%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM554+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n006.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 04:57:48 PM UTC 2026
% Result : Theorem 1.40s 1.77s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 65 ( 23 unt; 0 def)
% Number of atoms : 252 ( 55 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 300 ( 113 ~; 115 |; 52 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDiffCons,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
fof(mEOfElem,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aElementOf0(X2,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(mDefDiff,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElement0(X2) )
=> ! [X3] :
( X3 = sdtmndt0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aElement0(X4)
& aElementOf0(X4,X1)
& X4 != X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(m__2357,hypothesis,
( aSet0(sdtmndt0(xQ,xy))
& ! [X1] :
( aElementOf0(X1,sdtmndt0(xQ,xy))
<=> ( aElement0(X1)
& aElementOf0(X1,xQ)
& X1 != xy ) )
& aSet0(xP)
& ! [X1] :
( aElementOf0(X1,xP)
<=> ( aElement0(X1)
& ( aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx ) ) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
fof(m__2256,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(mFConsSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtpldt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
fof(m__2270,hypothesis,
( aSet0(xQ)
& ! [X1] :
( aElementOf0(X1,xQ)
=> aElementOf0(X1,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
fof(m__2323,hypothesis,
~ aElementOf0(xx,xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2323) ).
fof(mFDiffSet,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( ( aSet0(X2)
& isFinite0(X2) )
=> isFinite0(sdtmndt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
fof(m__,conjecture,
( ( ( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk )
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mCardDiff,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( ( isFinite0(X1)
& aElementOf0(X2,X1) )
=> szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
fof(m__2304,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
fof(m__2291,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& sbrdtbr0(xQ) = xk ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
fof(c_0_14,plain,
! [X1,X2] :
( ( aElement0(X1)
& aSet0(X2) )
=> ( ~ aElementOf0(X1,X2)
=> sdtmndt0(sdtpldt0(X2,X1),X1) = X2 ) ),
inference(fof_simplification,[status(thm)],[mDiffCons]) ).
fof(c_0_15,plain,
! [X126,X127] :
( ~ aSet0(X126)
| ~ aElementOf0(X127,X126)
| aElement0(X127) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEOfElem])])]) ).
fof(c_0_16,plain,
! [X154,X155,X156,X157,X158,X159] :
( ( aSet0(X156)
| X156 != sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( aElement0(X157)
| ~ aElementOf0(X157,X156)
| X156 != sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( aElementOf0(X157,X154)
| ~ aElementOf0(X157,X156)
| X156 != sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( X157 != X155
| ~ aElementOf0(X157,X156)
| X156 != sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( ~ aElement0(X158)
| ~ aElementOf0(X158,X154)
| X158 = X155
| aElementOf0(X158,X156)
| X156 != sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( ~ aElementOf0(esk4_3(X154,X155,X159),X159)
| ~ aElement0(esk4_3(X154,X155,X159))
| ~ aElementOf0(esk4_3(X154,X155,X159),X154)
| esk4_3(X154,X155,X159) = X155
| ~ aSet0(X159)
| X159 = sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( aElement0(esk4_3(X154,X155,X159))
| aElementOf0(esk4_3(X154,X155,X159),X159)
| ~ aSet0(X159)
| X159 = sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( aElementOf0(esk4_3(X154,X155,X159),X154)
| aElementOf0(esk4_3(X154,X155,X159),X159)
| ~ aSet0(X159)
| X159 = sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) )
& ( esk4_3(X154,X155,X159) != X155
| aElementOf0(esk4_3(X154,X155,X159),X159)
| ~ aSet0(X159)
| X159 = sdtmndt0(X154,X155)
| ~ aSet0(X154)
| ~ aElement0(X155) ) ),
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)],[mDefDiff])])])])])]) ).
fof(c_0_17,plain,
! [X163,X164] :
( ~ aElement0(X163)
| ~ aSet0(X164)
| aElementOf0(X163,X164)
| sdtmndt0(sdtpldt0(X164,X163),X163) = X164 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).
