%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM468+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:21:05 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 294 ( 115 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 396 ( 173 ~; 111 |; 75 &)
% ( 25 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 23 ( 23 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 63 ( 54 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xl_type,type,
xl: $i ).
tff(xn_type,type,
xn: $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( xl != sz00 )
=> ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xl))
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) )
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ) )
<=> ~ ( ( xl = sz00 )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
| ~ ( aNaturalNumber0(sdtsldt0(xn,xl))
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) )
| ~ ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( xl != sz00 )
=> ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xl))
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) )
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ( xl = sz00 )
| ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
| ~ ( aNaturalNumber0(sdtsldt0(xn,xl))
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) )
| ~ ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
<=> aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(10,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
( aNaturalNumber0(xl)
<=> aNaturalNumber0(xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1240) ).
tff(14,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aNaturalNumber0(xl),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aNaturalNumber0(xl),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAMDistr) ).
tff(25,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[28,18]) ).
tff(30,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) ) ),
inference(unit_resolution,[status(thm)],[32,29,16,11,7]) ).
tff(34,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtsldt0(xn,xl),xl)) )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(35,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) )
<=> ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
xn = sdtasdt0(xl,sdtsldt0(xn,xl)),
inference(and_elim,[status(thm)],[9]) ).
tff(39,plain,
xn = sdtasdt0(xl,sdtsldt0(xn,xl)),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )
<=> ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(and_elim,[status(thm)],[5]) ).
tff(42,plain,
xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
sdtpldt0(xm,xn) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtsldt0(xn,xl))),
inference(monotonicity,[status(thm)],[42,39]) ).
tff(44,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(transitivity,[status(thm)],[43,36]) ).
tff(45,plain,
( ( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) )
<=> ( sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(or_elim,[status(thm)],[4]) ).
tff(47,plain,
sdtpldt0(xm,xn) != sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM468+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 01:14:56 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------