(multiply(inverse(inverse(X1)),a1)))),a1) = 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(spm,[status(thm)],[c_0_6,c_0_86]),c_0_18]),c_0_43]),c_0_47]),c_0_53]),c_0_65]),c_0_54]),c_0_40]) ).
cnf(c_0_104,plain,
multiply(multiply(a1,a1),X1) = multiply(a1,multiply(a1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_49]),c_0_53]),c_0_100]) ).
cnf(c_0_105,plain,
multiply(inverse(multiply(X1,inverse(a1))),multiply(X1,X2)) = multiply(a1,multiply(multiply(a1,inverse(a1)),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_48]),c_0_40]) ).
cnf(c_0_106,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(X3,multiply(a1,inverse(a1)))))))),inverse(multiply(inverse(inverse(X4)),inverse(multiply(a1,multiply(inverse(a1),multiply(X1,X3)))))))),inverse(multiply(inverse(X5),inverse(multiply(X2,multiply(a1,inverse(a1)))))))),X4) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X5),inverse(a1))))),multiply(a1,a1)),
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_7,c_0_6]),c_0_23]),c_0_43]),c_0_16]),c_0_43]),c_0_47]),c_0_53]),c_0_23]),c_0_43]),c_0_23]),c_0_43]),c_0_44]) ).
cnf(c_0_107,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(inverse(X2)),inverse(multiply(X3,multiply(a1,inverse(a1)))))))),X4)),X2) = multiply(inverse(multiply(a1,X4)),multiply(a1,multiply(X1,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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_7]),c_0_3]),c_0_6]),c_0_23]),c_0_43]),c_0_8]),c_0_23]),c_0_43]),c_0_44]),c_0_68]) ).
cnf(c_0_108,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),inverse(multiply(a1,multiply(inverse(a1),multiply(X2,X3)))))))),multiply(a1,multiply(X2,X3))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),inverse(a1))))),multiply(a1,a1)),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_109,plain,
multiply(inverse(multiply(a1,multiply(multiply(a1,inverse(a1)),inverse(X1)))),a1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_74]) ).
cnf(c_0_110,plain,
multiply(X1,multiply(a1,inverse(a1))) = multiply(inverse(a1),multiply(a1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_45]),c_0_44]) ).
cnf(c_0_111,plain,
multiply(multiply(a1,inverse(a1)),multiply(a1,X1)) = multiply(a1,multiply(multiply(a1,inverse(a1)),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_105,c_0_106]),c_0_102]),c_0_47]),c_0_107]),c_0_108]),c_0_68]) ).
cnf(c_0_112,plain,
multiply(multiply(a1,inverse(a1)),multiply(multiply(a1,inverse(a1)),X1)) = multiply(X1,multiply(a1,inverse(a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_105]),c_0_48]),c_0_47]),c_0_47]) ).
cnf(c_0_113,plain,
multiply(a1,multiply(inverse(a1),inverse(X1))) = multiply(inverse(multiply(a1,X1)),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_49]),c_0_53]) ).
cnf(c_0_114,plain,
multiply(inverse(a1),multiply(multiply(a1,a1),X1)) = multiply(a1,multiply(multiply(a1,inverse(a1)),X1)),
inference(spm,[status(thm)],[c_0_105,c_0_86]) ).
cnf(c_0_115,plain,
multiply(inverse(a1),multiply(a1,X1)) = multiply(a1,multiply(inverse(a1),X1)),
inference(spm,[status(thm)],[c_0_53,c_0_110]) ).
cnf(c_0_116,plain,
multiply(a1,multiply(inverse(multiply(a1,X1)),a1)) = multiply(a1,inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_109]),c_0_111]),c_0_112]),c_0_53]),c_0_113]) ).
cnf(c_0_117,plain,
multiply(a1,multiply(multiply(a1,inverse(a1)),X1)) = multiply(a1,multiply(a1,multiply(inverse(a1),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_104]),c_0_115]),c_0_115]) ).
cnf(c_0_118,negated_conjecture,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
prove_these_axioms ).
cnf(c_0_119,plain,
multiply(a1,multiply(a1,multiply(inverse(a1),X1))) = multiply(a1,inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_116]),c_0_116]),c_0_74]),c_0_111]),c_0_117]) ).
cnf(c_0_120,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2 ),
inference(sr,[status(thm)],[c_0_118,c_0_16]) ).
cnf(c_0_121,plain,
multiply(a1,inverse(inverse(inverse(X1)))) = multiply(a1,inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_113]),c_0_116]) ).
