%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP701-1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:27:06 PM UTC 2026
% Result : Unsatisfiable 34.08s 20.44s
% Output : CNFRefutation 34.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 69
% Number of leaves : 11
% Syntax : Number of clauses : 284 ( 284 unt; 0 nHn; 3 RR)
% Number of literals : 284 ( 283 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 551 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c08,axiom,
mult(mult(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,mult(X2,mult(X2,X3))),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c10,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
cnf(c07,axiom,
mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c09,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(goals,negated_conjecture,
mult(a,i(mult(b,a))) != i(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_11,axiom,
mult(mult(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,mult(X2,mult(X2,X3))),X2),
c08 ).
cnf(c_0_12,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_13,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_14,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_15,plain,
mult(mult(X1,mult(X2,X2)),X2) = mult(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).
cnf(c_0_16,axiom,
mult(i(X1),X1) = unit,
c10 ).
cnf(c_0_17,plain,
rd(mult(mult(X1,X2),mult(X2,X2)),X2) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
mult(mult(i(mult(X1,X1)),X1),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_13]) ).
cnf(c_0_19,axiom,
mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
c07 ).
cnf(c_0_20,plain,
mult(i(X1),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_16]),c_0_13]),c_0_14]) ).
cnf(c_0_21,plain,
rd(X1,mult(X1,X1)) = mult(i(mult(X1,X1)),X1),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_22,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_23,axiom,
mult(X1,i(X1)) = unit,
c09 ).
cnf(c_0_24,plain,
mult(mult(X1,X1),mult(X1,X2)) = mult(X1,mult(mult(X1,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_13]) ).
cnf(c_0_25,plain,
mult(i(mult(X1,X1)),X1) = i(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
ld(X1,unit) = i(X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
mult(X1,mult(mult(X1,X1),i(X1))) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_12]) ).
cnf(c_0_28,plain,
rd(i(X1),X1) = i(mult(X1,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).
cnf(c_0_29,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_16]),c_0_26]) ).
cnf(c_0_30,plain,
mult(mult(X1,mult(X1,X2)),X1) = mult(X1,mult(X1,mult(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_13]),c_0_13]) ).
cnf(c_0_31,plain,
mult(mult(X1,X1),i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_22]) ).
cnf(c_0_32,plain,
rd(X1,i(X1)) = i(mult(i(X1),i(X1))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
rd(mult(X1,mult(X1,mult(X2,X1))),X1) = mult(X1,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_34,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_35,plain,
i(mult(i(X1),i(X1))) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_31]),c_0_32]) ).
cnf(c_0_36,plain,
mult(X1,mult(X1,rd(X2,X1))) = rd(mult(X1,mult(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
mult(X1,mult(i(X1),i(X1))) = i(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_13]),c_0_14]) ).
cnf(c_0_38,plain,
mult(i(X1),i(X1)) = i(mult(X1,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_39,plain,
ld(i(X1),X1) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_40,plain,
ld(X1,rd(mult(X1,mult(X1,X2)),X1)) = mult(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_41,plain,
mult(X1,i(mult(X1,X1))) = i(X1),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
rd(unit,X1) = i(X1),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_43,plain,
ld(X1,i(X1)) = mult(i(X1),i(X1)),
inference(spm,[status(thm)],[c_0_39,c_0_29]) ).
cnf(c_0_44,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_45,plain,
mult(mult(mult(X1,X2),X1),X1) = mult(X1,mult(mult(X2,X1),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_12]) ).
cnf(c_0_46,plain,
mult(X1,rd(i(mult(X1,X1)),X1)) = i(mult(X1,X1)),
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_23]),c_0_42]),c_0_43]),c_0_38]) ).
cnf(c_0_47,plain,
mult(X1,mult(X1,mult(ld(X1,X2),X1))) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_48,plain,
rd(mult(X1,mult(mult(X2,X1),X1)),X1) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_45]) ).
cnf(c_0_49,plain,
rd(mult(mult(X1,X2),mult(X2,mult(X3,X2))),X2) = mult(X1,mult(X2,mult(X2,X3))),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_50,plain,
mult(i(X1),mult(X1,X2)) = mult(X1,mult(i(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_46]),c_0_25]),c_0_34]),c_0_25]) ).
cnf(c_0_51,plain,
mult(X1,mult(ld(X1,X2),X1)) = ld(X1,mult(mult(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_22,c_0_47]) ).
cnf(c_0_52,plain,
mult(mult(X1,rd(X2,X1)),X1) = rd(mult(X1,mult(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_48,c_0_34]) ).
cnf(c_0_53,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,mult(X1,mult(i(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_16]),c_0_13]),c_0_50]),c_0_50]) ).
cnf(c_0_54,plain,
ld(X1,ld(X1,mult(mult(X1,X2),X1))) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_55,plain,
mult(mult(X1,rd(X2,X1)),X1) = mult(X1,mult(X1,mult(i(X1),X2))),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,plain,
mult(X1,mult(mult(ld(X1,X2),X1),X1)) = mult(mult(X2,X1),X1),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_57,plain,
mult(ld(X1,rd(X2,X1)),X1) = mult(i(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_22]),c_0_22]) ).
cnf(c_0_58,plain,
mult(mult(ld(X1,X2),X1),X1) = ld(X1,mult(mult(X2,X1),X1)),
inference(spm,[status(thm)],[c_0_22,c_0_56]) ).
cnf(c_0_59,plain,
ld(X1,rd(X2,X1)) = rd(mult(i(X1),X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_57]) ).
