%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP507-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:39:58 PM UTC 2026
% Result : Unsatisfiable 66.56s 13.84s
% Output : CNFRefutation 66.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 2
% Syntax : Number of clauses : 98 ( 98 unt; 0 nHn; 6 RR)
% Number of literals : 98 ( 97 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 37 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 330 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,inverse(X6)),inverse(X4))))))),X6) = X5,
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(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,inverse(X6)),inverse(X4))))))),X6) = X5,
single_axiom ).
cnf(c_0_3,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6) = inverse(multiply(inverse(multiply(inverse(multiply(X7,X8)),multiply(X8,X7))),multiply(inverse(multiply(X9,X10)),multiply(X9,inverse(multiply(multiply(X5,inverse(inverse(X6))),inverse(X10))))))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6),inverse(X6)) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(X5,inverse(X4))))))),X6),X7),inverse(X7)) = multiply(X5,inverse(inverse(X6))),
inference(spm,[status(thm)],[c_0_4,c_0_3]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(multiply(X1,inverse(X3)),inverse(inverse(X3))),
inference(spm,[status(thm)],[c_0_5,c_0_2]) ).
cnf(c_0_7,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(multiply(X1,X3),inverse(X3)),
inference(spm,[status(thm)],[c_0_6,c_0_6]) ).
cnf(c_0_8,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,inverse(X4))),multiply(X3,inverse(multiply(multiply(X5,X6),inverse(X6))))))),X4) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(multiply(X3,multiply(multiply(X4,X5),inverse(X5))),inverse(X6))),multiply(multiply(X3,X7),inverse(X7))))),X6) = X4,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(X5,X6),inverse(X6))))))),X7),inverse(X7)) = multiply(X5,X4),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(X3),X3))),multiply(multiply(X4,X5),inverse(X5))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_4]),c_0_4]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))) = multiply(X3,inverse(multiply(multiply(X3,X4),inverse(X4)))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_13,plain,
multiply(multiply(multiply(X1,X2),inverse(X2)),inverse(inverse(X3))) = multiply(multiply(multiply(X1,X3),X4),inverse(X4)),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),multiply(multiply(X4,X5),inverse(X5))) = X4,
inference(spm,[status(thm)],[c_0_11,c_0_11]) ).
cnf(c_0_15,plain,
multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(inverse(X3))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_12]),c_0_4]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3,a3)),multiply(a3,a3))),multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X3,inverse(a3))))))),multiply(inverse(multiply(inverse(multiply(X4,X5)),multiply(X5,X4))),inverse(multiply(X6,inverse(multiply(inverse(multiply(X7,X8)),multiply(X7,inverse(multiply(X3,inverse(X8)))))))))))),X9) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3,a3)),multiply(a3,a3))),multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X6,inverse(a3))))))),X9),
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_17,plain,
multiply(multiply(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1)))),multiply(inverse(X3),X3))),X4),X5),inverse(X5)) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
multiply(X1,multiply(inverse(multiply(X2,X3)),multiply(X2,inverse(multiply(X4,inverse(X3)))))) = multiply(X1,multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X4,inverse(a3)))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_16]),c_0_4]) ).
cnf(c_0_19,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X3,inverse(a3))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_17]) ).
cnf(c_0_20,plain,
multiply(inverse(multiply(multiply(X1,multiply(X2,inverse(X3))),X3)),multiply(multiply(X1,X4),inverse(X4))) = multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X2,inverse(a3))))),
inference(spm,[status(thm)],[c_0_19,c_0_7]) ).
cnf(c_0_21,plain,
multiply(inverse(multiply(multiply(X1,multiply(multiply(X2,X3),inverse(X3))),X4)),multiply(multiply(X1,X5),inverse(X5))) = multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(multiply(X2,X4),inverse(a3))))),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
cnf(c_0_22,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(multiply(X2,inverse(multiply(multiply(X2,X3),inverse(X3)))),inverse(a3))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_4]),c_0_4]) ).
cnf(c_0_23,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_22,c_0_22]) ).
cnf(c_0_24,plain,
multiply(inverse(multiply(inverse(X1),X1)),multiply(multiply(X2,X3),inverse(X3))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_23]) ).
