TSTP Solution File: GRP056-1 by E---3.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : GRP056-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 17:37:18 EDT 2023
% Result : Unsatisfiable 1.82s 0.64s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X3),X3))) = X2,
file('/export/starexec/sandbox2/tmp/tmp.kmILeZ4i0A/E---3.1_18059.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/tmp/tmp.kmILeZ4i0A/E---3.1_18059.p',prove_these_axioms) ).
cnf(c_0_2,axiom,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X3),X3))) = X2,
single_axiom ).
cnf(c_0_3,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(inverse(multiply(inverse(X3),X3)))))),inverse(multiply(inverse(inverse(multiply(inverse(X3),X3))),inverse(multiply(inverse(X3),X3))))) = multiply(inverse(multiply(X4,inverse(multiply(inverse(X2),X3)))),multiply(X4,inverse(X3))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(X3),X3)))),X3)))),multiply(X1,inverse(X3))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_3]),c_0_2]) ).
cnf(c_0_5,plain,
multiply(inverse(multiply(a1,inverse(X1))),multiply(a1,inverse(multiply(X2,inverse(X3))))) = multiply(inverse(multiply(X4,inverse(X1))),multiply(X4,inverse(multiply(X2,inverse(X3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_4]),c_0_3]),c_0_4]) ).
cnf(c_0_6,plain,
multiply(inverse(multiply(a1,inverse(X1))),multiply(a1,inverse(X2))) = multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(X2))),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,inverse(X3))) = multiply(inverse(multiply(X4,inverse(X2))),multiply(X4,inverse(X3))),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(inverse(X1),multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3)))),inverse(X3)))),inverse(multiply(inverse(X3),X3))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(a1,inverse(X3))),multiply(a1,inverse(X3)))))),multiply(X2,inverse(X3)))))),multiply(X1,inverse(multiply(inverse(X4),inverse(X3))))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_7]),c_0_6]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(X1))),multiply(a1,inverse(X1)))))),multiply(a1,inverse(multiply(inverse(X2),inverse(X1)))))),inverse(multiply(inverse(multiply(a1,inverse(X1))),multiply(a1,inverse(X1))))) = multiply(inverse(X2),inverse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_7]),c_0_7]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),multiply(X3,inverse(X4)))))),multiply(X1,inverse(multiply(X3,inverse(X4)))))),inverse(multiply(inverse(multiply(X5,inverse(X4))),multiply(X5,inverse(X4))))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_12,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),inverse(X3))),multiply(a1,inverse(X3)))))),multiply(X1,inverse(multiply(a1,inverse(X3))))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(X3))),multiply(a1,inverse(X3)))))),multiply(a1,inverse(multiply(inverse(X2),inverse(X3))))),
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_13,plain,
multiply(inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(X1))),multiply(a1,inverse(X1)))))),multiply(a1,inverse(multiply(inverse(X2),inverse(X1)))))),inverse(multiply(inverse(multiply(X3,inverse(X1))),multiply(X3,inverse(X1))))) = multiply(inverse(X2),inverse(X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(multiply(inverse(X1),inverse(X2))),multiply(X3,inverse(X2)))))),multiply(a1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(X2))),multiply(a1,inverse(X2)))))),multiply(a1,inverse(multiply(inverse(X1),inverse(X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_13]),c_0_3]) ).
cnf(c_0_15,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),X1)))),multiply(a1,inverse(multiply(inverse(X1),X1))))))),multiply(a1,inverse(multiply(inverse(X2),inverse(multiply(inverse(X1),X1)))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_8]),c_0_4]) ).
cnf(c_0_16,plain,
multiply(inverse(X1),inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))),multiply(X2,inverse(multiply(inverse(X3),X3)))))) = multiply(inverse(X1),inverse(multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_17,plain,
multiply(inverse(X1),inverse(multiply(inverse(X2),X2))) = multiply(inverse(X1),inverse(multiply(inverse(X3),X3))),
inference(spm,[status(thm)],[c_0_16,c_0_2]) ).
