%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP770-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 04:27:15 PM UTC 2026
% Result : Unsatisfiable 94.81s 61.67s
% Output : CNFRefutation 95.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of clauses : 137 ( 137 unt; 0 nHn; 3 RR)
% Number of literals : 137 ( 136 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 268 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(sos24,axiom,
product(j(product(X1,X2)),X1) = j(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos24) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
cnf(sos17,axiom,
quotient(j(X1),X1) = product(j(X1),i(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos17) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(sos23,axiom,
product(X1,i(product(X2,X1))) = i(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos23) ).
cnf(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
cnf(sos14,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos11) ).
cnf(sos16,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos16) ).
cnf(sos13,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos13) ).
cnf(sos22,axiom,
product(j(j(X1)),j(product(X2,X1))) = j(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos22) ).
cnf(goals,negated_conjecture,
product(x0,product(x1,x2)) != product(quotient(product(x0,x1),x0),product(x0,x2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_20,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_21,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_22,plain,
product(X1,quotient(product(X2,product(X3,X1)),X1)) = product(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_24,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_25,plain,
product(product(X1,quotient(X2,product(X3,X1))),X3) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
product(one,X1) = X1,
sos02 ).
cnf(c_0_27,plain,
quotient(product(X1,quotient(X2,X1)),X3) = product(X1,quotient(X2,product(X3,X1))),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
quotient(X1,X1) = one,
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_29,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_30,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_31,plain,
product(X1,quotient(X1,product(X2,X1))) = quotient(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,axiom,
product(j(product(X1,X2)),X1) = j(X2),
sos24 ).
cnf(c_0_33,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_34,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08 ).
cnf(c_0_35,plain,
difference(X1,quotient(X1,X2)) = quotient(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,axiom,
quotient(j(X1),X1) = product(j(X1),i(X1)),
sos17 ).
cnf(c_0_37,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_38,plain,
product(quotient(one,product(X1,X2)),X1) = quotient(one,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]) ).
cnf(c_0_39,plain,
difference(product(X1,X2),product(X1,product(X2,quotient(X3,product(X1,X2))))) = quotient(quotient(X3,X2),X1),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_40,plain,
quotient(product(X1,X2),product(X2,product(X1,X2))) = difference(product(X1,X2),X1),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_41,plain,
product(X1,quotient(product(X2,X1),product(X3,X1))) = quotient(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_42,axiom,
product(X1,i(product(X2,X1))) = i(X2),
sos23 ).
cnf(c_0_43,plain,
quotient(quotient(one,X1),X1) = product(quotient(one,X1),difference(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_33]),c_0_33]) ).
cnf(c_0_44,plain,
quotient(quotient(one,X1),X2) = quotient(one,product(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_38]) ).
cnf(c_0_45,plain,
difference(product(X1,product(X2,X1)),product(X1,X2)) = quotient(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_20]),c_0_28]) ).
cnf(c_0_46,plain,
quotient(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_41,c_0_23]) ).
cnf(c_0_47,plain,
product(X1,difference(product(X2,X1),one)) = difference(X2,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_37]),c_0_37]) ).
cnf(c_0_48,plain,
product(quotient(one,X1),difference(X1,one)) = quotient(one,product(X1,X1)),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_50,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_20]) ).
cnf(c_0_51,plain,
difference(product(X1,product(difference(X1,X2),X1)),X2) = quotient(one,X1),
inference(spm,[status(thm)],[c_0_45,c_0_20]) ).
cnf(c_0_52,plain,
product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_53,plain,
product(quotient(X1,X2),product(X2,quotient(X1,product(X3,X2)))) = quotient(X1,quotient(X3,quotient(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_23]),c_0_27]) ).
cnf(c_0_54,plain,
product(difference(X1,one),product(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_49]) ).
cnf(c_0_55,plain,
product(X1,product(difference(X1,X2),X1)) = quotient(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
difference(product(X1,X2),product(X1,quotient(product(X2,X3),X1))) = quotient(X3,X1),
inference(spm,[status(thm)],[c_0_30,c_0_52]) ).
cnf(c_0_57,plain,
quotient(X1,one) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_58,plain,
quotient(X1,quotient(quotient(X2,X3),quotient(X1,X3))) = product(quotient(X1,X3),product(X3,quotient(X1,X2))),
inference(spm,[status(thm)],[c_0_53,c_0_23]) ).
