%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM631+3 : 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 : n005.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 04:58:12 PM UTC 2026
% Result : Theorem 74.03s 47.42s
% Output : CNFRefutation 74.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 161 ( 51 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 170 ( 49 ~; 51 |; 56 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 13 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 27 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__5164,hypothesis,
( aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(szmzizndt0(xQ),X1) )
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != szmzizndt0(xQ) ) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
fof(m__5147,hypothesis,
( aElementOf0(xp,xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> sdtlseqdt0(xp,X1) )
& xp = szmzizndt0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5147) ).
fof(m__4660,hypothesis,
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( aElementOf0(sdtlpdtrp0(xe,X1),sdtlpdtrp0(xN,X1))
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> sdtlseqdt0(sdtlpdtrp0(xe,X1),X2) )
& sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
fof(mConsDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> sdtpldt0(sdtmndt0(X1,X2),X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
fof(m__5078,hypothesis,
( aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5078) ).
fof(m__4730,hypothesis,
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ! [X2] :
( ( aSet0(X2)
& ( ( ( ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,sdtlpdtrp0(xN,szszuzczcdt0(X1))) )
| aSubsetOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X1))) )
& sbrdtbr0(X2) = xk )
| aElementOf0(X2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X1)),xk)) ) )
=> sdtlpdtrp0(xd,X1) = sdtlpdtrp0(sdtlpdtrp0(xC,X1),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4730) ).
fof(m__5632,hypothesis,
( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,xn))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X1) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ! [X1] :
( aElementOf0(X1,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
<=> ( aElement0(X1)
& ( aElementOf0(X1,xP)
| X1 = szmzizndt0(sdtlpdtrp0(xN,xn)) ) ) )
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5632) ).
fof(m__5309,hypothesis,
( aElementOf0(xn,szDzozmdt0(xd))
& sdtlpdtrp0(xd,xn) = szDzizrdt0(xd)
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& sdtlpdtrp0(xe,xn) = xp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
fof(m__5217,hypothesis,
sbrdtbr0(xP) = xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5217) ).
fof(m__5334,hypothesis,
( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5334) ).
fof(m__,conjecture,
sdtlpdtrp0(xc,xQ) = sdtlpdtrp0(xd,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_11,hypothesis,
! [X508,X509] :
( aSet0(xP)
& ( ~ aElementOf0(X508,xQ)
| sdtlseqdt0(szmzizndt0(xQ),X508) )
& ( aElement0(X509)
| ~ aElementOf0(X509,xP) )
& ( aElementOf0(X509,xQ)
| ~ aElementOf0(X509,xP) )
& ( X509 != szmzizndt0(xQ)
| ~ aElementOf0(X509,xP) )
& ( ~ aElement0(X509)
| ~ aElementOf0(X509,xQ)
| X509 = szmzizndt0(xQ)
| aElementOf0(X509,xP) )
& xP = sdtmndt0(xQ,szmzizndt0(xQ)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5164])])])]) ).
fof(c_0_12,hypothesis,
! [X507] :
( aElementOf0(xp,xQ)
& ( ~ aElementOf0(X507,xQ)
| sdtlseqdt0(xp,X507) )
& xp = szmzizndt0(xQ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5147])])]) ).
fof(c_0_13,hypothesis,
! [X481,X482] :
( aFunction0(xe)
& szDzozmdt0(xe) = szNzAzT0
& ( aElementOf0(sdtlpdtrp0(xe,X481),sdtlpdtrp0(xN,X481))
| ~ aElementOf0(X481,szNzAzT0) )
& ( ~ aElementOf0(X482,sdtlpdtrp0(xN,X481))
| sdtlseqdt0(sdtlpdtrp0(xe,X481),X482)
| ~ aElementOf0(X481,szNzAzT0) )
& ( sdtlpdtrp0(xe,X481) = szmzizndt0(sdtlpdtrp0(xN,X481))
| ~ aElementOf0(X481,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4660])])])]) ).
fof(c_0_14,plain,
! [X298,X299] :
( ~ aSet0(X298)
| ~ aElementOf0(X299,X298)
| sdtpldt0(sdtmndt0(X298,X299),X299) = X298 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mConsDiff])])]) ).
cnf(c_0_15,hypothesis,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
xp = szmzizndt0(xQ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_17,hypothesis,
! [X501] :
( aSet0(xQ)
& ( ~ aElementOf0(X501,xQ)
| aElementOf0(X501,xO) )
& aSubsetOf0(xQ,xO)
& sbrdtbr0(xQ) = xK
& aElementOf0(xQ,slbdtsldtrb0(xO,xK)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5078])])]) ).