cnf(c_0_18,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X4),X4))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_17]) ).
cnf(c_0_19,plain,
multiply(inverse(multiply(inverse(X1),X1)),inverse(multiply(inverse(a1),a1))) = multiply(inverse(X2),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_18]),c_0_17]) ).
cnf(c_0_20,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(a1,inverse(X2))),multiply(a1,inverse(X2)))))),multiply(X1,inverse(multiply(inverse(X3),inverse(X2)))))),inverse(multiply(inverse(multiply(a1,inverse(X2))),multiply(a1,inverse(X2))))) = multiply(inverse(X3),inverse(X2)),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_21,plain,
inverse(multiply(inverse(X1),X1)) = 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_15,c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_22,plain,
multiply(inverse(multiply(inverse(multiply(X1,multiply(inverse(a1),a1))),multiply(X1,inverse(multiply(inverse(X2),inverse(X3)))))),multiply(inverse(a1),a1)) = multiply(inverse(X2),inverse(X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_21]),c_0_21]) ).
cnf(c_0_23,plain,
multiply(inverse(a1),a1) = multiply(inverse(X1),X1),
inference(rw,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X4),multiply(inverse(X3),X3))))),X2)),inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X3),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_25,plain,
inverse(multiply(multiply(inverse(a1),a1),multiply(inverse(X1),X1))) = multiply(inverse(a1),a1),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_26,plain,
multiply(multiply(inverse(a1),a1),multiply(inverse(a1),a1)) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_23]),c_0_21]),c_0_23]) ).
cnf(c_0_27,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))),inverse(multiply(inverse(X4),multiply(inverse(X3),X3))))),X2)),multiply(inverse(a1),a1)) = X4,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_21]) ).
cnf(c_0_28,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(inverse(a1),a1),X2)))),multiply(X1,inverse(X2))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_21]),c_0_21]) ).
cnf(c_0_29,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3)))),multiply(inverse(a1),a1)) = X2,
inference(rw,[status(thm)],[c_0_18,c_0_21]) ).
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_25]),c_0_19]),c_0_19]),c_0_21]),c_0_21]),c_0_26]),c_0_21]),c_0_23]) ).
cnf(c_0_31,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(a1),a1),X1))) = multiply(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_27,c_0_28]),c_0_21]),c_0_29]),c_0_21]),c_0_30]) ).
cnf(c_0_32,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_23,c_0_23]) ).
cnf(c_0_33,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(X2),X2),X1))) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,plain,
multiply(multiply(inverse(a1),a1),multiply(inverse(inverse(multiply(multiply(inverse(a1),a1),X1))),inverse(X1))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_21]) ).
cnf(c_0_35,plain,
multiply(inverse(inverse(multiply(inverse(inverse(multiply(multiply(inverse(a1),a1),X1))),inverse(X1)))),multiply(inverse(a1),a1)) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_21]) ).
cnf(c_0_36,plain,
inverse(multiply(inverse(inverse(multiply(multiply(inverse(a1),a1),X1))),inverse(X1))) = 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_29,c_0_35]),c_0_21]),c_0_21]),c_0_23]),c_0_21]),c_0_30]) ).
cnf(c_0_37,plain,
multiply(inverse(multiply(X1,inverse(multiply(multiply(inverse(X2),X2),X3)))),multiply(X1,inverse(X3))) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_38,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,inverse(X4)))))),multiply(X2,inverse(X4)))))),multiply(X1,inverse(multiply(inverse(X5),inverse(X4))))) = X5,
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_39,plain,
multiply(inverse(inverse(multiply(multiply(inverse(a1),a1),X1))),inverse(X1)) = multiply(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_4,c_0_36]),c_0_21]),c_0_30]),c_0_21]),c_0_37]) ).
