TSTP Solution File: GRP764-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP764-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 : Thu Aug 31 00:23:39 EDT 2023
% Result : Unsatisfiable 9.24s 9.29s
% Output : CNFRefutation 9.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 150 ( 141 unt; 9 typ; 0 def)
% Number of atoms : 141 ( 140 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
one: $i ).
tff(decl_23,type,
product: ( $i * $i ) > $i ).
tff(decl_24,type,
difference: ( $i * $i ) > $i ).
tff(decl_25,type,
quotient: ( $i * $i ) > $i ).
tff(decl_26,type,
i: $i > $i ).
tff(decl_27,type,
j: $i > $i ).
tff(decl_28,type,
eta: $i > $i ).
tff(decl_29,type,
x0: $i ).
tff(decl_30,type,
x1: $i ).
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(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
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(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(goals,negated_conjecture,
product(x0,product(eta(x0),x1)) != product(j(j(x0)),x1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_13,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07 ).
cnf(c_0_14,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_15,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_16,plain,
quotient(product(difference(X1,X2),product(X3,X1)),X1) = difference(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
product(X1,quotient(product(X2,product(X3,X1)),X1)) = product(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(c_0_19,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_20,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_21,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_22,plain,
product(difference(X1,product(X2,X3)),X1) = product(difference(X1,X2),product(X3,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_23,axiom,
product(one,X1) = X1,
sos02 ).
cnf(c_0_24,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_25,plain,
product(product(X1,X2),quotient(X3,X1)) = product(X1,quotient(product(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_26,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_27,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_28,plain,
product(difference(X1,one),product(X2,X1)) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
quotient(product(X1,quotient(product(X2,X3),X1)),quotient(X3,X1)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,axiom,
product(X1,one) = X1,
sos01 ).
cnf(c_0_31,plain,
product(quotient(one,X1),quotient(one,quotient(one,X1))) = product(X1,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
difference(difference(X1,one),product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_33,plain,
quotient(product(X1,quotient(X2,X1)),quotient(one,X1)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
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,
quotient(product(X1,product(X2,quotient(X3,X1))),quotient(X3,X1)) = difference(quotient(X3,X1),product(X3,X2)),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_36,plain,
difference(quotient(one,X1),product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_37,plain,
difference(difference(X1,one),product(X2,X1)) = product(product(X1,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_38,plain,
quotient(product(X1,X2),quotient(one,X1)) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_39,plain,
difference(product(X1,quotient(X2,X3)),product(X1,X2)) = quotient(difference(quotient(X2,X3),product(X2,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_15]),c_0_35]) ).
cnf(c_0_40,plain,
product(X1,quotient(quotient(one,X1),X1)) = difference(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_36]),c_0_27]),c_0_15]),c_0_25]),c_0_30]) ).
cnf(c_0_41,plain,
difference(difference(X1,one),product(X1,quotient(one,X1))) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_42,plain,
product(product(X1,product(difference(X1,one),X2)),X1) = quotient(X2,difference(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_37]),c_0_14]),c_0_30]) ).
cnf(c_0_43,plain,
product(X1,product(difference(X1,X2),X1)) = quotient(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_38,c_0_14]) ).
cnf(c_0_44,plain,
product(difference(X1,quotient(X2,X1)),X1) = product(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_45,plain,
quotient(difference(quotient(quotient(one,X1),X1),one),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_15]) ).
cnf(c_0_46,plain,
quotient(quotient(X1,difference(X2,one)),X2) = product(X2,product(difference(X2,one),X1)),
inference(spm,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_47,plain,
quotient(quotient(X1,X2),quotient(one,X2)) = product(X2,product(difference(X2,one),X1)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
difference(X1,quotient(X2,quotient(one,X1))) = product(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_49,plain,
quotient(product(difference(X1,X2),X1),product(X2,X1)) = difference(X1,one),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_50,plain,
difference(X1,difference(X1,one)) = quotient(quotient(one,X1),X1),
inference(spm,[status(thm)],[c_0_21,c_0_40]) ).
cnf(c_0_51,plain,
difference(quotient(quotient(one,X1),X1),one) = product(X1,X1),
inference(spm,[status(thm)],[c_0_15,c_0_45]) ).
