%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX190-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n027.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 : Tue May 5 07:08:14 PM UTC 2026
% Result : Unsatisfiable 16.64s 16.90s
% Output : Proof 16.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 102
% Syntax : Number of formulae : 299 ( 216 unt; 0 typ; 0 def)
% Number of atoms : 442 ( 419 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 185 ( 64 ~; 51 |; 0 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 22 ( 22 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 433 ( 393 !; 0 ?; 433 :)
% Comments :
%------------------------------------------------------------------------------
tff(btrue_type,type,
btrue: $i ).
tff(eq3_type,type,
eq3: ( $i * $i ) > $i ).
tff(bfalse_type,type,
bfalse: $i ).
tff(prop4_type,type,
prop4: $i > $i ).
tff(x_type,type,
x: ( $i * $i ) > $i ).
tff(opt_type,type,
opt: $i > $i ).
tff(x2_type,type,
x2: $i ).
tff(n_type,type,
n: $i > $i ).
tff(s_type,type,
s: $i > $i ).
tff(z_type,type,
z: $i ).
tff(eq2_type,type,
eq2: ( $i * $i ) > $i ).
tff(aux_type,type,
aux: ( $i * $i * $i ) > $i ).
tff(fail4_type,type,
fail4: ( $i * $i ) > $i ).
tff(y_type,type,
y: ( $i * $i ) > $i ).
tff(d_type,type,
d: $i > $i ).
tff(fail_type,type,
fail: ( $i * $i ) > $i ).
tff(fail2_type,type,
fail2: ( $i * $i ) > $i ).
tff(fail1_type,type,
fail1: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( eq3(X,X) = btrue )
<=> ( eq3(X,X) = btrue ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( eq3(X,X) = btrue )
<=> ! [X: $i] : ( eq3(X,X) = btrue ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( eq3(X,X) = btrue )
<=> ! [X: $i] : ( eq3(X,X) = btrue ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( eq3(X,X) = btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_088) ).
tff(5,plain,
! [X: $i] : ( eq3(X,X) = btrue ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( eq3(X,X) = btrue ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( eq3(X,X) = btrue ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( eq3(X,X) = btrue )
| ( eq3(bfalse,bfalse) = btrue ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
eq3(bfalse,bfalse) = btrue,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( eq2(n(X),y(Y,Z)) = bfalse )
<=> ( eq2(n(X),y(Y,Z)) = bfalse ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse )
<=> ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse )
<=> ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_072) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),y(Y,Z)) = bfalse )
| ( eq2(n(s(z)),y(n(z),x2)) = bfalse ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
eq2(n(s(z)),y(n(z),x2)) = bfalse,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( opt(x2) = x2 )
<=> ( opt(x2) = x2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
opt(x2) = x2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_062) ).
tff(21,plain,
opt(x2) = x2,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
x2 = opt(x2),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
^ [X: $i] :
refl(( ( opt(n(X)) = n(X) )
<=> ( opt(n(X)) = n(X) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X: $i] : ( opt(n(X)) = n(X) )
<=> ! [X: $i] : ( opt(n(X)) = n(X) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X: $i] : ( opt(n(X)) = n(X) )
<=> ! [X: $i] : ( opt(n(X)) = n(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
! [X: $i] : ( opt(n(X)) = n(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_061) ).
tff(27,plain,
! [X: $i] : ( opt(n(X)) = n(X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] : ( opt(n(X)) = n(X) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i] : ( opt(n(X)) = n(X) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [X: $i] : ( opt(n(X)) = n(X) )
| ( opt(n(z)) = n(z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
opt(n(z)) = n(z),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
n(z) = opt(n(z)),
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
y(n(z),x2) = y(opt(n(z)),opt(x2)),
inference(monotonicity,[status(thm)],[32,22]) ).
tff(34,plain,
y(opt(n(z)),opt(x2)) = y(n(z),x2),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
^ [X5: $i,E2: $i] :
refl(( ( fail4(X5,E2) = y(opt(X5),opt(E2)) )
<=> ( fail4(X5,E2) = y(opt(X5),opt(E2)) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) )
<=> ! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) )
<=> ! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_018) ).
tff(39,plain,
! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [X5: $i,E2: $i] : ( fail4(X5,E2) = y(opt(X5),opt(E2)) )
| ( fail4(n(z),x2) = y(opt(n(z)),opt(x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
fail4(n(z),x2) = y(opt(n(z)),opt(x2)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
fail4(n(z),x2) = y(n(z),x2),
inference(transitivity,[status(thm)],[43,34]) ).
