TSTP Solution File: KLE131+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE131+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 : n029.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 05:26:29 EDT 2023
% Result : Theorem 0.57s 0.65s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 32
% Syntax : Number of formulae : 81 ( 60 unt; 18 typ; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 1 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 15 >; 8 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 1 sgn; 45 !; 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,
c: $i > $i ).
tff(decl_32,type,
domain_difference: ( $i * $i ) > $i ).
tff(decl_33,type,
forward_diamond: ( $i * $i ) > $i ).
tff(decl_34,type,
backward_diamond: ( $i * $i ) > $i ).
tff(decl_35,type,
forward_box: ( $i * $i ) > $i ).
tff(decl_36,type,
backward_box: ( $i * $i ) > $i ).
tff(decl_37,type,
divergence: $i > $i ).
tff(decl_38,type,
star: $i > $i ).
tff(decl_39,type,
esk1_0: $i ).
fof(forward_diamond,axiom,
! [X4,X5] : forward_diamond(X4,X5) = domain(multiplication(X4,domain(X5))),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',forward_diamond) ).
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(domain1,axiom,
! [X4] : multiplication(antidomain(X4),X4) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain1) ).
fof(additive_identity,axiom,
! [X1] : addition(X1,zero) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_identity) ).
fof(domain3,axiom,
! [X4] : addition(antidomain(antidomain(X4)),antidomain(X4)) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+4.ax',domain3) ).
fof(additive_commutativity,axiom,
! [X1,X2] : addition(X1,X2) = addition(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',additive_commutativity) ).
fof(divergence1,axiom,
! [X4] : forward_diamond(X4,divergence(X4)) = divergence(X4),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+7.ax',divergence1) ).
fof(goals,conjecture,
! [X4] :
( divergence(X4) = zero
<= ! [X5] : addition(domain(X5),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(domain_difference,axiom,
! [X4,X5] : domain_difference(X4,X5) = multiplication(domain(X4),antidomain(X5)),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+6.ax',domain_difference) ).
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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(multiplicative_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_identity) ).
fof(right_annihilation,axiom,
! [X1] : multiplication(X1,zero) = zero,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',right_annihilation) ).
fof(c_0_14,plain,
! [X42,X43] : forward_diamond(X42,X43) = domain(multiplication(X42,domain(X43))),
inference(variable_rename,[status(thm)],[forward_diamond]) ).
fof(c_0_15,plain,
! [X33] : domain(X33) = antidomain(antidomain(X33)),
inference(variable_rename,[status(thm)],[domain4]) ).
fof(c_0_16,plain,
! [X22,X23,X24] : multiplication(addition(X22,X23),X24) = addition(multiplication(X22,X24),multiplication(X23,X24)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_17,plain,
! [X29] : multiplication(antidomain(X29),X29) = zero,
inference(variable_rename,[status(thm)],[domain1]) ).
fof(c_0_18,plain,
! [X12] : addition(X12,zero) = X12,
inference(variable_rename,[status(thm)],[additive_identity]) ).
fof(c_0_19,plain,
! [X32] : addition(antidomain(antidomain(X32)),antidomain(X32)) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
fof(c_0_20,plain,
! [X7,X8] : addition(X7,X8) = addition(X8,X7),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_21,plain,
! [X50] : forward_diamond(X50,divergence(X50)) = divergence(X50),
inference(variable_rename,[status(thm)],[divergence1]) ).
cnf(c_0_22,plain,
forward_diamond(X1,X2) = domain(multiplication(X1,domain(X2))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
domain(X1) = antidomain(antidomain(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,plain,
multiplication(antidomain(X1),X1) = zero,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
addition(X1,zero) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,negated_conjecture,
~ ! [X4] :
( ! [X5] : addition(domain(X5),forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))) = forward_diamond(star(X4),domain_difference(domain(X5),forward_diamond(X4,domain(X5))))
=> divergence(X4) = zero ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goals])]) ).
fof(c_0_28,plain,
! [X40,X41] : domain_difference(X40,X41) = multiplication(domain(X40),antidomain(X41)),
inference(variable_rename,[status(thm)],[domain_difference]) ).
fof(c_0_29,plain,
! [X19,X20,X21] : multiplication(X19,addition(X20,X21)) = addition(multiplication(X19,X20),multiplication(X19,X21)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
cnf(c_0_30,plain,
addition(antidomain(antidomain(X1)),antidomain(X1)) = one,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_32,plain,
forward_diamond(X1,divergence(X1)) = divergence(X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,plain,
forward_diamond(X1,X2) = antidomain(antidomain(multiplication(X1,antidomain(antidomain(X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]) ).
