%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GRP054-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 12:41:40 PM UTC 2026
% Result : Unsatisfiable 12.48s 2.19s
% Output : CNFRefutation 12.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 2
% Syntax : Number of clauses : 67 ( 59 unt; 0 nHn; 13 RR)
% Number of literals : 78 ( 77 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 20 ( 4 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 146 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
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(X2),inverse(multiply(multiply(inverse(multiply(X3,inverse(multiply(X4,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X3,X5)),inverse(multiply(multiply(inverse(multiply(X6,inverse(multiply(inverse(X4),inverse(multiply(X7,inverse(multiply(inverse(X7),X7)))))))),multiply(X6,X7)),multiply(inverse(multiply(X3,inverse(multiply(X4,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X3,X5)))))))))),multiply(X1,multiply(inverse(multiply(X3,inverse(multiply(X4,inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X3,X5)))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X2),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_3]) ).
cnf(c_0_7,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_8,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_9,plain,
multiply(inverse(multiply(X1,inverse(multiply(inverse(X2),inverse(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(X3),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),inverse(multiply(X3,multiply(inverse(multiply(a1,inverse(multiply(inverse(X3),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)))))))))),multiply(X1,multiply(inverse(multiply(a1,inverse(multiply(inverse(X3),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)))) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X2),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),inverse(multiply(inverse(inverse(X2)),inverse(multiply(multiply(a1,a1),inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,a1))))))))),inverse(multiply(inverse(X3),inverse(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),inverse(multiply(X1,multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)))))))))),X2) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X3),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_11,plain,
multiply(inverse(multiply(a1,inverse(multiply(multiply(inverse(multiply(a1,inverse(multiply(inverse(X1),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)) = multiply(inverse(multiply(X2,inverse(multiply(multiply(inverse(multiply(X3,inverse(multiply(inverse(X1),inverse(multiply(X4,inverse(multiply(inverse(X4),X4)))))))),multiply(X3,X4)),inverse(multiply(X5,inverse(multiply(inverse(X5),X5)))))))),multiply(X2,X5)),
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_12,plain,
multiply(inverse(multiply(inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(inverse(X1)),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),inverse(multiply(inverse(inverse(X2)),inverse(multiply(multiply(a1,a1),inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,a1))))))))),inverse(multiply(inverse(X3),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))))),X2) = multiply(inverse(multiply(a1,inverse(multiply(inverse(X3),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_13,plain,
multiply(inverse(multiply(a1,inverse(multiply(X1,inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),multiply(a1,a1)) = multiply(inverse(multiply(X2,inverse(multiply(X1,inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))))),multiply(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_8]),c_0_8]) ).
cnf(c_0_14,plain,
inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))) = multiply(inverse(multiply(inverse(multiply(a1,inverse(multiply(inverse(inverse(X4)),inverse(multiply(a1,inverse(multiply(inverse(a1),a1)))))))),inverse(multiply(inverse(inverse(inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),inverse(multiply(multiply(a1,a1),inverse(multiply(inverse(multiply(a1,a1)),multiply(a1,a1))))))))),inverse(multiply(inverse(X2),inverse(multiply(X4,inverse(multiply(inverse(X4),X4))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_12]),c_0_3]),c_0_8]),c_0_8]) ).
cnf(c_0_15,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_8]),c_0_3]) ).
cnf(c_0_16,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(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_17,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_14]),c_0_15]),c_0_8]),c_0_8]) ).
cnf(c_0_18,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(multiply(X4,X2)),multiply(X4,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_8]) ).
cnf(c_0_19,plain,
multiply(inverse(multiply(inverse(multiply(X1,X2)),multiply(X1,X3))),multiply(inverse(multiply(X4,X2)),X5)) = multiply(inverse(multiply(X6,multiply(X4,X3))),multiply(X6,X5)),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_20,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(X4,multiply(X2,multiply(a1,a1)))),multiply(X4,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_7]),c_0_3]),c_0_8]) ).