fof(c_0_18,hypothesis,
! [X483,X484] :
( aFunction0(xd)
& szDzozmdt0(xd) = szNzAzT0
& ( aElementOf0(esk36_2(X483,X484),X484)
| sbrdtbr0(X484) != xk
| ~ aSet0(X484)
| sdtlpdtrp0(xd,X483) = sdtlpdtrp0(sdtlpdtrp0(xC,X483),X484)
| ~ aElementOf0(X483,szNzAzT0) )
& ( ~ aElementOf0(esk36_2(X483,X484),sdtlpdtrp0(xN,szszuzczcdt0(X483)))
| sbrdtbr0(X484) != xk
| ~ aSet0(X484)
| sdtlpdtrp0(xd,X483) = sdtlpdtrp0(sdtlpdtrp0(xC,X483),X484)
| ~ aElementOf0(X483,szNzAzT0) )
& ( ~ aSubsetOf0(X484,sdtlpdtrp0(xN,szszuzczcdt0(X483)))
| sbrdtbr0(X484) != xk
| ~ aSet0(X484)
| sdtlpdtrp0(xd,X483) = sdtlpdtrp0(sdtlpdtrp0(xC,X483),X484)
| ~ aElementOf0(X483,szNzAzT0) )
& ( ~ aElementOf0(X484,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X483)),xk))
| ~ aSet0(X484)
| sdtlpdtrp0(xd,X483) = sdtlpdtrp0(sdtlpdtrp0(xC,X483),X484)
| ~ aElementOf0(X483,szNzAzT0) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__4730])])])])]) ).
fof(c_0_19,hypothesis,
! [X517,X518] :
( ( ~ aElementOf0(X517,sdtlpdtrp0(xN,xn))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,xn)),X517) )
& aSet0(sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn))))
& ( aElement0(X518)
| ~ aElementOf0(X518,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
& ( aElementOf0(X518,xP)
| X518 = szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElementOf0(X518,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
& ( ~ aElementOf0(X518,xP)
| ~ aElement0(X518)
| aElementOf0(X518,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
& ( X518 != szmzizndt0(sdtlpdtrp0(xN,xn))
| ~ aElement0(X518)
| aElementOf0(X518,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) )
& sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5632])])])]) ).
cnf(c_0_20,hypothesis,
( sdtlpdtrp0(xe,X1) = szmzizndt0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,hypothesis,
aElementOf0(xn,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_22,hypothesis,
sdtlpdtrp0(xe,xn) = xp,
inference(split_conjunct,[status(thm)],[m__5309]) ).
cnf(c_0_23,plain,
( sdtpldt0(sdtmndt0(X1,X2),X2) = X1
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,hypothesis,
aElementOf0(xp,xQ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_25,hypothesis,
sdtmndt0(xQ,xp) = xP,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_26,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,hypothesis,
( sdtlpdtrp0(xd,X2) = sdtlpdtrp0(sdtlpdtrp0(xC,X2),X1)
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X2)))
| sbrdtbr0(X1) != xk
| ~ aSet0(X1)
| ~ aElementOf0(X2,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,hypothesis,
sbrdtbr0(xP) = xk,
inference(split_conjunct,[status(thm)],[m__5217]) ).
cnf(c_0_29,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,hypothesis,
sdtlpdtrp0(xc,sdtpldt0(xP,szmzizndt0(sdtlpdtrp0(xN,xn)))) = sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_31,hypothesis,
szmzizndt0(sdtlpdtrp0(xN,xn)) = xp,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_32,hypothesis,
sdtpldt0(xP,xp) = xQ,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26])]) ).
fof(c_0_33,hypothesis,
! [X513] :
( ( ~ aElementOf0(X513,xP)
| aElementOf0(X513,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
& aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__5334])])]) ).
fof(c_0_34,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_35,hypothesis,
( sdtlpdtrp0(sdtlpdtrp0(xC,X1),xP) = sdtlpdtrp0(xd,X1)
| ~ aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(X1)))
| ~ aElementOf0(X1,szNzAzT0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_36,hypothesis,
sdtlpdtrp0(sdtlpdtrp0(xC,xn),xP) = sdtlpdtrp0(xc,xQ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_37,hypothesis,
aSubsetOf0(xP,sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,negated_conjecture,
sdtlpdtrp0(xc,xQ) != sdtlpdtrp0(xd,xn),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_39,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_21]),c_0_36]),c_0_37])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM631+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 00:52:30 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 74.03/47.42 % Version : CSE_E---1.7
% 74.03/47.42 % Problem : theBenchmark.p
% 74.03/47.42 % SZS status Theorem for theBenchmark.p
% 74.03/47.42 % SZS output start CNFRefutation
% See solution above
% 74.13/47.57 % Total time : 40.921s
%------------------------------------------------------------------------------