%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP766-1 : TPTP v9.3.1. Released v4.1.0.
% 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 12:41:12 PM UTC 2026
% Result : Unsatisfiable 14.14s 2.57s
% Output : CNFRefutation 14.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of clauses : 118 ( 118 unt; 0 nHn; 6 RR)
% Number of literals : 118 ( 117 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 216 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(sos15,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos15) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos16,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
cnf(sos17,axiom,
product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos17) ).
cnf(sos19,axiom,
t(eta(X1),product(X2,X3)) = product(t(eta(X1),X2),t(eta(X1),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
cnf(sos18,axiom,
t(X1,X2) = quotient(product(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos18) ).
cnf(goals,negated_conjecture,
product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_18,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08 ).
cnf(c_0_19,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_20,plain,
quotient(difference(X1,product(product(X1,X2),X3)),X3) = difference(product(X3,X1),product(X3,product(X1,X2))),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_22,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_23,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_24,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_25,plain,
quotient(difference(X1,product(X2,X3)),X3) = difference(product(X3,X1),product(X3,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
difference(X1,X1) = one,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_28,plain,
difference(product(X1,product(X2,X1)),product(X1,X2)) = quotient(one,X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
quotient(product(X1,X2),quotient(one,X1)) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_31,axiom,
product(one,X1) = X1,
sos02 ).
cnf(c_0_32,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_33,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_34,plain,
product(X1,product(product(X2,quotient(one,X1)),X1)) = difference(quotient(one,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_29]),c_0_30]),c_0_31]) ).
cnf(c_0_35,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
sos15 ).
cnf(c_0_36,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_37,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_38,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_39,plain,
product(product(X1,product(X2,X1)),quotient(one,X1)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_40,plain,
difference(quotient(one,X1),quotient(X2,quotient(one,X1))) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_41,plain,
product(difference(X1,one),product(X2,difference(X1,one))) = quotient(product(difference(X1,one),X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_42,plain,
product(difference(difference(X1,one),one),X2) = product(product(difference(X1,one),X1),product(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_33]),c_0_33]),c_0_36]) ).
cnf(c_0_43,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_33]),c_0_38]) ).
cnf(c_0_44,plain,
product(product(X1,X2),quotient(one,X1)) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_45,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
sos16 ).
cnf(c_0_46,plain,
quotient(product(difference(X1,one),X2),X1) = difference(X1,quotient(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_41]) ).
cnf(c_0_47,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_48,plain,
product(product(X1,quotient(one,X1)),product(X1,X2)) = product(difference(difference(X1,one),one),X2),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_21]) ).
cnf(c_0_50,plain,
product(X1,product(product(difference(X1,one),X1),X2)) = product(quotient(one,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_38]),c_0_38]),c_0_36]) ).
cnf(c_0_51,plain,
difference(X1,quotient(difference(difference(X1,one),X2),X1)) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_21]) ).
cnf(c_0_52,plain,
product(quotient(one,X1),quotient(one,quotient(one,X1))) = product(X1,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_47]) ).
cnf(c_0_53,plain,
product(product(X1,quotient(one,X1)),X1) = difference(difference(X1,one),one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_23]),c_0_23]) ).
cnf(c_0_54,plain,
difference(X1,product(X2,quotient(one,X1))) = quotient(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_49]) ).
cnf(c_0_55,plain,
difference(one,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_56,plain,
product(X1,product(difference(X1,X2),X1)) = quotient(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_57,plain,
product(difference(X1,quotient(X2,X1)),X1) = product(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_30,c_0_46]) ).
cnf(c_0_58,plain,
quotient(difference(X1,product(X2,quotient(one,X2))),X2) = difference(product(X2,X1),one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_43]),c_0_21]) ).
cnf(c_0_59,plain,
product(X1,product(product(X1,quotient(one,X1)),X2)) = product(quotient(one,quotient(one,X1)),X2),
inference(rw,[status(thm)],[c_0_50,c_0_43]) ).
cnf(c_0_60,plain,
quotient(difference(difference(X1,one),X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_51]) ).
cnf(c_0_61,axiom,
product(X1,product(X2,eta(X1))) = product(product(X1,X2),eta(X1)),
sos17 ).
cnf(c_0_62,plain,
product(product(X1,quotient(one,X1)),product(quotient(one,X1),X2)) = product(difference(X1,one),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_52]),c_0_47]) ).