cnf(c_0_21,plain,
multiply(inverse(X1),X1) = multiply(inverse(multiply(X2,multiply(X3,multiply(a1,a1)))),multiply(X2,multiply(X3,multiply(a1,a1)))),
inference(spm,[status(thm)],[c_0_20,c_0_8]) ).
cnf(c_0_22,plain,
multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_21]) ).
cnf(c_0_23,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(X2,inverse(multiply(inverse(X2),X2)))))) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_24,plain,
inverse(multiply(inverse(inverse(multiply(inverse(X1),X1))),inverse(multiply(X2,inverse(multiply(inverse(X3),X3)))))) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_25,plain,
inverse(multiply(inverse(X1),X1)) = inverse(inverse(multiply(inverse(X2),X2))),
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_26,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_14]),c_0_15]),c_0_8]) ).
cnf(c_0_27,plain,
inverse(multiply(inverse(X1),X1)) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_25]),c_0_24]),c_0_22]) ).
cnf(c_0_28,plain,
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_26,c_0_27]),c_0_27]),c_0_27]) ).
cnf(c_0_29,plain,
multiply(multiply(inverse(a1),a1),multiply(inverse(a1),a1)) = multiply(inverse(a1),a1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_27]) ).
cnf(c_0_30,plain,
multiply(inverse(inverse(X1)),multiply(inverse(a1),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_8,c_0_29]),c_0_22]),c_0_27]),c_0_29]),c_0_27]),c_0_28]) ).
cnf(c_0_31,plain,
multiply(multiply(inverse(a1),a1),inverse(X1)) = inverse(X1),
inference(spm,[status(thm)],[c_0_28,c_0_30]) ).
cnf(c_0_32,plain,
multiply(multiply(inverse(a1),a1),X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_33,plain,
multiply(multiply(inverse(X1),X1),X2) = X2,
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_34,plain,
inverse(multiply(inverse(X1),multiply(inverse(a1),a1))) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_31]) ).
cnf(c_0_35,plain,
multiply(inverse(multiply(X1,X2)),multiply(X1,X3)) = multiply(inverse(X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_33]),c_0_33]) ).
cnf(c_0_36,plain,
inverse(multiply(inverse(X1),multiply(inverse(X2),X2))) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_37,plain,
multiply(inverse(inverse(X1)),multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_38,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_27]),c_0_32]) ).
cnf(c_0_39,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
inverse(multiply(X1,multiply(inverse(a1),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_39,c_0_24]),c_0_27]),c_0_27]),c_0_27]),c_0_31]) ).
cnf(c_0_41,plain,
multiply(X1,multiply(inverse(a1),a1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_40]),c_0_36]) ).
cnf(c_0_42,plain,
inverse(multiply(inverse(a1),X1)) = multiply(inverse(X1),a1),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_43,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(fof_simplification,[status(thm)],[prove_these_axioms]) ).
cnf(c_0_44,plain,
inverse(multiply(inverse(X1),a1)) = multiply(inverse(a1),X1),
inference(spm,[status(thm)],[c_0_39,c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
c_0_43 ).
cnf(c_0_46,plain,
multiply(inverse(a1),inverse(X1)) = inverse(multiply(X1,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_44,c_0_24]),c_0_27]),c_0_27]),c_0_27]),c_0_41]),c_0_33]) ).
cnf(c_0_47,negated_conjecture,
( multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(sr,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_48,plain,
multiply(a1,inverse(multiply(X1,a1))) = inverse(X1),
inference(spm,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( multiply(multiply(inverse(X1),X1),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(spm,[status(thm)],[c_0_47,c_0_22]) ).
cnf(c_0_50,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_51,plain,
multiply(inverse(multiply(inverse(inverse(X1)),inverse(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(spm,[status(thm)],[c_0_8,c_0_37]),c_0_27]),c_0_33]),c_0_27]),c_0_33]),c_0_27]),c_0_30]) ).
cnf(c_0_52,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_27]) ).
