%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 07:08:18 PM UTC 2026
% Result : Theorem 0.39s 0.58s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 36
% Syntax : Number of formulae : 87 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 298 ( 73 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 317 ( 123 ~; 80 |; 14 &)
% ( 97 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 190 ( 164 !; 7 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
tff(tc_type,type,
tc: ( $i * $i * $i ) > $o ).
tff(b_type,type,
b: $i ).
tff(var_type,type,
var: $i > $i ).
tff(zero_type,type,
zero: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(a_type,type,
a: $i ).
tff(arr_type,type,
arr: ( $i * $i ) > $i ).
tff(lam_type,type,
lam: $i > $i ).
tff(nf_type,type,
nf: $i > $o ).
tff(just_type,type,
just: $i > $i ).
tff(index_type,type,
index: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i,E: $i,Tx2: $i,T1: $i] :
refl(( ( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) )
<=> ( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) )
<=> ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) )
<=> ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_033) ).
tff(5,plain,
! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) )
| ( tc(cons(a,nil),lam(var(zero)),arr(b,b))
<=> tc(cons(b,cons(a,nil)),var(zero),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( tc(cons(a,nil),lam(var(zero)),arr(b,b))
<=> tc(cons(b,cons(a,nil)),var(zero),b) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [X: $i,E: $i,Tx2: $i,T1: $i] :
( tc(X,lam(E),arr(Tx2,T1))
<=> tc(cons(Tx2,X),E,T1) )
| ( tc(nil,lam(lam(var(zero))),arr(a,arr(b,b)))
<=> tc(cons(a,nil),lam(var(zero)),arr(b,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
( tc(nil,lam(lam(var(zero))),arr(a,arr(b,b)))
<=> tc(cons(a,nil),lam(var(zero)),arr(b,b)) ),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [E: $i] :
refl(( ( nf(lam(E))
<=> nf(E) )
<=> ( nf(lam(E))
<=> nf(E) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [E: $i] :
( nf(lam(E))
<=> nf(E) )
<=> ! [E: $i] :
( nf(lam(E))
<=> nf(E) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [E: $i] :
( nf(lam(E))
<=> nf(E) )
<=> ! [E: $i] :
( nf(lam(E))
<=> nf(E) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [E: $i] :
( nf(lam(E))
<=> nf(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_026) ).
tff(16,plain,
! [E: $i] :
( nf(lam(E))
<=> nf(E) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [E: $i] :
( nf(lam(E))
<=> nf(E) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [E: $i] :
( nf(lam(E))
<=> nf(E) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ~ ! [E: $i] :
( nf(lam(E))
<=> nf(E) )
| ( nf(lam(lam(var(zero))))
<=> nf(lam(var(zero))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( nf(lam(lam(var(zero))))
<=> nf(lam(var(zero))) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
( ~ ! [E: $i] :
( nf(lam(E))
<=> nf(E) )
| ( nf(lam(var(zero)))
<=> nf(var(zero)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( nf(lam(var(zero)))
<=> nf(var(zero)) ),
inference(unit_resolution,[status(thm)],[21,18]) ).
tff(23,plain,
^ [X4: $i] :
refl(( nf(var(X4))
<=> nf(var(X4)) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [X4: $i] : nf(var(X4))
<=> ! [X4: $i] : nf(var(X4)) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [X4: $i] : nf(var(X4))
<=> ! [X4: $i] : nf(var(X4)) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
! [X4: $i] : nf(var(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_027) ).
tff(27,plain,
! [X4: $i] : nf(var(X4)),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X4: $i] : nf(var(X4)),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X4: $i] : nf(var(X4)),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
( ~ ! [X4: $i] : nf(var(X4))
| nf(var(zero)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
nf(var(zero)),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ( nf(lam(var(zero)))
<=> nf(var(zero)) )
| nf(lam(var(zero)))
| ~ nf(var(zero)) ),
inference(tautology,[status(thm)],[]) ).
tff(33,plain,
( ~ ( nf(lam(var(zero)))
<=> nf(var(zero)) )
| nf(lam(var(zero))) ),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
nf(lam(var(zero))),
inference(unit_resolution,[status(thm)],[33,22]) ).
tff(35,plain,
( ~ ( nf(lam(lam(var(zero))))
<=> nf(lam(var(zero))) )
| nf(lam(lam(var(zero))))
| ~ nf(lam(var(zero))) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( nf(lam(lam(var(zero))))
<=> nf(lam(var(zero))) )
| nf(lam(lam(var(zero)))) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
nf(lam(lam(var(zero)))),
inference(unit_resolution,[status(thm)],[36,20]) ).
tff(38,plain,
^ [E: $i] :
refl(( ( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) )
<=> ( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) )
<=> ! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [E: $i] :
trans(monotonicity(rewrite(( ( nf(E)
& tc(nil,E,arr(a,arr(b,b))) )
<=> ~ ( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ) )),
( ~ ( nf(E)
& tc(nil,E,arr(a,arr(b,b))) )
<=> ~ ~ ( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ) )),
rewrite(( ~ ~ ( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) )
<=> ( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ) )),
( ~ ( nf(E)
& tc(nil,E,arr(a,arr(b,b))) )
<=> ( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [E: $i] :
~ ( nf(E)
& tc(nil,E,arr(a,arr(b,b))) )
<=> ! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ~ ? [E: $i] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) )
<=> ~ ? [E: $i] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
~ ? [E: $i] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_036) ).
tff(44,plain,
~ ? [E: $i] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ ? [E: $i] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
inference(modus_ponens,[status(thm)],[44,42]) ).
