%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 11:50:12 AM UTC 2026
% Result : Unsatisfiable 161.26s 24.08s
% Output : CNFRefutation 161.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of clauses : 103 ( 88 unt; 0 nHn; 37 RR)
% Number of literals : 124 ( 123 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(medial_law,axiom,
multiply(multiply(X1,X2),multiply(X3,X4)) = multiply(multiply(X1,X3),multiply(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',medial_law) ).
cnf(prove_quotient_condition3,negated_conjecture,
multiply(b,d0) = multiply(a,c0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition3) ).
cnf(prove_quotient_condition1,negated_conjecture,
multiply(b,b0) = multiply(a,a0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition1) ).
cnf(prove_quotient_condition2,negated_conjecture,
multiply(d,b0) = multiply(c,a0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition2) ).
cnf(right_cancelaation,axiom,
( multiply(X1,X4) != X3
| multiply(X1,X2) != X3
| X2 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancelaation) ).
cnf(left_cancellation,axiom,
( multiply(X4,X2) != X3
| multiply(X1,X2) != X3
| X1 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_cancellation) ).
cnf(prove_quotient_condition4,negated_conjecture,
multiply(d,d0) != multiply(c,c0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_quotient_condition4) ).
cnf(c_0_7,axiom,
multiply(multiply(X1,X2),multiply(X3,X4)) = multiply(multiply(X1,X3),multiply(X2,X4)),
medial_law ).
cnf(c_0_8,negated_conjecture,
multiply(b,d0) = multiply(a,c0),
prove_quotient_condition3 ).
cnf(c_0_9,negated_conjecture,
multiply(multiply(a,X1),multiply(c0,X2)) = multiply(multiply(b,d0),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,negated_conjecture,
multiply(b,b0) = multiply(a,a0),
prove_quotient_condition1 ).
cnf(c_0_11,negated_conjecture,
multiply(multiply(b,b0),multiply(c0,X1)) = multiply(multiply(b,a0),multiply(d0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_7]) ).
cnf(c_0_12,negated_conjecture,
multiply(multiply(X1,a),multiply(X2,a0)) = multiply(multiply(X1,X2),multiply(b,b0)),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
multiply(multiply(X1,a),multiply(X2,c0)) = multiply(multiply(X1,X2),multiply(b,d0)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
multiply(multiply(X1,X2),multiply(multiply(b,a0),multiply(d0,X3))) = multiply(multiply(X1,multiply(b,b0)),multiply(X2,multiply(c0,X3))),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
multiply(multiply(X1,a),multiply(X2,a0)) = multiply(multiply(X1,b),multiply(X2,b0)),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
multiply(d,b0) = multiply(c,a0),
prove_quotient_condition2 ).
cnf(c_0_17,negated_conjecture,
multiply(multiply(X1,a),multiply(X2,c0)) = multiply(multiply(X1,b),multiply(X2,d0)),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
multiply(multiply(X1,multiply(X2,a)),multiply(multiply(b,a0),multiply(d0,a0))) = multiply(multiply(X1,multiply(b,b0)),multiply(multiply(X2,b),multiply(c0,b0))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
multiply(multiply(d,X1),multiply(b0,X2)) = multiply(multiply(c,a0),multiply(X1,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
multiply(multiply(X1,multiply(X2,a)),multiply(multiply(b,a0),multiply(d0,c0))) = multiply(multiply(X1,multiply(b,b0)),multiply(multiply(X2,b),multiply(c0,d0))),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,b0)),multiply(multiply(b0,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,a0))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,b0)),multiply(multiply(b0,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,c0))),
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,a0))),
inference(spm,[status(thm)],[c_0_21,c_0_7]) ).
cnf(c_0_24,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,c0))),
inference(spm,[status(thm)],[c_0_22,c_0_7]) ).
cnf(c_0_25,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,a0))) = multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(X1,b0),multiply(c0,b0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_19]) ).
cnf(c_0_26,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,c0))) = multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(X1,b0),multiply(c0,d0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_24]),c_0_19]) ).
cnf(c_0_27,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,a0))) = multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,b0))),
inference(spm,[status(thm)],[c_0_7,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,a)),multiply(multiply(b,a0),multiply(d0,c0))) = multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,d0))),
inference(spm,[status(thm)],[c_0_7,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(X1,b),multiply(d0,b0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_27]),c_0_15]) ).
