TSTP Solution File: RNG091+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG091+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 : n008.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 13:49:04 EDT 2023
% Result : Theorem 0.59s 0.84s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 39
% Syntax : Number of formulae : 62 ( 15 unt; 31 typ; 0 def)
% Number of atoms : 145 ( 21 equ)
% Maximal formula atoms : 52 ( 4 avg)
% Number of connectives : 188 ( 74 ~; 81 |; 26 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 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 : 40 ( 0 sgn; 23 !; 2 ?; 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(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__870,hypothesis,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
fof(m__,conjecture,
( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
& aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1021,hypothesis,
( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1021) ).
fof(m__1098,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1098) ).
fof(m__994,hypothesis,
( aElementOf0(sdtpldt0(xk,xm),xI)
& aElementOf0(sdtpldt0(xl,xn),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__994) ).
fof(m__1061,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1061) ).
fof(c_0_8,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_9,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_10,plain,
( aElementOf0(X5,X6)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X4)
| sdtpldt0(X1,X3) != X5
| X6 != sdtpldt1(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( aSet0(X1)
| ~ aIdeal0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,hypothesis,
aIdeal0(xJ),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_13,negated_conjecture,
~ ( aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
& aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_14,plain,
( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(X3,X4))
| ~ aElementOf0(X2,X4)
| ~ aElementOf0(X1,X3)
| ~ aSet0(X4)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_15,hypothesis,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(split_conjunct,[status(thm)],[m__1021]) ).
cnf(c_0_16,hypothesis,
aSet0(xJ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,hypothesis,
aIdeal0(xI),
inference(split_conjunct,[status(thm)],[m__870]) ).
fof(c_0_18,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
inference(fof_nnf,[status(thm)],[c_0_13]) ).
cnf(c_0_19,hypothesis,
( aElementOf0(sdtpldt0(X1,sdtasdt0(xz,xl)),sdtpldt1(X2,xJ))
| ~ aElementOf0(X1,X2)
| ~ aSet0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_20,hypothesis,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(split_conjunct,[status(thm)],[m__1021]) ).
cnf(c_0_21,hypothesis,
sdtasdt0(xz,xx) = sdtpldt0(sdtasdt0(xz,xk),sdtasdt0(xz,xl)),
inference(split_conjunct,[status(thm)],[m__1098]) ).
cnf(c_0_22,hypothesis,
aSet0(xI),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_23,hypothesis,
aElementOf0(sdtpldt0(xl,xn),xJ),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ))
| ~ aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,hypothesis,
aElementOf0(sdtasdt0(xz,xx),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22])]) ).
cnf(c_0_26,hypothesis,
( aElementOf0(sdtpldt0(X1,sdtpldt0(xl,xn)),sdtpldt1(X2,xJ))
| ~ aElementOf0(X1,X2)
| ~ aSet0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_16])]) ).
cnf(c_0_27,hypothesis,
aElementOf0(sdtpldt0(xk,xm),xI),
inference(split_conjunct,[status(thm)],[m__994]) ).
cnf(c_0_28,hypothesis,
sdtpldt0(xx,xy) = sdtpldt0(sdtpldt0(xk,xm),sdtpldt0(xl,xn)),
inference(split_conjunct,[status(thm)],[m__1061]) ).
cnf(c_0_29,negated_conjecture,
~ aElementOf0(sdtpldt0(xx,xy),sdtpldt1(xI,xJ)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_30,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_22])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG091+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
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 03:02:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.59/0.84 % Version : CSE_E---1.5
% 0.59/0.84 % Problem : theBenchmark.p
% 0.59/0.84 % Proof found
% 0.59/0.84 % SZS status Theorem for theBenchmark.p
% 0.59/0.84 % SZS output start Proof
% See solution above
% 0.59/0.85 % Total time : 0.274000 s
% 0.59/0.85 % SZS output end Proof
% 0.59/0.85 % Total time : 0.276000 s
%------------------------------------------------------------------------------