cnf(c_0_63,plain,
product(product(X1,quotient(one,X1)),quotient(one,X1)) = difference(X1,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_52]),c_0_47]) ).
cnf(c_0_64,plain,
quotient(quotient(difference(X1,X2),X1),quotient(one,X1)) = product(quotient(one,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_54]),c_0_30]),c_0_55]) ).
cnf(c_0_65,plain,
quotient(quotient(X1,X2),quotient(one,X2)) = product(X2,product(difference(X2,one),X1)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,axiom,
t(eta(X1),product(X2,X3)) = product(t(eta(X1),X2),t(eta(X1),X3)),
sos19 ).
cnf(c_0_67,axiom,
t(X1,X2) = quotient(product(X1,X2),X1),
sos18 ).
cnf(c_0_68,plain,
difference(X1,product(X2,quotient(one,X2))) = product(difference(product(X2,X1),one),X2),
inference(spm,[status(thm)],[c_0_30,c_0_58]) ).
cnf(c_0_69,plain,
product(X1,product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_23]),c_0_23]) ).
cnf(c_0_70,plain,
difference(X1,product(product(X1,X2),quotient(X3,X1))) = quotient(product(X2,X3),X1),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_71,plain,
product(product(X1,quotient(X2,X1)),X1) = difference(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_30,c_0_60]) ).
cnf(c_0_72,plain,
product(X1,product(X2,product(difference(X1,one),X1))) = product(product(X1,X2),product(difference(X1,one),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_36]),c_0_36]) ).
cnf(c_0_73,plain,
product(difference(X1,one),difference(quotient(one,X1),X2)) = product(product(X1,quotient(one,X1)),X2),
inference(spm,[status(thm)],[c_0_62,c_0_21]) ).
cnf(c_0_74,plain,
product(quotient(one,X1),quotient(X2,quotient(one,X1))) = quotient(difference(X1,X2),quotient(one,X1)),
inference(spm,[status(thm)],[c_0_60,c_0_47]) ).
cnf(c_0_75,plain,
quotient(difference(X1,one),quotient(one,X1)) = product(X1,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_63]) ).
cnf(c_0_76,plain,
product(X1,product(difference(X1,one),difference(X1,X2))) = product(quotient(one,X1),X2),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_77,plain,
quotient(product(product(difference(X1,one),X1),product(X2,X3)),product(difference(X1,one),X1)) = product(quotient(product(product(difference(X1,one),X1),X2),product(difference(X1,one),X1)),quotient(product(product(difference(X1,one),X1),X3),product(difference(X1,one),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)],[c_0_66,c_0_36]),c_0_36]),c_0_36]),c_0_67]),c_0_67]),c_0_67]) ).
cnf(c_0_78,plain,
product(X1,product(difference(product(X2,X1),one),X2)) = product(X2,quotient(one,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_68]) ).
cnf(c_0_79,plain,
product(product(X1,quotient(one,X1)),quotient(one,quotient(one,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_52]),c_0_47]) ).
cnf(c_0_80,plain,
product(difference(X1,one),product(X1,quotient(one,X1))) = quotient(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_27]),c_0_43]) ).
cnf(c_0_81,plain,
product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_21,c_0_70]) ).
cnf(c_0_82,plain,
difference(X1,difference(quotient(one,X1),X2)) = product(product(X2,quotient(one,X1)),X1),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_83,plain,
difference(difference(X1,one),difference(X1,X2)) = product(product(X2,quotient(one,X1)),X1),
inference(spm,[status(thm)],[c_0_71,c_0_49]) ).
cnf(c_0_84,plain,
product(product(X1,X2),product(X1,quotient(one,X1))) = product(X1,product(X2,product(X1,quotient(one,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_43]),c_0_43]) ).
cnf(c_0_85,plain,
product(quotient(X1,X2),product(X2,quotient(X1,X2))) = quotient(X1,quotient(one,quotient(X1,X2))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_86,plain,
product(difference(difference(X1,one),one),quotient(one,X1)) = product(difference(X1,one),quotient(one,quotient(one,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_52]),c_0_52]),c_0_48]),c_0_47]) ).
