%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:05:54 PM UTC 2026
% Result : Theorem 0.16s 15.61s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 42 ( 15 unt; 0 def)
% Number of atoms : 346 ( 136 equ)
% Maximal formula atoms : 135 ( 8 avg)
% Number of connectives : 474 ( 170 ~; 187 |; 99 &)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 21 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ( ! [X2] :
( ( X2 != sz00
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ( iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
=> ? [X3] :
( ! [X4] :
( ( X4 != sz00
& ( aElementOf0(X4,xI)
| ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) )
& X3 != sz00
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ) )
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(c_0_1,negated_conjecture,
~ ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ( ! [X2] :
( ( X2 != sz00
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ( iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
=> ? [X3] :
( ! [X4] :
( ( X4 != sz00
& ( aElementOf0(X4,xI)
| ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) )
& X3 != sz00
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ) )
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_2,negated_conjecture,
~ ! [X1] :
( ( X1 != sz00
& aElementOf0(X1,xI)
& ? [X2,X3] :
( sdtpldt0(X2,X3) = X1
& aElementOf0(X3,slsdtgt0(xb))
& aElementOf0(X2,slsdtgt0(xa)) ) )
=> ( ! [X2] :
( ( X2 != sz00
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) )
=> ( iLess0(sbrdtbr0(X2),sbrdtbr0(X1))
=> ? [X3] :
( ! [X4] :
( ( X4 != sz00
& ( aElementOf0(X4,xI)
| ? [X5,X6] :
( sdtpldt0(X5,X6) = X4
& aElementOf0(X6,slsdtgt0(xb))
& aElementOf0(X5,slsdtgt0(xa)) ) ) )
=> ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X3)) )
& X3 != sz00
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) ) ) )
=> ? [X2] :
( ! [X3] :
( ( X3 != sz00
& aElementOf0(X3,xI)
& ? [X4,X5] :
( sdtpldt0(X4,X5) = X3
& aElementOf0(X5,slsdtgt0(xb))
& aElementOf0(X4,slsdtgt0(xa)) ) )
=> ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
& X2 != sz00
& ( aElementOf0(X2,xI)
| ? [X3,X4] :
( sdtpldt0(X3,X4) = X2
& aElementOf0(X4,slsdtgt0(xb))
& aElementOf0(X3,slsdtgt0(xa)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_1]) ).
fof(c_0_3,negated_conjecture,
! [X155,X156,X157,X161,X162,X163,X164,X165,X166] :
( ( X164 = sz00
| ~ aElementOf0(X164,xI)
| iLess0(sbrdtbr0(esk43_1(X164)),sbrdtbr0(X164)) )
& ( X164 = sz00
| ~ aElementOf0(X164,xI)
| esk43_1(X164) != sz00 )
& ( X164 = sz00
| ~ aElementOf0(X164,xI)
| aElementOf0(esk43_1(X164),xI) )
& ( X164 = sz00
| ~ aElementOf0(X164,xI)
| sdtpldt0(esk44_1(X164),esk45_1(X164)) = esk43_1(X164) )
& ( X164 = sz00
| ~ aElementOf0(X164,xI)
| aElementOf0(esk45_1(X164),slsdtgt0(xb)) )
& ( X164 = sz00
| ~ aElementOf0(X164,xI)
| aElementOf0(esk44_1(X164),slsdtgt0(xa)) )
& ( X164 = sz00
| sdtpldt0(X165,X166) != X164
| ~ aElementOf0(X166,slsdtgt0(xb))
| ~ aElementOf0(X165,slsdtgt0(xa))
| iLess0(sbrdtbr0(esk43_1(X164)),sbrdtbr0(X164)) )
& ( X164 = sz00
| sdtpldt0(X165,X166) != X164
| ~ aElementOf0(X166,slsdtgt0(xb))
| ~ aElementOf0(X165,slsdtgt0(xa))
| esk43_1(X164) != sz00 )
& ( X164 = sz00
| sdtpldt0(X165,X166) != X164
| ~ aElementOf0(X166,slsdtgt0(xb))
| ~ aElementOf0(X165,slsdtgt0(xa))
| aElementOf0(esk43_1(X164),xI) )
& ( X164 = sz00
| sdtpldt0(X165,X166) != X164