cnf(c_0_52,plain,
quotient(product(X1,quotient(one,X1)),X1) = difference(X1,one),
inference(spm,[status(thm)],[c_0_24,c_0_26]) ).
cnf(c_0_53,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_54,plain,
product(product(X1,quotient(X2,product(X3,X1))),X3) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_55,plain,
product(quotient(one,X1),product(X1,X2)) = product(X1,product(difference(X1,one),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_27]),c_0_47]) ).
cnf(c_0_56,plain,
product(X1,quotient(product(difference(X1,X2),X3),X1)) = product(X2,quotient(X3,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_14]) ).
cnf(c_0_57,plain,
difference(X1,difference(quotient(one,X1),X2)) = product(product(X2,quotient(one,X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_35]),c_0_23]),c_0_21]) ).
cnf(c_0_58,plain,
quotient(product(difference(X1,one),X2),X1) = difference(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_24,c_0_44]) ).
cnf(c_0_59,plain,
quotient(quotient(one,X1),product(X1,quotient(one,X1))) = difference(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_26]),c_0_50]),c_0_15]) ).
cnf(c_0_60,plain,
difference(product(X1,X1),one) = quotient(quotient(one,X1),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_32,c_0_51]),c_0_51]),c_0_25]),c_0_52]),c_0_14]),c_0_23]) ).
cnf(c_0_61,plain,
quotient(quotient(one,X1),X1) = quotient(one,product(X1,X1)),
inference(spm,[status(thm)],[c_0_53,c_0_51]) ).
cnf(c_0_62,plain,
quotient(product(X1,quotient(X2,X1)),X3) = product(X1,quotient(X2,product(X3,X1))),
inference(spm,[status(thm)],[c_0_24,c_0_54]) ).
cnf(c_0_63,plain,
product(X1,product(difference(X1,one),difference(X1,X2))) = product(quotient(one,X1),X2),
inference(spm,[status(thm)],[c_0_55,c_0_14]) ).
cnf(c_0_64,plain,
product(product(X1,quotient(X2,X1)),X1) = difference(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_37,c_0_15]) ).
cnf(c_0_65,plain,
product(X1,quotient(difference(X1,X2),X1)) = product(X2,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_56,c_0_30]) ).
cnf(c_0_66,plain,
difference(difference(X1,one),difference(X1,X2)) = product(product(X2,X1),difference(X1,one)),
inference(spm,[status(thm)],[c_0_57,c_0_53]) ).
cnf(c_0_67,plain,
product(difference(X1,one),product(X2,difference(X1,one))) = difference(X1,quotient(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_53]),c_0_58]) ).
cnf(c_0_68,plain,
quotient(product(X1,X2),product(product(X2,X1),X2)) = difference(X2,one),
inference(spm,[status(thm)],[c_0_49,c_0_21]) ).
cnf(c_0_69,plain,
difference(difference(X1,one),quotient(one,X1)) = product(X1,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_27,c_0_59]) ).
cnf(c_0_70,plain,
difference(product(X1,X1),one) = quotient(one,product(X1,X1)),
inference(rw,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,plain,
product(X1,quotient(product(X2,X1),product(X3,X1))) = quotient(product(X1,X2),X3),
inference(spm,[status(thm)],[c_0_62,c_0_24]) ).
cnf(c_0_72,plain,
difference(X1,product(quotient(one,X1),X2)) = product(difference(X1,one),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_63]) ).
cnf(c_0_73,plain,
difference(X1,product(X2,quotient(X3,X1))) = quotient(product(difference(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_74,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_64,c_0_65]),c_0_66]) ).
cnf(c_0_75,plain,
quotient(product(X1,difference(X2,one)),X2) = product(quotient(X1,X2),quotient(one,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_67]),c_0_65]),c_0_23]) ).
cnf(c_0_76,plain,
quotient(product(quotient(X1,product(X2,X2)),X2),product(X2,quotient(X1,X2))) = difference(X2,one),
inference(spm,[status(thm)],[c_0_68,c_0_54]) ).
cnf(c_0_77,plain,
difference(X1,quotient(one,quotient(one,X1))) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_27]),c_0_31]) ).