cnf(c_0_30,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(X1,b),multiply(d0,d0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_28]),c_0_17]) ).
cnf(c_0_31,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,b0)),multiply(multiply(b0,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,b0))),
inference(rw,[status(thm)],[c_0_21,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,b0))),
inference(spm,[status(thm)],[c_0_7,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,b0)),multiply(multiply(b0,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,d0))),
inference(rw,[status(thm)],[c_0_22,c_0_28]) ).
cnf(c_0_34,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,d0))),
inference(spm,[status(thm)],[c_0_7,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,b0)),multiply(multiply(b0,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,b0))),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
multiply(multiply(X1,multiply(b,b0)),multiply(X2,multiply(c0,X3))) = multiply(multiply(X1,multiply(b,a0)),multiply(X2,multiply(d0,X3))),
inference(spm,[status(thm)],[c_0_7,c_0_14]) ).
cnf(c_0_37,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,b0)),multiply(multiply(b0,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,d0))),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,a0)),multiply(multiply(b0,b),multiply(d0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,b0))),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
multiply(multiply(multiply(d,X1),multiply(b,a0)),multiply(multiply(b0,b),multiply(d0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,d0))),
inference(rw,[status(thm)],[c_0_37,c_0_36]) ).
cnf(c_0_40,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,a0)),multiply(multiply(b0,b),multiply(d0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,b0))),
inference(spm,[status(thm)],[c_0_38,c_0_7]) ).
cnf(c_0_41,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,a0)),multiply(multiply(b0,b),multiply(d0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,d0))),
inference(spm,[status(thm)],[c_0_39,c_0_7]) ).
cnf(c_0_42,plain,
( multiply(X1,X4) != X3
| multiply(X1,X2) != X3
| X2 = X4 ),
inference(fof_simplification,[status(thm)],[right_cancelaation]) ).
cnf(c_0_43,negated_conjecture,
multiply(multiply(X1,d),multiply(X2,b0)) = multiply(multiply(X1,X2),multiply(c,a0)),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_44,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,b0))),
inference(rw,[status(thm)],[c_0_23,c_0_27]) ).
cnf(c_0_45,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,b0))) = multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(X1,a0),multiply(d0,b0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_40]),c_0_19]) ).
cnf(c_0_46,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,d0))),
inference(rw,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_47,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,d0))) = multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(X1,a0),multiply(d0,d0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_41]),c_0_19]) ).
cnf(c_0_48,plain,
( multiply(X1,X4) != X3
| multiply(X1,X2) != X3
| X2 = X4 ),
c_0_42 ).
cnf(c_0_49,negated_conjecture,
multiply(multiply(X1,d),multiply(X2,b0)) = multiply(multiply(X1,c),multiply(X2,a0)),
inference(spm,[status(thm)],[c_0_7,c_0_43]) ).
cnf(c_0_50,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,b0))),
inference(rw,[status(thm)],[c_0_44,c_0_32]) ).
cnf(c_0_51,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,a0)),multiply(multiply(b,b),multiply(d0,b0))),
inference(spm,[status(thm)],[c_0_7,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,d0))),
inference(rw,[status(thm)],[c_0_46,c_0_34]) ).
cnf(c_0_53,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b)),multiply(multiply(b,a0),multiply(d0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,a0)),multiply(multiply(b,b),multiply(d0,d0))),
inference(spm,[status(thm)],[c_0_7,c_0_47]) ).
cnf(c_0_54,plain,
( multiply(X3,X1) != multiply(X3,X2)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_55,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(c,a0),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(d,b),multiply(d0,b0))),
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_49]),c_0_7]),c_0_7]),c_0_19]),c_0_7]),c_0_15]) ).
cnf(c_0_56,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(X1,a0)),multiply(multiply(b,b),multiply(d0,b0))),
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_57,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(c,a0),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(d,b),multiply(d0,d0))),
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_49]),c_0_7]),c_0_7]),c_0_19]),c_0_7]),c_0_17]) ).