| ~ aElementOf0(X166,slsdtgt0(xb))
| ~ aElementOf0(X165,slsdtgt0(xa))
| sdtpldt0(esk44_1(X164),esk45_1(X164)) = esk43_1(X164) )
& ( X164 = sz00
| sdtpldt0(X165,X166) != X164
| ~ aElementOf0(X166,slsdtgt0(xb))
| ~ aElementOf0(X165,slsdtgt0(xa))
| aElementOf0(esk45_1(X164),slsdtgt0(xb)) )
& ( X164 = sz00
| sdtpldt0(X165,X166) != X164
| ~ aElementOf0(X166,slsdtgt0(xb))
| ~ aElementOf0(X165,slsdtgt0(xa))
| aElementOf0(esk44_1(X164),slsdtgt0(xa)) )
& ( X155 = sz00
| ~ aElementOf0(X155,xI)
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| ~ iLess0(sbrdtbr0(X161),sbrdtbr0(esk40_1(X155)))
| X161 = sz00
| ~ aElementOf0(X161,xI) )
& ( X155 = sz00
| ~ aElementOf0(X155,xI)
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| ~ iLess0(sbrdtbr0(X161),sbrdtbr0(esk40_1(X155)))
| X161 = sz00
| sdtpldt0(X162,X163) != X161
| ~ aElementOf0(X163,slsdtgt0(xb))
| ~ aElementOf0(X162,slsdtgt0(xa)) )
& ( X155 = sz00
| ~ aElementOf0(X155,xI)
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| esk40_1(X155) != sz00 )
& ( X155 = sz00
| ~ aElementOf0(X155,xI)
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| aElementOf0(esk40_1(X155),xI) )
& ( X155 = sz00
| ~ aElementOf0(X155,xI)
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| sdtpldt0(esk41_1(X155),esk42_1(X155)) = esk40_1(X155) )
& ( X155 = sz00
| ~ aElementOf0(X155,xI)
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| aElementOf0(esk42_1(X155),slsdtgt0(xb)) )
& ( X155 = sz00
| ~ aElementOf0(X155,xI)
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| aElementOf0(esk41_1(X155),slsdtgt0(xa)) )
& ( X155 = sz00
| sdtpldt0(X156,X157) != X155
| ~ aElementOf0(X157,slsdtgt0(xb))
| ~ aElementOf0(X156,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| ~ iLess0(sbrdtbr0(X161),sbrdtbr0(esk40_1(X155)))
| X161 = sz00
| ~ aElementOf0(X161,xI) )
& ( X155 = sz00
| sdtpldt0(X156,X157) != X155
| ~ aElementOf0(X157,slsdtgt0(xb))
| ~ aElementOf0(X156,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| ~ iLess0(sbrdtbr0(X161),sbrdtbr0(esk40_1(X155)))
| X161 = sz00
| sdtpldt0(X162,X163) != X161
| ~ aElementOf0(X163,slsdtgt0(xb))
| ~ aElementOf0(X162,slsdtgt0(xa)) )
& ( X155 = sz00
| sdtpldt0(X156,X157) != X155
| ~ aElementOf0(X157,slsdtgt0(xb))
| ~ aElementOf0(X156,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| esk40_1(X155) != sz00 )
& ( X155 = sz00
| sdtpldt0(X156,X157) != X155
| ~ aElementOf0(X157,slsdtgt0(xb))
| ~ aElementOf0(X156,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| aElementOf0(esk40_1(X155),xI) )
& ( X155 = sz00
| sdtpldt0(X156,X157) != X155
| ~ aElementOf0(X157,slsdtgt0(xb))
| ~ aElementOf0(X156,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| sdtpldt0(esk41_1(X155),esk42_1(X155)) = esk40_1(X155) )
& ( X155 = sz00
| sdtpldt0(X156,X157) != X155
| ~ aElementOf0(X157,slsdtgt0(xb))
| ~ aElementOf0(X156,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| aElementOf0(esk42_1(X155),slsdtgt0(xb)) )
& ( X155 = sz00
| sdtpldt0(X156,X157) != X155
| ~ aElementOf0(X157,slsdtgt0(xb))
| ~ aElementOf0(X156,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X155),sbrdtbr0(esk37_0))
| aElementOf0(esk41_1(X155),slsdtgt0(xa)) )
& esk37_0 != sz00
& aElementOf0(esk37_0,xI)
& sdtpldt0(esk38_0,esk39_0) = esk37_0
& aElementOf0(esk39_0,slsdtgt0(xb))
& aElementOf0(esk38_0,slsdtgt0(xa)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])])]) ).