cnf(c_0_78,plain,
difference(difference(X1,one),product(product(X1,quotient(one,X1)),X2)) = quotient(product(X1,product(X2,difference(X1,one))),difference(X1,one)),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_79,plain,
difference(product(X1,X2),product(X1,X3)) = quotient(difference(X2,product(X3,X1)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_14]),c_0_16]) ).
cnf(c_0_80,plain,
product(product(X1,X1),quotient(one,product(X1,X1))) = one,
inference(spm,[status(thm)],[c_0_14,c_0_70]) ).
cnf(c_0_81,plain,
difference(X1,quotient(product(X1,X2),X3)) = quotient(product(X2,X1),product(X3,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_71]) ).
cnf(c_0_82,plain,
difference(X1,quotient(X2,quotient(one,quotient(one,X1)))) = product(difference(X1,one),product(X2,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)],[inference(spm,[status(thm)],[c_0_72,c_0_43]),c_0_73]),c_0_57]),c_0_74]),c_0_30]),c_0_75]),c_0_24]) ).
cnf(c_0_83,plain,
product(difference(X1,one),product(X1,quotient(X2,X1))) = product(quotient(X2,product(X1,X1)),X1),
inference(spm,[status(thm)],[c_0_15,c_0_76]) ).
cnf(c_0_84,plain,
product(quotient(one,quotient(one,X1)),X1) = quotient(X1,difference(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_77]),c_0_78]),c_0_14]),c_0_30]) ).
cnf(c_0_85,plain,
difference(product(product(X1,X1),X2),one) = quotient(difference(X2,one),product(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_15]) ).
cnf(c_0_86,plain,
quotient(product(X1,X2),quotient(X2,difference(X2,one))) = product(quotient(X1,product(X2,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_25]),c_0_30]),c_0_83]),c_0_84]) ).
cnf(c_0_87,plain,
product(X1,product(X1,quotient(one,X1))) = quotient(one,quotient(one,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_77]) ).
cnf(c_0_88,plain,
quotient(one,quotient(difference(X1,one),product(X2,X2))) = product(product(X2,X2),X1),
inference(spm,[status(thm)],[c_0_53,c_0_85]) ).
cnf(c_0_89,plain,
difference(product(X1,X2),X1) = quotient(difference(X2,X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_30]),c_0_23]) ).
cnf(c_0_90,plain,
difference(product(quotient(X1,product(X2,X2)),X2),product(X1,X2)) = quotient(X2,difference(X2,one)),
inference(spm,[status(thm)],[c_0_27,c_0_86]) ).
cnf(c_0_91,plain,
quotient(difference(product(X1,quotient(one,X1)),product(X2,X1)),X1) = difference(quotient(one,quotient(one,X1)),product(X1,X2)),
inference(spm,[status(thm)],[c_0_79,c_0_87]) ).
cnf(c_0_92,plain,
quotient(one,quotient(X1,product(X2,X2))) = product(product(X2,X2),quotient(one,X1)),
inference(spm,[status(thm)],[c_0_88,c_0_27]) ).
cnf(c_0_93,plain,
quotient(X1,one) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_15]) ).
cnf(c_0_94,plain,
product(product(X1,X2),quotient(one,product(X1,X1))) = product(X1,quotient(product(X2,quotient(one,X1)),X1)),
inference(spm,[status(thm)],[c_0_25,c_0_61]) ).
cnf(c_0_95,plain,
product(X1,quotient(one,product(X1,X1))) = difference(X1,one),
inference(rw,[status(thm)],[c_0_40,c_0_61]) ).
cnf(c_0_96,plain,
difference(one,X1) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_97,plain,
difference(product(X1,X2),product(product(X1,X3),X4)) = quotient(difference(X2,product(X3,product(X4,X1))),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_17]),c_0_15]) ).
cnf(c_0_98,plain,
quotient(X1,quotient(difference(X2,X1),X1)) = product(X1,X2),
inference(spm,[status(thm)],[c_0_53,c_0_89]) ).
cnf(c_0_99,plain,
difference(X1,quotient(difference(difference(X1,one),X2),X1)) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_58,c_0_14]) ).