cnf(c_0_87,plain,
quotient(product(product(X1,quotient(one,X1)),X2),difference(quotient(one,X1),X2)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_88,plain,
product(product(X1,quotient(one,X1)),product(quotient(one,quotient(one,X1)),X2)) = product(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_74]),c_0_75]),c_0_47]) ).
cnf(c_0_89,plain,
difference(X1,product(quotient(one,X1),X2)) = product(difference(X1,one),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_76]) ).
cnf(c_0_90,plain,
product(quotient(product(product(X1,quotient(one,X1)),X2),product(X1,quotient(one,X1))),quotient(product(product(X1,quotient(one,X1)),X3),product(X1,quotient(one,X1)))) = quotient(product(product(X1,quotient(one,X1)),product(X2,X3)),product(X1,quotient(one,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)],[c_0_77,c_0_43]),c_0_43]),c_0_43]),c_0_43]),c_0_43]),c_0_43]) ).
cnf(c_0_91,plain,
product(product(X1,quotient(one,X1)),quotient(one,product(X1,quotient(one,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]),c_0_30]) ).
cnf(c_0_92,plain,
product(X1,quotient(product(difference(X1,X2),X3),X1)) = product(X2,quotient(X3,X1)),
inference(spm,[status(thm)],[c_0_81,c_0_21]) ).
cnf(c_0_93,plain,
product(product(X1,quotient(one,X2)),X2) = product(product(X1,X2),difference(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_27]),c_0_83]) ).
cnf(c_0_94,plain,
difference(product(X1,quotient(one,X1)),product(difference(difference(X1,one),one),X2)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_48]) ).
cnf(c_0_95,plain,
product(difference(X1,one),quotient(one,quotient(one,X1))) = product(X1,quotient(one,quotient(one,quotient(one,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_84]),c_0_85]),c_0_86]) ).
cnf(c_0_96,plain,
quotient(product(X1,X2),product(X1,difference(quotient(one,X1),X2))) = difference(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_47]) ).
cnf(c_0_97,plain,
difference(quotient(product(product(X1,quotient(one,X1)),X2),product(X1,quotient(one,X1))),quotient(product(product(X1,quotient(one,X1)),product(X2,X3)),product(X1,quotient(one,X1)))) = quotient(product(product(X1,quotient(one,X1)),X3),product(X1,quotient(one,X1))),
inference(spm,[status(thm)],[c_0_22,c_0_90]) ).
cnf(c_0_98,plain,
quotient(one,product(X1,quotient(one,X1))) = difference(product(X1,quotient(one,X1)),one),
inference(spm,[status(thm)],[c_0_22,c_0_91]) ).
cnf(c_0_99,plain,
quotient(product(difference(X1,X2),X3),X1) = difference(X1,product(X2,quotient(X3,X1))),
inference(spm,[status(thm)],[c_0_22,c_0_92]) ).
cnf(c_0_100,plain,
difference(difference(X1,one),difference(X1,X2)) = product(product(X2,X1),difference(X1,one)),
inference(rw,[status(thm)],[c_0_83,c_0_93]) ).
cnf(c_0_101,plain,
difference(product(X1,quotient(one,X1)),product(product(X1,quotient(one,quotient(one,quotient(one,X1)))),X2)) = product(product(X1,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_84]),c_0_19]),c_0_53]),c_0_19]),c_0_48]),c_0_94]),c_0_30]),c_0_86]),c_0_95]) ).
cnf(c_0_102,plain,
quotient(product(X1,product(quotient(one,X1),X2)),product(X1,X2)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_96,c_0_22]) ).
cnf(c_0_103,plain,
product(X1,difference(product(X2,quotient(one,X2)),one)) = quotient(X1,product(X2,quotient(one,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_76]),c_0_21]),c_0_98]),c_0_98]),c_0_99]),c_0_31]),c_0_100]),c_0_30]),c_0_21]) ).
cnf(c_0_104,plain,
product(difference(X1,one),quotient(X2,difference(X1,one))) = product(product(difference(X1,one),X2),X1),
inference(spm,[status(thm)],[c_0_44,c_0_27]) ).
cnf(c_0_105,plain,
difference(difference(product(X1,quotient(one,X1)),one),one) = product(X1,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_98]) ).
cnf(c_0_106,negated_conjecture,
product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
inference(fof_simplification,[status(thm)],[goals]) ).