cnf(c_0_25,plain,
multiply(multiply(multiply(inverse(multiply(inverse(X1),X1)),X2),X3),inverse(X3)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_24]),c_0_15]) ).
cnf(c_0_26,plain,
multiply(X1,inverse(inverse(inverse(X1)))) = multiply(X2,inverse(inverse(inverse(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_15]),c_0_4]) ).
cnf(c_0_27,plain,
multiply(multiply(multiply(inverse(X1),X1),X2),inverse(X2)) = multiply(inverse(X3),X3),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_28,plain,
inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(X3,X4)),multiply(X3,inverse(multiply(multiply(multiply(X5,X6),inverse(X6)),inverse(X4))))))) = X5,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_7]),c_0_2]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,inverse(inverse(inverse(X1)))),inverse(inverse(inverse(inverse(X2))))) = multiply(multiply(X2,X3),inverse(X3)),
inference(spm,[status(thm)],[c_0_7,c_0_26]) ).
cnf(c_0_30,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_27]),c_0_28]) ).
cnf(c_0_31,plain,
multiply(multiply(inverse(X1),a3),inverse(a3)) = inverse(inverse(inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_29]) ).
cnf(c_0_32,plain,
multiply(multiply(X1,a3),inverse(a3)) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_28]) ).
cnf(c_0_33,plain,
multiply(multiply(X1,X2),inverse(X2)) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_7,c_0_32]) ).
cnf(c_0_34,plain,
inverse(inverse(multiply(inverse(X1),X1))) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_23]) ).
cnf(c_0_35,plain,
inverse(multiply(inverse(a3),a3)) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_34]),c_0_30]),c_0_34]),c_0_34]) ).
cnf(c_0_36,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(X1),X1),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_37,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(multiply(X4,X5)),multiply(X4,inverse(multiply(X3,inverse(X5))))),
inference(spm,[status(thm)],[c_0_19,c_0_19]) ).
cnf(c_0_38,plain,
multiply(multiply(X1,inverse(multiply(multiply(X1,X2),inverse(X2)))),inverse(multiply(X3,inverse(inverse(inverse(X3)))))) = multiply(X4,inverse(multiply(multiply(X4,X5),inverse(X5)))),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_39,plain,
inverse(inverse(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_36]),c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_36]),c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_30]),c_0_36]),c_0_36]),c_0_33]),c_0_30]) ).
cnf(c_0_40,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,inverse(multiply(X3,inverse(X2))))) = multiply(inverse(X3),multiply(X4,inverse(multiply(multiply(X4,X5),inverse(X5))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_15]) ).
cnf(c_0_41,plain,
multiply(X1,inverse(inverse(inverse(X1)))) = multiply(inverse(a3),a3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_34]),c_0_30]),c_0_34]) ).
cnf(c_0_42,plain,
multiply(inverse(inverse(X1)),inverse(inverse(X2))) = inverse(inverse(multiply(X1,X2))),
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
cnf(c_0_43,plain,
multiply(multiply(X1,inverse(inverse(inverse(X2)))),X2) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_44,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),multiply(X4,X3))),multiply(inverse(multiply(X5,X6)),multiply(X5,inverse(multiply(multiply(X7,inverse(inverse(multiply(multiply(X8,inverse(X9)),inverse(X10))))),inverse(X6))))))),X10)),X7))),X9) = X8,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_45,plain,
inverse(inverse(multiply(X1,inverse(multiply(X2,X1))))) = multiply(inverse(X2),multiply(inverse(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_40,c_0_41]),c_0_36]),c_0_39]),c_0_30]),c_0_33]),c_0_41]) ).
cnf(c_0_46,plain,
inverse(inverse(multiply(inverse(inverse(X1)),X2))) = multiply(X1,inverse(inverse(X2))),
inference(spm,[status(thm)],[c_0_42,c_0_39]) ).
cnf(c_0_47,plain,
inverse(inverse(multiply(X1,inverse(inverse(X2))))) = multiply(inverse(inverse(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_43]),c_0_39]) ).
cnf(c_0_48,plain,
multiply(inverse(inverse(multiply(X1,inverse(X2)))),X2) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_42]),c_0_39]) ).