cnf(c_0_100,plain,
quotient(quotient(product(X1,product(product(X1,X2),X1)),X1),X2) = quotient(X1,difference(X1,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(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_93]),c_0_30]),c_0_21]),c_0_94]),c_0_62]),c_0_95]),c_0_14]),c_0_96]),c_0_97]),c_0_13]) ).
cnf(c_0_101,plain,
product(difference(X1,X2),product(difference(X2,X3),X1)) = product(difference(X1,X3),X1),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_102,plain,
difference(X1,difference(quotient(one,X1),X2)) = product(product(X2,X1),difference(X1,one)),
inference(rw,[status(thm)],[c_0_57,c_0_74]) ).
cnf(c_0_103,plain,
quotient(X1,quotient(X2,X1)) = product(X1,quotient(X1,X2)),
inference(spm,[status(thm)],[c_0_98,c_0_27]) ).
cnf(c_0_104,plain,
quotient(difference(difference(X1,one),X2),X1) = product(X1,quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_99]) ).
cnf(c_0_105,plain,
quotient(product(X1,product(product(X1,X2),X1)),X1) = product(quotient(X1,difference(X1,one)),X2),
inference(spm,[status(thm)],[c_0_15,c_0_100]) ).
cnf(c_0_106,plain,
quotient(product(X1,X2),difference(X2,one)) = product(quotient(X1,quotient(one,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_101]),c_0_43]),c_0_96]) ).
cnf(c_0_107,plain,
product(product(product(quotient(one,X1),X2),X1),difference(X1,one)) = difference(X1,X2),
inference(spm,[status(thm)],[c_0_102,c_0_21]) ).
cnf(c_0_108,plain,
product(X1,quotient(X1,product(X2,X1))) = quotient(X1,X2),
inference(spm,[status(thm)],[c_0_103,c_0_24]) ).
cnf(c_0_109,plain,
product(X1,quotient(product(X2,difference(difference(X1,one),X3)),X1)) = product(product(X1,X2),product(X1,quotient(X3,X1))),
inference(spm,[status(thm)],[c_0_25,c_0_104]) ).
cnf(c_0_110,plain,
product(quotient(X1,difference(X1,one)),difference(X1,X2)) = quotient(product(X1,product(X2,X1)),X1),
inference(spm,[status(thm)],[c_0_105,c_0_14]) ).
cnf(c_0_111,plain,
quotient(difference(X1,X2),difference(X1,one)) = product(product(quotient(one,X1),X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_63]) ).
cnf(c_0_112,plain,
quotient(difference(X1,X2),difference(difference(X1,one),one)) = product(product(quotient(one,X1),X2),difference(X1,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_53]),c_0_24]) ).
cnf(c_0_113,plain,
product(quotient(one,X1),difference(X1,one)) = quotient(one,product(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_59]),c_0_61]) ).
cnf(c_0_114,plain,
product(X1,product(quotient(one,X1),quotient(X2,X1))) = product(quotient(X2,product(X1,X1)),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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_67]),c_0_111]),c_0_24]),c_0_112]),c_0_30]),c_0_113]),c_0_95]),c_0_83]) ).
cnf(c_0_115,plain,
product(quotient(product(X1,X2),product(X2,X2)),X2) = product(difference(X2,one),product(X2,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_81]) ).
cnf(c_0_116,plain,
product(difference(X1,one),product(X1,X2)) = product(X1,product(quotient(one,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_24]),c_0_115]) ).
cnf(c_0_117,plain,
difference(product(X1,X2),product(X3,quotient(one,X1))) = quotient(difference(X2,difference(X1,X3)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_65]),c_0_15]) ).
cnf(c_0_118,plain,
product(X1,product(quotient(one,X1),difference(X1,X2))) = product(difference(X1,one),X2),
inference(spm,[status(thm)],[c_0_116,c_0_14]) ).
cnf(c_0_119,plain,
quotient(difference(X1,product(difference(X2,one),X3)),X2) = difference(product(X2,X1),quotient(X3,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_42]),c_0_27]),c_0_27]),c_0_55]),c_0_21]) ).
cnf(c_0_120,plain,
difference(X1,product(difference(X1,one),X2)) = product(quotient(one,X1),difference(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_118]) ).