cnf(c_0_58,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(X1,b0)),multiply(multiply(b0,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,a0)),multiply(multiply(b,b),multiply(d0,d0))),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(d,b),multiply(d0,b0))) != multiply(multiply(multiply(c,a0),multiply(b,b)),X1)
| multiply(multiply(c,a0),multiply(c0,b0)) = X1 ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(d,a0),multiply(d0,b0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(d,b),multiply(d0,b0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_16]),c_0_7]),c_0_19]),c_0_55]),c_0_7]) ).
cnf(c_0_61,negated_conjecture,
( multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(d,b),multiply(d0,d0))) != multiply(multiply(multiply(c,a0),multiply(b,b)),X1)
| multiply(multiply(c,a0),multiply(c0,d0)) = X1 ),
inference(spm,[status(thm)],[c_0_54,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(d,a0),multiply(d0,d0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(d,b),multiply(d0,d0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_16]),c_0_7]),c_0_19]),c_0_57]),c_0_7]) ).
cnf(c_0_63,negated_conjecture,
multiply(multiply(d,a0),multiply(d0,b0)) = multiply(multiply(c,a0),multiply(c0,b0)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
multiply(multiply(d,a0),multiply(d0,d0)) = multiply(multiply(c,a0),multiply(c0,d0)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,negated_conjecture,
multiply(multiply(X1,X2),multiply(multiply(c,a0),multiply(c0,b0))) = multiply(multiply(X1,multiply(d,a0)),multiply(X2,multiply(d0,b0))),
inference(spm,[status(thm)],[c_0_7,c_0_63]) ).
cnf(c_0_66,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(c0,d0)),multiply(X1,X2)) = multiply(multiply(multiply(d,a0),X1),multiply(multiply(d0,d0),X2)),
inference(spm,[status(thm)],[c_0_7,c_0_64]) ).
cnf(c_0_67,negated_conjecture,
multiply(multiply(X1,multiply(d,a0)),multiply(X2,multiply(d0,b0))) = multiply(multiply(X1,multiply(c,a0)),multiply(X2,multiply(c0,b0))),
inference(spm,[status(thm)],[c_0_7,c_0_65]) ).
cnf(c_0_68,plain,
( multiply(X4,X2) != X3
| multiply(X1,X2) != X3
| X1 = X4 ),
inference(fof_simplification,[status(thm)],[left_cancellation]) ).
cnf(c_0_69,negated_conjecture,
multiply(multiply(multiply(d,a0),X1),multiply(multiply(d0,d0),X2)) = multiply(multiply(multiply(c,a0),X1),multiply(multiply(c0,d0),X2)),
inference(spm,[status(thm)],[c_0_7,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
multiply(multiply(multiply(d,a0),multiply(d0,c0)),multiply(multiply(c,a0),multiply(d0,b0))) = multiply(multiply(multiply(c,a0),multiply(c0,d0)),multiply(multiply(c,a0),multiply(c0,b0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_63]),c_0_7]),c_0_7]) ).
cnf(c_0_71,plain,
( multiply(X4,X2) != X3
| multiply(X1,X2) != X3
| X1 = X4 ),
c_0_68 ).
cnf(c_0_72,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(c0,d0)),multiply(multiply(c,a0),multiply(c0,b0))) = multiply(multiply(multiply(c,a0),multiply(c0,c0)),multiply(multiply(c,a0),multiply(d0,b0))),
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_67,c_0_69]),c_0_67]),c_0_7]),c_0_7]),c_0_70]),c_0_7]),c_0_7]) ).
cnf(c_0_73,plain,
( multiply(X1,X3) != multiply(X2,X3)
| X1 = X2 ),
inference(er,[status(thm)],[c_0_71]) ).
cnf(c_0_74,negated_conjecture,
multiply(multiply(multiply(d,a0),multiply(d0,c0)),multiply(multiply(c,a0),multiply(d0,b0))) = multiply(multiply(multiply(c,a0),multiply(c0,c0)),multiply(multiply(c,a0),multiply(d0,b0))),
inference(rw,[status(thm)],[c_0_70,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( multiply(multiply(multiply(c,a0),multiply(c0,c0)),multiply(multiply(c,a0),multiply(d0,b0))) != multiply(X1,multiply(multiply(c,a0),multiply(d0,b0)))
| multiply(multiply(d,a0),multiply(d0,c0)) = X1 ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_76,negated_conjecture,
multiply(multiply(d,a0),multiply(d0,c0)) = multiply(multiply(c,a0),multiply(c0,c0)),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_77,negated_conjecture,
multiply(multiply(X1,X2),multiply(multiply(c,a0),multiply(c0,c0))) = multiply(multiply(X1,multiply(d,a0)),multiply(X2,multiply(d0,c0))),
inference(spm,[status(thm)],[c_0_7,c_0_76]) ).