cnf(c_0_59,plain,
quotient(X1,quotient(X2,X1)) = product(X1,quotient(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_60,plain,
product(X1,quotient(product(quotient(X1,product(X2,X1)),X3),X1)) = product(quotient(X1,X2),quotient(X3,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_31]) ).
cnf(c_0_61,plain,
quotient(X1,product(X1,X1)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_24,c_0_54]) ).
cnf(c_0_62,plain,
product(product(X1,X2),product(quotient(X3,X1),product(X1,X2))) = product(X1,product(X2,product(X3,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_27]),c_0_38]),c_0_46]),c_0_57]) ).
cnf(c_0_63,plain,
product(quotient(X1,X2),product(X2,X1)) = product(X1,X1),
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_44]),c_0_23]),c_0_59]),c_0_57]),c_0_57]) ).
cnf(c_0_64,plain,
product(X1,quotient(product(difference(X1,one),X2),X1)) = quotient(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_28]),c_0_26]) ).
cnf(c_0_65,plain,
product(product(X1,X2),product(X2,X2)) = product(X1,product(X2,product(X2,X2))),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,plain,
quotient(one,difference(X1,X2)) = product(quotient(one,X2),X1),
inference(spm,[status(thm)],[c_0_38,c_0_20]) ).
cnf(c_0_67,plain,
difference(product(X1,X1),X1) = quotient(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_54]),c_0_28]),c_0_20]),c_0_29]) ).
cnf(c_0_68,plain,
quotient(one,product(X1,difference(X2,one))) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_50]) ).
cnf(c_0_69,plain,
quotient(product(difference(X1,one),X2),X1) = difference(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_64]) ).
cnf(c_0_70,plain,
product(difference(product(X1,X2),product(X1,product(X2,X3))),X1) = quotient(product(X3,product(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_71,plain,
product(quotient(X1,X2),product(X2,product(X2,X2))) = product(X1,product(X2,X2)),
inference(spm,[status(thm)],[c_0_65,c_0_23]) ).
cnf(c_0_72,plain,
difference(product(quotient(one,X1),X2),one) = difference(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_66]) ).
cnf(c_0_73,plain,
difference(quotient(X1,X2),one) = product(X2,difference(X1,one)),
inference(spm,[status(thm)],[c_0_47,c_0_23]) ).
cnf(c_0_74,plain,
quotient(X1,quotient(one,X1)) = product(X1,X1),
inference(spm,[status(thm)],[c_0_50,c_0_67]) ).
cnf(c_0_75,plain,
quotient(X1,quotient(X2,difference(X1,one))) = quotient(one,X2),
inference(spm,[status(thm)],[c_0_68,c_0_23]) ).
cnf(c_0_76,plain,
product(X1,quotient(X2,product(product(X1,quotient(X2,X1)),X1))) = one,
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_77,plain,
difference(product(X1,X2),product(X1,quotient(X2,X1))) = quotient(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_31]),c_0_28]) ).
cnf(c_0_78,plain,
product(quotient(one,X1),quotient(X1,X2)) = quotient(one,X2),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_79,plain,
difference(product(X1,quotient(X1,X2)),X1) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_49,c_0_59]) ).
cnf(c_0_80,plain,
product(difference(X1,quotient(X2,X1)),X1) = product(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_23,c_0_69]) ).
cnf(c_0_81,plain,
quotient(product(product(X1,X1),X2),X1) = product(X1,quotient(product(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_70,c_0_71]),c_0_23]),c_0_30]),c_0_52]),c_0_23]) ).
cnf(c_0_82,plain,
difference(difference(product(X1,quotient(one,X2)),one),X2) = difference(difference(X1,one),one),
inference(spm,[status(thm)],[c_0_72,c_0_47]) ).
cnf(c_0_83,plain,
product(product(X1,quotient(X1,X2)),X2) = product(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_63]),c_0_24]) ).
cnf(c_0_84,plain,
difference(product(X1,X1),one) = quotient(one,product(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_48]) ).
cnf(c_0_85,plain,
difference(quotient(one,X1),X2) = quotient(X1,difference(X2,one)),
inference(spm,[status(thm)],[c_0_49,c_0_75]) ).
