TSTP Solution File: KLE029+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : KLE029+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 05:25:46 EDT 2023
% Result : Theorem 178.90s 179.12s
% Output : CNFRefutation 178.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 70 ( 16 unt; 12 typ; 0 def)
% Number of atoms : 172 ( 13 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 185 ( 71 ~; 91 |; 16 &)
% ( 6 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 7 >; 11 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 113 ( 6 sgn; 41 !; 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,
ismeet: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
ismeetu: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
esk3_0: $i ).
tff(decl_32,type,
esk4_0: $i ).
tff(decl_33,type,
esk5_0: $i ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ismeet(X4,X5,X6)
<=> ismeetu(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(additive_associativity,axiom,
! [X3,X2,X1] : addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_associativity) ).
fof(additive_idempotence,axiom,
! [X1] : addition(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',additive_idempotence) ).
fof(ismeetu,axiom,
! [X4,X5,X6] :
( ismeetu(X6,X4,X5)
<=> ! [X7] :
( ( leq(X7,X4)
& leq(X7,X5) )
<=> leq(X7,X6) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+3.ax',ismeetu) ).
fof(order,axiom,
! [X1,X2] :
( leq(X1,X2)
<=> addition(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+0.ax',order) ).
fof(ismeet,axiom,
! [X4,X5,X6] :
( ismeet(X6,X4,X5)
<=> ( leq(X6,X4)
& leq(X6,X5)
& ! [X7] :
( ( leq(X7,X4)
& leq(X7,X5) )
=> leq(X7,X6) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE001+3.ax',ismeet) ).
fof(c_0_6,negated_conjecture,
~ ! [X4,X5,X6] :
( ismeet(X4,X5,X6)
<=> ismeetu(X4,X5,X6) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_7,plain,
! [X10,X11,X12] : addition(X12,addition(X11,X10)) = addition(addition(X12,X11),X10),
inference(variable_rename,[status(thm)],[additive_associativity]) ).
fof(c_0_8,plain,
! [X14] : addition(X14,X14) = X14,
inference(variable_rename,[status(thm)],[additive_idempotence]) ).
fof(c_0_9,plain,
! [X38,X39,X40,X41,X42,X43,X44,X45] :
( ( ~ leq(X41,X38)
| ~ leq(X41,X39)
| leq(X41,X40)
| ~ ismeetu(X40,X38,X39) )
& ( leq(X42,X38)
| ~ leq(X42,X40)
| ~ ismeetu(X40,X38,X39) )
& ( leq(X42,X39)
| ~ leq(X42,X40)
| ~ ismeetu(X40,X38,X39) )
& ( ~ leq(esk2_3(X43,X44,X45),X43)
| ~ leq(esk2_3(X43,X44,X45),X44)
| ~ leq(esk2_3(X43,X44,X45),X45)
| ismeetu(X45,X43,X44) )
& ( leq(esk2_3(X43,X44,X45),X43)
| leq(esk2_3(X43,X44,X45),X45)
| ismeetu(X45,X43,X44) )
& ( leq(esk2_3(X43,X44,X45),X44)
| leq(esk2_3(X43,X44,X45),X45)
| ismeetu(X45,X43,X44) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ismeetu])])])])])]) ).
fof(c_0_10,negated_conjecture,
( ( ~ ismeet(esk3_0,esk4_0,esk5_0)
| ~ ismeetu(esk3_0,esk4_0,esk5_0) )
& ( ismeet(esk3_0,esk4_0,esk5_0)
| ismeetu(esk3_0,esk4_0,esk5_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_11,plain,
! [X28,X29] :
( ( ~ leq(X28,X29)
| addition(X28,X29) = X29 )
& ( addition(X28,X29) != X29
| leq(X28,X29) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[order])]) ).
cnf(c_0_12,plain,
addition(X1,addition(X2,X3)) = addition(addition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
addition(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeetu(X3,X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| ismeetu(esk3_0,esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( leq(X1,X2)
| addition(X1,X2) != X2 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X30,X31,X32,X33,X34,X35,X36] :
( ( leq(X32,X30)
| ~ ismeet(X32,X30,X31) )
& ( leq(X32,X31)
| ~ ismeet(X32,X30,X31) )
& ( ~ leq(X33,X30)
| ~ leq(X33,X31)
| leq(X33,X32)
| ~ ismeet(X32,X30,X31) )
& ( leq(esk1_3(X34,X35,X36),X34)
| ~ leq(X36,X34)
| ~ leq(X36,X35)
| ismeet(X36,X34,X35) )
& ( leq(esk1_3(X34,X35,X36),X35)
| ~ leq(X36,X34)
| ~ leq(X36,X35)
| ismeet(X36,X34,X35) )
& ( ~ leq(esk1_3(X34,X35,X36),X36)
| ~ leq(X36,X34)
| ~ leq(X36,X35)
| ismeet(X36,X34,X35) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[ismeet])])])])])]) ).