cnf(c_0_60,plain,
ld(X1,mult(X2,X1)) = mult(mult(i(X1),X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_34]),c_0_34]) ).
cnf(c_0_61,plain,
rd(mult(i(X1),mult(X2,X1)),X1) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_59,c_0_14]) ).
cnf(c_0_62,plain,
mult(mult(i(X1),rd(X2,X1)),X1) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_60,c_0_34]) ).
cnf(c_0_63,plain,
mult(ld(X1,X2),X1) = mult(i(X1),mult(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_61]) ).
cnf(c_0_64,plain,
mult(mult(X1,i(X2)),X2) = mult(mult(X1,X2),i(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_46]),c_0_41]),c_0_34]),c_0_41]) ).
cnf(c_0_65,plain,
rd(ld(X1,X2),X1) = mult(i(X1),rd(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_62]) ).
cnf(c_0_66,plain,
mult(i(X1),mult(mult(X1,X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_63,c_0_22]) ).
cnf(c_0_67,plain,
mult(X1,mult(mult(X1,X1),mult(X2,X1))) = mult(X1,mult(X1,mult(mult(X1,X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_30]),c_0_24]) ).
cnf(c_0_68,plain,
rd(mult(mult(X1,X2),i(X2)),X2) = mult(X1,i(X2)),
inference(spm,[status(thm)],[c_0_14,c_0_64]) ).
cnf(c_0_69,plain,
mult(X1,rd(mult(i(X1),X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_59]) ).
cnf(c_0_70,plain,
mult(i(X1),rd(mult(X1,X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_22]) ).
cnf(c_0_71,plain,
rd(mult(X1,X2),mult(mult(X2,X1),X2)) = i(X2),
inference(spm,[status(thm)],[c_0_14,c_0_66]) ).
cnf(c_0_72,plain,
mult(mult(X1,X1),mult(X2,X1)) = mult(X1,mult(mult(X1,X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_67]),c_0_22]) ).
cnf(c_0_73,plain,
mult(rd(X1,X2),i(X2)) = rd(mult(X1,i(X2)),X2),
inference(spm,[status(thm)],[c_0_68,c_0_34]) ).
cnf(c_0_74,plain,
mult(X1,rd(rd(X2,X1),X1)) = rd(rd(mult(X1,X2),X1),X1),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
rd(X1,mult(X2,mult(X2,mult(i(X2),X1)))) = i(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_55]),c_0_34]) ).
cnf(c_0_76,plain,
mult(X1,mult(X1,mult(X1,mult(i(X1),X2)))) = mult(mult(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_34]),c_0_52]),c_0_53]) ).
cnf(c_0_77,plain,
mult(rd(X1,i(X2)),X2) = rd(mult(X1,X2),i(X2)),
inference(spm,[status(thm)],[c_0_73,c_0_29]) ).
cnf(c_0_78,plain,
mult(rd(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_74]),c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_79,plain,
rd(mult(X1,X2),mult(mult(X1,X1),X2)) = i(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_50]),c_0_76]) ).
cnf(c_0_80,plain,
mult(mult(X1,mult(i(X1),X2)),X1) = mult(X1,mult(i(X1),mult(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_60]),c_0_50]),c_0_63]) ).
cnf(c_0_81,plain,
rd(rd(mult(X1,X2),i(X2)),X2) = rd(X1,i(X2)),
inference(spm,[status(thm)],[c_0_14,c_0_77]) ).
cnf(c_0_82,plain,
rd(mult(X1,X2),X1) = mult(X1,mult(X2,i(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_23]),c_0_12]) ).
cnf(c_0_83,plain,
mult(i(X1),mult(mult(X1,X1),X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_79]) ).
cnf(c_0_84,plain,
mult(mult(mult(X1,X1),X2),X1) = mult(X1,mult(mult(X1,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_76]),c_0_80]),c_0_76]),c_0_72]) ).
cnf(c_0_85,plain,
rd(rd(X1,i(X2)),X2) = rd(rd(X1,X2),i(X2)),
inference(spm,[status(thm)],[c_0_81,c_0_34]) ).
cnf(c_0_86,plain,
rd(mult(X1,X2),i(X1)) = mult(X1,mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_29]),c_0_84]),c_0_50]),c_0_66]) ).
cnf(c_0_87,plain,
mult(X1,rd(rd(X2,X1),i(X1))) = rd(rd(mult(X1,X2),X1),i(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_69]),c_0_85]),c_0_29]),c_0_85]) ).
cnf(c_0_88,plain,
rd(mult(X1,mult(X2,i(X1))),i(X1)) = ld(i(X1),X2),
inference(spm,[status(thm)],[c_0_61,c_0_29]) ).
cnf(c_0_89,plain,
rd(rd(X1,X2),i(X2)) = mult(X2,mult(i(X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_69]),c_0_34]) ).
cnf(c_0_90,plain,
mult(mult(i(mult(X1,mult(X1,X2))),X1),mult(X1,mult(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_16]),c_0_13]) ).
cnf(c_0_91,plain,
mult(X1,mult(X1,mult(i(X1),X2))) = ld(i(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_82]),c_0_88]),c_0_89]) ).
cnf(c_0_92,plain,
mult(X1,mult(mult(i(X1),X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_60]) ).
cnf(c_0_93,plain,
mult(mult(i(ld(i(X1),X2)),X1),mult(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_94,plain,
mult(i(ld(i(X1),X2)),X1) = rd(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_93]) ).
cnf(c_0_95,plain,
rd(rd(X1,mult(X2,X1)),X1) = i(ld(i(X1),X2)),
inference(spm,[status(thm)],[c_0_14,c_0_94]) ).