cnf(c_0_86,plain,
quotient(product(X1,X1),X2) = product(X1,quotient(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_63]),c_0_23]),c_0_30]),c_0_23]) ).
cnf(c_0_87,plain,
difference(product(X1,quotient(X1,X2)),one) = product(quotient(X2,X1),difference(X1,one)),
inference(spm,[status(thm)],[c_0_73,c_0_59]) ).
cnf(c_0_88,plain,
quotient(X1,product(product(X2,quotient(X1,X2)),X2)) = difference(X2,one),
inference(spm,[status(thm)],[c_0_30,c_0_76]) ).
cnf(c_0_89,plain,
difference(X1,product(X2,quotient(difference(X2,X1),X2))) = quotient(one,X2),
inference(spm,[status(thm)],[c_0_77,c_0_20]) ).
cnf(c_0_90,plain,
quotient(one,quotient(X1,difference(X2,one))) = product(quotient(one,X2),quotient(one,X1)),
inference(spm,[status(thm)],[c_0_78,c_0_75]) ).
cnf(c_0_91,plain,
quotient(difference(X1,X2),X2) = difference(product(X2,X1),X2),
inference(spm,[status(thm)],[c_0_79,c_0_50]) ).
cnf(c_0_92,plain,
difference(X1,difference(X2,one)) = difference(product(X2,X1),one),
inference(spm,[status(thm)],[c_0_30,c_0_47]) ).
cnf(c_0_93,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_94,plain,
product(difference(X1,one),product(product(X1,X1),X2)) = product(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_30]),c_0_23]) ).
cnf(c_0_95,plain,
difference(difference(X1,one),product(X1,X2)) = product(X1,quotient(X1,difference(X2,one))),
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_82,c_0_83]),c_0_84]),c_0_85]),c_0_86]),c_0_87]),c_0_44]),c_0_72]) ).
cnf(c_0_96,plain,
difference(difference(X1,one),X2) = product(product(X1,quotient(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_49,c_0_88]) ).
cnf(c_0_97,plain,
product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_89]) ).
cnf(c_0_98,plain,
difference(one,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_99,plain,
product(X1,product(difference(X1,one),X2)) = product(quotient(one,X1),product(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_90,c_0_91]),c_0_92]),c_0_66]),c_0_57]),c_0_26]),c_0_92]),c_0_50]) ).
cnf(c_0_100,axiom,
product(X1,product(eta(X1),X2)) = product(j(j(X1)),X2),
sos14 ).
cnf(c_0_101,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_93,c_0_37]) ).
cnf(c_0_102,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_103,axiom,
product(eta(X1),product(X2,X3)) = product(product(eta(X1),X2),X3),
sos16 ).
cnf(c_0_104,axiom,
product(i(i(X1)),X2) = product(eta(X1),product(X1,X2)),
sos13 ).
cnf(c_0_105,plain,
product(X1,quotient(X1,difference(X2,one))) = product(product(X1,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_94]),c_0_95]) ).
cnf(c_0_106,plain,
difference(difference(X1,one),difference(X1,X2)) = product(product(X2,quotient(one,X1)),X1),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_107,plain,
quotient(one,product(product(X1,quotient(one,X2)),X2)) = quotient(X2,product(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_85,c_0_35]),c_0_44]),c_0_44]),c_0_73]),c_0_98]),c_0_29]) ).
cnf(c_0_108,plain,
product(product(X1,X2),difference(X2,one)) = product(product(X1,quotient(one,X2)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_99]),c_0_22]) ).
cnf(c_0_109,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_100,c_0_33]),c_0_33]),c_0_101]) ).
cnf(c_0_110,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_102,c_0_37]),c_0_33]) ).
cnf(c_0_111,plain,
product(product(difference(X1,one),X1),product(X2,X3)) = product(product(product(difference(X1,one),X1),X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_101]),c_0_101]) ).
cnf(c_0_112,axiom,
product(j(j(X1)),j(product(X2,X1))) = j(X2),
sos22 ).
cnf(c_0_113,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_104,c_0_37]),c_0_37]),c_0_101]) ).
cnf(c_0_114,plain,
product(quotient(X1,X2),product(X2,difference(X1,one))) = one,
inference(spm,[status(thm)],[c_0_20,c_0_73]) ).
cnf(c_0_115,plain,
quotient(product(X1,product(X2,X1)),X1) = quotient(X1,difference(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_105]),c_0_21]) ).