cnf(c_0_34,plain,
multiplication(addition(X1,antidomain(X2)),X2) = multiplication(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
fof(c_0_35,plain,
! [X18] : multiplication(one,X18) = X18,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_36,negated_conjecture,
! [X55] :
( addition(domain(X55),forward_diamond(star(esk1_0),domain_difference(domain(X55),forward_diamond(esk1_0,domain(X55))))) = forward_diamond(star(esk1_0),domain_difference(domain(X55),forward_diamond(esk1_0,domain(X55))))
& divergence(esk1_0) != zero ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])])]) ).
cnf(c_0_37,plain,
domain_difference(X1,X2) = multiplication(domain(X1),antidomain(X2)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,plain,
addition(antidomain(X1),antidomain(antidomain(X1))) = one,
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
antidomain(antidomain(multiplication(X1,antidomain(antidomain(divergence(X1)))))) = divergence(X1),
inference(rw,[status(thm)],[c_0_32,c_0_33]) ).
fof(c_0_41,plain,
! [X17] : multiplication(X17,one) = X17,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
cnf(c_0_42,plain,
multiplication(addition(antidomain(X1),X2),X1) = multiplication(X2,X1),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_43,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
addition(domain(X1),forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1))))) = forward_diamond(star(esk1_0),domain_difference(domain(X1),forward_diamond(esk1_0,domain(X1)))),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,plain,
domain_difference(X1,X2) = multiplication(antidomain(antidomain(X1)),antidomain(X2)),
inference(rw,[status(thm)],[c_0_37,c_0_23]) ).
cnf(c_0_46,plain,
multiplication(antidomain(X1),addition(X2,X1)) = multiplication(antidomain(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_25]),c_0_26]) ).
cnf(c_0_47,plain,
addition(divergence(X1),antidomain(divergence(X1))) = one,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
multiplication(antidomain(antidomain(X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_39]),c_0_43]) ).
cnf(c_0_50,negated_conjecture,
addition(antidomain(antidomain(X1)),antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(X1))))))))))))))) = antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(antidomain(antidomain(antidomain(antidomain(X1)))),antidomain(antidomain(antidomain(multiplication(esk1_0,antidomain(antidomain(antidomain(antidomain(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_45]),c_0_45]) ).
cnf(c_0_51,plain,
antidomain(antidomain(divergence(X1))) = divergence(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49]) ).
cnf(c_0_52,plain,
antidomain(antidomain(antidomain(X1))) = antidomain(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_39]),c_0_48]),c_0_49]) ).
cnf(c_0_53,plain,
antidomain(one) = zero,
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_54,plain,
addition(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
fof(c_0_55,plain,
! [X25] : multiplication(X25,zero) = zero,
inference(variable_rename,[status(thm)],[right_annihilation]) ).
cnf(c_0_56,negated_conjecture,
addition(divergence(X1),antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(divergence(X1),antidomain(multiplication(esk1_0,divergence(X1)))))))))) = antidomain(antidomain(multiplication(star(esk1_0),antidomain(antidomain(multiplication(divergence(X1),antidomain(multiplication(esk1_0,divergence(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_50,c_0_40]),c_0_51]),c_0_51]),c_0_52]),c_0_51]),c_0_51]),c_0_52]) ).
cnf(c_0_57,plain,
antidomain(multiplication(X1,divergence(X1))) = antidomain(divergence(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_40]),c_0_51]) ).
cnf(c_0_58,plain,
multiplication(divergence(X1),antidomain(divergence(X1))) = zero,
inference(spm,[status(thm)],[c_0_25,c_0_51]) ).
cnf(c_0_59,plain,
antidomain(zero) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_53]),c_0_54]) ).
cnf(c_0_60,plain,
multiplication(X1,zero) = zero,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_61,negated_conjecture,
divergence(esk1_0) != zero,
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(sr,[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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_59]),c_0_53]),c_0_60]),c_0_59]),c_0_53]),c_0_26]),c_0_58]),c_0_59]),c_0_53]),c_0_60]),c_0_59]),c_0_53]),c_0_61]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE131+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
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 11:41:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.57/0.65 % Version : CSE_E---1.5
% 0.57/0.65 % Problem : theBenchmark.p
% 0.57/0.65 % Proof found
% 0.57/0.65 % SZS status Theorem for theBenchmark.p
% 0.57/0.65 % SZS output start Proof
% See solution above
% 0.57/0.66 % Total time : 0.102000 s
% 0.57/0.66 % SZS output end Proof
% 0.57/0.66 % Total time : 0.105000 s
%------------------------------------------------------------------------------