tff(46,plain,
~ ? [E: $i] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
~ ? [E: $i] :
( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
^ [E: $i] :
refl($oeq(~ ( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
~ ( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ))),
inference(bind,[status(th)],[]) ).
tff(49,plain,
! [E: $i] :
~ ( nf(E)
& tc(nil,E,arr(a,arr(b,b))) ),
inference(nnf-neg,[status(sab)],[47,48]) ).
tff(50,plain,
! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ),
inference(modus_ponens,[status(thm)],[49,41]) ).
tff(51,plain,
! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) ),
inference(modus_ponens,[status(thm)],[50,39]) ).
tff(52,plain,
( ( ~ ! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) )
| ~ nf(lam(lam(var(zero))))
| ~ tc(nil,lam(lam(var(zero))),arr(a,arr(b,b))) )
<=> ( ~ ! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) )
| ~ nf(lam(lam(var(zero))))
| ~ tc(nil,lam(lam(var(zero))),arr(a,arr(b,b))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) )
| ~ nf(lam(lam(var(zero))))
| ~ tc(nil,lam(lam(var(zero))),arr(a,arr(b,b))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [E: $i] :
( ~ nf(E)
| ~ tc(nil,E,arr(a,arr(b,b))) )
| ~ nf(lam(lam(var(zero))))
| ~ tc(nil,lam(lam(var(zero))),arr(a,arr(b,b))) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ tc(nil,lam(lam(var(zero))),arr(a,arr(b,b))),
inference(unit_resolution,[status(thm)],[54,51,37]) ).
tff(56,plain,
( ~ ( tc(nil,lam(lam(var(zero))),arr(a,arr(b,b)))
<=> tc(cons(a,nil),lam(var(zero)),arr(b,b)) )
| tc(nil,lam(lam(var(zero))),arr(a,arr(b,b)))
| ~ tc(cons(a,nil),lam(var(zero)),arr(b,b)) ),
inference(tautology,[status(thm)],[]) ).
tff(57,plain,
( ~ ( tc(nil,lam(lam(var(zero))),arr(a,arr(b,b)))
<=> tc(cons(a,nil),lam(var(zero)),arr(b,b)) )
| ~ tc(cons(a,nil),lam(var(zero)),arr(b,b)) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
~ tc(cons(a,nil),lam(var(zero)),arr(b,b)),
inference(unit_resolution,[status(thm)],[57,11]) ).
tff(59,plain,
( ~ ( tc(cons(a,nil),lam(var(zero)),arr(b,b))
<=> tc(cons(b,cons(a,nil)),var(zero),b) )
| tc(cons(a,nil),lam(var(zero)),arr(b,b))
| ~ tc(cons(b,cons(a,nil)),var(zero),b) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
( ~ ( tc(cons(a,nil),lam(var(zero)),arr(b,b))
<=> tc(cons(b,cons(a,nil)),var(zero),b) )
| ~ tc(cons(b,cons(a,nil)),var(zero),b) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
~ tc(cons(b,cons(a,nil)),var(zero),b),
inference(unit_resolution,[status(thm)],[60,9]) ).
tff(62,plain,
^ [Z: $i,Xs: $i] :
refl(( ( index(cons(Z,Xs),zero) = just(Z) )
<=> ( index(cons(Z,Xs),zero) = just(Z) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) )
<=> ! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) )
<=> ! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_029) ).
tff(66,plain,
! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
( ~ ! [Z: $i,Xs: $i] : ( index(cons(Z,Xs),zero) = just(Z) )
| ( index(cons(b,cons(a,nil)),zero) = just(b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
index(cons(b,cons(a,nil)),zero) = just(b),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
^ [X: $i,Z: $i,X3: $i,Tx3: $i] :
refl(( ( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
<=> ( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
<=> ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
<=> ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
^ [X: $i,Z: $i,X3: $i,Tx3: $i] :
rewrite(( ( ( index(X,X3) = just(Tx3) )
=> ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
<=> ( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) = just(Tx3) )
=> ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
<=> ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) = just(Tx3) )
=> ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_035) ).
tff(77,plain,
! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| tc(cons(b,cons(a,nil)),var(zero),b) )
<=> ( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| tc(cons(b,cons(a,nil)),var(zero),b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ( ( index(cons(b,cons(a,nil)),zero) != just(b) )
| ( tc(cons(b,cons(a,nil)),var(zero),b)
<=> ( b = b ) ) )
<=> ( ( index(cons(b,cons(a,nil)),zero) != just(b) )
| tc(cons(b,cons(a,nil)),var(zero),b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| ( tc(cons(b,cons(a,nil)),var(zero),b)
<=> ( b = b ) ) )
<=> ( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| tc(cons(b,cons(a,nil)),var(zero),b) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| ( tc(cons(b,cons(a,nil)),var(zero),b)
<=> ( b = b ) ) )
<=> ( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| tc(cons(b,cons(a,nil)),var(zero),b) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| ( tc(cons(b,cons(a,nil)),var(zero),b)
<=> ( b = b ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(86,plain,
( ~ ! [X: $i,Z: $i,X3: $i,Tx3: $i] :
( ( index(X,X3) != just(Tx3) )
| ( tc(X,var(X3),Z)
<=> ( Tx3 = Z ) ) )
| ( index(cons(b,cons(a,nil)),zero) != just(b) )
| tc(cons(b,cons(a,nil)),var(zero),b) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,80,70,61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.13/0.32 % Computer : n011.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 5 12:33:34 EDT 2026
% 0.13/0.32 % CPUTime :
% 0.39/0.58 % SZS status Theorem
% 0.39/0.58 % SZS output start Proof
% See solution above
% 0.39/0.59 % E exiting
%------------------------------------------------------------------------------