cnf(c_0_121,plain,
quotient(product(quotient(one,X1),difference(X1,X2)),X1) = difference(product(X1,X1),quotient(X2,X1)),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_122,plain,
quotient(difference(difference(X1,X2),product(X3,X1)),X1) = difference(X2,product(X1,X3)),
inference(spm,[status(thm)],[c_0_79,c_0_14]) ).
cnf(c_0_123,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(c_0_124,plain,
difference(product(X1,X1),quotient(product(X1,X2),X1)) = quotient(product(quotient(one,X1),X2),X1),
inference(spm,[status(thm)],[c_0_121,c_0_21]) ).
cnf(c_0_125,plain,
difference(X1,X1) = one,
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_126,plain,
difference(difference(X1,X2),product(X3,X1)) = product(difference(X2,product(X1,X3)),X1),
inference(spm,[status(thm)],[c_0_15,c_0_122]) ).
cnf(c_0_127,plain,
product(product(product(X1,X2),X1),difference(X1,one)) = difference(difference(X1,one),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_37]),c_0_14]),c_0_30]) ).
cnf(c_0_128,plain,
product(X1,product(product(X2,X1),difference(X1,one))) = difference(quotient(one,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_38]),c_0_23]),c_0_74]) ).
cnf(c_0_129,negated_conjecture,
product(x0,product(eta(x0),x1)) != product(j(j(x0)),x1),
goals ).
cnf(c_0_130,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[c_0_123,c_0_19]) ).
cnf(c_0_131,plain,
quotient(product(quotient(one,X1),quotient(X2,X1)),X1) = quotient(product(quotient(one,X1),X2),product(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_62]),c_0_73]),c_0_89]),c_0_125]) ).
cnf(c_0_132,plain,
difference(difference(X1,one),product(quotient(one,X1),X2)) = product(difference(difference(X1,one),one),difference(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_111]),c_0_126]),c_0_96]),c_0_127]) ).
cnf(c_0_133,plain,
product(difference(difference(X1,one),one),difference(X1,X2)) = product(difference(X1,one),difference(quotient(one,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_66]),c_0_53]),c_0_128]) ).
cnf(c_0_134,plain,
difference(quotient(one,X1),quotient(X2,X1)) = product(X1,product(X2,difference(X1,one))),
inference(spm,[status(thm)],[c_0_128,c_0_15]) ).
cnf(c_0_135,plain,
product(difference(X1,one),product(X2,product(X3,difference(X1,one)))) = quotient(product(product(difference(X1,one),X2),X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_17]),c_0_46]),c_0_21]) ).
cnf(c_0_136,negated_conjecture,
product(x0,product(product(difference(x0,one),x0),x1)) != product(quotient(one,quotient(one,x0)),x1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_20]),c_0_20]),c_0_130]) ).
cnf(c_0_137,plain,
quotient(product(product(X1,quotient(one,X1)),X2),X1) = product(X1,quotient(product(quotient(one,X1),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(spm,[status(thm)],[c_0_64,c_0_131]),c_0_54]),c_0_132]),c_0_133]),c_0_134]),c_0_135]),c_0_26]) ).
cnf(c_0_138,negated_conjecture,
product(x0,product(product(x0,quotient(one,x0)),x1)) != product(quotient(one,quotient(one,x0)),x1),
inference(rw,[status(thm)],[c_0_136,c_0_26]) ).
cnf(c_0_139,plain,
product(X1,product(product(X1,quotient(one,X1)),X2)) = product(quotient(one,quotient(one,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_137]),c_0_17]),c_0_87]) ).
cnf(c_0_140,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_138,c_0_139])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP764-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 21:54:10 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 9.24/9.28 % Version : CSE_E---1.5
% 9.24/9.28 % Problem : theBenchmark.p
% 9.24/9.28 % Proof found
% 9.24/9.29 % SZS status Theorem for theBenchmark.p
% 9.24/9.29 % SZS output start Proof
% See solution above
% 9.24/9.29 % Total time : 8.708000 s
% 9.24/9.29 % SZS output end Proof
% 9.24/9.29 % Total time : 8.711000 s
%------------------------------------------------------------------------------