TSTP Solution File: RNG088+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG088+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 : n024.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 13:49:03 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 38
% Syntax : Number of formulae : 67 ( 17 unt; 31 typ; 0 def)
% Number of atoms : 97 ( 5 equ)
% Maximal formula atoms : 29 ( 2 avg)
% Number of connectives : 97 ( 36 ~; 37 |; 17 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 20 >; 21 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 11 con; 0-4 aty)
% Number of variables : 27 ( 0 sgn; 17 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aElement0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
smndt0: $i > $i ).
tff(decl_26,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_28,type,
aSet0: $i > $o ).
tff(decl_29,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_30,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(decl_31,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(decl_32,type,
aIdeal0: $i > $o ).
tff(decl_33,type,
xI: $i ).
tff(decl_34,type,
xJ: $i ).
tff(decl_35,type,
xx: $i ).
tff(decl_36,type,
xy: $i ).
tff(decl_37,type,
xz: $i ).
tff(decl_38,type,
xk: $i ).
tff(decl_39,type,
xl: $i ).
tff(decl_40,type,
xm: $i ).
tff(decl_41,type,
xn: $i ).
tff(decl_42,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_45,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_46,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk9_1: $i > $i ).
tff(decl_51,type,
esk10_1: $i > $i ).
tff(decl_52,type,
esk11_1: $i > $i ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
fof(m__967,hypothesis,
( aElementOf0(xm,xI)
& aElementOf0(xn,xJ)
& xy = sdtpldt0(xm,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__967) ).
fof(m__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(m__,conjecture,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__934,hypothesis,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& xx = sdtpldt0(xk,xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_7,plain,
! [X60,X61,X62,X63,X64] :
( ( aSet0(X60)
| ~ aIdeal0(X60) )
& ( ~ aElementOf0(X62,X60)
| aElementOf0(sdtpldt0(X61,X62),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( ~ aElement0(X63)
| aElementOf0(sdtasdt0(X63,X61),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( aElementOf0(esk9_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) ) ),
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)],[mDefIdeal])])])])])]) ).
cnf(c_0_8,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_9,hypothesis,
aElementOf0(xn,xJ),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_10,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_11,plain,
! [X32,X33] :
( ~ aSet0(X32)
| ~ aElementOf0(X33,X32)
| aElement0(X33) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
cnf(c_0_12,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_13,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,hypothesis,
( aElementOf0(sdtpldt0(xn,X1),xJ)
| ~ aElementOf0(X1,xJ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_15,hypothesis,
aElementOf0(xl,xJ),
inference(split_conjunct,[status(thm)],[m__934]) ).
fof(c_0_16,plain,
! [X12,X13] :
( ~ aElement0(X12)
| ~ aElement0(X13)
| sdtpldt0(X12,X13) = sdtpldt0(X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_17,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_19,hypothesis,
aElementOf0(xm,xI),
inference(split_conjunct,[status(thm)],[m__967]) ).
cnf(c_0_20,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_21,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(fof_nnf,[status(thm)],[c_0_13]) ).
cnf(c_0_22,hypothesis,
aElementOf0(sdtpldt0(xn,xl),xJ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,hypothesis,
aElement0(xl),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_18])]) ).
cnf(c_0_25,hypothesis,
aElement0(xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_9]),c_0_18])]) ).
cnf(c_0_26,hypothesis,
( aElementOf0(sdtpldt0(xm,X1),xI)
| ~ aElementOf0(X1,xI) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_19]),c_0_20])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(xk,xI),
inference(split_conjunct,[status(thm)],[m__934]) ).
cnf(c_0_28,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xk,xm),xI)
| ~ aElementOf0(sdtpldt0(xl,xn),xJ) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_31,hypothesis,
aElementOf0(sdtpldt0(xm,xk),xI),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,hypothesis,
aElement0(xk),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_27]),c_0_28])]) ).
cnf(c_0_33,hypothesis,
aElement0(xm),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_28])]) ).
cnf(c_0_34,negated_conjecture,
~ aElementOf0(sdtpldt0(xk,xm),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_35,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_32]),c_0_33])]),c_0_34]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG088+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 03:08:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.20/0.65 % Version : CSE_E---1.5
% 0.20/0.65 % Problem : theBenchmark.p
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark.p
% 0.20/0.65 % SZS output start Proof
% See solution above
% 0.20/0.66 % Total time : 0.054000 s
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time : 0.057000 s
%------------------------------------------------------------------------------