cnf(c_0_49,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),multiply(X4,X3))),multiply(inverse(multiply(X5,X6)),multiply(X5,inverse(multiply(X7,inverse(X6))))))),X8)),inverse(multiply(inverse(multiply(inverse(multiply(X9,X10)),multiply(X10,X9))),multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3,a3)),multiply(a3,a3))),multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X11,inverse(a3))))))),multiply(multiply(X7,inverse(inverse(inverse(multiply(multiply(X12,inverse(X13)),inverse(X8)))))),inverse(X14))),X14)),X11)))))),X13) = X12,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_44]),c_0_3]) ).
cnf(c_0_50,plain,
multiply(multiply(X1,multiply(inverse(a3),a3)),multiply(inverse(X2),X2)) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_36]),c_0_34]) ).
cnf(c_0_51,plain,
multiply(X1,inverse(multiply(inverse(inverse(X2)),X1))) = multiply(inverse(X2),multiply(inverse(a3),a3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_52,plain,
multiply(multiply(inverse(X1),multiply(inverse(a3),a3)),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_48,c_0_45]) ).
cnf(c_0_53,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),multiply(X4,X3))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X6)),multiply(X6,X5))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X7,X8)),multiply(X8,X7))),multiply(inverse(multiply(X9,X10)),multiply(X9,inverse(multiply(X11,inverse(X10))))))),X12)),inverse(multiply(inverse(multiply(inverse(multiply(X13,X14)),multiply(X14,X13))),multiply(inverse(multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X15,inverse(a3)))))))),multiply(multiply(X11,inverse(inverse(inverse(multiply(multiply(X16,inverse(inverse(multiply(multiply(X17,inverse(inverse(multiply(multiply(X18,inverse(X19)),inverse(X20))))),inverse(X21))))),inverse(X12)))))),inverse(X22))),X22)),X15)))))),X21)),X16))),X20)),X17))),X19) = X18,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_49]),c_0_23]),c_0_36]),c_0_30]) ).
cnf(c_0_54,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X2,X1))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3,X4)),multiply(X4,X3))),multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5,X6)),multiply(X6,X5))),multiply(inverse(multiply(X7,X8)),multiply(X7,inverse(multiply(X9,inverse(X8))))))),X10)),inverse(multiply(inverse(multiply(inverse(multiply(X11,X12)),multiply(X12,X11))),multiply(inverse(multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X13,inverse(a3)))))))),multiply(multiply(X9,inverse(inverse(inverse(multiply(multiply(X14,inverse(inverse(multiply(multiply(X15,inverse(X16)),inverse(X17))))),inverse(X10)))))),inverse(X18))),X18)),X13)))))),X17)),X14))),X16) = X15,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_49]),c_0_23]),c_0_36]),c_0_30]) ).
cnf(c_0_55,plain,
inverse(multiply(X1,multiply(inverse(X2),X2))) = multiply(inverse(X1),multiply(inverse(a3),a3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_30]),c_0_39]) ).
cnf(c_0_56,plain,
multiply(multiply(X1,multiply(inverse(X2),X2)),multiply(inverse(X3),X3)) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_57,plain,
multiply(X1,inverse(multiply(inverse(X2),X1))) = multiply(X2,multiply(inverse(a3),a3)),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_58,plain,
multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),multiply(X1,X3)) = X3,
inference(spm,[status(thm)],[c_0_52,c_0_23]) ).
cnf(c_0_59,plain,
multiply(inverse(multiply(X1,X2)),multiply(X2,X1)) = multiply(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_38]),c_0_33]),c_0_41]),c_0_30]),c_0_39]),c_0_54]),c_0_55]),c_0_41]),c_0_56]),c_0_39]),c_0_33]),c_0_41]) ).
cnf(c_0_60,plain,
multiply(inverse(multiply(X1,inverse(X2))),multiply(inverse(a3),a3)) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_48]) ).
cnf(c_0_61,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_56]),c_0_39]) ).
cnf(c_0_62,plain,
multiply(multiply(X1,inverse(X2)),multiply(multiply(X2,inverse(X1)),X3)) = X3,
inference(spm,[status(thm)],[c_0_58,c_0_60]) ).