cnf(c_0_40,plain,
multiply(inverse(multiply(X1,multiply(inverse(a1),a1))),multiply(X1,inverse(multiply(inverse(X2),multiply(inverse(a1),a1))))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_41,plain,
multiply(inverse(inverse(multiply(multiply(inverse(X1),X1),X2))),inverse(X2)) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_42,plain,
multiply(multiply(inverse(a1),a1),multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(X1),multiply(inverse(a1),a1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_32]),c_0_21]),c_0_21]) ).
cnf(c_0_43,plain,
multiply(inverse(X1),multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3)))),inverse(X3))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X3),X3)))),multiply(a1,inverse(X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_2]),c_0_3]) ).
cnf(c_0_44,plain,
multiply(inverse(inverse(X1)),inverse(multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(X1),multiply(inverse(a1),a1)))))) = multiply(inverse(a1),a1),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
multiply(inverse(multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,inverse(X1)))),multiply(inverse(a1),a1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_43]),c_0_21]),c_0_21]) ).
cnf(c_0_46,plain,
multiply(multiply(inverse(a1),a1),multiply(inverse(inverse(X1)),inverse(inverse(multiply(inverse(X1),multiply(inverse(a1),a1)))))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_44]),c_0_21]) ).
cnf(c_0_47,plain,
multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,inverse(X1))) = multiply(multiply(inverse(a1),a1),multiply(multiply(inverse(a1),a1),inverse(X1))),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_48,plain,
multiply(multiply(inverse(a1),a1),inverse(multiply(inverse(inverse(X1)),inverse(inverse(multiply(inverse(X1),multiply(inverse(a1),a1))))))) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_46]),c_0_21]),c_0_21]) ).
cnf(c_0_49,plain,
multiply(inverse(multiply(multiply(inverse(a1),a1),multiply(multiply(inverse(a1),a1),inverse(X1)))),multiply(inverse(a1),a1)) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_47]) ).
cnf(c_0_50,plain,
multiply(multiply(inverse(X1),X1),multiply(multiply(inverse(X1),X1),inverse(multiply(inverse(X2),multiply(inverse(X1),X1))))) = X2,
inference(spm,[status(thm)],[c_0_42,c_0_32]) ).
cnf(c_0_51,plain,
inverse(inverse(multiply(inverse(X1),multiply(inverse(a1),a1)))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_48]),c_0_21]),c_0_49]) ).
cnf(c_0_52,plain,
inverse(multiply(inverse(X1),multiply(inverse(a1),a1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_50]) ).
cnf(c_0_53,plain,
multiply(inverse(multiply(X1,multiply(inverse(a1),a1))),multiply(X1,X2)) = X2,
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_15]),c_0_19]),c_0_19]),c_0_21]),c_0_21]),c_0_52]) ).
cnf(c_0_54,plain,
multiply(inverse(multiply(X1,multiply(inverse(X2),X2))),multiply(X1,inverse(multiply(inverse(X3),multiply(inverse(X2),X2))))) = X3,
inference(spm,[status(thm)],[c_0_40,c_0_32]) ).
cnf(c_0_55,plain,
multiply(inverse(a1),multiply(inverse(a1),a1)) = inverse(a1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,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_57,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(multiply(inverse(X2),inverse(multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,inverse(X4)))))),multiply(X5,inverse(X4)))))),multiply(X1,inverse(multiply(X5,inverse(X4))))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_58,plain,
multiply(inverse(multiply(inverse(multiply(X1,inverse(X2))),multiply(X1,multiply(inverse(a1),a1)))),multiply(inverse(a1),a1)) = multiply(inverse(multiply(X3,inverse(multiply(inverse(X2),X4)))),multiply(X3,inverse(X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_17]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_59,plain,
inverse(inverse(a1)) = a1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_53]) ).
cnf(c_0_60,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_55]),c_0_52]) ).
cnf(c_0_61,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_56,c_0_23]) ).
cnf(c_0_62,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(a1),a1))),a1)))),multiply(a1,inverse(a1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_58]),c_0_17]),c_0_21]),c_0_58]) ).
