TSTP Solution File: RNG087+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG087+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 : n003.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 13:49:02 EDT 2023
% Result : Theorem 2.64s 2.90s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 34
% Syntax : Number of formulae : 55 ( 9 unt; 29 typ; 0 def)
% Number of atoms : 151 ( 25 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 207 ( 82 ~; 90 |; 28 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 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 : 25 ( 25 usr; 9 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn; 25 !; 6 ?; 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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_43,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk9_1: $i > $i ).
tff(decl_49,type,
esk10_1: $i > $i ).
tff(decl_50,type,
esk11_1: $i > $i ).
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( aElementOf0(X5,X1)
& aElementOf0(X6,X2)
& sdtpldt0(X5,X6) = X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
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__,conjecture,
? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xy = sdtpldt0(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(m__901,hypothesis,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
fof(c_0_5,plain,
! [X38,X39,X40,X41,X44,X45,X46,X47,X49,X50] :
( ( aSet0(X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk3_4(X38,X39,X40,X41),X38)
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk4_4(X38,X39,X40,X41),X39)
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( sdtpldt0(esk3_4(X38,X39,X40,X41),esk4_4(X38,X39,X40,X41)) = X41
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( ~ aElementOf0(X45,X38)
| ~ aElementOf0(X46,X39)
| sdtpldt0(X45,X46) != X44
| aElementOf0(X44,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( ~ aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aElementOf0(X49,X38)
| ~ aElementOf0(X50,X39)
| sdtpldt0(X49,X50) != esk5_3(X38,X39,X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk6_3(X38,X39,X47),X38)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk7_3(X38,X39,X47),X39)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( sdtpldt0(esk6_3(X38,X39,X47),esk7_3(X38,X39,X47)) = esk5_3(X38,X39,X47)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) ) ),
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)],[mDefSSum])])])])])]) ).
fof(c_0_6,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])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ? [X1,X2] :
( aElementOf0(X1,xI)
& aElementOf0(X2,xJ)
& xy = sdtpldt0(X1,X2) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_8,plain,
( sdtpldt0(esk3_4(X1,X2,X3,X4),esk4_4(X1,X2,X3,X4)) = X4
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_11,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
cnf(c_0_12,plain,
( aElementOf0(esk4_4(X1,X2,X3,X4),X2)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( aElementOf0(esk3_4(X1,X2,X3,X4),X1)
| ~ aElementOf0(X4,X3)
| X3 != sdtpldt1(X1,X2)
| ~ aSet0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_14,negated_conjecture,
! [X68,X69] :
( ~ aElementOf0(X68,xI)
| ~ aElementOf0(X69,xJ)
| xy != sdtpldt0(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
cnf(c_0_15,plain,
( sdtpldt0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),esk4_4(X1,X2,sdtpldt1(X1,X2),X3)) = X3
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xy,sdtpldt1(xI,xJ)),
inference(split_conjunct,[status(thm)],[m__901]) ).
cnf(c_0_17,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_18,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_19,plain,
( aElementOf0(esk4_4(X1,X2,sdtpldt1(X1,X2),X3),X2)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( aElementOf0(esk3_4(X1,X2,sdtpldt1(X1,X2),X3),X1)
| ~ aElementOf0(X3,sdtpldt1(X1,X2))
| ~ aSet0(X2)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ aElementOf0(X2,xJ)
| xy != sdtpldt0(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,hypothesis,
sdtpldt0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xy),esk4_4(xI,xJ,sdtpldt1(xI,xJ),xy)) = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_23,hypothesis,
aElementOf0(esk4_4(xI,xJ,sdtpldt1(xI,xJ),xy),xJ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_24,hypothesis,
aElementOf0(esk3_4(xI,xJ,sdtpldt1(xI,xJ),xy),xI),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG087+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 01:39:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.61 start to proof: theBenchmark
% 2.64/2.90 % Version : CSE_E---1.5
% 2.64/2.90 % Problem : theBenchmark.p
% 2.64/2.90 % Proof found
% 2.64/2.90 % SZS status Theorem for theBenchmark.p
% 2.64/2.90 % SZS output start Proof
% See solution above
% 2.64/2.90 % Total time : 2.276000 s
% 2.64/2.90 % SZS output end Proof
% 2.64/2.90 % Total time : 2.279000 s
%------------------------------------------------------------------------------