cnf(c_0_122,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(X1),X1),a2) != a2 ),
inference(spm,[status(thm)],[c_0_120,c_0_18]) ).
cnf(c_0_123,plain,
multiply(a1,inverse(inverse(X1))) = multiply(a1,X1),
inference(spm,[status(thm)],[c_0_121,c_0_25]) ).
cnf(c_0_124,negated_conjecture,
( multiply(multiply(X1,multiply(inverse(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_122,c_0_22]) ).
cnf(c_0_125,plain,
multiply(a1,multiply(multiply(a1,inverse(a1)),X1)) = multiply(a1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_119]),c_0_123]) ).
cnf(c_0_126,negated_conjecture,
( multiply(multiply(X1,multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_124,c_0_18]) ).
cnf(c_0_127,plain,
multiply(inverse(multiply(a1,inverse(X1))),a1) = X1,
inference(spm,[status(thm)],[c_0_109,c_0_125]) ).
cnf(c_0_128,negated_conjecture,
( multiply(multiply(X1,multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(X1,inverse(multiply(inverse(X3),X3)))))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_126,c_0_18]) ).
cnf(c_0_129,plain,
multiply(inverse(multiply(a1,X1)),a1) = inverse(X1),
inference(spm,[status(thm)],[c_0_127,c_0_123]) ).
cnf(c_0_130,negated_conjecture,
( multiply(multiply(X1,multiply(multiply(inverse(a1),a1),inverse(multiply(X1,multiply(inverse(X2),X2))))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_131,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[c_0_127,c_0_129]) ).
cnf(c_0_132,negated_conjecture,
( multiply(multiply(X1,multiply(multiply(inverse(X2),X2),inverse(multiply(X1,multiply(inverse(X3),X3))))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_130,c_0_18]) ).
cnf(c_0_133,plain,
multiply(multiply(a1,inverse(a1)),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)],[c_0_19,c_0_131]),c_0_43]),c_0_23]),c_0_43]),c_0_53]),c_0_113]),c_0_129]),c_0_131]) ).
cnf(c_0_134,negated_conjecture,
( multiply(multiply(inverse(multiply(inverse(X1),X2)),multiply(multiply(a1,inverse(a1)),inverse(multiply(inverse(multiply(X3,X2)),multiply(X3,X1))))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_11]),c_0_43]) ).
cnf(c_0_135,plain,
multiply(X1,multiply(a1,inverse(a1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_133]),c_0_131]) ).
cnf(c_0_136,negated_conjecture,
( multiply(multiply(inverse(multiply(a1,X1)),multiply(multiply(a1,inverse(a1)),multiply(a1,X1))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_44]),c_0_47]),c_0_11]),c_0_74]) ).
cnf(c_0_137,plain,
multiply(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,X3)),inverse(X3)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_131]),c_0_23]),c_0_43]),c_0_135]) ).
cnf(c_0_138,negated_conjecture,
( multiply(multiply(inverse(multiply(a1,X1)),multiply(a1,multiply(multiply(a1,inverse(a1)),X1))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_74]),c_0_11]) ).
cnf(c_0_139,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_133]),c_0_133]),c_0_131]) ).
cnf(c_0_140,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_135]),c_0_135]) ).
cnf(c_0_141,negated_conjecture,
( multiply(multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(multiply(a1,inverse(a1)),X2))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_138,c_0_11]) ).
cnf(c_0_142,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_143,negated_conjecture,
( multiply(multiply(multiply(a1,inverse(a1)),multiply(inverse(X1),multiply(multiply(a1,inverse(a1)),X1))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_43]),c_0_47]) ).
cnf(c_0_144,plain,
multiply(multiply(X1,multiply(X2,X3)),inverse(X3)) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_142]),c_0_131]) ).
cnf(c_0_145,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_143,c_0_133]),c_0_133]),c_0_43]),c_0_133])]) ).
cnf(c_0_146,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_144]),c_0_131]) ).
cnf(c_0_147,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_145,c_0_146])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP054-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n015.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 : Mon Aug 28 23:18:40 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.53 start to proof: theBenchmark
% 2.83/2.88 % Version : CSE_E---1.5
% 2.83/2.88 % Problem : theBenchmark.p
% 2.83/2.88 % Proof found
% 2.83/2.88 % SZS status Theorem for theBenchmark.p
% 2.83/2.88 % SZS output start Proof
% See solution above
% 2.83/2.90 % Total time : 2.340000 s
% 2.83/2.90 % SZS output end Proof
% 2.83/2.90 % Total time : 2.343000 s
%------------------------------------------------------------------------------