cnf(c_0_63,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_32,c_0_59]) ).
cnf(c_0_64,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,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)],[c_0_48,c_0_60]),c_0_52]),c_0_32]),c_0_60]),c_0_60]) ).
cnf(c_0_65,plain,
multiply(multiply(a1,inverse(a1)),multiply(a1,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)],[c_0_46,c_0_60]),c_0_52]),c_0_32]),c_0_60]),c_0_60]) ).
cnf(c_0_66,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_61,c_0_32]) ).
cnf(c_0_67,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),a1)))),multiply(a1,inverse(a1))) = multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,inverse(X1))),
inference(spm,[status(thm)],[c_0_62,c_0_45]) ).
cnf(c_0_68,plain,
multiply(multiply(inverse(a1),a1),multiply(multiply(inverse(a1),a1),inverse(X1))) = inverse(X1),
inference(rw,[status(thm)],[c_0_47,c_0_53]) ).
cnf(c_0_69,plain,
multiply(X1,multiply(a1,inverse(a1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_63]),c_0_52]) ).
cnf(c_0_70,plain,
inverse(multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_64]),c_0_60]),c_0_65]),c_0_32]),c_0_60]) ).
cnf(c_0_71,plain,
multiply(inverse(a1),multiply(a1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_53]),c_0_52]) ).
cnf(c_0_72,negated_conjecture,
( multiply(multiply(multiply(inverse(a1),a1),multiply(inverse(X1),X1)),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_66,c_0_21]) ).
cnf(c_0_73,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),X3)))),multiply(X1,inverse(X3))) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_58]),c_0_67]),c_0_47]),c_0_68]) ).
cnf(c_0_74,plain,
inverse(inverse(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_69]),c_0_70]),c_0_70]),c_0_69]),c_0_70]),c_0_70]),c_0_69]),c_0_63]),c_0_70]),c_0_69]),c_0_70]),c_0_70]),c_0_69]),c_0_71]) ).
cnf(c_0_75,negated_conjecture,
( multiply(multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2)),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_72,c_0_32]) ).
cnf(c_0_76,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),a1)))),multiply(a1,inverse(a1))) = multiply(multiply(inverse(a1),a1),multiply(multiply(inverse(a1),a1),inverse(X1))),
inference(rw,[status(thm)],[c_0_67,c_0_47]) ).
cnf(c_0_77,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X1),multiply(inverse(multiply(inverse(multiply(X2,inverse(multiply(inverse(X1),X3)))),multiply(X2,inverse(X3)))),inverse(X3)))),inverse(multiply(inverse(X4),multiply(inverse(X3),X3))))),X3)),inverse(multiply(inverse(multiply(inverse(X3),X3)),multiply(inverse(X3),X3)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_78,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_70]),c_0_69]),c_0_74]),c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( multiply(multiply(multiply(inverse(X1),X1),multiply(multiply(inverse(a1),a1),multiply(inverse(X2),X2))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_75,c_0_21]) ).
cnf(c_0_80,plain,
multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),a1)))),multiply(a1,inverse(a1))) = inverse(X1),
inference(rw,[status(thm)],[c_0_76,c_0_68]) ).
cnf(c_0_81,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,multiply(inverse(a1),a1))),multiply(a1,inverse(X1)))),inverse(multiply(inverse(X2),multiply(inverse(X1),X1))))),X1)),multiply(inverse(a1),a1)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_17]),c_0_43]),c_0_21]),c_0_21]) ).
cnf(c_0_82,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_52]),c_0_52]) ).
cnf(c_0_83,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_78]),c_0_74]) ).
cnf(c_0_84,negated_conjecture,
( multiply(multiply(multiply(inverse(X1),X1),multiply(multiply(inverse(X2),X2),multiply(inverse(X3),X3))),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_79,c_0_32]) ).
cnf(c_0_85,plain,
inverse(multiply(a1,inverse(multiply(X1,a1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_52]),c_0_69]) ).