cnf(c_0_107,plain,
quotient(product(product(X1,quotient(one,X1)),product(product(X2,product(X1,quotient(one,X1))),X3)),product(X1,quotient(one,X1))) = product(product(X1,quotient(one,X1)),quotient(product(X2,product(product(X1,quotient(one,X1)),X3)),product(X1,quotient(one,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_90,c_0_19]),c_0_48]),c_0_86]),c_0_95]),c_0_101]),c_0_81]) ).
cnf(c_0_108,plain,
product(difference(X1,one),product(X1,X2)) = product(X1,product(quotient(one,X1),X2)),
inference(spm,[status(thm)],[c_0_30,c_0_102]) ).
cnf(c_0_109,plain,
product(difference(product(X1,quotient(one,X1)),one),X2) = difference(product(X1,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_103]),c_0_104]),c_0_24]),c_0_105]) ).
cnf(c_0_110,negated_conjecture,
product(eta(x0),product(x1,x2)) != product(product(eta(x0),x1),x2),
c_0_106 ).
cnf(c_0_111,plain,
difference(difference(X1,product(product(X1,X2),X3)),product(X2,product(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_19]) ).
cnf(c_0_112,plain,
product(product(X1,product(X2,quotient(one,X2))),X3) = product(X1,product(product(X2,quotient(one,X2)),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_107]),c_0_22]),c_0_30]),c_0_108]),c_0_98]),c_0_109]),c_0_21]) ).
cnf(c_0_113,negated_conjecture,
product(product(difference(x0,one),x0),product(x1,x2)) != product(product(product(difference(x0,one),x0),x1),x2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_36]),c_0_36]) ).
cnf(c_0_114,plain,
difference(product(product(X1,quotient(one,X1)),X2),product(product(X1,quotient(one,X1)),product(X2,X3))) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_22]) ).
cnf(c_0_115,negated_conjecture,
product(product(product(x0,quotient(one,x0)),x1),x2) != product(product(x0,quotient(one,x0)),product(x1,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_43]),c_0_43]) ).
cnf(c_0_116,plain,
product(product(product(X1,quotient(one,X1)),X2),X3) = product(product(X1,quotient(one,X1)),product(X2,X3)),
inference(spm,[status(thm)],[c_0_21,c_0_114]) ).
cnf(c_0_117,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_116])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP766-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n026.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 20 20:41:36 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 14.14/2.57 % Version: 3.5.1
% 14.14/2.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.14/2.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.14/2.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.14/2.57 % Starting new_bool_3 with 300s (1) cores
% 14.14/2.57 % Starting new_bool_1 with 300s (1) cores
% 14.14/2.57 % Starting sh5l with 300s (1) cores
% 14.14/2.57 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 559314 completed with status 0
% 14.14/2.57 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 14.14/2.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.14/2.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.14/2.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.14/2.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.14/2.57 % No SInE strategy applied
% 14.14/2.57 % Search class: FUUPM-FFMF22-MFFFFFNN
% 14.14/2.57 % partial match(1): FUUPM-FFSF22-MFFFFFNN
% 14.14/2.57 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 14.14/2.57 % Starting SubtermCWHack with 136s (1) cores
% 14.14/2.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.14/2.57 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 14.14/2.57 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 14.14/2.57 % Starting U----_102_C09_12_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 14.14/2.57 % U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 559322 completed with status 0
% 14.14/2.57 % Result found by U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 14.14/2.57 % Preprocessing class: FSMSSMSSSSSNFFN.
% 14.14/2.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.14/2.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 14.14/2.57 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.14/2.57 % No SInE strategy applied
% 14.14/2.57 % Search class: FUUPM-FFMF22-MFFFFFNN
% 14.14/2.57 % partial match(1): FUUPM-FFSF22-MFFFFFNN
% 14.14/2.57 % Scheduled 10 strats onto 5 cores with 1500 seconds (1500 total)
% 14.14/2.57 % Starting SubtermCWHack with 136s (1) cores
% 14.14/2.57 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 14.14/2.57 % Starting E---G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 136s (1) cores
% 14.14/2.57 % Starting U----_206d_05_C11_08_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 14.14/2.57 % Preprocessing time : 0.001 s
% 14.14/2.57 % Presaturation interreduction done
% 14.14/2.57
% 14.14/2.57 % Proof found!