fof(c_0_18,hypothesis,
! [X259,X260] :
( aSet0(sdtmndt0(xQ,xy))
& ( aElement0(X259)
| ~ aElementOf0(X259,sdtmndt0(xQ,xy)) )
& ( aElementOf0(X259,xQ)
| ~ aElementOf0(X259,sdtmndt0(xQ,xy)) )
& ( X259 != xy
| ~ aElementOf0(X259,sdtmndt0(xQ,xy)) )
& ( ~ aElement0(X259)
| ~ aElementOf0(X259,xQ)
| X259 = xy
| aElementOf0(X259,sdtmndt0(xQ,xy)) )
& aSet0(xP)
& ( aElement0(X260)
| ~ aElementOf0(X260,xP) )
& ( aElementOf0(X260,sdtmndt0(xQ,xy))
| X260 = xx
| ~ aElementOf0(X260,xP) )
& ( ~ aElementOf0(X260,sdtmndt0(xQ,xy))
| ~ aElement0(X260)
| aElementOf0(X260,xP) )
& ( X260 != xx
| ~ aElement0(X260)
| aElementOf0(X260,xP) )
& xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2357])])])]) ).
cnf(c_0_19,plain,
( aElement0(X2)
| ~ aSet0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,hypothesis,
aElementOf0(xx,xS),
inference(split_conjunct,[status(thm)],[m__2256]) ).
cnf(c_0_21,hypothesis,
aSet0(xS),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
fof(c_0_22,plain,
! [X169,X170] :
( ~ aElement0(X169)
| ~ aSet0(X170)
| ~ isFinite0(X170)
| isFinite0(sdtpldt0(X170,X169)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFConsSet])])]) ).
cnf(c_0_23,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,X3)
| X3 != sdtmndt0(X2,X4)
| ~ aSet0(X2)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( aElementOf0(X1,X2)
| sdtmndt0(sdtpldt0(X2,X1),X1) = X2
| ~ aElement0(X1)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,hypothesis,
xP = sdtpldt0(sdtmndt0(xQ,xy),xx),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,hypothesis,
aSet0(sdtmndt0(xQ,xy)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,hypothesis,
aElement0(xx),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
fof(c_0_28,hypothesis,
! [X258] :
( aSet0(xQ)
& ( ~ aElementOf0(X258,xQ)
| aElementOf0(X258,xS) )
& aSubsetOf0(xQ,xS)
& sbrdtbr0(xQ) = xk
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2270])])]) ).
fof(c_0_29,hypothesis,
~ aElementOf0(xx,xQ),
inference(fof_simplification,[status(thm)],[m__2323]) ).
cnf(c_0_30,plain,
( isFinite0(sdtpldt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_31,plain,
! [X171,X172] :
( ~ aElement0(X171)
| ~ aSet0(X172)
| ~ isFinite0(X172)
| isFinite0(sdtmndt0(X172,X171)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mFDiffSet])])]) ).
cnf(c_0_32,hypothesis,
( aElementOf0(X1,xP)
| X1 != xx
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_33,negated_conjecture,
~ ( ( ( ! [X1] :
( aElementOf0(X1,xP)
=> aElementOf0(X1,xS) )
| aSubsetOf0(xP,xS) )
& sbrdtbr0(xP) = xk )
| aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_34,plain,
! [X198,X199] :
( ~ aSet0(X198)
| ~ isFinite0(X198)
| ~ aElementOf0(X199,X198)
| szszuzczcdt0(sbrdtbr0(sdtmndt0(X198,X199))) = sbrdtbr0(X198) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCardDiff])])]) ).
cnf(c_0_35,plain,
( aElementOf0(X1,X2)
| ~ aElementOf0(X1,sdtmndt0(X2,X3))
| ~ aElement0(X3)
| ~ aSet0(X2) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_36,hypothesis,
( sdtmndt0(xP,xx) = sdtmndt0(xQ,xy)
| aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27])]) ).