cnf(c_0_78,negated_conjecture,
multiply(multiply(X1,multiply(d,a0)),multiply(X2,multiply(d0,c0))) = multiply(multiply(X1,multiply(c,a0)),multiply(X2,multiply(c0,c0))),
inference(spm,[status(thm)],[c_0_7,c_0_77]) ).
cnf(c_0_79,negated_conjecture,
multiply(multiply(multiply(X1,b),multiply(c,b0)),multiply(X2,multiply(c0,c0))) = multiply(multiply(multiply(X1,b),multiply(c,a0)),multiply(X2,multiply(d0,c0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_15]),c_0_16]),c_0_15]) ).
cnf(c_0_80,negated_conjecture,
multiply(multiply(multiply(X1,b),multiply(c,a0)),multiply(X2,multiply(d0,c0))) = multiply(multiply(multiply(X1,b),X2),multiply(multiply(c,b0),multiply(c0,c0))),
inference(spm,[status(thm)],[c_0_7,c_0_79]) ).
cnf(c_0_81,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(c,a0)),multiply(multiply(b0,X1),multiply(d0,c0))) = multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,b0),multiply(c0,c0))),
inference(spm,[status(thm)],[c_0_80,c_0_19]) ).
cnf(c_0_82,negated_conjecture,
multiply(multiply(multiply(d,b),multiply(c,a0)),multiply(multiply(b0,X1),multiply(d0,c0))) = multiply(multiply(multiply(c,a0),multiply(c,b0)),multiply(multiply(b,X1),multiply(c0,c0))),
inference(spm,[status(thm)],[c_0_7,c_0_81]) ).
cnf(c_0_83,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,a0)),multiply(multiply(b,b),multiply(d0,d0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(X1,b),multiply(d0,d0))),
inference(spm,[status(thm)],[c_0_7,c_0_53]) ).
cnf(c_0_84,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(c,b0)),multiply(multiply(b,X1),multiply(c0,c0))) = multiply(multiply(multiply(c,a0),multiply(b,d0)),multiply(multiply(c,a0),multiply(X1,c0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_7]),c_0_7]),c_0_19]) ).
cnf(c_0_85,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(c,b0)),multiply(multiply(b,X1),multiply(c0,c0))) = multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,a0),multiply(d0,c0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_82]),c_0_19]) ).
cnf(c_0_86,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(X1,b0)),multiply(multiply(b,b),multiply(c0,d0))) = multiply(multiply(multiply(c,a0),multiply(X1,a0)),multiply(multiply(b,b),multiply(d0,d0))),
inference(rw,[status(thm)],[c_0_34,c_0_53]) ).
cnf(c_0_87,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,b)),multiply(multiply(X1,a0),multiply(d0,d0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(X1,b),multiply(d0,d0))),
inference(spm,[status(thm)],[c_0_7,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,d0)),multiply(multiply(c,a0),multiply(X1,c0))) = multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,b0),multiply(c0,c0))),
inference(spm,[status(thm)],[c_0_7,c_0_84]) ).
cnf(c_0_89,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,d0)),multiply(multiply(c,a0),multiply(X1,c0))) = multiply(multiply(multiply(c,a0),multiply(b,c0)),multiply(multiply(c,b0),multiply(X1,c0))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_7]),c_0_7]) ).
cnf(c_0_90,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,d0)),multiply(multiply(c,a0),multiply(X1,c0))) = multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,a0),multiply(d0,c0))),
inference(rw,[status(thm)],[c_0_85,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,a)),multiply(multiply(c,a0),multiply(d0,c0))) = multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(c,b),multiply(d0,d0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_17]),c_0_86]),c_0_7]),c_0_87]) ).