cnf(c_0_4,negated_conjecture,
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| X1 = sz00
| sdtpldt0(esk44_1(X1),esk45_1(X1)) = esk43_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_5,negated_conjecture,
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| X1 = sz00
| iLess0(sbrdtbr0(esk43_1(X1)),sbrdtbr0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| X1 = sz00
| aElementOf0(esk45_1(X1),slsdtgt0(xb)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,negated_conjecture,
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| X1 = sz00
| aElementOf0(esk44_1(X1),slsdtgt0(xa)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,negated_conjecture,
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| esk43_1(X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
( sdtpldt0(X2,X3) != X1
| ~ aElementOf0(X3,slsdtgt0(xb))
| ~ aElementOf0(X2,slsdtgt0(xa))
| X1 = sz00
| aElementOf0(esk43_1(X1),xI) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_10,negated_conjecture,
( sdtpldt0(X3,X4) != X2
| ~ aElementOf0(X4,slsdtgt0(xb))
| ~ aElementOf0(X3,slsdtgt0(xa))
| ~ iLess0(sbrdtbr0(X2),sbrdtbr0(esk37_0))
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk40_1(X2)))
| ~ aElementOf0(X1,xI)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_11,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| sdtpldt0(X1,X2) = sz00
| sdtpldt0(esk44_1(sdtpldt0(X1,X2)),esk45_1(sdtpldt0(X1,X2))) = esk43_1(sdtpldt0(X1,X2)) ),
inference(er,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
sdtpldt0(esk38_0,esk39_0) = esk37_0,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,negated_conjecture,
aElementOf0(esk39_0,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_14,negated_conjecture,
aElementOf0(esk38_0,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_15,negated_conjecture,
esk37_0 != sz00,
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_16,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| iLess0(sbrdtbr0(esk43_1(sdtpldt0(X1,X2))),sbrdtbr0(sdtpldt0(X1,X2)))
| sdtpldt0(X1,X2) = sz00 ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| aElementOf0(esk45_1(sdtpldt0(X1,X2)),slsdtgt0(xb))
| sdtpldt0(X1,X2) = sz00 ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| aElementOf0(esk44_1(sdtpldt0(X1,X2)),slsdtgt0(xa))
| sdtpldt0(X1,X2) = sz00 ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| esk43_1(sdtpldt0(X1,X2)) != sz00
| sdtpldt0(X1,X2) = sz00 ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_20,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk37_0))
| X1 = sz00
| aElementOf0(esk40_1(X1),xI) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| iLess0(sbrdtbr0(esk43_1(X1)),sbrdtbr0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_22,negated_conjecture,
aElementOf0(esk37_0,xI),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_23,negated_conjecture,
( ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| aElementOf0(esk43_1(sdtpldt0(X1,X2)),xI)
| sdtpldt0(X1,X2) = sz00 ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_24,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk37_0))
| esk40_1(X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_25,negated_conjecture,
( ~ aElementOf0(X3,xI)
| ~ aElementOf0(X1,slsdtgt0(xa))
| ~ aElementOf0(X2,slsdtgt0(xb))
| ~ iLess0(sbrdtbr0(sdtpldt0(X1,X2)),sbrdtbr0(esk37_0))
| ~ iLess0(sbrdtbr0(X3),sbrdtbr0(esk40_1(sdtpldt0(X1,X2))))
| X3 = sz00
| sdtpldt0(X1,X2) = sz00 ),
inference(er,[status(thm)],[c_0_10]) ).
cnf(c_0_26,negated_conjecture,
sdtpldt0(esk44_1(esk37_0),esk45_1(esk37_0)) = esk43_1(esk37_0),
inference(sr,[status(thm)],[inference(cn,[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]) ).