cnf(c_0_96,plain,
ld(i(X1),rd(X2,X1)) = rd(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_70]) ).
cnf(c_0_97,plain,
rd(rd(X1,X2),X1) = i(mult(X1,mult(X2,i(X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_34]),c_0_96]),c_0_82]) ).
cnf(c_0_98,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_44]) ).
cnf(c_0_99,plain,
i(mult(X1,mult(ld(X2,X1),i(X1)))) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_100,plain,
mult(X1,mult(X1,mult(i(X1),mult(i(X1),X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_75]),c_0_50]),c_0_50]) ).
cnf(c_0_101,plain,
mult(mult(X1,mult(X2,i(X1))),X1) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_82]) ).
cnf(c_0_102,plain,
mult(X1,mult(ld(X2,X1),i(X1))) = i(rd(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_99]) ).
cnf(c_0_103,plain,
mult(mult(rd(X1,mult(X2,mult(X2,X3))),X2),mult(X2,mult(X3,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_34]) ).
cnf(c_0_104,plain,
mult(mult(i(X1),X2),mult(mult(i(X2),X1),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_100]),c_0_92]) ).
cnf(c_0_105,plain,
mult(i(rd(X1,X2)),X2) = mult(X2,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_106,plain,
mult(rd(X1,mult(X2,mult(X2,X3))),X2) = rd(mult(X1,X2),mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_14,c_0_103]) ).
cnf(c_0_107,plain,
mult(mult(X1,ld(X2,X1)),ld(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_62]) ).
cnf(c_0_108,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_109,plain,
rd(X1,mult(mult(i(X1),X2),X1)) = mult(i(X2),X1),
inference(spm,[status(thm)],[c_0_94,c_0_22]) ).
cnf(c_0_110,plain,
mult(rd(X1,ld(i(X2),X3)),X2) = rd(mult(X1,X2),mult(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_91]),c_0_92]) ).
cnf(c_0_111,plain,
rd(X1,ld(X1,X2)) = mult(X1,ld(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_107]) ).
cnf(c_0_112,plain,
ld(mult(i(X1),X2),X2) = mult(mult(i(X2),X1),X2),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_113,plain,
mult(mult(i(X1),ld(X2,i(X1))),X1) = i(mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_16]),c_0_42]) ).
cnf(c_0_114,plain,
ld(mult(X1,X2),X2) = mult(mult(i(X2),i(X1)),X2),
inference(spm,[status(thm)],[c_0_112,c_0_29]) ).
cnf(c_0_115,plain,
ld(i(X1),mult(X1,X2)) = mult(mult(X1,X1),X2),
inference(spm,[status(thm)],[c_0_108,c_0_79]) ).
cnf(c_0_116,plain,
mult(ld(X1,i(X2)),X2) = mult(X2,i(mult(X1,X2))),
inference(spm,[status(thm)],[c_0_92,c_0_113]) ).
cnf(c_0_117,plain,
mult(mult(i(X1),i(rd(X2,X1))),X1) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_114,c_0_34]) ).
cnf(c_0_118,plain,
mult(X1,ld(mult(X1,X1),X2)) = mult(i(X1),X2),
inference(spm,[status(thm)],[c_0_83,c_0_44]) ).
cnf(c_0_119,plain,
ld(X1,mult(i(X1),X2)) = mult(i(mult(X1,X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_29]),c_0_38]) ).
cnf(c_0_120,plain,
mult(X1,i(mult(rd(i(X1),X2),X1))) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_116,c_0_108]) ).
cnf(c_0_121,plain,
rd(ld(X1,X2),X2) = mult(i(X2),i(rd(X1,X2))),
inference(spm,[status(thm)],[c_0_14,c_0_117]) ).
cnf(c_0_122,plain,
ld(mult(X1,X1),X2) = mult(i(mult(X1,X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_118]),c_0_119]) ).
cnf(c_0_123,plain,
i(mult(rd(i(X1),X2),X1)) = mult(mult(i(X1),X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_120]),c_0_60]) ).
cnf(c_0_124,plain,
mult(i(X1),i(rd(mult(X2,X2),X1))) = i(mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_14]) ).
cnf(c_0_125,plain,
mult(rd(i(X1),X2),X1) = i(mult(mult(i(X1),X2),X1)),
inference(spm,[status(thm)],[c_0_29,c_0_123]) ).
cnf(c_0_126,plain,
ld(i(mult(X1,X1)),X2) = mult(mult(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_38]),c_0_29]) ).
cnf(c_0_127,plain,
mult(mult(X1,X1),mult(i(mult(X1,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_115,c_0_83]),c_0_29]),c_0_22]),c_0_38]),c_0_50]) ).
cnf(c_0_128,plain,
ld(i(X1),i(mult(X2,X2))) = i(rd(mult(X2,X2),X1)),
inference(spm,[status(thm)],[c_0_22,c_0_124]) ).
cnf(c_0_129,plain,
mult(rd(X1,X2),i(X1)) = i(mult(mult(X1,X2),i(X1))),
inference(spm,[status(thm)],[c_0_125,c_0_29]) ).
cnf(c_0_130,plain,
rd(X1,mult(mult(X2,X2),X1)) = i(mult(X2,X2)),
inference(spm,[status(thm)],[c_0_98,c_0_126]) ).
cnf(c_0_131,plain,
mult(mult(X1,mult(X2,X1)),i(X1)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_86]) ).
cnf(c_0_132,plain,
rd(rd(mult(X1,i(X2)),X2),i(X2)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_73]) ).
