TSTP Solution File: NUM441+6 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM441+6 : 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 : n021.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 10:37:32 EDT 2023
% Result : Theorem 0.20s 0.68s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 48
% Syntax : Number of formulae : 63 ( 7 unt; 44 typ; 0 def)
% Number of atoms : 554 ( 42 equ)
% Maximal formula atoms : 116 ( 29 avg)
% Number of connectives : 711 ( 176 ~; 182 |; 284 &)
% ( 30 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 67 ( 18 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 38 >; 27 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-3 aty)
% Number of variables : 112 ( 0 sgn; 92 !; 18 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aInteger0: $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,
aDivisorOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
isPrime0: $i > $o ).
tff(decl_31,type,
aSet0: $i > $o ).
tff(decl_32,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_33,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_34,type,
isFinite0: $i > $o ).
tff(decl_35,type,
cS1395: $i ).
tff(decl_36,type,
sdtbsmnsldt0: ( $i * $i ) > $i ).
tff(decl_37,type,
sdtslmnbsdt0: ( $i * $i ) > $i ).
tff(decl_38,type,
sbsmnsldt0: $i > $i ).
tff(decl_39,type,
stldt0: $i > $i ).
tff(decl_40,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(decl_41,type,
isOpen0: $i > $o ).
tff(decl_42,type,
isClosed0: $i > $o ).
tff(decl_43,type,
xA: $i ).
tff(decl_44,type,
xB: $i ).
tff(decl_45,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk2_1: $i > $i ).
tff(decl_47,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk6_1: $i > $i ).
tff(decl_51,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk13_1: $i > $i ).
tff(decl_58,type,
esk14_1: $i > $i ).
tff(decl_59,type,
esk15_1: $i > $i ).
tff(decl_60,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk17_1: $i > $i ).
tff(decl_62,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk19_0: $i ).
tff(decl_64,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk21_1: $i > $i ).
fof(m__1883,hypothesis,
( aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& aElementOf0(X1,stldt0(xA))
& aElementOf0(X1,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(m__1826,hypothesis,
( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,xA)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xB)
& ! [X1] :
( aElementOf0(X1,xB)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1826) ).
fof(m__,conjecture,
( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) ) )
=> ( ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mInterOpen,axiom,
! [X1,X2] :
( ( aSubsetOf0(X1,cS1395)
& aSubsetOf0(X2,cS1395)
& isOpen0(X1)
& isOpen0(X2) )
=> isOpen0(sdtslmnbsdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mInterOpen) ).
fof(c_0_4,hypothesis,
( aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& aElementOf0(X1,stldt0(xA))
& aElementOf0(X1,stldt0(xB)) ) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(fof_simplification,[status(thm)],[m__1883]) ).
fof(c_0_5,hypothesis,
( aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xA)
& ! [X1] :
( aElementOf0(X1,xA)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ! [X1] :
( aElementOf0(X1,cS1395)
<=> aInteger0(X1) )
& aSet0(xB)
& ! [X1] :
( aElementOf0(X1,xB)
=> aElementOf0(X1,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xA) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xA))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xA)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xA)) ) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,xB) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(xB))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(xB)) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(xB)) ) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
inference(fof_simplification,[status(thm)],[m__1826]) ).
fof(c_0_6,negated_conjecture,
~ ( ( aSet0(sdtbsmnsldt0(xA,xB))
& ! [X1] :
( aElementOf0(X1,sdtbsmnsldt0(xA,xB))
<=> ( aInteger0(X1)
& ( aElementOf0(X1,xA)
| aElementOf0(X1,xB) ) ) ) )
=> ( ( ( aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sdtbsmnsldt0(xA,xB)) ) ) )
=> ( ! [X1] :
( aElementOf0(X1,stldt0(sdtbsmnsldt0(xA,xB)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) ) )
=> ( ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sdtbsmnsldt0(xA,xB))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sdtbsmnsldt0(xA,xB))) ) ) ) )
| isOpen0(stldt0(sdtbsmnsldt0(xA,xB))) ) )
| isClosed0(sdtbsmnsldt0(xA,xB)) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
fof(c_0_7,plain,
! [X105,X106] :
( ~ aSubsetOf0(X105,cS1395)
| ~ aSubsetOf0(X106,cS1395)
| ~ isOpen0(X105)
| ~ isOpen0(X106)
| isOpen0(sdtslmnbsdt0(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mInterOpen])]) ).