cnf(c_0_63,plain,
multiply(X1,multiply(inverse(multiply(X1,multiply(inverse(a3),a3))),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_48]),c_0_36]) ).
cnf(c_0_64,plain,
multiply(inverse(X1),multiply(X2,X1)) = inverse(inverse(X2)),
inference(rw,[status(thm)],[c_0_33,c_0_61]) ).
cnf(c_0_65,plain,
multiply(X1,inverse(multiply(multiply(X2,inverse(X3)),X1))) = inverse(inverse(multiply(X3,inverse(X2)))),
inference(spm,[status(thm)],[c_0_33,c_0_62]) ).
cnf(c_0_66,plain,
inverse(multiply(X1,multiply(inverse(a3),a3))) = multiply(inverse(X1),multiply(inverse(a3),a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_63]),c_0_33]),c_0_39]) ).
cnf(c_0_67,plain,
multiply(inverse(a3),multiply(a3,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_39]) ).
cnf(c_0_68,plain,
multiply(X1,inverse(multiply(multiply(X2,X3),X1))) = multiply(inverse(X3),inverse(inverse(inverse(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_39]),c_0_46]) ).
cnf(c_0_69,plain,
multiply(inverse(multiply(X1,inverse(inverse(X2)))),multiply(X1,inverse(multiply(X3,inverse(inverse(inverse(X3))))))) = multiply(inverse(multiply(a3,a3)),multiply(a3,inverse(multiply(X2,inverse(a3))))),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_70,plain,
multiply(X1,multiply(multiply(inverse(X1),multiply(inverse(a3),a3)),X2)) = X2,
inference(spm,[status(thm)],[c_0_63,c_0_66]) ).
cnf(c_0_71,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_61]),c_0_64]) ).
cnf(c_0_72,plain,
multiply(inverse(multiply(a3,inverse(multiply(X1,inverse(a3))))),multiply(a3,a3)) = inverse(inverse(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(spm,[status(thm)],[c_0_68,c_0_69]),c_0_68]),c_0_39]),c_0_41]),c_0_36]),c_0_66]),c_0_47]),c_0_46]),c_0_58]) ).
cnf(c_0_73,plain,
multiply(multiply(X1,inverse(multiply(X2,X1))),multiply(inverse(inverse(X2)),X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_43]),c_0_39]) ).
cnf(c_0_74,plain,
multiply(X1,multiply(multiply(inverse(X1),multiply(inverse(X2),X2)),X3)) = X3,
inference(spm,[status(thm)],[c_0_70,c_0_23]) ).
cnf(c_0_75,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(rw,[status(thm)],[c_0_64,c_0_71]) ).
cnf(c_0_76,plain,
multiply(inverse(multiply(a3,inverse(X1))),multiply(a3,a3)) = multiply(X1,inverse(inverse(a3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_48]),c_0_47]),c_0_46]) ).
cnf(c_0_77,plain,
multiply(multiply(X1,inverse(multiply(X2,X1))),multiply(inverse(a3),a3)) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_41]),c_0_39]) ).
cnf(c_0_78,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_71]),c_0_61]) ).
cnf(c_0_79,plain,
multiply(multiply(X1,multiply(inverse(a3),a3)),multiply(inverse(inverse(inverse(X1))),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_43]),c_0_34]),c_0_36]) ).
cnf(c_0_80,plain,
multiply(X1,inverse(multiply(X1,X2))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_75]),c_0_61]) ).
cnf(c_0_81,plain,
multiply(inverse(multiply(a3,X1)),multiply(a3,a3)) = inverse(inverse(multiply(inverse(X1),a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_39]),c_0_42]) ).
cnf(c_0_82,plain,
inverse(multiply(X1,inverse(multiply(X2,X1)))) = multiply(X2,multiply(inverse(a3),a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_77]),c_0_30]),c_0_39]) ).
cnf(c_0_83,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(spm,[status(thm)],[c_0_62,c_0_78]) ).
cnf(c_0_84,plain,
inverse(multiply(inverse(X1),X2)) = multiply(X1,inverse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_61]),c_0_78]),c_0_71]) ).
cnf(c_0_85,plain,
multiply(multiply(X1,multiply(inverse(a3),a3)),multiply(a3,a3)) = multiply(multiply(X1,a3),inverse(inverse(a3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_46]) ).
