%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG077+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:24:06 AM UTC 2025
% Result : Theorem 14.21s 14.41s
% Output : Proof 14.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 36
% Syntax : Number of formulae : 113 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 818 ( 374 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 1257 ( 598 ~; 444 |; 139 &)
% ( 67 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 46 ( 46 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 : 149 ( 134 !; 0 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xH_type,type,
xH: $i ).
tff(xE_type,type,
xE: $i ).
tff(xP_type,type,
xP: $i ).
tff(xB_type,type,
xB: $i ).
tff(xA_type,type,
xA: $i ).
tff(sdtasasdt0_type,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(xp_type,type,
xp: $i ).
tff(aScalar0_type,type,
aScalar0: $i > $o ).
tff(sz0z00_type,type,
sz0z00: $i ).
tff(1,plain,
( ( xH = sdtasdt0(xA,xB) )
<=> ( xH = sdtasdt0(xA,xB) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aScalar0(xH)
& ( xH = sdtasdt0(xA,xB) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
tff(3,plain,
xH = sdtasdt0(xA,xB),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xH = sdtasdt0(xA,xB),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtasdt0(xA,xB) = xH,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( xE = sdtasasdt0(xp,xq) )
<=> ( xE = sdtasasdt0(xp,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( aScalar0(xE)
& ( xE = sdtasasdt0(xp,xq) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
tff(8,plain,
xE = sdtasasdt0(xp,xq),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
xE = sdtasasdt0(xp,xq),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
sdtasasdt0(xp,xq) = xE,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) = sdtasdt0(xE,xH),
inference(monotonicity,[status(thm)],[10,5]) ).
tff(12,plain,
( aScalar0(sdtasasdt0(xp,xq))
<=> aScalar0(xE) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(13,plain,
( aScalar0(xE)
<=> aScalar0(sdtasasdt0(xp,xq)) ),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
( aScalar0(xE)
<=> aScalar0(xE) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,plain,
aScalar0(xE),
inference(and_elim,[status(thm)],[7]) ).
tff(16,plain,
aScalar0(xE),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
aScalar0(sdtasasdt0(xp,xq)),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( aScalar0(sdtasdt0(xA,xB))
<=> aScalar0(xH) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(19,plain,
( aScalar0(xH)
<=> aScalar0(sdtasdt0(xA,xB)) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( aScalar0(xH)
<=> aScalar0(xH) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
aScalar0(xH),
inference(and_elim,[status(thm)],[2]) ).
tff(22,plain,
aScalar0(xH),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
aScalar0(sdtasdt0(xA,xB)),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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)],[26]) ).
tff(28,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(29,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(30,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)],[29]) ).
tff(31,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(32,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)],[31,30]) ).
tff(33,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)],[32,28]) ).
tff(34,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)],[33]) ).
tff(35,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)],[34,27]) ).
tff(36,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)],[35,25]) ).
tff(37,plain,
( aScalar0(sz0z00)
<=> aScalar0(sz0z00) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
aScalar0(sz0z00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSZeroSc) ).
tff(39,plain,
aScalar0(sz0z00),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,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(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) )
<=> ( ~ ! [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(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) )
<=> ( ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ aScalar0(sz0z00)
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,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(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) )
<=> ( ~ ! [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(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,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(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) )
<=> ( ~ ! [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(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ) ),
inference(transitivity,[status(thm)],[45,40]) ).
tff(47,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(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,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(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasasdt0(xp,xq))
| ~ aScalar0(sz0z00)
| ~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ),
inference(unit_resolution,[status(thm)],[48,39,36,23,17]) ).
tff(50,plain,
( ( sdtpldt0(sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtpldt0(sdtasasdt0(xp,xq),sdtpldt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtpldt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtpldt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),sz0z00) != sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(sdtasdt0(xA,xB),sz0z00)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) != sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) )
| ( sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) = sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)) = sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)) = sdtasdt0(sdtasasdt0(xp,xq),sdtasdt0(xA,xB)),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
sdtasdt0(xH,xE) = sdtasdt0(sdtasdt0(xA,xB),sdtasasdt0(xp,xq)),
inference(monotonicity,[status(thm)],[4,9]) ).
tff(54,plain,
sdtasdt0(xH,xE) = sdtasdt0(xE,xH),
inference(transitivity,[status(thm)],[53,52,11]) ).