fof(c_0_8,hypothesis,
! [X127,X128,X129,X130,X131,X132,X133,X134,X135,X136,X137] :
( aSet0(stldt0(xA))
& ( aInteger0(X127)
| ~ aElementOf0(X127,stldt0(xA)) )
& ( ~ aElementOf0(X127,xA)
| ~ aElementOf0(X127,stldt0(xA)) )
& ( ~ aInteger0(X127)
| aElementOf0(X127,xA)
| aElementOf0(X127,stldt0(xA)) )
& aSet0(cS1395)
& ( ~ aElementOf0(X128,cS1395)
| aInteger0(X128) )
& ( ~ aInteger0(X128)
| aElementOf0(X128,cS1395) )
& ( ~ aElementOf0(X129,stldt0(xA))
| aElementOf0(X129,cS1395) )
& aSubsetOf0(stldt0(xA),cS1395)
& aSet0(stldt0(xB))
& ( aInteger0(X130)
| ~ aElementOf0(X130,stldt0(xB)) )
& ( ~ aElementOf0(X130,xB)
| ~ aElementOf0(X130,stldt0(xB)) )
& ( ~ aInteger0(X130)
| aElementOf0(X130,xB)
| aElementOf0(X130,stldt0(xB)) )
& aSet0(cS1395)
& ( ~ aElementOf0(X131,cS1395)
| aInteger0(X131) )
& ( ~ aInteger0(X131)
| aElementOf0(X131,cS1395) )
& ( ~ aElementOf0(X132,stldt0(xB))
| aElementOf0(X132,cS1395) )
& aSubsetOf0(stldt0(xB),cS1395)
& aSet0(sdtbsmnsldt0(xA,xB))
& ( aInteger0(X133)
| ~ aElementOf0(X133,sdtbsmnsldt0(xA,xB)) )
& ( aElementOf0(X133,xA)
| aElementOf0(X133,xB)
| ~ aElementOf0(X133,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X133,xA)
| ~ aInteger0(X133)
| aElementOf0(X133,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X133,xB)
| ~ aInteger0(X133)
| aElementOf0(X133,sdtbsmnsldt0(xA,xB)) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ( aInteger0(X134)
| ~ aElementOf0(X134,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aElementOf0(X134,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X134,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X134)
| aElementOf0(X134,sdtbsmnsldt0(xA,xB))
| aElementOf0(X134,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aInteger0(X135)
| ~ aElementOf0(X135,stldt0(xA)) )
& ( ~ aElementOf0(X135,xA)
| ~ aElementOf0(X135,stldt0(xA)) )
& ( ~ aInteger0(X135)
| aElementOf0(X135,xA)
| aElementOf0(X135,stldt0(xA)) )
& ( aInteger0(X136)
| ~ aElementOf0(X136,stldt0(xB)) )
& ( ~ aElementOf0(X136,xB)
| ~ aElementOf0(X136,stldt0(xB)) )
& ( ~ aInteger0(X136)
| aElementOf0(X136,xB)
| aElementOf0(X136,stldt0(xB)) )
& ( aInteger0(X137)
| ~ aElementOf0(X137,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aElementOf0(X137,stldt0(xA))
| ~ aElementOf0(X137,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( aElementOf0(X137,stldt0(xB))
| ~ aElementOf0(X137,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X137)
| ~ aElementOf0(X137,stldt0(xA))
| ~ aElementOf0(X137,stldt0(xB))
| aElementOf0(X137,stldt0(sdtbsmnsldt0(xA,xB))) )
& stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_9,hypothesis,
! [X107,X108,X109,X110,X111,X112,X114,X116,X117,X118,X119,X120,X122,X124,X125,X126] :
( aSet0(cS1395)
& ( ~ aElementOf0(X107,cS1395)
| aInteger0(X107) )
& ( ~ aInteger0(X107)
| aElementOf0(X107,cS1395) )
& aSet0(xA)
& ( ~ aElementOf0(X108,xA)
| aElementOf0(X108,cS1395) )
& aSubsetOf0(xA,cS1395)
& aSet0(cS1395)
& ( ~ aElementOf0(X109,cS1395)
| aInteger0(X109) )
& ( ~ aInteger0(X109)
| aElementOf0(X109,cS1395) )
& aSet0(xB)
& ( ~ aElementOf0(X110,xB)
| aElementOf0(X110,cS1395) )
& aSubsetOf0(xB,cS1395)
& aSet0(stldt0(xA))
& ( aInteger0(X111)
| ~ aElementOf0(X111,stldt0(xA)) )
& ( ~ aElementOf0(X111,xA)
| ~ aElementOf0(X111,stldt0(xA)) )
& ( ~ aInteger0(X111)
| aElementOf0(X111,xA)
| aElementOf0(X111,stldt0(xA)) )
& ( aInteger0(esk15_1(X112))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( esk15_1(X112) != sz00
