%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG059+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 : Sat Jun 21 05:24:02 AM UTC 2025
% Result : Theorem 1.59s 1.78s
% Output : Proof 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 106 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 668 ( 328 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 938 ( 426 ~; 292 |; 153 &)
% ( 55 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 50 ( 50 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 130 ( 113 !; 0 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xR_type,type,
xR: $i ).
tff(xS_type,type,
xS: $i ).
tff(xD_type,type,
xD: $i ).
tff(xF_type,type,
xF: $i ).
tff(xG_type,type,
xG: $i ).
tff(xC_type,type,
xC: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(1,plain,
( ( xS = sdtasdt0(xF,xD) )
<=> ( xS = sdtasdt0(xF,xD) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xS)
& ( xS = sdtasdt0(xF,xD) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).
tff(3,plain,
xS = sdtasdt0(xF,xD),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xS = sdtasdt0(xF,xD),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasdt0(xF,xD) = xS,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( xR = sdtasdt0(xC,xG) )
<=> ( xR = sdtasdt0(xC,xG) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( aScalar0(xR)
& ( xR = sdtasdt0(xC,xG) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).
tff(8,plain,
xR = sdtasdt0(xC,xG),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
xR = sdtasdt0(xC,xG),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
sdtasdt0(xC,xG) = xR,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)) = sdtasdt0(xR,xS),
inference(monotonicity,[status(thm)],[10,5]) ).
tff(12,plain,
sdtasdt0(xR,xS) = sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( ( xN = sdtasdt0(xR,xS) )
<=> ( xN = sdtasdt0(xR,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
( aScalar0(xN)
& ( xN = sdtasdt0(xR,xS) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
tff(15,plain,
xN = sdtasdt0(xR,xS),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
xN = sdtasdt0(xR,xS),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
xN = sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD)),
inference(transitivity,[status(thm)],[16,12]) ).
tff(18,plain,
smndt0(xN) = smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) = smndt0(xN),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( aScalar0(sdtasdt0(xF,xD))
<=> aScalar0(xS) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(21,plain,
( aScalar0(xS)
<=> aScalar0(sdtasdt0(xF,xD)) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( aScalar0(xS)
<=> aScalar0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
aScalar0(xS),
inference(and_elim,[status(thm)],[2]) ).
tff(24,plain,
aScalar0(xS),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
aScalar0(sdtasdt0(xF,xD)),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
( aScalar0(sdtasdt0(xC,xG))
<=> aScalar0(xR) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(27,plain,
( aScalar0(xR)
<=> aScalar0(sdtasdt0(xC,xG)) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( aScalar0(xR)
<=> aScalar0(xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
aScalar0(xR),
inference(and_elim,[status(thm)],[7]) ).
tff(30,plain,
aScalar0(xR),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
aScalar0(sdtasdt0(xC,xG)),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) )
<=> ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
rewrite(( ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMNeg) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [W0: $i,W1: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1) )
| ( ( sdtasdt0(W0,smndt0(W1)) = smndt0(sdtasdt0(W0,W1)) )
& ( sdtasdt0(smndt0(W0),W1) = smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[43,33]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtasdt0(sdtasdt0(xC,xG),smndt0(sdtasdt0(xF,xD))) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtasdt0(sdtasdt0(xC,xG),smndt0(sdtasdt0(xF,xD))) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtasdt0(sdtasdt0(xC,xG),smndt0(sdtasdt0(xF,xD))) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtasdt0(sdtasdt0(xC,xG),smndt0(sdtasdt0(xF,xD))) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ ( ( sdtasdt0(sdtasdt0(xC,xG),smndt0(sdtasdt0(xF,xD))) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ) ),
inference(unit_resolution,[status(thm)],[47,44]) ).
tff(49,plain,
~ ( ( sdtasdt0(sdtasdt0(xC,xG),smndt0(sdtasdt0(xF,xD))) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ),
inference(unit_resolution,[status(thm)],[48,31,25]) ).
tff(50,plain,
( ( sdtasdt0(sdtasdt0(xC,xG),smndt0(sdtasdt0(xF,xD))) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) = smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) = smndt0(sdtasdt0(sdtasdt0(xC,xG),sdtasdt0(xF,xD))),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [W0: $i] :
refl(( ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [W0: $i] :
rewrite(( ( aScalar0(W0)
=> aScalar0(smndt0(W0)) )
<=> ( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W0: $i] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) )
<=> ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [W0: $i] :
( aScalar0(W0)
=> aScalar0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNegSc) ).
