TSTP Solution File: GRP777+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 00:23:42 EDT 2023
% Result : Theorem 0.19s 0.67s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 96 ( 88 unt; 8 typ; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn; 38 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
product: ( $i * $i ) > $i ).
tff(decl_23,type,
difference: ( $i * $i ) > $i ).
tff(decl_24,type,
quotient: ( $i * $i ) > $i ).
tff(decl_25,type,
bigC: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
a: $i ).
tff(decl_27,type,
c: $i ).
tff(decl_28,type,
b: $i ).
tff(decl_29,type,
esk1_0: $i ).
fof(sos05,axiom,
! [X3,X4,X1,X2] : product(product(X2,X1),product(X4,X3)) = product(product(X2,X4),product(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
fof(sos06,axiom,
! [X2] : product(X2,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
fof(sos03,axiom,
! [X1,X2] : quotient(product(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
fof(sos04,axiom,
! [X1,X2] : product(quotient(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
fof(sos09,axiom,
product(product(a,c),product(c,b)) = product(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
fof(sos01,axiom,
! [X1,X2] : difference(X2,product(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
fof(sos07,axiom,
! [X1,X2] : product(product(product(X2,X1),X1),product(X1,product(X1,X2))) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos07) ).
fof(sos02,axiom,
! [X1,X2] : product(X2,difference(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
fof(goals,conjecture,
! [X5] : bigC(a,b,X5) = bigC(c,c,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(sos08,axiom,
! [X4,X1,X2] : bigC(X2,X1,X4) = product(product(X2,X1),product(X4,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos08) ).
fof(c_0_10,plain,
! [X14,X15,X16,X17] : product(product(X17,X16),product(X15,X14)) = product(product(X17,X15),product(X16,X14)),
inference(variable_rename,[status(thm)],[sos05]) ).
fof(c_0_11,plain,
! [X18] : product(X18,X18) = X18,
inference(variable_rename,[status(thm)],[sos06]) ).
cnf(c_0_12,plain,
product(product(X1,X2),product(X3,X4)) = product(product(X1,X3),product(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
product(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,plain,
! [X10,X11] : quotient(product(X11,X10),X10) = X11,
inference(variable_rename,[status(thm)],[sos03]) ).
cnf(c_0_15,plain,
product(product(X1,X2),product(X3,X2)) = product(product(X1,X3),X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
quotient(product(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
product(product(X1,X2),X1) = product(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
fof(c_0_18,plain,
! [X12,X13] : product(quotient(X13,X12),X12) = X13,
inference(variable_rename,[status(thm)],[sos04]) ).
cnf(c_0_19,plain,
product(product(X1,X2),product(X1,X3)) = product(X1,product(X2,X3)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_20,plain,
product(product(a,c),product(c,b)) = product(a,b),
inference(split_conjunct,[status(thm)],[sos09]) ).
cnf(c_0_21,plain,
quotient(product(X1,product(X2,X1)),X1) = product(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
product(quotient(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_23,plain,
! [X6,X7] : difference(X7,product(X7,X6)) = X6,
inference(variable_rename,[status(thm)],[sos01]) ).
cnf(c_0_24,plain,
product(product(product(a,c),X1),product(a,b)) = product(product(a,c),product(X1,product(c,b))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
product(X1,quotient(X2,X1)) = quotient(product(X1,X2),X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
difference(X1,product(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
product(a,product(product(c,a),b)) = product(a,product(c,product(c,b))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_17]),c_0_19]),c_0_19]) ).
cnf(c_0_28,plain,
quotient(quotient(product(X1,X2),X1),quotient(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_29,plain,
quotient(product(a,b),product(c,b)) = product(a,c),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_30,plain,
product(product(c,a),b) = product(c,product(c,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_26]) ).
cnf(c_0_31,plain,
quotient(c,product(a,c)) = product(c,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_15]),c_0_30]),c_0_16]) ).