cnf(c_0_133,plain,
rd(X1,i(mult(X2,X2))) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_127]),c_0_92]) ).
cnf(c_0_134,plain,
ld(i(X1),mult(X1,mult(i(X1),X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_50]) ).
cnf(c_0_135,plain,
i(rd(i(mult(X1,X1)),X2)) = ld(i(X2),mult(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_38]),c_0_29]) ).
cnf(c_0_136,plain,
mult(i(mult(X1,X1)),i(X2)) = i(mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).
cnf(c_0_137,plain,
rd(X1,mult(X2,X2)) = mult(X1,i(mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_34]) ).
cnf(c_0_138,plain,
mult(mult(X1,X2),i(X2)) = mult(X2,mult(i(X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_101]),c_0_50]),c_0_64]) ).
cnf(c_0_139,plain,
mult(ld(i(X1),X2),X1) = mult(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_44]) ).
cnf(c_0_140,plain,
mult(i(X1),ld(X2,i(X1))) = rd(i(mult(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_14,c_0_113]) ).
cnf(c_0_141,plain,
mult(X1,rd(X2,i(X1))) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_101,c_0_34]) ).
cnf(c_0_142,plain,
ld(X1,rd(X2,i(X1))) = rd(mult(i(X1),X2),i(X1)),
inference(spm,[status(thm)],[c_0_96,c_0_29]) ).
cnf(c_0_143,plain,
mult(mult(X1,X1),mult(i(X1),X2)) = mult(X1,X2),
inference(rw,[status(thm)],[c_0_134,c_0_115]) ).
cnf(c_0_144,plain,
i(ld(i(X1),mult(X2,X2))) = rd(i(mult(X2,X2)),X1),
inference(spm,[status(thm)],[c_0_29,c_0_135]) ).
cnf(c_0_145,plain,
ld(X1,mult(X2,X2)) = mult(i(X1),mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_136]),c_0_137]),c_0_64]),c_0_138]),c_0_127]) ).
cnf(c_0_146,plain,
mult(ld(X1,X2),i(X1)) = mult(i(X1),mult(X2,i(X1))),
inference(spm,[status(thm)],[c_0_139,c_0_29]) ).
cnf(c_0_147,plain,
rd(i(mult(X1,i(X2))),i(X2)) = mult(X2,ld(X1,X2)),
inference(spm,[status(thm)],[c_0_140,c_0_29]) ).
cnf(c_0_148,plain,
mult(i(X1),rd(X2,X1)) = mult(mult(i(X1),X2),i(X1)),
inference(spm,[status(thm)],[c_0_141,c_0_29]) ).
cnf(c_0_149,plain,
rd(rd(mult(X1,X2),mult(X3,X2)),X2) = rd(X1,ld(i(X2),X3)),
inference(spm,[status(thm)],[c_0_14,c_0_110]) ).
cnf(c_0_150,plain,
ld(X1,rd(X2,i(X1))) = mult(i(X1),mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_142,c_0_82]),c_0_29]) ).
cnf(c_0_151,plain,
rd(mult(i(X1),X2),mult(X1,X2)) = i(mult(X1,X1)),
inference(spm,[status(thm)],[c_0_130,c_0_143]) ).
cnf(c_0_152,plain,
rd(i(mult(X1,X1)),X2) = i(mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_145]),c_0_29]) ).
cnf(c_0_153,plain,
mult(mult(i(X1),mult(X2,i(X1))),X1) = mult(i(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_146]),c_0_29]),c_0_29]),c_0_44]) ).
cnf(c_0_154,plain,
mult(X1,ld(rd(X2,i(X1)),X1)) = rd(i(X2),i(X1)),
inference(spm,[status(thm)],[c_0_147,c_0_34]) ).
cnf(c_0_155,plain,
mult(X1,mult(mult(i(X1),X2),i(X1))) = mult(X2,i(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_34]),c_0_148]) ).
cnf(c_0_156,plain,
rd(X1,mult(X2,mult(X1,X1))) = rd(i(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_79]),c_0_145]),c_0_29]) ).
cnf(c_0_157,plain,
ld(X1,ld(i(X1),X2)) = mult(mult(X2,X1),i(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_61]),c_0_29]),c_0_66]),c_0_64]) ).
cnf(c_0_158,plain,
rd(X1,mult(i(mult(X2,X2)),X1)) = mult(X2,X2),
inference(spm,[status(thm)],[c_0_98,c_0_122]) ).
cnf(c_0_159,plain,
rd(i(X1),ld(i(X2),X1)) = i(mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_151]),c_0_152]) ).
cnf(c_0_160,plain,
i(mult(i(X1),mult(X2,X2))) = mult(i(mult(X2,X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_130]),c_0_153]) ).
cnf(c_0_161,plain,
ld(rd(X1,X2),i(X2)) = mult(X2,mult(i(X1),i(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_154]),c_0_29]),c_0_148]),c_0_155]),c_0_29]) ).
cnf(c_0_162,plain,
ld(rd(i(X1),X2),X1) = mult(X2,mult(X1,X1)),
inference(spm,[status(thm)],[c_0_108,c_0_156]) ).
cnf(c_0_163,plain,
ld(X1,ld(i(X1),X2)) = mult(X1,mult(i(X1),X2)),
inference(rw,[status(thm)],[c_0_157,c_0_138]) ).
cnf(c_0_164,plain,
i(mult(X1,i(mult(X2,X2)))) = mult(mult(X2,X2),i(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_158]),c_0_131]) ).