cnf(c_0_86,plain,
multiply(multiply(multiply(X1,X2),inverse(multiply(X1,multiply(X2,inverse(X3))))),multiply(inverse(multiply(X4,X5)),multiply(multiply(X4,multiply(X5,inverse(X3))),inverse(X6)))) = multiply(inverse(multiply(X7,X8)),multiply(X7,multiply(X8,inverse(X6)))),
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_37,c_0_37]),c_0_83]),c_0_84]),c_0_83]),c_0_83]),c_0_83]) ).
cnf(c_0_87,plain,
multiply(multiply(a3,a3),inverse(multiply(multiply(X1,a3),inverse(inverse(a3))))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_85]),c_0_36]),c_0_30]),c_0_39]) ).
cnf(c_0_88,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(fof_simplification,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_0_89,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_78]),c_0_71]) ).
cnf(c_0_90,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,multiply(X2,inverse(X3)))) = multiply(inverse(multiply(a3,a3)),multiply(a3,multiply(a3,inverse(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(spm,[status(thm)],[c_0_37,c_0_37]),c_0_83]),c_0_83]),c_0_84]),c_0_83]),c_0_83]),c_0_86]) ).
cnf(c_0_91,plain,
multiply(multiply(a3,a3),X1) = multiply(a3,multiply(X1,a3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_87]),c_0_71]),c_0_47]),c_0_71]),c_0_61]) ).
cnf(c_0_92,plain,
multiply(X1,multiply(X2,inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_75,c_0_71]) ).
cnf(c_0_93,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
c_0_88 ).
cnf(c_0_94,plain,
multiply(X1,multiply(X2,multiply(X3,inverse(X1)))) = 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)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_84]),c_0_91]),c_0_61]),c_0_80]),c_0_83]),c_0_92]),c_0_71]),c_0_61]) ).
cnf(c_0_95,negated_conjecture,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(rw,[status(thm)],[c_0_93,c_0_61]) ).
cnf(c_0_96,plain,
multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_94]),c_0_61]),c_0_78]),c_0_71]),c_0_71]) ).
cnf(c_0_97,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96]),c_0_61]),c_0_96]),c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP507-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:15:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 66.56/13.84 % Version: 3.5.1
% 66.56/13.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 66.56/13.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.56/13.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 66.56/13.84 % Starting new_bool_3 with 300s (1) cores
% 66.56/13.84 % Starting new_bool_1 with 300s (1) cores
% 66.56/13.84 % Starting sh5l with 300s (1) cores
% 66.56/13.84 % new_bool_3 with pid 3422469 completed with status 9
% 66.56/13.84 % new_bool_1 with pid 3422470 completed with status 9
% 66.56/13.84 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3422468 completed with status 0
% 66.56/13.84 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 66.56/13.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 66.56/13.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.56/13.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 66.56/13.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 66.56/13.84 % No SInE strategy applied
% 66.56/13.84 % Search class: FUUPF-FFSF21-DFFFFFNN
% 66.56/13.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 66.56/13.84 % Starting SubtermCWHack with 136s (1) cores
% 66.56/13.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 66.56/13.84 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 66.56/13.84 % Starting new_bool_3 with 136s (1) cores
% 66.56/13.84 % Starting new_bool_1 with 136s (1) cores
% 66.56/13.84 % U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 3422476 completed with status 0
% 66.56/13.84 % Result found by U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 66.56/13.84 % Preprocessing class: FSSSSMSSSSSNFFN.
% 66.56/13.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.56/13.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 66.56/13.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 66.56/13.84 % No SInE strategy applied
% 66.56/13.84 % Search class: FUUPF-FFSF21-DFFFFFNN
% 66.56/13.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 66.56/13.84 % Starting SubtermCWHack with 136s (1) cores
% 66.56/13.84 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 66.56/13.84 % Starting U----_116XG_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 66.56/13.84 % Preprocessing time : 0.001 s
% 66.56/13.84 % Presaturation interreduction done
% 66.56/13.84
% 66.56/13.84 % Proof found!