tff(45,plain,
eq2(n(s(z)),fail4(n(z),x2)) = eq2(n(s(z)),y(n(z),x2)),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
eq2(n(s(z)),fail4(n(z),x2)) = bfalse,
inference(transitivity,[status(thm)],[45,18]) ).
tff(47,plain,
^ [Z: $i,Y: $i,X: $i,X2: $i] :
refl(( ( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) )
<=> ( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) )
<=> ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) )
<=> ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_067) ).
tff(51,plain,
! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) )
| ( eq2(n(s(z)),fail4(n(z),x2)) != bfalse )
| ( eq2(x(n(s(z)),n(s(z))),x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))))) = bfalse ) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) )
| ( eq2(n(s(z)),fail4(n(z),x2)) != bfalse )
| ( eq2(x(n(s(z)),n(s(z))),x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))))) = bfalse ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) )
| ( eq2(n(s(z)),fail4(n(z),x2)) != bfalse )
| ( eq2(x(n(s(z)),n(s(z))),x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))))) = bfalse ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i,X2: $i] :
( ( eq2(X,Z) != bfalse )
| ( eq2(x(X,Y),x(Z,X2)) = bfalse ) )
| ( eq2(n(s(z)),fail4(n(z),x2)) != bfalse )
| ( eq2(x(n(s(z)),n(s(z))),x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))))) = bfalse ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
eq2(x(n(s(z)),n(s(z))),x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))))) = bfalse,
inference(unit_resolution,[status(thm)],[56,53,46]) ).
tff(58,plain,
( ~ ! [X: $i] : ( opt(n(X)) = n(X) )
| ( opt(n(s(z))) = n(s(z)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
opt(n(s(z))) = n(s(z)),
inference(unit_resolution,[status(thm)],[58,29]) ).
tff(60,plain,
n(s(z)) = opt(n(s(z))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( ( d(x2) = n(s(z)) )
<=> ( d(x2) = n(s(z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
d(x2) = n(s(z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_046) ).
tff(63,plain,
d(x2) = n(s(z)),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
d(x2) = opt(n(s(z))),
inference(transitivity,[status(thm)],[63,60]) ).
tff(65,plain,
y(n(s(s(z))),d(x2)) = y(n(s(s(z))),opt(n(s(z)))),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
y(n(s(s(z))),opt(n(s(z)))) = y(n(s(s(z))),d(x2)),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
^ [Y: $i,E: $i] :
refl(( ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) )
<=> ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) )
<=> ! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) )
<=> ! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
tff(71,plain,
! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ~ ! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) )
| ( aux(n(s(z)),n(s(z)),btrue) = y(n(s(s(z))),opt(n(s(z)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
aux(n(s(z)),n(s(z)),btrue) = y(n(s(s(z))),opt(n(s(z)))),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
^ [X: $i] :
refl(( ( eq2(X,X) = btrue )
<=> ( eq2(X,X) = btrue ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [X: $i] : ( eq2(X,X) = btrue )
<=> ! [X: $i] : ( eq2(X,X) = btrue ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [X: $i] : ( eq2(X,X) = btrue )
<=> ! [X: $i] : ( eq2(X,X) = btrue ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
! [X: $i] : ( eq2(X,X) = btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_087) ).
tff(80,plain,
! [X: $i] : ( eq2(X,X) = btrue ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X: $i] : ( eq2(X,X) = btrue ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X: $i] : ( eq2(X,X) = btrue ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [X: $i] : ( eq2(X,X) = btrue )
| ( eq2(n(s(z)),n(s(z))) = btrue ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
eq2(n(s(z)),n(s(z))) = btrue,
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
btrue = eq2(n(s(z)),n(s(z))),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
aux(n(s(z)),n(s(z)),btrue) = aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))) = aux(n(s(z)),n(s(z)),btrue),
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))) = y(n(s(s(z))),d(x2)),
inference(transitivity,[status(thm)],[87,75,66]) ).
tff(89,plain,
^ [Y: $i] :
refl(( ( d(n(Y)) = n(z) )
<=> ( d(n(Y)) = n(z) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [Y: $i] : ( d(n(Y)) = n(z) )
<=> ! [Y: $i] : ( d(n(Y)) = n(z) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [Y: $i] : ( d(n(Y)) = n(z) )
<=> ! [Y: $i] : ( d(n(Y)) = n(z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,axiom,
! [Y: $i] : ( d(n(Y)) = n(z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_043) ).