cnf(c_0_86,plain,
multiply(multiply(inverse(X1),X1),multiply(inverse(X2),X2)) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_87,plain,
inverse(multiply(inverse(multiply(X1,X2)),X1)) = 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)],[c_0_81,c_0_53]),c_0_60]),c_0_74]),c_0_63]),c_0_69]),c_0_74]),c_0_69]) ).
cnf(c_0_88,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_89,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_82]),c_0_23]),c_0_63]),c_0_69]),c_0_74]) ).
cnf(c_0_90,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,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_78,c_0_54]),c_0_63]),c_0_69]),c_0_63]),c_0_69]),c_0_74]) ).
cnf(c_0_91,negated_conjecture,
( multiply(multiply(X1,multiply(a1,inverse(multiply(X1,a1)))),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_84,c_0_85]),c_0_86]),c_0_63]),c_0_69]) ).
cnf(c_0_92,plain,
multiply(multiply(a1,inverse(a1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_87]),c_0_63]) ).
cnf(c_0_93,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,X3))) = 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_38,c_0_88]),c_0_21]),c_0_63]),c_0_69]),c_0_89]),c_0_90]),c_0_90]),c_0_74]) ).
cnf(c_0_94,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(spm,[status(thm)],[c_0_91,c_0_92]),c_0_69]),c_0_92])]) ).
cnf(c_0_95,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_93]),c_0_63]),c_0_69]),c_0_74]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP056-1 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n005.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.31 % CPULimit : 2400
% 0.16/0.31 % WCLimit : 300
% 0.16/0.31 % DateTime : Tue Oct 3 02:33:46 EDT 2023
% 0.16/0.31 % CPUTime :
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.kmILeZ4i0A/E---3.1_18059.p
% 1.82/0.64 # Version: 3.1pre001
% 1.82/0.64 # Preprocessing class: FSSSSMSSSSSNFFN.
% 1.82/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.82/0.64 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.82/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.82/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.82/0.64 # Starting sh5l with 300s (1) cores
% 1.82/0.64 # new_bool_1 with pid 18139 completed with status 0
% 1.82/0.64 # Result found by new_bool_1
% 1.82/0.64 # Preprocessing class: FSSSSMSSSSSNFFN.
% 1.82/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.82/0.64 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.82/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.82/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.82/0.64 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.82/0.64 # Search class: FUHPF-FFSF21-DFFFFFNN
% 1.82/0.64 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.82/0.64 # Starting G-E--_208_C18_F2_SE_CS_SP_PS_S5PRR_RG_S04A with 181s (1) cores
% 1.82/0.64 # G-E--_208_C18_F2_SE_CS_SP_PS_S5PRR_RG_S04A with pid 18144 completed with status 0
% 1.82/0.64 # Result found by G-E--_208_C18_F2_SE_CS_SP_PS_S5PRR_RG_S04A
% 1.82/0.64 # Preprocessing class: FSSSSMSSSSSNFFN.
% 1.82/0.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.82/0.64 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 1.82/0.64 # Starting new_bool_3 with 300s (1) cores
% 1.82/0.64 # Starting new_bool_1 with 300s (1) cores
% 1.82/0.64 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 1.82/0.64 # Search class: FUHPF-FFSF21-DFFFFFNN
% 1.82/0.64 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.82/0.64 # Starting G-E--_208_C18_F2_SE_CS_SP_PS_S5PRR_RG_S04A with 181s (1) cores
% 1.82/0.64 # Preprocessing time : 0.001 s
% 1.82/0.64 # Presaturation interreduction done
% 1.82/0.64
% 1.82/0.64 # Proof found!
