TSTP Solution File: KLE055+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE055+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 : n006.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 05:25:53 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of formulae : 40 ( 30 unt; 7 typ; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 45 ( 2 sgn; 26 !; 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,
domain: $i > $i ).
tff(decl_28,type,
esk1_0: $i ).
fof(goals,conjecture,
! [X4] :
( addition(X4,one) = one
=> addition(X4,domain(X4)) = domain(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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_right_identity,axiom,
! [X1] : multiplication(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_right_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(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(multiplicative_left_identity,axiom,
! [X1] : multiplication(one,X1) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+0.ax',multiplicative_left_identity) ).
fof(domain3,axiom,
! [X4] : addition(domain(X4),one) = one,
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain3) ).
fof(domain1,axiom,
! [X4] : addition(X4,multiplication(domain(X4),X4)) = multiplication(domain(X4),X4),
file('/export/starexec/sandbox2/benchmark/Axioms/KLE001+5.ax',domain1) ).
fof(c_0_8,negated_conjecture,
~ ! [X4] :
( addition(X4,one) = one
=> addition(X4,domain(X4)) = domain(X4) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_9,plain,
! [X18,X19,X20] : multiplication(X18,addition(X19,X20)) = addition(multiplication(X18,X19),multiplication(X18,X20)),
inference(variable_rename,[status(thm)],[right_distributivity]) ).
fof(c_0_10,plain,
! [X16] : multiplication(X16,one) = X16,
inference(variable_rename,[status(thm)],[multiplicative_right_identity]) ).
fof(c_0_11,negated_conjecture,
( addition(esk1_0,one) = one
& addition(esk1_0,domain(esk1_0)) != domain(esk1_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_12,plain,
! [X6,X7] : addition(X6,X7) = addition(X7,X6),
inference(variable_rename,[status(thm)],[additive_commutativity]) ).
fof(c_0_13,plain,
! [X21,X22,X23] : multiplication(addition(X21,X22),X23) = addition(multiplication(X21,X23),multiplication(X22,X23)),
inference(variable_rename,[status(thm)],[left_distributivity]) ).
fof(c_0_14,plain,
! [X17] : multiplication(one,X17) = X17,
inference(variable_rename,[status(thm)],[multiplicative_left_identity]) ).
fof(c_0_15,plain,
! [X31] : addition(domain(X31),one) = one,
inference(variable_rename,[status(thm)],[domain3]) ).
cnf(c_0_16,plain,
multiplication(X1,addition(X2,X3)) = addition(multiplication(X1,X2),multiplication(X1,X3)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
multiplication(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
addition(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,plain,
addition(X1,X2) = addition(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_20,plain,
! [X28] : addition(X28,multiplication(domain(X28),X28)) = multiplication(domain(X28),X28),
inference(variable_rename,[status(thm)],[domain1]) ).
cnf(c_0_21,plain,
multiplication(addition(X1,X2),X3) = addition(multiplication(X1,X3),multiplication(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
multiplication(one,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
addition(domain(X1),one) = one,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
addition(X1,multiplication(X1,X2)) = multiplication(X1,addition(one,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
addition(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,plain,
addition(X1,multiplication(domain(X1),X1)) = multiplication(domain(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
addition(X1,multiplication(X2,X1)) = multiplication(addition(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19]) ).
cnf(c_0_28,plain,
addition(one,domain(X1)) = one,
inference(rw,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_29,negated_conjecture,
addition(X1,multiplication(X1,esk1_0)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17]) ).
cnf(c_0_30,plain,
multiplication(domain(X1),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]),c_0_28]),c_0_22]) ).
cnf(c_0_31,negated_conjecture,
addition(esk1_0,domain(esk1_0)) != domain(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_19]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE055+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n006.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 11:41:21 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 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 : 0.045000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.048000 s
%------------------------------------------------------------------------------