cnf(c_0_27,negated_conjecture,
iLess0(sbrdtbr0(esk43_1(esk37_0)),sbrdtbr0(esk37_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_28,negated_conjecture,
aElementOf0(esk45_1(esk37_0),slsdtgt0(xb)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_29,negated_conjecture,
aElementOf0(esk44_1(esk37_0),slsdtgt0(xa)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_30,negated_conjecture,
esk43_1(esk37_0) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_31,negated_conjecture,
( ~ aElementOf0(esk43_1(esk37_0),xI)
| aElementOf0(esk40_1(esk43_1(esk37_0)),xI)
| esk43_1(esk37_0) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),c_0_15]) ).
cnf(c_0_32,negated_conjecture,
aElementOf0(esk43_1(esk37_0),xI),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( ~ aElementOf0(esk43_1(esk37_0),xI)
| esk40_1(esk43_1(esk37_0)) != sz00
| esk43_1(esk37_0) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_22])]),c_0_15]) ).
cnf(c_0_34,negated_conjecture,
( ~ aElementOf0(X1,xI)
| ~ iLess0(sbrdtbr0(X1),sbrdtbr0(esk40_1(esk43_1(esk37_0))))
| X1 = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_35,negated_conjecture,
aElementOf0(esk40_1(esk43_1(esk37_0)),xI),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32])]),c_0_30]) ).
cnf(c_0_36,negated_conjecture,
esk40_1(esk43_1(esk37_0)) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_32])]),c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( ~ aElementOf0(esk43_1(esk40_1(esk43_1(esk37_0))),xI)
| esk43_1(esk40_1(esk43_1(esk37_0))) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_21]),c_0_35])]),c_0_36]) ).
cnf(c_0_38,negated_conjecture,
( ~ aElementOf0(X1,xI)
| X1 = sz00
| aElementOf0(esk43_1(X1),xI) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_39,negated_conjecture,
( ~ aElementOf0(X1,xI)
| esk43_1(X1) != sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_40,negated_conjecture,
esk43_1(esk40_1(esk43_1(esk37_0))) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_35])]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_35])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG111+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/15.40 % Computer : n010.cluster.edu
% 0.13/15.40 % Model : x86_64 x86_64
% 0.13/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/15.40 % Memory : 8046.5625MB
% 0.13/15.40 % OS : Linux 6.8.0-71-generic
% 0.13/15.40 % CPULimit : 300
% 0.13/15.40 % WCLimit : 300
% 0.13/15.40 % DateTime : Mon Sep 21 04:21:11 UTC 2026
% 0.13/15.40 % CPUTime :
% 0.13/15.40 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/15.47 Running first-order theorem proving
% 0.13/15.47 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/15.61 % Version: 3.5.1
% 0.16/15.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/15.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/15.61 % Starting new_bool_3 with 300s (1) cores
% 0.16/15.61 % Starting new_bool_1 with 300s (1) cores
% 0.16/15.61 % Starting sh5l with 300s (1) cores
% 0.16/15.61 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 13456 completed with status 0
% 0.16/15.61 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.16/15.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/15.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/15.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/15.61 % No SInE strategy applied
% 0.16/15.61 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.16/15.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/15.61 % Starting SubtermCWHack with 136s (1) cores
% 0.16/15.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/15.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/15.61 % Starting SAT001_MinMin_p005000_rr_RG with 136s (1) cores
% 0.16/15.61 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S070I with 136s (1) cores
% 0.16/15.61 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 13464 completed with status 0
% 0.16/15.61 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.16/15.61 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.16/15.61 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.16/15.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.16/15.61 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.16/15.61 % No SInE strategy applied
% 0.16/15.61 % Search class: FGHSF-FSLM31-MFFFFFNN
% 0.16/15.61 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.16/15.61 % Starting SubtermCWHack with 136s (1) cores
% 0.16/15.61 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.16/15.61 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.16/15.61 % Preprocessing time : 0.006 s
% 0.16/15.61 % Presaturation interreduction done
% 0.16/15.61
% 0.16/15.61 % Proof found!