| ~ aElementOf0(X112,stldt0(xA)) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( aInteger0(X114)
| ~ aElementOf0(X114,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( aInteger0(esk16_2(X112,X114))
| ~ aElementOf0(X114,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( sdtasdt0(esk15_1(X112),esk16_2(X112,X114)) = sdtpldt0(X114,smndt0(X112))
| ~ aElementOf0(X114,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( aDivisorOf0(esk15_1(X112),sdtpldt0(X114,smndt0(X112)))
| ~ aElementOf0(X114,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( sdteqdtlpzmzozddtrp0(X114,X112,esk15_1(X112))
| ~ aElementOf0(X114,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( ~ aInteger0(X117)
| sdtasdt0(esk15_1(X112),X117) != sdtpldt0(X116,smndt0(X112))
| ~ aInteger0(X116)
| aElementOf0(X116,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( ~ aDivisorOf0(esk15_1(X112),sdtpldt0(X116,smndt0(X112)))
| ~ aInteger0(X116)
| aElementOf0(X116,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( ~ sdteqdtlpzmzozddtrp0(X116,X112,esk15_1(X112))
| ~ aInteger0(X116)
| aElementOf0(X116,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( ~ aElementOf0(X118,szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)))
| aElementOf0(X118,stldt0(xA))
| ~ aElementOf0(X112,stldt0(xA)) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X112,esk15_1(X112)),stldt0(xA))
| ~ aElementOf0(X112,stldt0(xA)) )
& isOpen0(stldt0(xA))
& isClosed0(xA)
& aSet0(stldt0(xB))
& ( aInteger0(X119)
| ~ aElementOf0(X119,stldt0(xB)) )
& ( ~ aElementOf0(X119,xB)
| ~ aElementOf0(X119,stldt0(xB)) )
& ( ~ aInteger0(X119)
| aElementOf0(X119,xB)
| aElementOf0(X119,stldt0(xB)) )
& ( aInteger0(esk17_1(X120))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( esk17_1(X120) != sz00
| ~ aElementOf0(X120,stldt0(xB)) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( aInteger0(X122)
| ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( aInteger0(esk18_2(X120,X122))
| ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( sdtasdt0(esk17_1(X120),esk18_2(X120,X122)) = sdtpldt0(X122,smndt0(X120))
| ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( aDivisorOf0(esk17_1(X120),sdtpldt0(X122,smndt0(X120)))
| ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( sdteqdtlpzmzozddtrp0(X122,X120,esk17_1(X120))
| ~ aElementOf0(X122,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( ~ aInteger0(X125)
| sdtasdt0(esk17_1(X120),X125) != sdtpldt0(X124,smndt0(X120))
| ~ aInteger0(X124)
| aElementOf0(X124,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( ~ aDivisorOf0(esk17_1(X120),sdtpldt0(X124,smndt0(X120)))
| ~ aInteger0(X124)
| aElementOf0(X124,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( ~ sdteqdtlpzmzozddtrp0(X124,X120,esk17_1(X120))
| ~ aInteger0(X124)
| aElementOf0(X124,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( ~ aElementOf0(X126,szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)))
| aElementOf0(X126,stldt0(xB))
| ~ aElementOf0(X120,stldt0(xB)) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X120,esk17_1(X120)),stldt0(xB))
| ~ aElementOf0(X120,stldt0(xB)) )
& isOpen0(stldt0(xB))
& isClosed0(xB) ),
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)],[c_0_5])])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X138,X139,X141,X142,X144] :
( aSet0(sdtbsmnsldt0(xA,xB))
& ( aInteger0(X138)
| ~ aElementOf0(X138,sdtbsmnsldt0(xA,xB)) )
& ( aElementOf0(X138,xA)
| aElementOf0(X138,xB)