cnf(c_0_165,plain,
rd(i(X1),ld(X2,X1)) = mult(i(mult(X1,X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_29]),c_0_160]) ).
cnf(c_0_166,plain,
mult(X1,mult(i(X1),ld(X2,X1))) = ld(mult(X1,mult(i(X1),X2)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_89]),c_0_29]),c_0_29]),c_0_105]),c_0_50]) ).
cnf(c_0_167,plain,
mult(X1,ld(mult(X1,X2),X1)) = mult(i(mult(X1,mult(X2,i(X1)))),X1),
inference(spm,[status(thm)],[c_0_105,c_0_82]) ).
cnf(c_0_168,plain,
i(mult(rd(X1,X2),rd(X1,X2))) = rd(mult(i(rd(X1,X2)),X2),X1),
inference(spm,[status(thm)],[c_0_151,c_0_34]) ).
cnf(c_0_169,plain,
rd(mult(mult(X1,X2),mult(X2,X3)),X2) = mult(X1,mult(X2,mult(mult(X2,X3),i(X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_34]),c_0_36]),c_0_82]) ).
cnf(c_0_170,plain,
rd(mult(X1,mult(i(X1),X2)),mult(X1,X2)) = i(X1),
inference(spm,[status(thm)],[c_0_14,c_0_50]) ).
cnf(c_0_171,plain,
mult(ld(X1,i(X2)),mult(X2,X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_162,c_0_98]) ).
cnf(c_0_172,plain,
mult(X1,mult(i(X1),mult(X2,X2))) = mult(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_145]),c_0_29]),c_0_22]) ).
cnf(c_0_173,plain,
rd(mult(X1,X1),X2) = mult(mult(X1,X1),i(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_38]),c_0_29]),c_0_164]) ).
cnf(c_0_174,plain,
ld(mult(i(mult(X1,X1)),X2),i(X1)) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_108,c_0_165]) ).
cnf(c_0_175,plain,
mult(i(mult(X1,X1)),ld(i(X1),X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_119,c_0_44]) ).
cnf(c_0_176,plain,
ld(i(X1),ld(X2,X1)) = mult(i(mult(X2,i(X1))),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_166]),c_0_167]),c_0_155]) ).
cnf(c_0_177,plain,
mult(mult(i(mult(X1,X1)),X2),ld(X2,X1)) = i(X1),
inference(spm,[status(thm)],[c_0_34,c_0_165]) ).
cnf(c_0_178,plain,
ld(i(ld(i(X1),X2)),rd(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_94]) ).
cnf(c_0_179,plain,
i(mult(rd(X1,X2),rd(X1,X2))) = rd(mult(X2,ld(X1,X2)),X1),
inference(rw,[status(thm)],[c_0_168,c_0_105]) ).
cnf(c_0_180,plain,
rd(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,i(X2)))),
inference(spm,[status(thm)],[c_0_169,c_0_100]) ).
cnf(c_0_181,plain,
mult(mult(X1,X1),i(ld(X2,X1))) = i(ld(X2,i(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_171]),c_0_172]),c_0_173]) ).
cnf(c_0_182,plain,
ld(ld(i(X1),X2),X1) = ld(ld(X1,X2),i(X1)),
inference(spm,[status(thm)],[c_0_174,c_0_175]) ).
cnf(c_0_183,plain,
ld(X1,ld(X2,i(X1))) = mult(i(mult(X2,X1)),i(X1)),
inference(spm,[status(thm)],[c_0_176,c_0_29]) ).
cnf(c_0_184,plain,
i(rd(X1,mult(X2,X1))) = rd(X1,mult(i(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_177,c_0_178]),c_0_179]),c_0_60]),c_0_180]),c_0_138]),c_0_100]),c_0_181]),c_0_94]) ).
cnf(c_0_185,plain,
ld(ld(X1,ld(X2,X1)),i(X1)) = mult(i(X1),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_182,c_0_183]),c_0_29]),c_0_114]),c_0_29]),c_0_153]),c_0_29]) ).
cnf(c_0_186,plain,
rd(X1,mult(X1,ld(X2,X1))) = i(rd(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_34]),c_0_105]) ).
cnf(c_0_187,plain,
ld(X1,ld(X2,X1)) = rd(i(X1),mult(i(X1),X2)),
inference(spm,[status(thm)],[c_0_98,c_0_185]) ).
cnf(c_0_188,plain,
rd(X1,ld(X2,i(X1))) = mult(mult(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_29]),c_0_38]),c_0_29]) ).
cnf(c_0_189,plain,
ld(i(rd(X1,X2)),X1) = mult(X1,ld(X2,X1)),
inference(spm,[status(thm)],[c_0_108,c_0_186]) ).
cnf(c_0_190,plain,
mult(X1,rd(i(X1),mult(i(X1),X2))) = ld(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_187]) ).
cnf(c_0_191,plain,
mult(X1,mult(i(mult(X1,X1)),X2)) = mult(i(X1),X2),
inference(spm,[status(thm)],[c_0_44,c_0_119]) ).
cnf(c_0_192,plain,
ld(mult(X1,X2),mult(X2,mult(i(X2),X1))) = i(X2),
inference(spm,[status(thm)],[c_0_22,c_0_138]) ).
cnf(c_0_193,plain,
mult(mult(X1,X1),rd(i(X1),X2)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_188,c_0_108]) ).
cnf(c_0_194,plain,
mult(X1,ld(ld(X2,X1),X1)) = ld(i(X2),X1),
inference(spm,[status(thm)],[c_0_189,c_0_98]) ).