tff(93,plain,
! [Y: $i] : ( d(n(Y)) = n(z) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [Y: $i] : ( d(n(Y)) = n(z) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [Y: $i] : ( d(n(Y)) = n(z) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [Y: $i] : ( d(n(Y)) = n(z) )
| ( d(n(s(s(z)))) = n(z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
d(n(s(s(z)))) = n(z),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
d(n(s(s(z)))) = opt(n(z)),
inference(transitivity,[status(thm)],[97,32]) ).
tff(99,plain,
y(d(n(s(s(z)))),x2) = y(opt(n(z)),opt(x2)),
inference(monotonicity,[status(thm)],[98,22]) ).
tff(100,plain,
y(opt(n(z)),opt(x2)) = y(d(n(s(s(z)))),x2),
inference(symmetry,[status(thm)],[99]) ).
tff(101,plain,
fail4(n(z),x2) = y(d(n(s(s(z)))),x2),
inference(transitivity,[status(thm)],[43,100]) ).
tff(102,plain,
x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z))))) = x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))),
inference(monotonicity,[status(thm)],[101,88]) ).
tff(103,plain,
x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))) = x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z))))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
^ [E: $i] :
refl(( ( opt(x(n(z),E)) = E )
<=> ( opt(x(n(z),E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [E: $i] : ( opt(x(n(z),E)) = E )
<=> ! [E: $i] : ( opt(x(n(z),E)) = E ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [E: $i] : ( opt(x(n(z),E)) = E )
<=> ! [E: $i] : ( opt(x(n(z),E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
! [E: $i] : ( opt(x(n(z),E)) = E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_052) ).
tff(108,plain,
! [E: $i] : ( opt(x(n(z),E)) = E ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [E: $i] : ( opt(x(n(z),E)) = E ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [E: $i] : ( opt(x(n(z),E)) = E ),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ~ ! [E: $i] : ( opt(x(n(z),E)) = E )
| ( opt(x(n(z),x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))))) = x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
opt(x(n(z),x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))))) = x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
x(x2,x2) = x(opt(x2),opt(x2)),
inference(monotonicity,[status(thm)],[22,22]) ).
tff(114,plain,
x(opt(x2),opt(x2)) = x(x2,x2),
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
opt(x(opt(x2),opt(x2))) = opt(x(x2,x2)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
opt(x(x2,x2)) = opt(x(opt(x2),opt(x2))),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
^ [E: $i] :
refl(( ( opt(x(x2,E)) = fail(x2,E) )
<=> ( opt(x(x2,E)) = fail(x2,E) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) )
<=> ! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
( ! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) )
<=> ! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,axiom,
! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_055) ).
tff(121,plain,
! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
( ~ ! [E: $i] : ( opt(x(x2,E)) = fail(x2,E) )
| ( opt(x(x2,x2)) = fail(x2,x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(125,plain,
opt(x(x2,x2)) = fail(x2,x2),
inference(unit_resolution,[status(thm)],[124,123]) ).
tff(126,plain,
fail(x2,x2) = opt(x(x2,x2)),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
fail(x2,x2) = opt(x(opt(x2),opt(x2))),
inference(transitivity,[status(thm)],[126,116]) ).
tff(128,plain,
d(fail(x2,x2)) = d(opt(x(opt(x2),opt(x2)))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
d(opt(x(opt(x2),opt(x2)))) = d(fail(x2,x2)),
inference(symmetry,[status(thm)],[128]) ).
tff(130,plain,
y(n(s(s(z))),x2) = y(n(s(s(z))),opt(x2)),
inference(monotonicity,[status(thm)],[22]) ).
tff(131,plain,
y(n(s(s(z))),opt(x2)) = y(n(s(s(z))),x2),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ~ ! [Y: $i,E: $i] : ( aux(Y,E,btrue) = y(n(s(s(z))),opt(Y)) )
| ( aux(x2,x2,btrue) = y(n(s(s(z))),opt(x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
aux(x2,x2,btrue) = y(n(s(s(z))),opt(x2)),
inference(unit_resolution,[status(thm)],[132,73]) ).
tff(134,plain,
( ~ ! [X: $i] : ( eq2(X,X) = btrue )
| ( eq2(x2,x2) = btrue ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
eq2(x2,x2) = btrue,
inference(unit_resolution,[status(thm)],[134,82]) ).
