%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM474+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:21:06 AM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 80 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 327 ( 140 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 395 ( 171 ~; 108 |; 74 &)
% ( 36 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 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 : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 63 ( 54 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(xq_type,type,
xq: $i ).
tff(xl_type,type,
xl: $i ).
tff(sdtsldt0_type,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xn_type,type,
xn: $i ).
tff(xr_type,type,
xr: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(1,plain,
( ( sdtpldt0(sdtasdt0(xl,xp),xn) = sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) )
<=> ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( xr = sdtmndt0(xq,xp) )
<=> ( xr = sdtmndt0(xq,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
( aNaturalNumber0(xr)
& ( sdtpldt0(xp,xr) = xq )
& ( xr = sdtmndt0(xq,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
tff(4,plain,
xr = sdtmndt0(xq,xp),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
xr = sdtmndt0(xq,xp),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
sdtmndt0(xq,xp) = xr,
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
sdtasdt0(xl,sdtmndt0(xq,xp)) = sdtasdt0(xl,xr),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ( xp = sdtsldt0(xm,xl) )
<=> ( xp = sdtsldt0(xm,xl) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( aNaturalNumber0(xp)
& ( xm = sdtasdt0(xl,xp) )
& ( xp = sdtsldt0(xm,xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
tff(10,plain,
xp = sdtsldt0(xm,xl),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
xp = sdtsldt0(xm,xl),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
sdtsldt0(xm,xl) = xp,
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
sdtasdt0(xl,sdtsldt0(xm,xl)) = sdtasdt0(xl,xp),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)),
inference(monotonicity,[status(thm)],[13,7]) ).
tff(15,plain,
( ( xm = sdtasdt0(xl,xp) )
<=> ( xm = sdtasdt0(xl,xp) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( aNaturalNumber0(xp)
& ( xm = sdtasdt0(xl,xp) ) ),
inference(and_elim,[status(thm)],[9]) ).
tff(17,plain,
xm = sdtasdt0(xl,xp),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
xm = sdtasdt0(xl,xp),
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,plain,
sdtasdt0(xl,xp) = xm,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
sdtpldt0(sdtasdt0(xl,xp),xn) = sdtpldt0(xm,xn),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
sdtpldt0(xm,xn) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
<=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
( aNaturalNumber0(xq)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
& ( xq = sdtsldt0(sdtpldt0(xm,xn),xl) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
tff(24,plain,
( aNaturalNumber0(xq)
& ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) ) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
sdtasdt0(xl,xq) = sdtpldt0(xm,xn),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ( sdtpldt0(xp,xr) = xq )
<=> ( sdtpldt0(xp,xr) = xq ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( aNaturalNumber0(xr)
& ( sdtpldt0(xp,xr) = xq ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(30,plain,
sdtpldt0(xp,xr) = xq,
inference(and_elim,[status(thm)],[29]) ).
tff(31,plain,
sdtpldt0(xp,xr) = xq,
inference(modus_ponens,[status(thm)],[30,28]) ).
tff(32,plain,
sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)) = sdtpldt0(xp,xr),
inference(monotonicity,[status(thm)],[12,6]) ).
tff(33,plain,
sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)) = xq,
inference(transitivity,[status(thm)],[32,31]) ).
tff(34,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) = sdtasdt0(xl,xq),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(transitivity,[status(thm)],[34,27,21]) ).
tff(36,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
<=> ( sdtpldt0(sdtasdt0(xl,xp),xn) = sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) ) ),
inference(monotonicity,[status(thm)],[35,14]) ).
tff(37,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
<=> ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn) ) ),
inference(transitivity,[status(thm)],[36,1]) ).
tff(38,plain,
( ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn) )
<=> ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) ) ),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn) )
<=> ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn) )
<=> ( sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(42,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
( aNaturalNumber0(sdtmndt0(xq,xp))
<=> aNaturalNumber0(xr) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(45,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(sdtmndt0(xq,xp)) ),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
( aNaturalNumber0(xr)
<=> aNaturalNumber0(xr) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
aNaturalNumber0(xr),
inference(and_elim,[status(thm)],[29]) ).
tff(48,plain,
aNaturalNumber0(xr),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
aNaturalNumber0(sdtmndt0(xq,xp)),
inference(modus_ponens,[status(thm)],[48,45]) ).
tff(50,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
<=> aNaturalNumber0(xp) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(51,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
( aNaturalNumber0(xp)
<=> aNaturalNumber0(xp) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
aNaturalNumber0(xp),
inference(and_elim,[status(thm)],[16]) ).
tff(54,plain,
aNaturalNumber0(xp),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(modus_ponens,[status(thm)],[54,51]) ).
tff(56,plain,
( aNaturalNumber0(xl)
<=> aNaturalNumber0(xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
tff(58,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
aNaturalNumber0(xl),
inference(and_elim,[status(thm)],[58]) ).
tff(60,plain,
aNaturalNumber0(xl),
inference(modus_ponens,[status(thm)],[59,56]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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(64,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)],[63]) ).
tff(65,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(66,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(67,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)],[66]) ).
tff(68,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/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
tff(69,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)],[68,67]) ).
tff(70,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)],[69,65]) ).
tff(71,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)],[70]) ).
tff(72,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)],[71,64]) ).
tff(73,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)],[72,62]) ).
tff(74,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(sdtmndt0(xq,xp))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtmndt0(xq,xp),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(sdtmndt0(xq,xp))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtmndt0(xq,xp),xl)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,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(sdtmndt0(xq,xp))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtmndt0(xq,xp),xl)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,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(sdtmndt0(xq,xp))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xl)
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtmndt0(xq,xp),xl)) ) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ aNaturalNumber0(sdtmndt0(xq,xp))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtmndt0(xq,xp),xl)) ) ) ),
inference(unit_resolution,[status(thm)],[76,73,60]) ).
tff(78,plain,
~ ( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtmndt0(xq,xp),xl)) ) ),
inference(unit_resolution,[status(thm)],[77,55,49]) ).
tff(79,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) != sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) )
| ( sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp)),xl) != sdtpldt0(sdtasdt0(sdtsldt0(xm,xl),xl),sdtasdt0(sdtmndt0(xq,xp),xl)) )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtmndt0(xq,xp))) = sdtpldt0(sdtasdt0(xl,sdtsldt0(xm,xl)),sdtasdt0(xl,sdtmndt0(xq,xp))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(80,plain,
$false,
inference(unit_resolution,[status(thm)],[79,78,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM474+2 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:13:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% See solution above
% 0.21/0.45 % E exiting
%------------------------------------------------------------------------------