fof(c_0_32,plain,
! [X19,X20] : product(product(product(X20,X19),X19),product(X19,product(X19,X20))) = X19,
inference(variable_rename,[status(thm)],[sos07]) ).
cnf(c_0_33,plain,
product(product(a,c),product(product(c,a),product(b,c))) = product(a,product(b,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_12]),c_0_19]) ).
cnf(c_0_34,plain,
product(product(c,a),product(b,c)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_31]),c_0_12]) ).
cnf(c_0_35,plain,
product(product(product(X1,X2),X2),product(X2,product(X2,X1))) = X2,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,plain,
product(product(a,c),c) = product(a,product(b,c)),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_37,plain,
! [X8,X9] : product(X9,difference(X9,X8)) = X8,
inference(variable_rename,[status(thm)],[sos02]) ).
cnf(c_0_38,plain,
product(product(a,c),product(product(b,c),product(c,a))) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_12]) ).
cnf(c_0_39,plain,
product(X1,difference(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_40,plain,
product(product(b,c),product(c,a)) = difference(product(a,c),c),
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
cnf(c_0_41,plain,
product(X1,product(difference(X1,X2),X3)) = product(X2,product(X1,X3)),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
cnf(c_0_42,plain,
product(difference(product(a,c),c),product(b,c)) = product(product(b,c),c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_40]),c_0_34]) ).
cnf(c_0_43,plain,
product(X1,product(difference(X1,X2),X1)) = product(X2,X1),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_44,plain,
product(product(a,product(b,c)),c) = product(c,product(product(a,b),c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_15]),c_0_15]) ).
cnf(c_0_45,plain,
product(difference(X1,X2),X1) = difference(X1,product(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_46,plain,
difference(product(X1,X2),product(product(X1,X3),X2)) = product(X3,X2),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_47,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_48,plain,
product(a,product(b,c)) = product(c,product(a,b)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_44]),c_0_21]) ).
cnf(c_0_49,plain,
product(product(X1,difference(X2,X1)),product(difference(X2,X1),difference(X2,product(X1,X2)))) = difference(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_45]) ).
cnf(c_0_50,plain,
difference(product(c,b),product(c,product(c,b))) = product(a,b),
inference(spm,[status(thm)],[c_0_46,c_0_30]) ).
cnf(c_0_51,plain,
difference(product(c,b),c) = product(a,c),
inference(spm,[status(thm)],[c_0_47,c_0_31]) ).
cnf(c_0_52,plain,
product(difference(X1,product(product(X2,X1),X1)),product(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_39]),c_0_45]),c_0_45]) ).
cnf(c_0_53,plain,
product(product(a,c),c) = product(c,product(a,b)),
inference(rw,[status(thm)],[c_0_36,c_0_48]) ).
cnf(c_0_54,plain,
difference(product(product(X1,X2),X2),X2) = product(X2,product(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_35]) ).
cnf(c_0_55,plain,
product(product(c,a),product(a,b)) = product(a,c),
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_49,c_0_50]),c_0_51]),c_0_51]),c_0_19]),c_0_51]),c_0_12]),c_0_20]) ).
cnf(c_0_56,plain,
difference(product(a,product(c,b)),product(a,b)) = product(c,product(c,b)),
inference(spm,[status(thm)],[c_0_46,c_0_20]) ).
cnf(c_0_57,plain,
product(product(a,c),product(b,a)) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_26]),c_0_12]) ).
cnf(c_0_58,plain,
product(product(a,b),product(product(a,c),product(b,a))) = product(c,product(c,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_19]),c_0_56]),c_0_12]) ).
cnf(c_0_59,plain,
difference(product(a,c),c) = product(b,a),
inference(spm,[status(thm)],[c_0_26,c_0_57]) ).
cnf(c_0_60,plain,
product(product(a,b),c) = product(c,product(c,b)),
inference(rw,[status(thm)],[c_0_58,c_0_57]) ).