% 0.16/15.61 % SZS status Theorem
% 0.16/15.61 % SZS output start CNFRefutation
% See solution above
% 0.16/15.61 % Parsed axioms : 45
% 0.16/15.61 % Removed by relevancy pruning/SinE : 0
% 0.16/15.61 % Initial clauses : 203
% 0.16/15.61 % Removed in clause preprocessing : 4
% 0.16/15.61 % Initial clauses in saturation : 199
% 0.16/15.61 % Processed clauses : 564
% 0.16/15.61 % ...of these trivial : 10
% 0.16/15.61 % ...subsumed : 28
% 0.16/15.61 % ...remaining for further processing : 526
% 0.16/15.61 % Other redundant clauses eliminated : 98
% 0.16/15.61 % Clauses deleted for lack of memory : 0
% 0.16/15.61 % Backward-subsumed : 15
% 0.16/15.61 % Backward-rewritten : 12
% 0.16/15.61 % Generated clauses : 1100
% 0.16/15.61 % ...of the previous two non-redundant : 828
% 0.16/15.61 % ...aggressively subsumed : 0
% 0.16/15.61 % Contextual simplify-reflections : 7
% 0.16/15.61 % Paramodulations : 1005
% 0.16/15.61 % Factorizations : 0
% 0.16/15.61 % NegExts : 0
% 0.16/15.61 % Equation resolutions : 98
% 0.16/15.61 % Disequality decompositions : 0
% 0.16/15.61 % Total rewrite steps : 899
% 0.16/15.61 % ...of those cached : 836
% 0.16/15.61 % Propositional unsat checks : 0
% 0.16/15.61 % Propositional check models : 0
% 0.16/15.61 % Propositional check unsatisfiable : 0
% 0.16/15.61 % Propositional clauses : 0
% 0.16/15.61 % Propositional clauses after purity: 0
% 0.16/15.61 % Propositional unsat core size : 0
% 0.16/15.61 % Propositional preprocessing time : 0.000
% 0.16/15.61 % Propositional encoding time : 0.000
% 0.16/15.61 % Propositional solver time : 0.000
% 0.16/15.61 % Success case prop preproc time : 0.000
% 0.16/15.61 % Success case prop encoding time : 0.000
% 0.16/15.61 % Success case prop solver time : 0.000
% 0.16/15.61 % Current number of processed clauses : 270
% 0.16/15.61 % Positive orientable unit clauses : 87
% 0.16/15.61 % Positive unorientable unit clauses: 0
% 0.16/15.61 % Negative unit clauses : 9
% 0.16/15.61 % Non-unit-clauses : 174
% 0.16/15.61 % Current number of unprocessed clauses: 596
% 0.16/15.61 % ...number of literals in the above : 2892
% 0.16/15.61 % Current number of archived formulas : 0
% 0.16/15.61 % Current number of archived clauses : 223
% 0.16/15.61 % Clause-clause subsumption calls (NU) : 9039
% 0.16/15.61 % Rec. Clause-clause subsumption calls : 3011
% 0.16/15.61 % Non-unit clause-clause subsumptions : 36
% 0.16/15.61 % Unit Clause-clause subsumption calls : 1530
% 0.16/15.61 % Rewrite failures with RHS unbound : 0
% 0.16/15.61 % BW rewrite match attempts : 13
% 0.16/15.61 % BW rewrite match successes : 10
% 0.16/15.61 % Condensation attempts : 0
% 0.16/15.61 % Condensation successes : 0
% 0.16/15.61 % Termbank termtop insertions : 32607
% 0.16/15.61 % Search garbage collected termcells : 2977
% 0.16/15.61
% 0.16/15.61 % -------------------------------------------------
% 0.16/15.61 % User time : 0.097 s
% 0.16/15.61 % System time : 0.010 s
% 0.16/15.61 % Total time : 0.106 s
% 0.16/15.61 % Maximum resident set size: 4228 pages
% 0.16/15.61
% 0.16/15.61 % -------------------------------------------------
% 0.16/15.61 % User time : 0.422 s
% 0.16/15.61 % System time : 0.049 s
% 0.16/15.61 % Total time : 0.471 s
% 0.16/15.61 % Maximum resident set size: 4608 pages
% 0.16/15.61 % E exiting
%------------------------------------------------------------------------------