| ~ aElementOf0(X138,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X138,xA)
| ~ aInteger0(X138)
| aElementOf0(X138,sdtbsmnsldt0(xA,xB)) )
& ( ~ aElementOf0(X138,xB)
| ~ aInteger0(X138)
| aElementOf0(X138,sdtbsmnsldt0(xA,xB)) )
& aSet0(stldt0(sdtbsmnsldt0(xA,xB)))
& ( aInteger0(X139)
| ~ aElementOf0(X139,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aElementOf0(X139,sdtbsmnsldt0(xA,xB))
| ~ aElementOf0(X139,stldt0(sdtbsmnsldt0(xA,xB))) )
& ( ~ aInteger0(X139)
| aElementOf0(X139,sdtbsmnsldt0(xA,xB))
| aElementOf0(X139,stldt0(sdtbsmnsldt0(xA,xB))) )
& aElementOf0(esk19_0,stldt0(sdtbsmnsldt0(xA,xB)))
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( aInteger0(X142)
| ~ aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( aInteger0(esk20_2(X141,X142))
| ~ aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( sdtasdt0(X141,esk20_2(X141,X142)) = sdtpldt0(X142,smndt0(esk19_0))
| ~ aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( aDivisorOf0(X141,sdtpldt0(X142,smndt0(esk19_0)))
| ~ aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X142,esk19_0,X141)
| ~ aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( ~ aInteger0(X144)
| sdtasdt0(X141,X144) != sdtpldt0(X142,smndt0(esk19_0))
| ~ aInteger0(X142)
| aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( ~ aDivisorOf0(X141,sdtpldt0(X142,smndt0(esk19_0)))
| ~ aInteger0(X142)
| aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( ~ sdteqdtlpzmzozddtrp0(X142,esk19_0,X141)
| ~ aInteger0(X142)
| aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( aElementOf0(esk21_1(X141),szAzrzSzezqlpdtcmdtrp0(esk19_0,X141))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( ~ aElementOf0(esk21_1(X141),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X141)
| X141 = sz00 )
& ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(esk19_0,X141),stldt0(sdtbsmnsldt0(xA,xB)))
| ~ aInteger0(X141)
| X141 = sz00 )
& ~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB)))
& ~ isClosed0(sdtbsmnsldt0(xA,xB)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
cnf(c_0_11,plain,
( isOpen0(sdtslmnbsdt0(X1,X2))
| ~ aSubsetOf0(X1,cS1395)
| ~ aSubsetOf0(X2,cS1395)
| ~ isOpen0(X1)
| ~ isOpen0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
stldt0(sdtbsmnsldt0(xA,xB)) = sdtslmnbsdt0(stldt0(xA),stldt0(xB)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
isOpen0(stldt0(xB)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,hypothesis,
isOpen0(stldt0(xA)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,hypothesis,
aSubsetOf0(stldt0(xB),cS1395),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,hypothesis,
aSubsetOf0(stldt0(xA),cS1395),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
~ isOpen0(stldt0(sdtbsmnsldt0(xA,xB))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM441+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n021.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 : Fri Aug 25 15:19:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.63 start to proof: theBenchmark
% 0.20/0.68 % Version : CSE_E---1.5
% 0.20/0.68 % Problem : theBenchmark.p
% 0.20/0.68 % Proof found
% 0.20/0.68 % SZS status Theorem for theBenchmark.p
% 0.20/0.68 % SZS output start Proof
% See solution above
% 0.20/0.69 % Total time : 0.044000 s
% 0.20/0.69 % SZS output end Proof
% 0.20/0.69 % Total time : 0.049000 s
%------------------------------------------------------------------------------