% 66.56/13.84 % SZS status Unsatisfiable
% 66.56/13.84 % SZS output start CNFRefutation
% See solution above
% 66.56/13.84 % Parsed axioms : 2
% 66.56/13.84 % Removed by relevancy pruning/SinE : 0
% 66.56/13.84 % Initial clauses : 2
% 66.56/13.84 % Removed in clause preprocessing : 0
% 66.56/13.84 % Initial clauses in saturation : 2
% 66.56/13.84 % Processed clauses : 3504
% 66.56/13.84 % ...of these trivial : 586
% 66.56/13.84 % ...subsumed : 2631
% 66.56/13.84 % ...remaining for further processing : 287
% 66.56/13.84 % Other redundant clauses eliminated : 0
% 66.56/13.84 % Clauses deleted for lack of memory : 0
% 66.56/13.84 % Backward-subsumed : 14
% 66.56/13.84 % Backward-rewritten : 249
% 66.56/13.84 % Generated clauses : 289438
% 66.56/13.84 % ...of the previous two non-redundant : 280636
% 66.56/13.84 % ...aggressively subsumed : 0
% 66.56/13.84 % Contextual simplify-reflections : 0
% 66.56/13.84 % Paramodulations : 289438
% 66.56/13.84 % Factorizations : 0
% 66.56/13.84 % NegExts : 0
% 66.56/13.84 % Equation resolutions : 0
% 66.56/13.84 % Disequality decompositions : 0
% 66.56/13.84 % Total rewrite steps : 391813
% 66.56/13.84 % ...of those cached : 360385
% 66.56/13.84 % Propositional unsat checks : 0
% 66.56/13.84 % Propositional check models : 0
% 66.56/13.84 % Propositional check unsatisfiable : 0
% 66.56/13.84 % Propositional clauses : 0
% 66.56/13.84 % Propositional clauses after purity: 0
% 66.56/13.84 % Propositional unsat core size : 0
% 66.56/13.84 % Propositional preprocessing time : 0.000
% 66.56/13.84 % Propositional encoding time : 0.000
% 66.56/13.84 % Propositional solver time : 0.000
% 66.56/13.84 % Success case prop preproc time : 0.000
% 66.56/13.84 % Success case prop encoding time : 0.000
% 66.56/13.84 % Success case prop solver time : 0.000
% 66.56/13.84 % Current number of processed clauses : 22
% 66.56/13.84 % Positive orientable unit clauses : 18
% 66.56/13.84 % Positive unorientable unit clauses: 4
% 66.56/13.84 % Negative unit clauses : 0
% 66.56/13.84 % Non-unit-clauses : 0
% 66.56/13.84 % Current number of unprocessed clauses: 97732
% 66.56/13.84 % ...number of literals in the above : 97732
% 66.56/13.84 % Current number of archived formulas : 0
% 66.56/13.84 % Current number of archived clauses : 265
% 66.56/13.84 % Clause-clause subsumption calls (NU) : 0
% 66.56/13.84 % Rec. Clause-clause subsumption calls : 0
% 66.56/13.84 % Non-unit clause-clause subsumptions : 0
% 66.56/13.84 % Unit Clause-clause subsumption calls : 1985
% 66.56/13.84 % Rewrite failures with RHS unbound : 0
% 66.56/13.84 % BW rewrite match attempts : 9074
% 66.56/13.84 % BW rewrite match successes : 1104
% 66.56/13.84 % Condensation attempts : 0
% 66.56/13.84 % Condensation successes : 0
% 66.56/13.84 % Termbank termtop insertions : 25326330
% 66.56/13.84 % Search garbage collected termcells : 2
% 66.56/13.84
% 66.56/13.84 % -------------------------------------------------
% 66.56/13.84 % User time : 12.727 s
% 66.56/13.84 % System time : 0.455 s
% 66.56/13.84 % Total time : 13.183 s
% 66.56/13.84 % Maximum resident set size: 3584 pages
% 66.56/13.84
% 66.56/13.84 % -------------------------------------------------
% 66.56/13.84 % User time : 64.146 s
% 66.56/13.84 % System time : 2.262 s
% 66.56/13.84 % Total time : 66.408 s
% 66.56/13.84 % Maximum resident set size: 4864 pages
% 66.56/13.84 % E exiting
%------------------------------------------------------------------------------