tff(136,plain,
btrue = eq2(x2,x2),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
aux(x2,x2,btrue) = aux(x2,x2,eq2(x2,x2)),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
aux(x2,x2,eq2(x2,x2)) = aux(x2,x2,btrue),
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
^ [Y: $i,E: $i] :
refl(( ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) )
<=> ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) ) )),
inference(bind,[status(th)],[]) ).
tff(140,plain,
( ! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) )
<=> ! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,plain,
( ! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) )
<=> ! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,axiom,
! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
tff(143,plain,
! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
( ~ ! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) )
| ( fail2(x2,x2) = aux(x2,x2,eq2(x2,x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,plain,
fail2(x2,x2) = aux(x2,x2,eq2(x2,x2)),
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
^ [E: $i] :
refl(( ( fail1(x2,E) = fail2(x2,E) )
<=> ( fail1(x2,E) = fail2(x2,E) ) )),
inference(bind,[status(th)],[]) ).
tff(149,plain,
( ! [E: $i] : ( fail1(x2,E) = fail2(x2,E) )
<=> ! [E: $i] : ( fail1(x2,E) = fail2(x2,E) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,plain,
( ! [E: $i] : ( fail1(x2,E) = fail2(x2,E) )
<=> ! [E: $i] : ( fail1(x2,E) = fail2(x2,E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,axiom,
! [E: $i] : ( fail1(x2,E) = fail2(x2,E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_012) ).
tff(152,plain,
! [E: $i] : ( fail1(x2,E) = fail2(x2,E) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [E: $i] : ( fail1(x2,E) = fail2(x2,E) ),
inference(skolemize,[status(sab)],[152]) ).
tff(154,plain,
! [E: $i] : ( fail1(x2,E) = fail2(x2,E) ),
inference(modus_ponens,[status(thm)],[153,149]) ).
tff(155,plain,
( ~ ! [E: $i] : ( fail1(x2,E) = fail2(x2,E) )
| ( fail1(x2,x2) = fail2(x2,x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
fail1(x2,x2) = fail2(x2,x2),
inference(unit_resolution,[status(thm)],[155,154]) ).
tff(157,plain,
^ [Y: $i] :
refl(( ( fail(Y,x2) = fail1(Y,x2) )
<=> ( fail(Y,x2) = fail1(Y,x2) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) )
<=> ! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
( ! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) )
<=> ! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,axiom,
! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_017) ).
tff(161,plain,
! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
( ~ ! [Y: $i] : ( fail(Y,x2) = fail1(Y,x2) )
| ( fail(x2,x2) = fail1(x2,x2) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(165,plain,
fail(x2,x2) = fail1(x2,x2),
inference(unit_resolution,[status(thm)],[164,163]) ).
tff(166,plain,
opt(x(opt(x2),opt(x2))) = y(n(s(s(z))),x2),
inference(transitivity,[status(thm)],[115,125,165,156,147,138,133,131]) ).
tff(167,plain,
d(opt(x(opt(x2),opt(x2)))) = d(y(n(s(s(z))),x2)),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
d(y(n(s(s(z))),x2)) = d(opt(x(opt(x2),opt(x2)))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
^ [G2: $i,H: $i] :
refl(( ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) )
<=> ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) ) )),
inference(bind,[status(th)],[]) ).
tff(170,plain,
( ! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) )
<=> ! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) ) ),
inference(quant_intro,[status(thm)],[169]) ).
tff(171,plain,
( ! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) )
<=> ! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(172,axiom,
! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_045) ).
tff(173,plain,
! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) ),
inference(skolemize,[status(sab)],[173]) ).
tff(175,plain,
! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) ),
inference(modus_ponens,[status(thm)],[174,170]) ).
tff(176,plain,
( ~ ! [G2: $i,H: $i] : ( d(y(H,G2)) = x(y(d(H),G2),y(H,d(G2))) )
| ( d(y(n(s(s(z))),x2)) = x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(177,plain,
d(y(n(s(s(z))),x2)) = x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))),
inference(unit_resolution,[status(thm)],[176,175]) ).
tff(178,plain,
x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))) = d(y(n(s(s(z))),x2)),
inference(symmetry,[status(thm)],[177]) ).
tff(179,plain,
x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))) = d(fail(x2,x2)),
inference(transitivity,[status(thm)],[178,168,129]) ).