cnf(c_0_195,plain,
ld(ld(X1,i(X2)),X2) = mult(X2,i(rd(i(X2),X1))),
inference(spm,[status(thm)],[c_0_190,c_0_186]) ).
cnf(c_0_196,plain,
mult(mult(i(X1),X2),mult(X1,X1)) = mult(i(X1),mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_41]),c_0_133]),c_0_29]),c_0_191]) ).
cnf(c_0_197,plain,
mult(i(rd(X1,X2)),mult(X1,X1)) = i(rd(i(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_172]),c_0_145]) ).
cnf(c_0_198,plain,
ld(ld(X1,X2),X2) = rd(i(X2),mult(i(X2),i(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_194]),c_0_187]) ).
cnf(c_0_199,plain,
mult(i(X1),i(rd(i(X1),X2))) = rd(i(X1),mult(i(X1),i(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_171,c_0_195]),c_0_29]),c_0_196]),c_0_197]),c_0_29]),c_0_198]) ).
cnf(c_0_200,plain,
mult(mult(X1,X2),ld(X1,rd(X1,X2))) = X1,
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_201,plain,
mult(X1,i(rd(X1,X2))) = rd(X1,mult(X1,i(X2))),
inference(spm,[status(thm)],[c_0_199,c_0_29]) ).
cnf(c_0_202,plain,
ld(X1,rd(X1,X2)) = ld(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_200]) ).
cnf(c_0_203,plain,
ld(rd(X1,X2),i(X1)) = mult(X2,i(mult(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_29]),c_0_38]) ).
cnf(c_0_204,plain,
ld(mult(X1,mult(X1,i(X2))),X1) = i(rd(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_201]),c_0_202]) ).
cnf(c_0_205,plain,
ld(mult(mult(X1,X1),X2),X1) = ld(X2,i(X1)),
inference(spm,[status(thm)],[c_0_108,c_0_188]) ).
cnf(c_0_206,plain,
rd(i(mult(mult(i(X1),X2),X1)),X1) = rd(i(X1),X2),
inference(spm,[status(thm)],[c_0_14,c_0_125]) ).
cnf(c_0_207,plain,
mult(X1,mult(i(X1),ld(X1,X2))) = mult(i(X1),X2),
inference(spm,[status(thm)],[c_0_50,c_0_44]) ).
cnf(c_0_208,plain,
mult(mult(X1,X2),i(mult(X1,X1))) = mult(X1,mult(X2,i(mult(X1,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_38]),c_0_29]),c_0_29]) ).
cnf(c_0_209,plain,
mult(ld(X1,X2),i(mult(X2,X2))) = ld(X1,i(X2)),
inference(spm,[status(thm)],[c_0_203,c_0_98]) ).
cnf(c_0_210,plain,
ld(mult(X1,mult(X1,X2)),X1) = i(rd(X1,i(X2))),
inference(spm,[status(thm)],[c_0_204,c_0_29]) ).
cnf(c_0_211,plain,
ld(mult(i(X1),X2),i(X1)) = ld(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_205,c_0_143]) ).
cnf(c_0_212,plain,
rd(i(X1),i(rd(X2,X1))) = rd(i(ld(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_206,c_0_117]) ).
cnf(c_0_213,plain,
mult(i(X1),ld(X1,X2)) = ld(X1,mult(i(X1),X2)),
inference(spm,[status(thm)],[c_0_22,c_0_207]) ).
cnf(c_0_214,plain,
ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_66]) ).
cnf(c_0_215,plain,
rd(i(mult(i(X1),X2)),X1) = rd(i(X1),mult(X2,i(X1))),
inference(spm,[status(thm)],[c_0_206,c_0_153]) ).
cnf(c_0_216,plain,
ld(i(rd(X1,X2)),i(X1)) = mult(X1,ld(X2,i(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_186]),c_0_208]),c_0_209]) ).
cnf(c_0_217,plain,
ld(ld(X1,X2),i(X2)) = mult(i(X2),i(rd(X2,X1))),
inference(spm,[status(thm)],[c_0_195,c_0_29]) ).
cnf(c_0_218,plain,
i(rd(i(ld(X1,X2)),X2)) = ld(mult(X1,i(X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_148]),c_0_211]),c_0_155]),c_0_212]) ).
cnf(c_0_219,plain,
mult(X1,ld(i(X1),X2)) = ld(i(X1),mult(X1,X2)),
inference(spm,[status(thm)],[c_0_213,c_0_29]) ).
cnf(c_0_220,plain,
mult(mult(X1,X2),mult(X1,X1)) = mult(X1,mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_196]),c_0_126]),c_0_143]),c_0_143]) ).
cnf(c_0_221,plain,
rd(i(mult(X1,X2)),i(X1)) = rd(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_215,c_0_29]) ).
cnf(c_0_222,plain,
mult(X1,mult(i(X1),i(rd(X1,X2)))) = ld(i(X2),i(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_98]),c_0_217]) ).
cnf(c_0_223,plain,
rd(i(ld(X1,X2)),X2) = i(ld(mult(X1,i(X2)),X2)),
inference(spm,[status(thm)],[c_0_29,c_0_218]) ).
cnf(c_0_224,plain,
ld(X1,ld(i(X1),mult(X1,X2))) = ld(i(X1),X2),
inference(spm,[status(thm)],[c_0_22,c_0_219]) ).
cnf(c_0_225,plain,
mult(mult(X1,mult(mult(mult(X2,X1),X1),X1)),X1) = mult(X1,mult(mult(mult(X2,X1),X1),mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_19]),c_0_45]),c_0_220]) ).
