TSTP Solution File: KLE088+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE088+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 05:26:04 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 26
% Syntax : Number of formulae : 89 ( 75 unt; 11 typ; 0 def)
% Number of atoms : 81 ( 80 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 7 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 96 ( 3 sgn; 52 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
addition: ( $i * $i ) > $i ).
tff(decl_23,type,
zero: $i ).
tff(decl_24,type,
multiplication: ( $i * $i ) > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
leq: ( $i * $i ) > $o ).
tff(decl_27,type,
antidomain: $i > $i ).
tff(decl_28,type,
domain: $i > $i ).
tff(decl_29,type,
coantidomain: $i > $i ).
tff(decl_30,type,
codomain: $i > $i ).
tff(decl_31,type,
esk1_0: $i ).
tff(decl_32,type,
esk2_0: $i ).
fof(goals,conjecture,
! [X4,X5] :
( multiplication(domain(X4),X5) = zero
=> addition(domain(X4),antidomain(X5)) = antidomain(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(domain4,axiom,
! [X4] : domain(X4) = antidomain(antidomain(X4)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain4) ).
fof(left_distributivity,axiom,
! [X1,X2,X3] : multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_distributivity) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(multiplicative_associativity,axiom,
! [X1,X2,X3] : multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_associativity) ).
fof(left_annihilation,axiom,
! [X1] : multiplication(zero,X1) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',left_annihilation) ).
fof(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(domain2,axiom,
! [X4,X5] : addition(antidomain(multiplication(X4,X5)),antidomain(multiplication(X4,antidomain(antidomain(X5))))) = antidomain(multiplication(X4,antidomain(antidomain(X5)))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain2) ).
fof(right_distributivity,axiom,
! [X1,X2,X3] : multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_distributivity) ).
fof(c_0_15,negated_conjecture,
~ ! [X4,X5] :
( multiplication(domain(X4),X5) = zero
=> addition(domain(X4),antidomain(X5)) = antidomain(X5) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_16,negated_conjecture,
( multiplication(domain(esk1_0),esk2_0) = zero
& addition(domain(esk1_0),antidomain(esk2_0)) != antidomain(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_17,plain,
! [X32] : domain(X32) = antidomain(antidomain(X32)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_18,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
cnf(c_0_19,negated_conjecture,
multiplication(domain(esk1_0),esk2_0) = zero,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,plain,
! [X11] : addition(X11,zero) = X11,
inference(variable_rename,[status(thm)],[additive_identity]) ).
cnf(c_0_22,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),esk2_0) = zero,
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_25,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_26,plain,
! [X31] : addition(antidomain(antidomain(X31)),antidomain(X31)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_27,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_28,plain,
! [X28] : multiplication(antidomain(X28),X28) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_29,plain,
! [X13,X14,X15] : multiplication(X13,multiplication(X14,X15)) = multiplication(multiplication(X13,X14),X15),
inference(variable_rename,[status(thm)],[multiplicative_associativity]) ).
fof(c_0_30,plain,
! [X25] : multiplication(zero,X25) = zero,
inference(variable_rename,[status(thm)],[left_annihilation]) ).
cnf(c_0_31,negated_conjecture,
multiplication(addition(X1,antidomain(antidomain(esk1_0))),esk2_0) = multiplication(X1,esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_32,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_34,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_0_35,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_37,plain,
! [X8,X9,X10] : addition(X10,addition(X9,X8)) = addition(addition(X10,X9),X8),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_38,plain,
! [X12] : addition(X12,X12) = X12,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
cnf(c_0_39,plain,
multiplication(X1,multiplication(X2,X3)) = multiplication(multiplication(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,plain,
multiplication(zero,X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_41,negated_conjecture,
multiplication(addition(antidomain(antidomain(esk1_0)),X1),esk2_0) = multiplication(X1,esk2_0),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_42,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_43,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_44,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_47,plain,
! [X29,X30] : addition(antidomain(multiplication(X29,X30)),antidomain(multiplication(X29,antidomain(antidomain(X30))))) = antidomain(multiplication(X29,antidomain(antidomain(X30)))),
inference(variable_rename,[status(thm)],[domain2]) ).
cnf(c_0_48,plain,
multiplication(antidomain(X1),multiplication(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_36]),c_0_40]) ).
cnf(c_0_49,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(esk1_0))),esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_50,plain,
addition(zero,antidomain(zero)) = one,
inference(spm,[status(thm)],[c_0_42,c_0_44]) ).
cnf(c_0_51,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_52,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,plain,
addition(antidomain(multiplication(X1,X2)),antidomain(multiplication(X1,antidomain(antidomain(X2))))) = antidomain(multiplication(X1,antidomain(antidomain(X2)))),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(esk1_0)))),esk2_0) = zero,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
addition(one,antidomain(X1)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_42]),c_0_32]) ).
cnf(c_0_57,negated_conjecture,
antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(esk1_0)))),antidomain(antidomain(esk2_0)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_56]) ).
cnf(c_0_58,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(esk1_0)))),antidomain(antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_57]),c_0_43]) ).
cnf(c_0_59,negated_conjecture,
antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(esk1_0)))),antidomain(antidomain(antidomain(antidomain(esk2_0)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_58]),c_0_55]),c_0_56]) ).
fof(c_0_60,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_61,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_36]),c_0_24]) ).
cnf(c_0_62,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(esk1_0)))),antidomain(antidomain(antidomain(antidomain(esk2_0))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_59]),c_0_43]) ).
cnf(c_0_63,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_64,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_61,c_0_32]) ).
cnf(c_0_65,negated_conjecture,
antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(esk1_0)))),antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0)))))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_62]),c_0_55]),c_0_56]) ).
cnf(c_0_66,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_36]),c_0_24]) ).
cnf(c_0_67,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_42]),c_0_43]) ).
cnf(c_0_68,negated_conjecture,
multiplication(antidomain(antidomain(antidomain(antidomain(esk1_0)))),antidomain(antidomain(antidomain(antidomain(antidomain(antidomain(esk2_0))))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_65]),c_0_43]) ).
cnf(c_0_69,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_42]),c_0_35]),c_0_67]) ).
cnf(c_0_70,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),antidomain(antidomain(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_69]),c_0_69]) ).
cnf(c_0_71,negated_conjecture,
addition(domain(esk1_0),antidomain(esk2_0)) != antidomain(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_72,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),addition(antidomain(antidomain(esk2_0)),X1)) = multiplication(antidomain(antidomain(esk1_0)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_70]),c_0_51]) ).
cnf(c_0_73,negated_conjecture,
addition(antidomain(antidomain(esk1_0)),antidomain(esk2_0)) != antidomain(esk2_0),
inference(rw,[status(thm)],[c_0_71,c_0_20]) ).
cnf(c_0_74,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_43]),c_0_32]) ).
cnf(c_0_75,negated_conjecture,
multiplication(antidomain(antidomain(esk1_0)),antidomain(esk2_0)) = antidomain(antidomain(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_42]),c_0_35]),c_0_69]) ).
cnf(c_0_76,negated_conjecture,
addition(antidomain(esk2_0),antidomain(antidomain(esk1_0))) != antidomain(esk2_0),
inference(rw,[status(thm)],[c_0_73,c_0_32]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_32]),c_0_56]),c_0_43]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE088+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 29 11:08:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.51 start to proof: theBenchmark
% 0.19/0.61 % Version : CSE_E---1.5
% 0.19/0.61 % Problem : theBenchmark.p
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark.p
% 0.19/0.61 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.091000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.094000 s
%------------------------------------------------------------------------------