tff(180,plain,
( ~ ! [Y: $i] : ( d(n(Y)) = n(z) )
| ( d(n(s(z))) = n(z) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
d(n(s(z))) = n(z),
inference(unit_resolution,[status(thm)],[180,95]) ).
tff(182,plain,
n(z) = d(n(s(z))),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
x(n(z),x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2)))) = x(d(n(s(z))),d(fail(x2,x2))),
inference(monotonicity,[status(thm)],[182,179]) ).
tff(184,plain,
x(d(n(s(z))),d(fail(x2,x2))) = x(n(z),x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2)))),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
^ [F: $i,G: $i] :
refl(( ( d(x(F,G)) = x(d(F),d(G)) )
<=> ( d(x(F,G)) = x(d(F),d(G)) ) )),
inference(bind,[status(th)],[]) ).
tff(186,plain,
( ! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) )
<=> ! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) ) ),
inference(quant_intro,[status(thm)],[185]) ).
tff(187,plain,
( ! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) )
<=> ! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,axiom,
! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_044) ).
tff(189,plain,
! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) ),
inference(skolemize,[status(sab)],[189]) ).
tff(191,plain,
! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) ),
inference(modus_ponens,[status(thm)],[190,186]) ).
tff(192,plain,
( ~ ! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) )
| ( d(x(n(s(z)),fail(x2,x2))) = x(d(n(s(z))),d(fail(x2,x2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(193,plain,
d(x(n(s(z)),fail(x2,x2))) = x(d(n(s(z))),d(fail(x2,x2))),
inference(unit_resolution,[status(thm)],[192,191]) ).
tff(194,plain,
x(n(s(z)),fail(x2,x2)) = x(opt(n(s(z))),opt(x(opt(x2),opt(x2)))),
inference(monotonicity,[status(thm)],[60,127]) ).
tff(195,plain,
x(opt(n(s(z))),opt(x(opt(x2),opt(x2)))) = x(n(s(z)),fail(x2,x2)),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
^ [E: $i,X: $i] :
refl(( ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) )
<=> ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) ) )),
inference(bind,[status(th)],[]) ).
tff(197,plain,
( ! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) )
<=> ! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
( ! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) )
<=> ! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,axiom,
! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
tff(200,plain,
! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) ),
inference(skolemize,[status(sab)],[200]) ).
tff(202,plain,
! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) ),
inference(modus_ponens,[status(thm)],[201,197]) ).
tff(203,plain,
( ~ ! [E: $i,X: $i] : ( aux(n(X),E,bfalse) = x(opt(n(X)),opt(E)) )
| ( aux(n(s(z)),x(opt(x2),opt(x2)),bfalse) = x(opt(n(s(z))),opt(x(opt(x2),opt(x2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
aux(n(s(z)),x(opt(x2),opt(x2)),bfalse) = x(opt(n(s(z))),opt(x(opt(x2),opt(x2)))),
inference(unit_resolution,[status(thm)],[203,202]) ).
tff(205,plain,
eq2(n(s(z)),x(opt(x2),opt(x2))) = eq2(n(s(z)),x(x2,x2)),
inference(monotonicity,[status(thm)],[114]) ).
tff(206,plain,
eq2(n(s(z)),x(x2,x2)) = eq2(n(s(z)),x(opt(x2),opt(x2))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( eq2(n(X),x(Y,Z)) = bfalse )
<=> ( eq2(n(X),x(Y,Z)) = bfalse ) )),
inference(bind,[status(th)],[]) ).
tff(208,plain,
( ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse )
<=> ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse ) ),
inference(quant_intro,[status(thm)],[207]) ).
tff(209,plain,
( ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse )
<=> ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,axiom,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_071) ).
tff(211,plain,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse ),
inference(skolemize,[status(sab)],[211]) ).
tff(213,plain,
! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse ),
inference(modus_ponens,[status(thm)],[212,208]) ).
tff(214,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( eq2(n(X),x(Y,Z)) = bfalse )
| ( eq2(n(s(z)),x(x2,x2)) = bfalse ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(215,plain,
eq2(n(s(z)),x(x2,x2)) = bfalse,
inference(unit_resolution,[status(thm)],[214,213]) ).
tff(216,plain,
bfalse = eq2(n(s(z)),x(x2,x2)),
inference(symmetry,[status(thm)],[215]) ).
tff(217,plain,
bfalse = eq2(n(s(z)),x(opt(x2),opt(x2))),
inference(transitivity,[status(thm)],[216,206]) ).