cnf(c_0_18,plain,
addition(X1,addition(X1,X2)) = addition(X1,X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( addition(X1,X2) = X2
| ~ leq(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(X1,esk5_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
leq(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_22,plain,
( leq(X1,X2)
| ~ ismeet(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeetu(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_24,plain,
leq(X1,addition(X1,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
cnf(c_0_25,plain,
( addition(X1,addition(X2,X3)) = X3
| ~ leq(addition(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_26,plain,
( leq(esk1_3(X1,X2,X3),X2)
| ismeet(X3,X1,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,negated_conjecture,
leq(esk3_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(X1,esk4_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_29,plain,
( leq(X1,X2)
| ~ ismeet(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_30,plain,
( leq(X1,X2)
| ~ leq(addition(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,plain,
( leq(X1,X4)
| ~ leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeetu(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_32,plain,
( leq(X1,X4)
| ~ leq(X1,X2)
| ~ leq(X1,X3)
| ~ ismeet(X4,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,negated_conjecture,
( ismeet(esk3_0,X1,esk5_0)
| leq(esk1_3(X1,esk5_0,esk3_0),esk5_0)
| ~ leq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_34,negated_conjecture,
leq(esk3_0,esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_21]),c_0_29]) ).
cnf(c_0_35,plain,
( leq(esk1_3(X1,X2,X3),X1)
| ismeet(X3,X1,X2)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_36,plain,
( leq(X1,X2)
| ~ leq(X3,X2)
| ~ leq(X1,X3) ),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_37,negated_conjecture,
( leq(X1,esk3_0)
| ~ leq(X1,esk5_0)
| ~ leq(X1,esk4_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_15]),c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(esk1_3(esk4_0,esk5_0,esk3_0),esk5_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,negated_conjecture,
( ismeet(esk3_0,X1,esk5_0)
| leq(esk1_3(X1,esk5_0,esk3_0),X1)
| ~ leq(esk3_0,X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_40,negated_conjecture,
( leq(X1,esk4_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(esk1_3(esk4_0,esk5_0,esk3_0),esk3_0)
| ~ leq(esk1_3(esk4_0,esk5_0,esk3_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(esk1_3(esk4_0,esk5_0,esk3_0),esk4_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_21])]) ).
cnf(c_0_43,plain,
( leq(esk2_3(X1,X2,X3),X2)
| leq(esk2_3(X1,X2,X3),X3)
| ismeetu(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_44,plain,
( ismeet(X3,X1,X2)
| ~ leq(esk1_3(X1,X2,X3),X3)
| ~ leq(X3,X1)
| ~ leq(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_45,negated_conjecture,
( ismeet(esk3_0,esk4_0,esk5_0)
| leq(esk1_3(esk4_0,esk5_0,esk3_0),esk3_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( ismeetu(X1,X2,esk5_0)
| leq(esk2_3(X2,esk5_0,X1),esk3_0)
| leq(esk2_3(X2,esk5_0,X1),X1)
| ~ leq(esk2_3(X2,esk5_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_43]) ).
cnf(c_0_47,plain,
( leq(esk2_3(X1,X2,X3),X1)
| leq(esk2_3(X1,X2,X3),X3)
| ismeetu(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_48,negated_conjecture,
( ~ ismeet(esk3_0,esk4_0,esk5_0)
| ~ ismeetu(esk3_0,esk4_0,esk5_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_49,negated_conjecture,
ismeet(esk3_0,esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_27]),c_0_34])]) ).
cnf(c_0_50,negated_conjecture,
( ismeetu(X1,esk4_0,esk5_0)
| leq(esk2_3(esk4_0,esk5_0,X1),esk3_0)
| leq(esk2_3(esk4_0,esk5_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,negated_conjecture,
~ ismeetu(esk3_0,esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]) ).
cnf(c_0_52,plain,
( ismeetu(X3,X1,X2)
| ~ leq(esk2_3(X1,X2,X3),X1)
| ~ leq(esk2_3(X1,X2,X3),X2)
| ~ leq(esk2_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_53,negated_conjecture,
leq(esk2_3(esk4_0,esk5_0,esk3_0),esk3_0),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_50]),c_0_51]) ).
cnf(c_0_54,negated_conjecture,
( ~ leq(esk2_3(esk4_0,esk5_0,esk3_0),esk5_0)
| ~ leq(esk2_3(esk4_0,esk5_0,esk3_0),esk4_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( leq(X1,esk5_0)
| ~ leq(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_27]) ).
cnf(c_0_56,negated_conjecture,
~ leq(esk2_3(esk4_0,esk5_0,esk3_0),esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_53])]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_40]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE029+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n016.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 12:16:00 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.18/0.54 start to proof: theBenchmark
% 178.90/179.12 % Version : CSE_E---1.5
% 178.90/179.12 % Problem : theBenchmark.p
% 178.90/179.12 % Proof found
% 178.90/179.12 % SZS status Theorem for theBenchmark.p
% 178.90/179.12 % SZS output start Proof
% See solution above
% 178.90/179.12 % Total time : 178.427000 s
% 178.90/179.12 % SZS output end Proof
% 178.90/179.12 % Total time : 178.436000 s
%------------------------------------------------------------------------------