cnf(c_0_92,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,c0)),multiply(multiply(c,b0),multiply(X1,c0))) = multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,b0),multiply(c0,c0))),
inference(rw,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,c0)),multiply(multiply(c,b0),multiply(X1,c0))) = multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,a0),multiply(d0,c0))),
inference(rw,[status(thm)],[c_0_90,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( multiply(multiply(c,a0),multiply(X1,X3)) != multiply(X2,multiply(b0,X3))
| multiply(d,X1) = X2 ),
inference(spm,[status(thm)],[c_0_73,c_0_19]) ).
cnf(c_0_95,negated_conjecture,
( multiply(multiply(multiply(c,a0),multiply(b,a0)),multiply(multiply(c,b),multiply(d0,d0))) != multiply(multiply(multiply(c,a0),multiply(b,a)),X1)
| multiply(multiply(c,a0),multiply(d0,c0)) = X1 ),
inference(spm,[status(thm)],[c_0_54,c_0_91]) ).
cnf(c_0_96,negated_conjecture,
multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,b0),multiply(c0,c0))) = multiply(multiply(multiply(c,a0),multiply(b,X1)),multiply(multiply(c,a0),multiply(d0,c0))),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( multiply(multiply(c,a0),multiply(X1,X4)) != multiply(multiply(X2,b0),multiply(X3,X4))
| multiply(d,X1) = multiply(X2,X3) ),
inference(spm,[status(thm)],[c_0_94,c_0_7]) ).
cnf(c_0_98,negated_conjecture,
multiply(multiply(c,b0),multiply(c0,c0)) = multiply(multiply(c,a0),multiply(d0,c0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_91])]) ).
cnf(c_0_99,negated_conjecture,
multiply(d,d0) != multiply(c,c0),
inference(fof_simplification,[status(thm)],[prove_quotient_condition4]) ).
cnf(c_0_100,negated_conjecture,
( multiply(multiply(c,a0),multiply(X1,c0)) != multiply(multiply(c,a0),multiply(d0,c0))
| multiply(d,X1) = multiply(c,c0) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_101,negated_conjecture,
multiply(d,d0) != multiply(c,c0),
c_0_99 ).
cnf(c_0_102,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_100]),c_0_101]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ALG004-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.21/0.47 % Computer : n026.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Mon Sep 21 12:54:51 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.54 Running first-order theorem proving
% 0.26/0.54 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
% 161.26/24.08 % Version: 3.5.1
% 161.26/24.08 % Preprocessing class: FSSSSMSMSSSNFFN.
% 161.26/24.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 161.26/24.08 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 161.26/24.08 % Starting new_bool_3 with 300s (1) cores
% 161.26/24.08 % Starting new_bool_1 with 300s (1) cores
% 161.26/24.08 % Starting sh5l with 300s (1) cores
% 161.26/24.08 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 2304669 completed with status 0
% 161.26/24.08 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 161.26/24.08 % Preprocessing class: FSSSSMSMSSSNFFN.
% 161.26/24.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 161.26/24.08 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 161.26/24.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 161.26/24.08 % No SInE strategy applied
% 161.26/24.08 % Search class: FHUPF-FFSS22-SFFFFFNN
% 161.26/24.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 161.26/24.08 % Starting SubtermCWHack with 136s (1) cores
% 161.26/24.08 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 161.26/24.08 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S0Y with 169s (1) cores
% 161.26/24.08 % Starting new_bool_3 with 169s (1) cores
% 161.26/24.08 % Starting new_bool_1 with 169s (1) cores
% 161.26/24.08 % G----_0031_C18_F1_SE_CS_SP_S0Y with pid 2304674 completed with status 0
% 161.26/24.08 % Result found by G----_0031_C18_F1_SE_CS_SP_S0Y
% 161.26/24.08 % Preprocessing class: FSSSSMSMSSSNFFN.
% 161.26/24.08 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 161.26/24.08 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 1500s (5) cores
% 161.26/24.08 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 161.26/24.08 % No SInE strategy applied
% 161.26/24.08 % Search class: FHUPF-FFSS22-SFFFFFNN
% 161.26/24.08 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 161.26/24.08 % Starting SubtermCWHack with 136s (1) cores
% 161.26/24.08 % Starting G----_0031_C18_F1_SE_CS_SP_S0Y with 151s (1) cores
% 161.26/24.08 % Preprocessing time : 0.002 s
% 161.26/24.08
% 161.26/24.08 % Proof found!