tff(58,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG)) )
<=> ( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [W0: $i] :
( aScalar0(smndt0(W0))
| ~ aScalar0(W0) )
| aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ aScalar0(sdtasdt0(xC,xG)) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
aScalar0(smndt0(sdtasdt0(xC,xG))),
inference(unit_resolution,[status(thm)],[64,61,31]) ).
tff(66,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ~ ~ ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
rewrite(( ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
( ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
<=> ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) ) )),
trans(monotonicity(rewrite(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ) )),
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
( ( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
tff(74,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aScalar0(W0)
& aScalar0(W1)
& aScalar0(W2) )
| ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
& ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
& ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) )
& ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[77,67]) ).
tff(79,plain,
( aScalar0(sz0z00)
<=> aScalar0(sz0z00) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
tff(81,plain,
aScalar0(sz0z00),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) )
| ( sdtasdt0(sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) )
| ( sdtasdt0(sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) )
| ( sdtasdt0(sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aScalar0(W2)
| ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtpldt0(sdtpldt0(W0,W1),W2) != sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ( sdtpldt0(W0,W1) != sdtpldt0(W1,W0) )
| ( sdtasdt0(sdtasdt0(W0,W1),W2) != sdtasdt0(W0,sdtasdt0(W1,W2)) )
| ( sdtasdt0(W0,W1) != sdtasdt0(W1,W0) ) ) )
| ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ aScalar0(smndt0(sdtasdt0(xC,xG)))
| ~ ( ( sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) )
| ( sdtasdt0(sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) ) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
~ ( ( sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) )
| ( sdtasdt0(sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) ) ),
inference(unit_resolution,[status(thm)],[84,81,78,25,65]) ).
tff(86,plain,
( ( sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtpldt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtpldt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtpldt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) )
| ( sdtasdt0(sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),sz0z00) != sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(sdtasdt0(xF,xD),sz0z00)) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) != sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) = sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)) = sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) = sdtasdt0(smndt0(sdtasdt0(xC,xG)),sdtasdt0(xF,xD)),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ ( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ ( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ ( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aScalar0(W1)
| ~ aScalar0(W0)
| ~ ( ( sdtasdt0(W0,smndt0(W1)) != smndt0(sdtasdt0(W0,W1)) )
| ( sdtasdt0(smndt0(W0),W1) != smndt0(sdtasdt0(W0,W1)) ) ) )
| ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ ( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ aScalar0(sdtasdt0(xC,xG))
| ~ aScalar0(sdtasdt0(xF,xD))
| ~ ( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ) ),
inference(unit_resolution,[status(thm)],[91,44]) ).
tff(93,plain,
~ ( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ),
inference(unit_resolution,[status(thm)],[92,31,25]) ).
tff(94,plain,
( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) = smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(95,plain,
sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) = smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) = sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
( ( sdtasdt0(sdtasdt0(xF,xD),smndt0(sdtasdt0(xC,xG))) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) != smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) )
| ( sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) = smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(98,plain,
sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) = smndt0(sdtasdt0(sdtasdt0(xF,xD),sdtasdt0(xC,xG))),
inference(unit_resolution,[status(thm)],[97,93]) ).
tff(99,plain,
smndt0(sdtasdt0(xF,xD)) = smndt0(xS),
inference(monotonicity,[status(thm)],[5]) ).
tff(100,plain,
sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)) = sdtasdt0(smndt0(xS),xR),
inference(monotonicity,[status(thm)],[99,10]) ).
tff(101,plain,
sdtasdt0(smndt0(xS),xR) = sdtasdt0(smndt0(sdtasdt0(xF,xD)),sdtasdt0(xC,xG)),
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(transitivity,[status(thm)],[101,98,96,88,51,19]) ).
tff(103,plain,
( ( sdtasdt0(smndt0(xS),xR) != smndt0(xN) )
<=> ( sdtasdt0(smndt0(xS),xR) != smndt0(xN) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,axiom,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(105,plain,
sdtasdt0(smndt0(xS),xR) != smndt0(xN),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
$false,
inference(unit_resolution,[status(thm)],[105,102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG059+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:16:54 EDT 2025
% 0.12/0.33 % CPUTime :
% 1.59/1.78 % SZS status Theorem
% 1.59/1.78 % SZS output start Proof
% See solution above
% 1.59/1.80 % E exiting
%------------------------------------------------------------------------------