tff(218,plain,
aux(n(s(z)),x(opt(x2),opt(x2)),bfalse) = aux(n(s(z)),x(opt(x2),opt(x2)),eq2(n(s(z)),x(opt(x2),opt(x2)))),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
aux(n(s(z)),x(opt(x2),opt(x2)),eq2(n(s(z)),x(opt(x2),opt(x2)))) = aux(n(s(z)),x(opt(x2),opt(x2)),bfalse),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
( ~ ! [Y: $i,E: $i] : ( fail2(Y,E) = aux(Y,E,eq2(Y,E)) )
| ( fail2(n(s(z)),x(opt(x2),opt(x2))) = aux(n(s(z)),x(opt(x2),opt(x2)),eq2(n(s(z)),x(opt(x2),opt(x2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(221,plain,
fail2(n(s(z)),x(opt(x2),opt(x2))) = aux(n(s(z)),x(opt(x2),opt(x2)),eq2(n(s(z)),x(opt(x2),opt(x2)))),
inference(unit_resolution,[status(thm)],[220,145]) ).
tff(222,plain,
fail2(n(s(z)),x(opt(x2),opt(x2))) = fail2(n(s(z)),x(x2,x2)),
inference(monotonicity,[status(thm)],[114]) ).
tff(223,plain,
fail2(n(s(z)),x(x2,x2)) = fail2(n(s(z)),x(opt(x2),opt(x2))),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
( ! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) )
<=> ! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(225,plain,
^ [A2: $i,X: $i,X2: $i] :
refl(( ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) )
<=> ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ) )),
inference(bind,[status(th)],[]) ).
tff(226,plain,
( ! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) )
<=> ! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ) ),
inference(quant_intro,[status(thm)],[225]) ).
tff(227,plain,
( ! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) )
<=> ! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,axiom,
! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
tff(229,plain,
! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ),
inference(skolemize,[status(sab)],[229]) ).
tff(231,plain,
! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ),
inference(modus_ponens,[status(thm)],[230,226]) ).
tff(232,plain,
! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) ),
inference(modus_ponens,[status(thm)],[231,224]) ).
tff(233,plain,
( ~ ! [A2: $i,X: $i,X2: $i] : ( fail1(n(A2),x(X,X2)) = fail2(n(A2),x(X,X2)) )
| ( fail1(n(s(z)),x(x2,x2)) = fail2(n(s(z)),x(x2,x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(234,plain,
fail1(n(s(z)),x(x2,x2)) = fail2(n(s(z)),x(x2,x2)),
inference(unit_resolution,[status(thm)],[233,232]) ).
tff(235,plain,
^ [Y: $i,X: $i,X2: $i] :
refl(( ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) )
<=> ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) ) )),
inference(bind,[status(th)],[]) ).
tff(236,plain,
( ! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) )
<=> ! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) ) ),
inference(quant_intro,[status(thm)],[235]) ).
tff(237,plain,
( ! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) )
<=> ! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(238,axiom,
! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_015) ).
tff(239,plain,
! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) ),
inference(modus_ponens,[status(thm)],[238,237]) ).
tff(240,plain,
! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) ),
inference(skolemize,[status(sab)],[239]) ).
tff(241,plain,
! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) ),
inference(modus_ponens,[status(thm)],[240,236]) ).
tff(242,plain,
( ~ ! [Y: $i,X: $i,X2: $i] : ( fail(Y,x(X,X2)) = fail1(Y,x(X,X2)) )
| ( fail(n(s(z)),x(x2,x2)) = fail1(n(s(z)),x(x2,x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(243,plain,
fail(n(s(z)),x(x2,x2)) = fail1(n(s(z)),x(x2,x2)),
inference(unit_resolution,[status(thm)],[242,241]) ).
tff(244,plain,
fail(n(s(z)),x(opt(x2),opt(x2))) = fail(n(s(z)),x(x2,x2)),
inference(monotonicity,[status(thm)],[114]) ).
tff(245,plain,
^ [E: $i,X4: $i] :
refl(( ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) )
<=> ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ) )),
inference(bind,[status(th)],[]) ).
tff(246,plain,
( ! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) )
<=> ! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ) ),
inference(quant_intro,[status(thm)],[245]) ).
tff(247,plain,
( ! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) )
<=> ! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(248,axiom,
! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_051) ).
tff(249,plain,
! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ),
inference(skolemize,[status(sab)],[249]) ).
tff(251,plain,
! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) ),
inference(modus_ponens,[status(thm)],[250,246]) ).