% 1.82/0.64 # SZS status Unsatisfiable
% 1.82/0.64 # SZS output start CNFRefutation
% See solution above
% 1.82/0.64 # Parsed axioms : 2
% 1.82/0.64 # Removed by relevancy pruning/SinE : 0
% 1.82/0.64 # Initial clauses : 2
% 1.82/0.64 # Removed in clause preprocessing : 0
% 1.82/0.64 # Initial clauses in saturation : 2
% 1.82/0.64 # Processed clauses : 691
% 1.82/0.64 # ...of these trivial : 118
% 1.82/0.64 # ...subsumed : 381
% 1.82/0.64 # ...remaining for further processing : 192
% 1.82/0.64 # Other redundant clauses eliminated : 0
% 1.82/0.64 # Clauses deleted for lack of memory : 0
% 1.82/0.64 # Backward-subsumed : 26
% 1.82/0.64 # Backward-rewritten : 148
% 1.82/0.64 # Generated clauses : 8180
% 1.82/0.64 # ...of the previous two non-redundant : 6997
% 1.82/0.64 # ...aggressively subsumed : 0
% 1.82/0.64 # Contextual simplify-reflections : 0
% 1.82/0.64 # Paramodulations : 8179
% 1.82/0.64 # Factorizations : 0
% 1.82/0.64 # NegExts : 0
% 1.82/0.64 # Equation resolutions : 0
% 1.82/0.64 # Total rewrite steps : 15373
% 1.82/0.64 # Propositional unsat checks : 0
% 1.82/0.64 # Propositional check models : 0
% 1.82/0.64 # Propositional check unsatisfiable : 0
% 1.82/0.64 # Propositional clauses : 0
% 1.82/0.64 # Propositional clauses after purity: 0
% 1.82/0.64 # Propositional unsat core size : 0
% 1.82/0.64 # Propositional preprocessing time : 0.000
% 1.82/0.64 # Propositional encoding time : 0.000
% 1.82/0.64 # Propositional solver time : 0.000
% 1.82/0.64 # Success case prop preproc time : 0.000
% 1.82/0.64 # Success case prop encoding time : 0.000
% 1.82/0.64 # Success case prop solver time : 0.000
% 1.82/0.64 # Current number of processed clauses : 15
% 1.82/0.64 # Positive orientable unit clauses : 14
% 1.82/0.64 # Positive unorientable unit clauses: 1
% 1.82/0.64 # Negative unit clauses : 0
% 1.82/0.64 # Non-unit-clauses : 0
% 1.82/0.64 # Current number of unprocessed clauses: 4436
% 1.82/0.64 # ...number of literals in the above : 4436
% 1.82/0.64 # Current number of archived formulas : 0
% 1.82/0.64 # Current number of archived clauses : 177
% 1.82/0.64 # Clause-clause subsumption calls (NU) : 497
% 1.82/0.64 # Rec. Clause-clause subsumption calls : 497
% 1.82/0.64 # Non-unit clause-clause subsumptions : 214
% 1.82/0.64 # Unit Clause-clause subsumption calls : 120
% 1.82/0.64 # Rewrite failures with RHS unbound : 0
% 1.82/0.64 # BW rewrite match attempts : 856
% 1.82/0.64 # BW rewrite match successes : 179
% 1.82/0.64 # Condensation attempts : 0
% 1.82/0.64 # Condensation successes : 0
% 1.82/0.64 # Termbank termtop insertions : 326236
% 1.82/0.64
% 1.82/0.64 # -------------------------------------------------
% 1.82/0.64 # User time : 0.200 s
% 1.82/0.64 # System time : 0.009 s
% 1.82/0.64 # Total time : 0.209 s
% 1.82/0.64 # Maximum resident set size: 1648 pages
% 1.82/0.64
% 1.82/0.64 # -------------------------------------------------
% 1.82/0.64 # User time : 0.201 s
% 1.82/0.64 # System time : 0.011 s
% 1.82/0.64 # Total time : 0.211 s
% 1.82/0.64 # Maximum resident set size: 1676 pages
% 1.82/0.64 % E---3.1 exiting
% 1.82/0.64 % E---3.1 exiting
%------------------------------------------------------------------------------