cnf(c_0_53,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_54,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(X1,multiply(inverse(inverse(multiply(inverse(multiply(X2,X1)),multiply(X2,X3)))),inverse(multiply(X3,inverse(multiply(inverse(X3),X3)))))),a2) != a2 ),
inference(spm,[status(thm)],[c_0_49,c_0_17]) ).
cnf(c_0_55,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_39]),c_0_39]) ).
cnf(c_0_56,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_22,c_0_52]) ).
cnf(c_0_57,plain,
inverse(multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_42,c_0_52]) ).
cnf(c_0_58,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_24]),c_0_27]),c_0_27]),c_0_27]),c_0_41]),c_0_33]) ).
cnf(c_0_59,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(spm,[status(thm)],[c_0_33,c_0_39]) ).
cnf(c_0_60,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(X1,multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(X1,inverse(multiply(inverse(X1),X1)))))),a2) != a2 ),
inference(spm,[status(thm)],[c_0_54,c_0_22]) ).
cnf(c_0_61,plain,
multiply(multiply(X1,X2),inverse(X2)) = 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_55,c_0_24]),c_0_27]),c_0_56]),c_0_57]),c_0_27]),c_0_56]),c_0_58]),c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(X1,multiply(inverse(inverse(multiply(inverse(X2),X2))),inverse(multiply(X1,inverse(multiply(inverse(X3),X3)))))),a2) != a2 ),
inference(spm,[status(thm)],[c_0_60,c_0_22]) ).
cnf(c_0_63,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(spm,[status(thm)],[c_0_61,c_0_50]) ).
cnf(c_0_64,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_32]),c_0_27]),c_0_27]),c_0_27]),c_0_32]),c_0_27]),c_0_32]),c_0_32])]) ).
cnf(c_0_65,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_63]),c_0_39]),c_0_39]) ).
cnf(c_0_66,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP054-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:57:57 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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/benchmark/theBenchmark.p
% 12.48/2.19 % Version: 3.5.1
% 12.48/2.19 % Preprocessing class: FSSSSMSSSSSNFFN.
% 12.48/2.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.48/2.19 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 12.48/2.19 % Starting new_bool_3 with 300s (1) cores
% 12.48/2.19 % Starting new_bool_1 with 300s (1) cores
% 12.48/2.19 % Starting sh5l with 300s (1) cores
% 12.48/2.19 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 50454 completed with status 0
% 12.48/2.19 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 12.48/2.19 % Preprocessing class: FSSSSMSSSSSNFFN.
% 12.48/2.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.48/2.19 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 12.48/2.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.48/2.19 % No SInE strategy applied
% 12.48/2.19 % Search class: FUHPF-FFSF21-DFFFFFNN
% 12.48/2.19 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.48/2.19 % Starting SubtermCWHack with 136s (1) cores
% 12.48/2.19 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 12.48/2.19 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.48/2.19 % Starting new_bool_3 with 136s (1) cores
% 12.48/2.19 % Starting new_bool_1 with 136s (1) cores
% 12.48/2.19 % G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with pid 50460 completed with status 0
% 12.48/2.19 % Result found by G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN
% 12.48/2.19 % Preprocessing class: FSSSSMSSSSSNFFN.
% 12.48/2.19 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 12.48/2.19 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 12.48/2.19 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 12.48/2.19 % No SInE strategy applied
% 12.48/2.19 % Search class: FUHPF-FFSF21-DFFFFFNN
% 12.48/2.19 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 12.48/2.19 % Starting SubtermCWHack with 136s (1) cores
% 12.48/2.19 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 12.48/2.19 % Starting G-E--_208_C18_F1_SE_CS_SSP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 12.48/2.19 % Preprocessing time : 0.002 s
% 12.48/2.19 % Presaturation interreduction done
% 12.48/2.19
% 12.48/2.19 % Proof found!