tff(252,plain,
( ~ ! [E: $i,X4: $i] : ( opt(x(n(s(X4)),E)) = fail(n(s(X4)),E) )
| ( opt(x(n(s(z)),x(opt(x2),opt(x2)))) = fail(n(s(z)),x(opt(x2),opt(x2))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(253,plain,
opt(x(n(s(z)),x(opt(x2),opt(x2)))) = fail(n(s(z)),x(opt(x2),opt(x2))),
inference(unit_resolution,[status(thm)],[252,251]) ).
tff(254,plain,
opt(x(n(s(z)),x(opt(x2),opt(x2)))) = x(n(s(z)),fail(x2,x2)),
inference(transitivity,[status(thm)],[253,244,243,234,223,221,219,204,195]) ).
tff(255,plain,
d(opt(x(n(s(z)),x(opt(x2),opt(x2))))) = d(x(n(s(z)),fail(x2,x2))),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
d(opt(x(n(s(z)),x(opt(x2),opt(x2))))) = x(n(z),x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2)))),
inference(transitivity,[status(thm)],[255,193,184]) ).
tff(257,plain,
opt(d(opt(x(n(s(z)),x(opt(x2),opt(x2)))))) = opt(x(n(z),x(y(d(n(s(s(z)))),x2),y(n(s(s(z))),d(x2))))),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
opt(d(opt(x(n(s(z)),x(opt(x2),opt(x2)))))) = x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z))))),
inference(transitivity,[status(thm)],[257,112,103]) ).
tff(259,plain,
n(s(z)) = d(x2),
inference(symmetry,[status(thm)],[63]) ).
tff(260,plain,
x(n(s(z)),n(s(z))) = x(d(x2),d(x2)),
inference(monotonicity,[status(thm)],[259,259]) ).
tff(261,plain,
x(d(x2),d(x2)) = x(n(s(z)),n(s(z))),
inference(symmetry,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [E: $i] : ( opt(x(n(z),E)) = E )
| ( opt(x(n(z),x(d(x2),d(x2)))) = x(d(x2),d(x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
opt(x(n(z),x(d(x2),d(x2)))) = x(d(x2),d(x2)),
inference(unit_resolution,[status(thm)],[262,110]) ).
tff(264,plain,
d(x(opt(x2),opt(x2))) = d(x(x2,x2)),
inference(monotonicity,[status(thm)],[114]) ).
tff(265,plain,
d(x(x2,x2)) = d(x(opt(x2),opt(x2))),
inference(symmetry,[status(thm)],[264]) ).
tff(266,plain,
( ~ ! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) )
| ( d(x(x2,x2)) = x(d(x2),d(x2)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
d(x(x2,x2)) = x(d(x2),d(x2)),
inference(unit_resolution,[status(thm)],[266,191]) ).
tff(268,plain,
x(d(x2),d(x2)) = d(x(x2,x2)),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
x(d(x2),d(x2)) = d(x(opt(x2),opt(x2))),
inference(transitivity,[status(thm)],[268,265]) ).
tff(270,plain,
x(n(z),x(d(x2),d(x2))) = x(d(n(s(z))),d(x(opt(x2),opt(x2)))),
inference(monotonicity,[status(thm)],[182,269]) ).
tff(271,plain,
x(d(n(s(z))),d(x(opt(x2),opt(x2)))) = x(n(z),x(d(x2),d(x2))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
( ~ ! [F: $i,G: $i] : ( d(x(F,G)) = x(d(F),d(G)) )
| ( d(x(n(s(z)),x(opt(x2),opt(x2)))) = x(d(n(s(z))),d(x(opt(x2),opt(x2)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(273,plain,
d(x(n(s(z)),x(opt(x2),opt(x2)))) = x(d(n(s(z))),d(x(opt(x2),opt(x2)))),
inference(unit_resolution,[status(thm)],[272,191]) ).
tff(274,plain,
d(x(n(s(z)),x(opt(x2),opt(x2)))) = x(n(z),x(d(x2),d(x2))),
inference(transitivity,[status(thm)],[273,271]) ).
tff(275,plain,
opt(d(x(n(s(z)),x(opt(x2),opt(x2))))) = opt(x(n(z),x(d(x2),d(x2)))),
inference(monotonicity,[status(thm)],[274]) ).
tff(276,plain,
opt(d(x(n(s(z)),x(opt(x2),opt(x2))))) = x(n(s(z)),n(s(z))),
inference(transitivity,[status(thm)],[275,263,261]) ).