% 161.26/24.08 % SZS status Unsatisfiable
% 161.26/24.08 % SZS output start CNFRefutation
% See solution above
% 161.26/24.08 % Parsed axioms : 7
% 161.26/24.08 % Removed by relevancy pruning/SinE : 0
% 161.26/24.08 % Initial clauses : 7
% 161.26/24.08 % Removed in clause preprocessing : 0
% 161.26/24.08 % Initial clauses in saturation : 7
% 161.26/24.08 % Processed clauses : 36873
% 161.26/24.08 % ...of these trivial : 814
% 161.26/24.08 % ...subsumed : 24943
% 161.26/24.08 % ...remaining for further processing : 11116
% 161.26/24.08 % Other redundant clauses eliminated : 2
% 161.26/24.08 % Clauses deleted for lack of memory : 0
% 161.26/24.08 % Backward-subsumed : 518
% 161.26/24.08 % Backward-rewritten : 1133
% 161.26/24.08 % Generated clauses : 402024
% 161.26/24.08 % ...of the previous two non-redundant : 398311
% 161.26/24.08 % ...aggressively subsumed : 0
% 161.26/24.08 % Contextual simplify-reflections : 0
% 161.26/24.08 % Paramodulations : 401895
% 161.26/24.08 % Factorizations : 0
% 161.26/24.08 % NegExts : 0
% 161.26/24.08 % Equation resolutions : 129
% 161.26/24.08 % Disequality decompositions : 0
% 161.26/24.08 % Total rewrite steps : 50371
% 161.26/24.08 % ...of those cached : 43003
% 161.26/24.08 % Propositional unsat checks : 0
% 161.26/24.08 % Propositional check models : 0
% 161.26/24.08 % Propositional check unsatisfiable : 0
% 161.26/24.08 % Propositional clauses : 0
% 161.26/24.08 % Propositional clauses after purity: 0
% 161.26/24.08 % Propositional unsat core size : 0
% 161.26/24.08 % Propositional preprocessing time : 0.000
% 161.26/24.08 % Propositional encoding time : 0.000
% 161.26/24.08 % Propositional solver time : 0.000
% 161.26/24.08 % Success case prop preproc time : 0.000
% 161.26/24.08 % Success case prop encoding time : 0.000
% 161.26/24.08 % Success case prop solver time : 0.000
% 161.26/24.08 % Current number of processed clauses : 9463
% 161.26/24.08 % Positive orientable unit clauses : 459
% 161.26/24.08 % Positive unorientable unit clauses: 175
% 161.26/24.08 % Negative unit clauses : 1
% 161.26/24.08 % Non-unit-clauses : 8828
% 161.26/24.08 % Current number of unprocessed clauses: 355180
% 161.26/24.08 % ...number of literals in the above : 649074
% 161.26/24.08 % Current number of archived formulas : 0
% 161.26/24.08 % Current number of archived clauses : 1651
% 161.26/24.08 % Clause-clause subsumption calls (NU) : 3447847
% 161.26/24.08 % Rec. Clause-clause subsumption calls : 3446788
% 161.26/24.08 % Non-unit clause-clause subsumptions : 21058
% 161.26/24.08 % Unit Clause-clause subsumption calls : 11425
% 161.26/24.08 % Rewrite failures with RHS unbound : 0
% 161.26/24.08 % BW rewrite match attempts : 742452
% 161.26/24.08 % BW rewrite match successes : 2674
% 161.26/24.08 % Condensation attempts : 0
% 161.26/24.08 % Condensation successes : 0
% 161.26/24.08 % Termbank termtop insertions : 17138455
% 161.26/24.08 % Search garbage collected termcells : 12
% 161.26/24.08
% 161.26/24.08 % -------------------------------------------------
% 161.26/24.08 % User time : 22.658 s
% 161.26/24.08 % System time : 0.423 s
% 161.26/24.08 % Total time : 23.081 s
% 161.26/24.08 % Maximum resident set size: 3376 pages
% 161.26/24.08
% 161.26/24.08 % -------------------------------------------------
% 161.26/24.08 % User time : 110.957 s
% 161.26/24.08 % System time : 3.284 s
% 161.26/24.08 % Total time : 114.241 s
% 161.26/24.08 % Maximum resident set size: 4864 pages
% 161.26/24.08 % E exiting
%------------------------------------------------------------------------------