tff(55,plain,
sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH)),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH)),
inference(symmetry,[status(thm)],[55]) ).
tff(57,plain,
sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
( ( xP = sdtasdt0(xE,xH) )
<=> ( xP = sdtasdt0(xE,xH) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
( aScalar0(xP)
& ( xP = sdtasdt0(xE,xH) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
tff(60,plain,
xP = sdtasdt0(xE,xH),
inference(and_elim,[status(thm)],[59]) ).
tff(61,plain,
xP = sdtasdt0(xE,xH),
inference(modus_ponens,[status(thm)],[60,58]) ).
tff(62,plain,
sdtasdt0(xE,xH) = xP,
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( aScalar0(sdtasdt0(xE,xH))
<=> aScalar0(xP) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( aScalar0(xP)
<=> aScalar0(sdtasdt0(xE,xH)) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( aScalar0(xP)
<=> aScalar0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
aScalar0(xP),
inference(and_elim,[status(thm)],[59]) ).
tff(67,plain,
aScalar0(xP),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
aScalar0(sdtasdt0(xE,xH)),
inference(modus_ponens,[status(thm)],[67,64]) ).
tff(69,plain,
sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)) = sdtasdt0(xH,xH),
inference(monotonicity,[status(thm)],[5,5]) ).
tff(70,plain,
( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
<=> aScalar0(sdtasdt0(xH,xH)) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
^ [W0: $i,W1: $i] :
refl(( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,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) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
rewrite(( ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
( ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [W0: $i,W1: $i] :
( ( aScalar0(W0)
& aScalar0(W1) )
=> aScalar0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
tff(79,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ ( aScalar0(W0)
& aScalar0(W1) ) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) ),
inference(modus_ponens,[status(thm)],[82,72]) ).
tff(84,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ( aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) )
<=> ( ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB)))
| ~ aScalar0(sdtasdt0(xA,xB))
| ~ aScalar0(sdtasdt0(xA,xB)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [W0: $i,W1: $i] :
( aScalar0(sdtasdt0(W0,W1))
| ~ aScalar0(W1)
| ~ aScalar0(W0) )
| ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ aScalar0(sdtasdt0(xA,xB))
| aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))) ),
inference(unit_resolution,[status(thm)],[89,83]) ).
tff(91,plain,
aScalar0(sdtasdt0(sdtasdt0(xA,xB),sdtasdt0(xA,xB))),
inference(unit_resolution,[status(thm)],[90,23]) ).
tff(92,plain,
aScalar0(sdtasdt0(xH,xH)),
inference(modus_ponens,[status(thm)],[91,70]) ).
tff(93,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(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) )
<=> ( ~ ! [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(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,plain,
( ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) ) ) )
<=> ( ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,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(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) ) ) )
<=> ( ~ ! [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(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,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(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) ) ) )
<=> ( ~ ! [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(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ) ),
inference(transitivity,[status(thm)],[98,93]) ).
tff(100,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(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xE,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,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(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ aScalar0(sdtasdt0(xE,xH))
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ) ),
inference(unit_resolution,[status(thm)],[101,36]) ).
tff(103,plain,
~ ( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ),
inference(unit_resolution,[status(thm)],[102,92,68]) ).
tff(104,plain,
( ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtasdt0(sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) != sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) )
| ( sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(105,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xH,xH))),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)) = sdtpldt0(xP,xP),
inference(monotonicity,[status(thm)],[62,62]) ).
tff(107,plain,
sdtpldt0(xP,xP) = sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),
inference(symmetry,[status(thm)],[106]) ).
tff(108,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtpldt0(sdtasdt0(xE,xH),sdtasdt0(xE,xH)),sdtasdt0(xH,xH)),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) = sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(transitivity,[status(thm)],[108,105,57]) ).
tff(110,plain,
( ( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) )
<=> ( sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(112,plain,
sdtpldt0(sdtpldt0(xP,xP),sdtasdt0(xH,xH)) != sdtpldt0(sdtasdt0(xE,xH),sdtpldt0(sdtasdt0(xH,xE),sdtasdt0(xH,xH))),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
$false,
inference(unit_resolution,[status(thm)],[112,109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : RNG077+2 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:19:08 EDT 2025
% 0.13/0.35 % CPUTime :
% 14.21/14.41 % SZS status Theorem
% 14.21/14.41 % SZS output start Proof
% See solution above
% 14.26/14.45 % E exiting
%------------------------------------------------------------------------------