tff(277,plain,
eq2(opt(d(x(n(s(z)),x(opt(x2),opt(x2))))),opt(d(opt(x(n(s(z)),x(opt(x2),opt(x2))))))) = eq2(x(n(s(z)),n(s(z))),x(fail4(n(z),x2),aux(n(s(z)),n(s(z)),eq2(n(s(z)),n(s(z)))))),
inference(monotonicity,[status(thm)],[276,258]) ).
tff(278,plain,
^ [X: $i] :
refl(( ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) )
<=> ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ) )),
inference(bind,[status(th)],[]) ).
tff(279,plain,
( ! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) )
<=> ! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ) ),
inference(quant_intro,[status(thm)],[278]) ).
tff(280,plain,
( ! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) )
<=> ! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(281,axiom,
! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_063) ).
tff(282,plain,
! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ),
inference(skolemize,[status(sab)],[282]) ).
tff(284,plain,
! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) ),
inference(modus_ponens,[status(thm)],[283,279]) ).
tff(285,plain,
( ~ ! [X: $i] : ( prop4(X) = eq2(opt(d(X)),opt(d(opt(X)))) )
| ( prop4(x(n(s(z)),x(opt(x2),opt(x2)))) = eq2(opt(d(x(n(s(z)),x(opt(x2),opt(x2))))),opt(d(opt(x(n(s(z)),x(opt(x2),opt(x2))))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(286,plain,
prop4(x(n(s(z)),x(opt(x2),opt(x2)))) = eq2(opt(d(x(n(s(z)),x(opt(x2),opt(x2))))),opt(d(opt(x(n(s(z)),x(opt(x2),opt(x2))))))),
inference(unit_resolution,[status(thm)],[285,284]) ).
tff(287,plain,
prop4(x(n(s(z)),x(opt(x2),opt(x2)))) = bfalse,
inference(transitivity,[status(thm)],[286,277,57]) ).
tff(288,plain,
eq3(prop4(x(n(s(z)),x(opt(x2),opt(x2)))),bfalse) = eq3(bfalse,bfalse),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
eq3(prop4(x(n(s(z)),x(opt(x2),opt(x2)))),bfalse) = btrue,
inference(transitivity,[status(thm)],[288,9]) ).
tff(290,plain,
^ [X: $i] :
refl(( ( eq3(prop4(X),bfalse) != btrue )
<=> ( eq3(prop4(X),bfalse) != btrue ) )),
inference(bind,[status(th)],[]) ).
tff(291,plain,
( ! [X: $i] : ( eq3(prop4(X),bfalse) != btrue )
<=> ! [X: $i] : ( eq3(prop4(X),bfalse) != btrue ) ),
inference(quant_intro,[status(thm)],[290]) ).
tff(292,plain,
( ! [X: $i] : ( eq3(prop4(X),bfalse) != btrue )
<=> ! [X: $i] : ( eq3(prop4(X),bfalse) != btrue ) ),
inference(rewrite,[status(thm)],[]) ).
tff(293,axiom,
! [X: $i] : ( eq3(prop4(X),bfalse) != btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
tff(294,plain,
! [X: $i] : ( eq3(prop4(X),bfalse) != btrue ),
inference(modus_ponens,[status(thm)],[293,292]) ).
tff(295,plain,
! [X: $i] : ( eq3(prop4(X),bfalse) != btrue ),
inference(skolemize,[status(sab)],[294]) ).
tff(296,plain,
! [X: $i] : ( eq3(prop4(X),bfalse) != btrue ),
inference(modus_ponens,[status(thm)],[295,291]) ).
tff(297,plain,
( ~ ! [X: $i] : ( eq3(prop4(X),bfalse) != btrue )
| ( eq3(prop4(x(n(s(z)),x(opt(x2),opt(x2)))),bfalse) != btrue ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(298,plain,
eq3(prop4(x(n(s(z)),x(opt(x2),opt(x2)))),bfalse) != btrue,
inference(unit_resolution,[status(thm)],[297,296]) ).
tff(299,plain,
$false,
inference(unit_resolution,[status(thm)],[298,289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX190-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.17/0.33 % Computer : n027.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 09:58:36 EDT 2026
% 0.17/0.34 % CPUTime :
% 16.64/16.90 % SZS status Unsatisfiable
% 16.64/16.90 % SZS output start Proof
% See solution above
% 16.74/16.97 % E exiting
%------------------------------------------------------------------------------