cnf(c_0_61,plain,
product(product(b,c),product(c,a)) = product(b,a),
inference(rw,[status(thm)],[c_0_40,c_0_59]) ).
cnf(c_0_62,plain,
product(c,product(product(b,c),product(a,b))) = c,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_60]),c_0_17]),c_0_17]),c_0_26]),c_0_19]) ).
cnf(c_0_63,plain,
difference(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_64,plain,
difference(product(X1,X2),product(X1,product(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_65,plain,
product(product(c,b),product(b,a)) = product(b,c),
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_35,c_0_61]),c_0_34]),c_0_19]),c_0_12]),c_0_40]),c_0_59]) ).
cnf(c_0_66,plain,
product(product(b,c),product(a,b)) = c,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_62]),c_0_63]) ).
cnf(c_0_67,plain,
product(product(b,c),c) = product(b,product(a,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_59]),c_0_19]) ).
cnf(c_0_68,plain,
difference(c,product(b,product(a,c))) = product(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_12]),c_0_66]),c_0_19]) ).
cnf(c_0_69,plain,
quotient(product(b,product(a,c)),c) = product(b,c),
inference(spm,[status(thm)],[c_0_16,c_0_67]) ).
cnf(c_0_70,plain,
product(b,product(a,c)) = product(c,product(b,a)),
inference(spm,[status(thm)],[c_0_39,c_0_68]) ).
fof(c_0_71,negated_conjecture,
~ ! [X5] : bigC(a,b,X5) = bigC(c,c,X5),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_72,plain,
quotient(product(X1,product(X1,X2)),X1) = difference(product(X2,X1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_22]),c_0_25]),c_0_25]) ).
cnf(c_0_73,plain,
difference(X1,quotient(product(X1,X2),X1)) = quotient(X2,X1),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_74,plain,
quotient(product(c,product(b,a)),c) = product(b,c),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_75,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])])]) ).
fof(c_0_76,plain,
! [X21,X22,X23] : bigC(X23,X22,X21) = product(product(X23,X22),product(X21,X23)),
inference(variable_rename,[status(thm)],[sos08]) ).
cnf(c_0_77,plain,
quotient(difference(product(X1,X2),X2),X2) = difference(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_25]),c_0_25]),c_0_72]),c_0_22]) ).
cnf(c_0_78,plain,
quotient(product(b,a),c) = difference(c,product(b,c)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,negated_conjecture,
bigC(a,b,esk1_0) != bigC(c,c,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_80,plain,
bigC(X1,X2,X3) = product(product(X1,X2),product(X3,X1)),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_81,plain,
difference(c,product(b,c)) = difference(a,c),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_59]),c_0_78]) ).
cnf(c_0_82,negated_conjecture,
product(product(c,c),product(esk1_0,c)) != product(product(a,b),product(esk1_0,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_80]) ).
cnf(c_0_83,plain,
product(product(X1,X2),product(difference(X1,X3),X4)) = product(X3,product(X2,X4)),
inference(spm,[status(thm)],[c_0_12,c_0_39]) ).
cnf(c_0_84,plain,
product(difference(a,c),c) = product(b,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_81]),c_0_67]),c_0_70]),c_0_26]) ).
cnf(c_0_85,negated_conjecture,
product(product(a,esk1_0),product(b,a)) != product(c,product(esk1_0,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_12]),c_0_13]) ).
cnf(c_0_86,plain,
product(product(a,X1),product(b,a)) = product(c,product(X1,c)),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP777+1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n011.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 20:27:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.67 % Version : CSE_E---1.5
% 0.19/0.67 % Problem : theBenchmark.p
% 0.19/0.67 % Proof found
% 0.19/0.67 % SZS status Theorem for theBenchmark.p
% 0.19/0.67 % SZS output start Proof
% See solution above
% 0.19/0.68 % Total time : 0.109000 s
% 0.19/0.68 % SZS output end Proof
% 0.19/0.68 % Total time : 0.112000 s
%------------------------------------------------------------------------------