%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM607+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 : Tue May 5 04:58:00 PM UTC 2026
% Result : Theorem 1.49s 1.78s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 18 unt; 0 def)
% Number of atoms : 144 ( 23 equ)
% Maximal formula atoms : 39 ( 3 avg)
% Number of connectives : 181 ( 75 ~; 76 |; 22 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSel) ).
fof(m__5078,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(m__3418,hypothesis,
aElementOf0(xK,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3418) ).
fof(m__4891,hypothesis,
( aSet0(xO)
& xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
fof(mSubTrans,axiom,
! [X1,X2,X3] :
( ( aSet0(X1)
& aSet0(X2)
& aSet0(X3) )
=> ( ( aSubsetOf0(X1,X2)
& aSubsetOf0(X2,X3) )
=> aSubsetOf0(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
fof(m__3435,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3435) ).
fof(mNATSet,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
fof(m__,conjecture,
aElementOf0(xQ,szDzozmdt0(xc)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m__3453,hypothesis,
( aFunction0(xc)
& szDzozmdt0(xc) = slbdtsldtrb0(xS,xK)
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3453) ).
fof(m__4998,hypothesis,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4998) ).
fof(m__5093,hypothesis,
( aSubsetOf0(xQ,xO)
& xQ != slcrc0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
fof(c_0_12,plain,
! [X283,X284,X285,X286,X287,X288] :
( ( aSet0(X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( aSubsetOf0(X286,X283)
| ~ aElementOf0(X286,X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( sbrdtbr0(X286) = X284
| ~ aElementOf0(X286,X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( ~ aSubsetOf0(X287,X283)
| sbrdtbr0(X287) != X284
| aElementOf0(X287,X285)
| X285 != slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X283,X284,X288),X288)
| ~ aSubsetOf0(esk11_3(X283,X284,X288),X283)
| sbrdtbr0(esk11_3(X283,X284,X288)) != X284
| ~ aSet0(X288)
| X288 = slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X283,X284,X288),X283)
| aElementOf0(esk11_3(X283,X284,X288),X288)
| ~ aSet0(X288)
| X288 = slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X283,X284,X288)) = X284
| aElementOf0(esk11_3(X283,X284,X288),X288)
| ~ aSet0(X288)
| X288 = slbdtsldtrb0(X283,X284)
| ~ aSet0(X283)
| ~ aElementOf0(X284,szNzAzT0) ) ),
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)],[mDefSel])])])])])]) ).
cnf(c_0_13,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,X3)
| X3 != slbdtsldtrb0(X4,X2)
| ~ aSet0(X4)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_14,plain,
( aElementOf0(X1,X4)
| ~ aSubsetOf0(X1,X2)
| sbrdtbr0(X1) != X3
| X4 != slbdtsldtrb0(X2,X3)
| ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
( sbrdtbr0(X1) = X2
| ~ aElementOf0(X1,slbdtsldtrb0(X3,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_16,hypothesis,
aElementOf0(xQ,slbdtsldtrb0(xO,xK)),
inference(split_conjunct,[status(thm)],[m__5078]) ).
cnf(c_0_17,hypothesis,
aElementOf0(xK,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3418]) ).
cnf(c_0_18,hypothesis,
aSet0(xO),
inference(split_conjunct,[status(thm)],[m__4891]) ).
fof(c_0_19,plain,
! [X186,X187,X188,X189] :
( ( aSet0(X187)
| ~ aSubsetOf0(X187,X186)
| ~ aSet0(X186) )
& ( ~ aElementOf0(X188,X187)
| aElementOf0(X188,X186)
| ~ aSubsetOf0(X187,X186)
| ~ aSet0(X186) )
& ( aElementOf0(esk2_2(X186,X189),X189)
| ~ aSet0(X189)
| aSubsetOf0(X189,X186)
| ~ aSet0(X186) )
& ( ~ aElementOf0(esk2_2(X186,X189),X186)
| ~ aSet0(X189)
| aSubsetOf0(X189,X186)
| ~ aSet0(X186) ) ),
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)],[mDefSub])])])])])]) ).
fof(c_0_20,plain,
! [X196,X197,X198] :
( ~ aSet0(X196)
| ~ aSet0(X197)
| ~ aSet0(X198)
| ~ aSubsetOf0(X196,X197)
| ~ aSubsetOf0(X197,X198)
| aSubsetOf0(X196,X198) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSubTrans])]) ).
cnf(c_0_21,plain,
( aElementOf0(X1,slbdtsldtrb0(X2,sbrdtbr0(X1)))
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(sbrdtbr0(X1),szNzAzT0)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])]) ).
cnf(c_0_22,hypothesis,
sbrdtbr0(xQ) = xK,
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,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,hypothesis,
aSubsetOf0(xS,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__3435]) ).
cnf(c_0_25,plain,
aSet0(szNzAzT0),
inference(split_conjunct,[status(thm)],[mNATSet]) ).
fof(c_0_26,negated_conjecture,
~ aElementOf0(xQ,szDzozmdt0(xc)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_27,plain,
( aSubsetOf0(X1,X3)
| ~ aSet0(X1)
| ~ aSet0(X2)
| ~ aSet0(X3)
| ~ aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(X1,xK))
| ~ aSubsetOf0(xQ,X1)
| ~ aSet0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17])]) ).
cnf(c_0_29,hypothesis,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(split_conjunct,[status(thm)],[m__3453]) ).
cnf(c_0_30,hypothesis,
aSet0(xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_31,negated_conjecture,
~ aElementOf0(xQ,szDzozmdt0(xc)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
( aSubsetOf0(X1,X2)
| ~ aSubsetOf0(X3,X2)
| ~ aSubsetOf0(X1,X3)
| ~ aSet0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_27,c_0_23]),c_0_23]) ).
cnf(c_0_33,hypothesis,
aSubsetOf0(xO,xS),
inference(split_conjunct,[status(thm)],[m__4998]) ).
cnf(c_0_34,hypothesis,
~ aSubsetOf0(xQ,xS),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]),c_0_31]) ).
cnf(c_0_35,hypothesis,
( aSubsetOf0(X1,xS)
| ~ aSubsetOf0(X1,xO) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30])]) ).
cnf(c_0_36,hypothesis,
aSubsetOf0(xQ,xO),
inference(split_conjunct,[status(thm)],[m__5093]) ).
cnf(c_0_37,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM607+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n021.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 00:51:10 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.49/1.78 % Version : CSE_E---1.7
% 1.49/1.78 % Problem : theBenchmark.p
% 1.49/1.78 % SZS status Theorem for theBenchmark.p
% 1.49/1.78 % SZS output start CNFRefutation
% See solution above
% 1.49/1.78 % Total time : 1.372s
%------------------------------------------------------------------------------