cnf(c_0_226,plain,
mult(mult(rd(X1,X2),ld(mult(X1,X2),X1)),X2) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_202]) ).
cnf(c_0_227,plain,
i(ld(mult(i(X1),X2),i(X2))) = mult(rd(X2,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_223]),c_0_29]),c_0_109]),c_0_29]) ).
cnf(c_0_228,plain,
ld(i(X1),ld(X1,X2)) = ld(X1,ld(i(X1),X2)),
inference(spm,[status(thm)],[c_0_224,c_0_44]) ).
cnf(c_0_229,plain,
rd(ld(i(X1),X2),X1) = mult(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_69,c_0_44]) ).
cnf(c_0_230,plain,
rd(mult(mult(X1,X2),X1),i(X1)) = mult(mult(X1,mult(X2,X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_86]),c_0_29]),c_0_29]) ).
cnf(c_0_231,plain,
mult(mult(X1,mult(X2,X1)),X1) = mult(X1,mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_34]),c_0_34]) ).
cnf(c_0_232,plain,
ld(mult(i(X1),X2),i(X2)) = i(mult(rd(X2,X1),X2)),
inference(spm,[status(thm)],[c_0_29,c_0_227]) ).
cnf(c_0_233,plain,
ld(i(X1),ld(X1,X2)) = mult(mult(X2,X1),i(X1)),
inference(rw,[status(thm)],[c_0_228,c_0_157]) ).
cnf(c_0_234,plain,
ld(X1,i(rd(X2,X1))) = mult(ld(X2,X1),i(X1)),
inference(spm,[status(thm)],[c_0_22,c_0_102]) ).
cnf(c_0_235,plain,
mult(ld(X1,X2),i(X2)) = mult(i(X2),i(mult(X1,i(X2)))),
inference(spm,[status(thm)],[c_0_116,c_0_29]) ).
cnf(c_0_236,plain,
mult(X1,rd(mult(X2,i(X1)),X1)) = rd(mult(mult(X1,X2),i(X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_60]),c_0_29]) ).
cnf(c_0_237,plain,
rd(mult(mult(X1,X2),X1),i(X1)) = mult(X1,mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[c_0_230,c_0_231]) ).
cnf(c_0_238,plain,
i(mult(rd(X1,i(X2)),X1)) = ld(mult(X2,X1),i(X1)),
inference(spm,[status(thm)],[c_0_232,c_0_29]) ).
cnf(c_0_239,plain,
ld(i(X1),ld(X1,X2)) = mult(X1,mult(i(X1),X2)),
inference(rw,[status(thm)],[c_0_233,c_0_138]) ).
cnf(c_0_240,plain,
ld(X1,i(rd(X2,X1))) = mult(i(X1),i(mult(X2,i(X1)))),
inference(rw,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_241,plain,
mult(X1,mult(ld(X1,X2),mult(X1,X1))) = mult(X2,mult(X1,X1)),
inference(spm,[status(thm)],[c_0_220,c_0_44]) ).
cnf(c_0_242,plain,
mult(X1,rd(X2,X1)) = mult(mult(X1,X2),i(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_77]),c_0_29]),c_0_236]),c_0_34]),c_0_29]) ).
cnf(c_0_243,plain,
rd(mult(X1,X2),i(X2)) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_100]),c_0_220]),c_0_196]),c_0_196]),c_0_100]) ).
cnf(c_0_244,plain,
rd(i(X1),i(rd(X2,X1))) = i(ld(mult(X2,i(X1)),X1)),
inference(rw,[status(thm)],[c_0_212,c_0_223]) ).
cnf(c_0_245,plain,
i(ld(mult(X1,X2),i(X2))) = mult(rd(X2,i(X1)),X2),
inference(spm,[status(thm)],[c_0_29,c_0_238]) ).
cnf(c_0_246,plain,
ld(i(X1),rd(X2,X1)) = mult(X1,mult(X2,i(X1))),
inference(rw,[status(thm)],[c_0_96,c_0_82]) ).
cnf(c_0_247,plain,
mult(X1,mult(i(X1),i(rd(X2,X1)))) = i(mult(X2,i(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_22]) ).
cnf(c_0_248,plain,
rd(X1,ld(i(X1),X2)) = mult(X1,ld(X2,i(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_111]),c_0_143]) ).
cnf(c_0_249,plain,
mult(ld(X1,X2),mult(X1,X1)) = ld(X1,mult(X2,mult(X1,X1))),
inference(spm,[status(thm)],[c_0_22,c_0_241]) ).
cnf(c_0_250,plain,
mult(mult(mult(X1,i(mult(X2,X2))),X2),mult(X2,X2)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_34]),c_0_137]) ).
cnf(c_0_251,plain,
ld(mult(mult(X1,X2),X1),mult(X1,mult(mult(mult(X2,X1),X1),X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_252,plain,
i(rd(X1,i(X2))) = mult(mult(X1,i(mult(X2,X1))),i(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_205]),c_0_140]),c_0_242]),c_0_83]),c_0_210]) ).
cnf(c_0_253,plain,
mult(rd(X1,i(X2)),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[c_0_77,c_0_243]) ).
cnf(c_0_254,plain,
rd(X1,i(rd(X2,i(X1)))) = mult(rd(X1,i(X2)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_29]),c_0_245]) ).
cnf(c_0_255,plain,
mult(X1,i(mult(X2,mult(X1,X1)))) = mult(i(X1),i(X2)),
inference(spm,[status(thm)],[c_0_191,c_0_136]) ).