% 14.14/2.57 % SZS status Unsatisfiable
% 14.14/2.57 % SZS output start CNFRefutation
% See solution above
% 14.14/2.58 % Parsed axioms : 20
% 14.14/2.58 % Removed by relevancy pruning/SinE : 0
% 14.14/2.58 % Initial clauses : 20
% 14.14/2.58 % Removed in clause preprocessing : 5
% 14.14/2.58 % Initial clauses in saturation : 15
% 14.14/2.58 % Processed clauses : 1215
% 14.14/2.58 % ...of these trivial : 641
% 14.14/2.58 % ...subsumed : 0
% 14.14/2.58 % ...remaining for further processing : 574
% 14.14/2.58 % Other redundant clauses eliminated : 0
% 14.14/2.58 % Clauses deleted for lack of memory : 0
% 14.14/2.58 % Backward-subsumed : 0
% 14.14/2.58 % Backward-rewritten : 204
% 14.14/2.58 % Generated clauses : 67235
% 14.14/2.58 % ...of the previous two non-redundant : 47366
% 14.14/2.58 % ...aggressively subsumed : 0
% 14.14/2.58 % Contextual simplify-reflections : 0
% 14.14/2.58 % Paramodulations : 67235
% 14.14/2.58 % Factorizations : 0
% 14.14/2.58 % NegExts : 0
% 14.14/2.58 % Equation resolutions : 0
% 14.14/2.58 % Disequality decompositions : 0
% 14.14/2.58 % Total rewrite steps : 263095
% 14.14/2.58 % ...of those cached : 255363
% 14.14/2.58 % Propositional unsat checks : 0
% 14.14/2.58 % Propositional check models : 0
% 14.14/2.58 % Propositional check unsatisfiable : 0
% 14.14/2.58 % Propositional clauses : 0
% 14.14/2.58 % Propositional clauses after purity: 0
% 14.14/2.58 % Propositional unsat core size : 0
% 14.14/2.58 % Propositional preprocessing time : 0.000
% 14.14/2.58 % Propositional encoding time : 0.000
% 14.14/2.58 % Propositional solver time : 0.000
% 14.14/2.58 % Success case prop preproc time : 0.000
% 14.14/2.58 % Success case prop encoding time : 0.000
% 14.14/2.58 % Success case prop solver time : 0.000
% 14.14/2.58 % Current number of processed clauses : 355
% 14.14/2.58 % Positive orientable unit clauses : 355
% 14.14/2.58 % Positive unorientable unit clauses: 0
% 14.14/2.58 % Negative unit clauses : 0
% 14.14/2.58 % Non-unit-clauses : 0
% 14.14/2.58 % Current number of unprocessed clauses: 45449
% 14.14/2.58 % ...number of literals in the above : 45449
% 14.14/2.58 % Current number of archived formulas : 0
% 14.14/2.58 % Current number of archived clauses : 224
% 14.14/2.58 % Clause-clause subsumption calls (NU) : 0
% 14.14/2.58 % Rec. Clause-clause subsumption calls : 0
% 14.14/2.58 % Non-unit clause-clause subsumptions : 0
% 14.14/2.58 % Unit Clause-clause subsumption calls : 3
% 14.14/2.58 % Rewrite failures with RHS unbound : 0
% 14.14/2.58 % BW rewrite match attempts : 972
% 14.14/2.58 % BW rewrite match successes : 163
% 14.14/2.58 % Condensation attempts : 0
% 14.14/2.58 % Condensation successes : 0
% 14.14/2.58 % Termbank termtop insertions : 2031171
% 14.14/2.58 % Search garbage collected termcells : 2
% 14.14/2.58
% 14.14/2.58 % -------------------------------------------------
% 14.14/2.58 % User time : 1.956 s
% 14.14/2.58 % System time : 0.061 s
% 14.14/2.58 % Total time : 2.018 s
% 14.14/2.58 % Maximum resident set size: 3644 pages
% 14.14/2.58
% 14.14/2.58 % -------------------------------------------------
% 14.14/2.58 % User time : 9.998 s
% 14.14/2.58 % System time : 0.344 s
% 14.14/2.58 % Total time : 10.342 s
% 14.14/2.58 % Maximum resident set size: 4608 pages
% 14.14/2.58 % E exiting
%------------------------------------------------------------------------------