cnf(c_0_37,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_38,hypothesis,
aSet0(xQ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_39,hypothesis,
~ aElementOf0(xx,xQ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,hypothesis,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_26])]),c_0_27])]) ).
cnf(c_0_41,plain,
( isFinite0(sdtmndt0(X2,X1))
| ~ aElement0(X1)
| ~ aSet0(X2)
| ~ isFinite0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,hypothesis,
isFinite0(xQ),
inference(split_conjunct,[status(thm)],[m__2291]) ).
cnf(c_0_43,hypothesis,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(er,[status(thm)],[c_0_32]) ).
fof(c_0_44,negated_conjecture,
( ( aElementOf0(esk16_0,xP)
| sbrdtbr0(xP) != xk )
& ( ~ aElementOf0(esk16_0,xS)
| sbrdtbr0(xP) != xk )
& ( ~ aSubsetOf0(xP,xS)
| sbrdtbr0(xP) != xk )
& ~ aElementOf0(xP,slbdtsldtrb0(xS,xk)) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])]) ).
cnf(c_0_45,plain,
( szszuzczcdt0(sbrdtbr0(sdtmndt0(X1,X2))) = sbrdtbr0(X1)
| ~ aSet0(X1)
| ~ isFinite0(X1)
| ~ aElementOf0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,hypothesis,
sdtmndt0(xP,xx) = sdtmndt0(xQ,xy),
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_36]),c_0_37]),c_0_38])]),c_0_39]) ).
cnf(c_0_47,hypothesis,
isFinite0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_37]),c_0_38])]) ).
cnf(c_0_48,hypothesis,
aElementOf0(xx,xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_27])]) ).
cnf(c_0_49,hypothesis,
aSet0(xP),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_50,hypothesis,
( aElementOf0(X1,xQ)
| ~ aElementOf0(X1,sdtmndt0(xQ,xy)) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_51,hypothesis,
( aElementOf0(X1,sdtmndt0(xQ,xy))
| X1 = xx
| ~ aElementOf0(X1,xP) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_52,negated_conjecture,
( ~ aElementOf0(esk16_0,xS)
| sbrdtbr0(xP) != xk ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_53,hypothesis,
( aElementOf0(X1,xS)
| ~ aElementOf0(X1,xQ) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_54,hypothesis,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,xy))) = sbrdtbr0(xP),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48]),c_0_49])]) ).
cnf(c_0_55,hypothesis,
sbrdtbr0(xQ) = xk,
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_56,hypothesis,
aElementOf0(xy,xQ),
inference(split_conjunct,[status(thm)],[m__2304]) ).
cnf(c_0_57,hypothesis,
( X1 = xx
| aElementOf0(X1,xQ)
| ~ aElementOf0(X1,xP) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_58,negated_conjecture,
( aElementOf0(esk16_0,xP)
| sbrdtbr0(xP) != xk ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_59,negated_conjecture,
( sbrdtbr0(xP) != xk
| ~ aElementOf0(esk16_0,xQ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,hypothesis,
sbrdtbr0(xP) = xk,
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_45,c_0_54]),c_0_55]),c_0_42]),c_0_56]),c_0_38])]) ).
cnf(c_0_61,negated_conjecture,
( esk16_0 = xx
| sbrdtbr0(xP) != xk ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_62,negated_conjecture,
~ aElementOf0(esk16_0,xS),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_60])]) ).
cnf(c_0_63,negated_conjecture,
esk16_0 = xx,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_60])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : NUM554+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.10/0.29 % Computer : n006.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue May 5 00:45:01 EDT 2026
% 0.10/0.29 % CPUTime :
% 0.10/0.29 % start to proof: theBenchmark
% 1.40/1.77 % Version : CSE_E---1.7
% 1.40/1.77 % Problem : theBenchmark.p
% 1.40/1.77 % SZS status Theorem for theBenchmark.p
% 1.40/1.77 % SZS output start CNFRefutation
% See solution above
% 1.40/1.77 % Total time : 1.369s
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