cnf(c_0_256,plain,
rd(rd(mult(X1,X2),X3),X2) = rd(X1,mult(X2,mult(X3,i(X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_34]),c_0_246]) ).
cnf(c_0_257,plain,
mult(i(rd(X1,X2)),i(X2)) = rd(i(mult(X1,i(X2))),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_247]),c_0_155]) ).
cnf(c_0_258,plain,
ld(mult(i(X1),ld(X2,X1)),X1) = ld(X1,mult(X2,mult(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_248]),c_0_29]),c_0_29]),c_0_249]) ).
cnf(c_0_259,plain,
mult(i(X1),ld(X1,X2)) = mult(i(mult(X1,X1)),X2),
inference(rw,[status(thm)],[c_0_213,c_0_119]) ).
cnf(c_0_260,plain,
mult(mult(X1,i(mult(X2,X2))),X2) = mult(mult(X1,X2),i(mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_250]),c_0_137]) ).
cnf(c_0_261,plain,
mult(i(mult(X1,X1)),mult(X1,X2)) = mult(i(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_50]),c_0_29]),c_0_22]),c_0_38]) ).
cnf(c_0_262,plain,
mult(X1,ld(mult(mult(X2,X1),X1),X3)) = ld(mult(mult(X1,X2),X1),mult(X1,X3)),
inference(spm,[status(thm)],[c_0_251,c_0_44]) ).
cnf(c_0_263,plain,
ld(mult(X1,X2),i(X2)) = mult(mult(i(X2),i(X1)),i(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_253]),c_0_254]),c_0_238]),c_0_255]) ).
cnf(c_0_264,plain,
mult(X1,mult(i(mult(X2,X1)),X1)) = ld(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_116]),c_0_86]),c_0_171]) ).
cnf(c_0_265,plain,
rd(mult(X1,mult(X2,X2)),X2) = rd(X1,i(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_256,c_0_243]),c_0_38]),c_0_41]) ).
cnf(c_0_266,plain,
mult(i(rd(X1,i(X2))),X2) = rd(i(mult(X1,X2)),i(X2)),
inference(spm,[status(thm)],[c_0_257,c_0_29]) ).
cnf(c_0_267,plain,
mult(X1,ld(mult(X2,mult(X1,X1)),X1)) = mult(i(X1),ld(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_258]),c_0_111]) ).
cnf(c_0_268,plain,
mult(i(X1),ld(mult(X1,X2),X1)) = mult(i(mult(X1,X1)),rd(X1,X2)),
inference(spm,[status(thm)],[c_0_259,c_0_202]) ).
cnf(c_0_269,plain,
mult(i(mult(X1,X1)),rd(X1,X2)) = rd(i(X1),X2),
inference(spm,[status(thm)],[c_0_165,c_0_108]) ).
cnf(c_0_270,plain,
mult(mult(X1,mult(X2,X2)),i(X2)) = mult(mult(X1,i(X2)),mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260,c_0_38]),c_0_29]),c_0_29]) ).
cnf(c_0_271,plain,
ld(X1,i(rd(X2,i(X1)))) = mult(i(X1),i(mult(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_240]),c_0_29]),c_0_29]),c_0_261]) ).
cnf(c_0_272,plain,
mult(i(mult(X1,X2)),i(X2)) = i(mult(mult(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_262,c_0_263]),c_0_155]),c_0_23]),c_0_264]),c_0_12]),c_0_12]),c_0_13]) ).
cnf(c_0_273,plain,
rd(i(mult(X1,X2)),i(X2)) = mult(i(X2),ld(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_265]),c_0_266]),c_0_267]) ).
cnf(c_0_274,plain,
mult(i(X1),ld(mult(X1,X2),X1)) = rd(i(X1),X2),
inference(rw,[status(thm)],[c_0_268,c_0_269]) ).
cnf(c_0_275,plain,
mult(mult(X1,i(X2)),mult(X2,X2)) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_243]),c_0_270]) ).
cnf(c_0_276,plain,
mult(i(X1),i(mult(X2,i(X1)))) = mult(X1,i(mult(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_271,c_0_265]),c_0_29]),c_0_234]),c_0_235]),c_0_38]),c_0_260]),c_0_164]),c_0_83]) ).
cnf(c_0_277,plain,
rd(i(X1),X2) = i(mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_272]),c_0_273]),c_0_274]) ).
cnf(c_0_278,plain,
mult(mult(X1,X1),i(mult(X2,X1))) = i(mult(X2,i(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_275]),c_0_172]),c_0_173]) ).
cnf(c_0_279,plain,
ld(X1,i(rd(X2,X1))) = mult(X1,i(mult(X2,X1))),
inference(rw,[status(thm)],[c_0_240,c_0_276]) ).
cnf(c_0_280,plain,
rd(X1,X2) = i(mult(X2,i(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_193,c_0_277]),c_0_278]) ).
cnf(c_0_281,negated_conjecture,
mult(a,i(mult(b,a))) != i(b),
goals ).
cnf(c_0_282,plain,
mult(X1,i(mult(X2,X1))) = i(X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_279,c_0_280]),c_0_29]),c_0_22]) ).
cnf(c_0_283,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_281,c_0_282])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP701-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 19:03:29 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 34.08/20.44 % Version : CSE_E---1.7
% 34.08/20.44 % Problem : theBenchmark.p
% 34.08/20.44 % SZS status Unsatisfiable for theBenchmark.p
% 34.08/20.44 % SZS output start CNFRefutation
% See solution above
% 34.19/20.57 % Total time : 15.398s
%------------------------------------------------------------------------------