cnf(c_0_116,plain,
product(product(quotient(one,X1),quotient(one,X2)),X2) = quotient(X2,product(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_106]),c_0_107]),c_0_66]),c_0_108]) ).
cnf(c_0_117,plain,
product(X1,product(product(X1,quotient(one,X1)),X2)) = product(quotient(one,quotient(one,X1)),X2),
inference(rw,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_118,plain,
product(product(product(X1,quotient(one,X1)),X2),X3) = product(product(X1,quotient(one,X1)),product(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_111,c_0_110]),c_0_110]) ).
cnf(c_0_119,plain,
product(quotient(one,quotient(one,X1)),quotient(one,product(X2,X1))) = quotient(one,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_33]),c_0_33]),c_0_33]),c_0_33]) ).
cnf(c_0_120,plain,
product(difference(difference(X1,one),one),X2) = product(product(X1,quotient(one,X1)),product(X1,X2)),
inference(rw,[status(thm)],[c_0_113,c_0_110]) ).
cnf(c_0_121,plain,
product(difference(X1,one),quotient(X1,X2)) = product(X1,quotient(one,product(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_114]),c_0_23]),c_0_23]),c_0_110]),c_0_27]) ).
cnf(c_0_122,plain,
product(X1,quotient(difference(X1,one),X2)) = quotient(one,X2),
inference(spm,[status(thm)],[c_0_78,c_0_50]) ).
cnf(c_0_123,plain,
quotient(X1,quotient(X1,difference(X2,one))) = quotient(quotient(X1,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_31]),c_0_72]),c_0_85]) ).
cnf(c_0_124,plain,
product(product(quotient(one,quotient(one,X1)),X2),quotient(X3,X1)) = product(X1,quotient(product(product(X1,quotient(one,X1)),product(X2,X3)),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_117]),c_0_118]) ).
cnf(c_0_125,plain,
product(quotient(one,quotient(one,X1)),quotient(one,X2)) = quotient(one,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_119,c_0_23]) ).
cnf(c_0_126,plain,
product(product(X1,quotient(one,X1)),quotient(one,X2)) = product(X1,quotient(one,product(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_68]),c_0_121]),c_0_122]) ).
cnf(c_0_127,plain,
quotient(product(X1,quotient(one,X2)),X1) = quotient(X1,product(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_38]),c_0_49]) ).
cnf(c_0_128,plain,
product(X1,quotient(X1,product(X1,product(X2,X1)))) = quotient(quotient(X1,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_115]),c_0_59]) ).
cnf(c_0_129,plain,
quotient(product(X1,X2),product(product(X1,X1),X2)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_24,c_0_94]) ).
cnf(c_0_130,plain,
quotient(quotient(X1,quotient(X2,X3)),X1) = quotient(one,quotient(product(X1,X2),product(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_125]),c_0_44]),c_0_44]),c_0_125]),c_0_126]),c_0_127]),c_0_128]) ).
cnf(c_0_131,plain,
product(X1,product(X2,difference(X1,one))) = quotient(product(X1,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_129]),c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_132,plain,
quotient(product(X1,quotient(X2,X3)),X1) = quotient(product(X1,X2),product(X1,X3)),
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_73,c_0_130]),c_0_85]),c_0_98]),c_0_57]),c_0_73]),c_0_131]) ).
cnf(c_0_133,plain,
quotient(product(X1,product(X2,X3)),product(X1,X3)) = quotient(product(X1,X2),X1),
inference(spm,[status(thm)],[c_0_132,c_0_24]) ).
cnf(c_0_134,negated_conjecture,
product(x0,product(x1,x2)) != product(quotient(product(x0,x1),x0),product(x0,x2)),
goals ).
cnf(c_0_135,plain,
product(quotient(product(X1,X2),X1),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_23,c_0_133]) ).
cnf(c_0_136,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP770-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n017.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:04:27 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 94.81/61.67 % Version : CSE_E---1.7
% 94.81/61.67 % Problem : theBenchmark.p
% 94.81/61.67 % SZS status Unsatisfiable for theBenchmark.p
% 94.81/61.67 % SZS output start CNFRefutation
% See solution above
% 95.23/62.07 % Total time : 45.673s
%------------------------------------------------------------------------------