% 12.48/2.19 % SZS status Unsatisfiable
% 12.48/2.19 % SZS output start CNFRefutation
% See solution above
% 12.48/2.19 % Parsed axioms : 2
% 12.48/2.19 % Removed by relevancy pruning/SinE : 0
% 12.48/2.19 % Initial clauses : 2
% 12.48/2.19 % Removed in clause preprocessing : 0
% 12.48/2.19 % Initial clauses in saturation : 2
% 12.48/2.19 % Processed clauses : 473
% 12.48/2.19 % ...of these trivial : 85
% 12.48/2.19 % ...subsumed : 253
% 12.48/2.19 % ...remaining for further processing : 135
% 12.48/2.19 % Other redundant clauses eliminated : 0
% 12.48/2.19 % Clauses deleted for lack of memory : 0
% 12.48/2.19 % Backward-subsumed : 26
% 12.48/2.19 % Backward-rewritten : 91
% 12.48/2.19 % Generated clauses : 17936
% 12.48/2.19 % ...of the previous two non-redundant : 17390
% 12.48/2.19 % ...aggressively subsumed : 0
% 12.48/2.19 % Contextual simplify-reflections : 0
% 12.48/2.19 % Paramodulations : 17935
% 12.48/2.19 % Factorizations : 0
% 12.48/2.19 % NegExts : 0
% 12.48/2.19 % Equation resolutions : 0
% 12.48/2.19 % Disequality decompositions : 0
% 12.48/2.19 % Total rewrite steps : 36886
% 12.48/2.19 % ...of those cached : 35195
% 12.48/2.19 % Propositional unsat checks : 0
% 12.48/2.19 % Propositional check models : 0
% 12.48/2.19 % Propositional check unsatisfiable : 0
% 12.48/2.19 % Propositional clauses : 0
% 12.48/2.19 % Propositional clauses after purity: 0
% 12.48/2.19 % Propositional unsat core size : 0
% 12.48/2.19 % Propositional preprocessing time : 0.000
% 12.48/2.19 % Propositional encoding time : 0.000
% 12.48/2.19 % Propositional solver time : 0.000
% 12.48/2.19 % Success case prop preproc time : 0.000
% 12.48/2.19 % Success case prop encoding time : 0.000
% 12.48/2.19 % Success case prop solver time : 0.000
% 12.48/2.19 % Current number of processed clauses : 15
% 12.48/2.19 % Positive orientable unit clauses : 14
% 12.48/2.19 % Positive unorientable unit clauses: 1
% 12.48/2.19 % Negative unit clauses : 0
% 12.48/2.19 % Non-unit-clauses : 0
% 12.48/2.19 % Current number of unprocessed clauses: 15540
% 12.48/2.19 % ...number of literals in the above : 15540
% 12.48/2.19 % Current number of archived formulas : 0
% 12.48/2.19 % Current number of archived clauses : 120
% 12.48/2.19 % Clause-clause subsumption calls (NU) : 568
% 12.48/2.19 % Rec. Clause-clause subsumption calls : 568
% 12.48/2.19 % Non-unit clause-clause subsumptions : 159
% 12.48/2.19 % Unit Clause-clause subsumption calls : 275
% 12.48/2.19 % Rewrite failures with RHS unbound : 0
% 12.48/2.19 % BW rewrite match attempts : 1232
% 12.48/2.19 % BW rewrite match successes : 259
% 12.48/2.19 % Condensation attempts : 0
% 12.48/2.19 % Condensation successes : 0
% 12.48/2.19 % Termbank termtop insertions : 2418904
% 12.48/2.19 % Search garbage collected termcells : 8
% 12.48/2.19
% 12.48/2.19 % -------------------------------------------------
% 12.48/2.19 % User time : 1.498 s
% 12.48/2.19 % System time : 0.061 s
% 12.48/2.19 % Total time : 1.558 s
% 12.48/2.19 % Maximum resident set size: 3640 pages
% 12.48/2.19
% 12.48/2.19 % -------------------------------------------------
% 12.48/2.19 % User time : 7.741 s
% 12.48/2.19 % System time : 0.246 s
% 12.48/2.19 % Total time : 7.986 s
% 12.48/2.19 % Maximum resident set size: 4864 pages
% 12.48/2.19 % E exiting
%------------------------------------------------------------------------------