TSTP Solution File: SWC014-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC014-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 Sep 20 11:54:39 EDT 2022
% Result : Unsatisfiable 0.55s 0.63s
% Output : Proof 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 75
% Syntax : Number of formulae : 166 ( 36 unt; 13 typ; 0 def)
% Number of atoms : 1140 ( 396 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 1779 ( 878 ~; 788 |; 0 &)
% ( 113 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 86 ( 86 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 2 prp; 0-5 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 210 ( 186 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk4_type,type,
sk4: $i ).
tff(nil_type,type,
nil: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk6_type,type,
sk6: $i ).
tff(tl_type,type,
tl: $i > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ( nil = sk4 )
<=> ( sk4 = nil ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( sk4 = nil )
<=> ( nil = sk4 ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( sk4 != nil )
<=> ( nil != sk4 ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(8,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[9,4]) ).
tff(11,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
tff(14,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(22,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(28,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ neq(sk4,nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ neq(sk4,nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ neq(sk4,nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ neq(sk4,nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ neq(sk4,nil)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 != nil ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
sk4 != nil,
inference(unit_resolution,[status(thm)],[34,28,25,15,10]) ).
tff(36,plain,
nil != sk4,
inference(modus_ponens,[status(thm)],[35,3]) ).
tff(37,plain,
( ( ssList(sk6)
| $false )
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[10]) ).
tff(40,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ( ssList(sk6)
| $false ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ssList(sk6) ),
inference(transitivity,[status(thm)],[42,37]) ).
tff(44,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ( ssList(sk6)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
tff(46,plain,
( ssList(sk6)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[46,43]) ).
tff(48,plain,
( ( ssItem(sk5)
| $false )
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(50,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ssItem(sk5) ),
inference(transitivity,[status(thm)],[49,48]) ).
tff(51,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(53,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
tff(61,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( tl(cons(sk5,sk6)) = sk6 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( tl(cons(sk5,sk6)) = sk6 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( tl(cons(sk5,sk6)) = sk6 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( tl(cons(U,V)) = V ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( tl(cons(sk5,sk6)) = sk6 ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
tl(cons(sk5,sk6)) = sk6,
inference(unit_resolution,[status(thm)],[67,64,54,47]) ).
tff(69,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(cons(sk5,nil),sk6) = cons(sk5,sk6) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(cons(sk5,nil),sk6) = cons(sk5,sk6) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(cons(sk5,nil),sk6) = cons(sk5,sk6) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ( app(cons(sk5,nil),sk6) = cons(sk5,sk6) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
app(cons(sk5,nil),sk6) = cons(sk5,sk6),
inference(unit_resolution,[status(thm)],[81,78,54,47]) ).
tff(83,plain,
( ( $false
| ( cons(sk5,nil) = sk3 ) )
<=> ( cons(sk5,nil) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( $false
| ( cons(sk5,nil) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(85,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( cons(sk5,nil) = sk3 ) ),
inference(transitivity,[status(thm)],[84,83]) ).
tff(86,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
tff(89,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[89,86]) ).
tff(91,plain,
cons(sk5,nil) = sk3,
inference(modus_ponens,[status(thm)],[90,85]) ).
tff(92,plain,
app(cons(sk5,nil),sk6) = app(sk3,sk6),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
app(sk3,sk6) = app(cons(sk5,nil),sk6),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ( $false
| ( app(sk3,sk6) = sk4 ) )
<=> ( app(sk3,sk6) = sk4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
<=> ( app(sk3,sk6) = sk4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk6) = sk4 ) )
<=> ( $false
| ( app(sk3,sk6) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[41,95]) ).
tff(97,plain,
( ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk6) = sk4 ) )
<=> ( app(sk3,sk6) = sk4 ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk6) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk6) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk6) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
tff(101,plain,
( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk6) = sk4 ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
( ~ neq(sk4,nil)
| ( app(cons(sk5,nil),sk6) = sk4 ) ),
inference(modus_ponens,[status(thm)],[101,98]) ).
tff(103,plain,
app(sk3,sk6) = sk4,
inference(modus_ponens,[status(thm)],[102,97]) ).
tff(104,plain,
sk4 = app(sk3,sk6),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
sk4 = cons(sk5,sk6),
inference(transitivity,[status(thm)],[104,93,82]) ).
tff(106,plain,
tl(sk4) = tl(cons(sk5,sk6)),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
tl(sk4) = sk6,
inference(transitivity,[status(thm)],[106,68]) ).
tff(108,plain,
^ [B: $i,A: $i] :
refl(
( ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
<=> ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
^ [B: $i,A: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(
mp(
mp(
mp(
asserted(
( neq(sk2,nil)
| neq(sk2,nil) )),
rewrite(
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk4,nil) )),
neq(sk4,nil)),
( neq(sk4,nil)
<=> $true )),
( ~ neq(sk4,nil)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ neq(sk4,nil)
<=> $false )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
<=> ( ~ ssList(A)
| $false
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) )),
rewrite(
( ( ~ ssList(A)
| $false
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
<=> ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
^ [B: $i,A: $i] :
trans(
monotonicity(
rewrite(
( ~ neq(nil,sk2)
<=> ~ neq(nil,sk4) )),
rewrite(
( ( app(sk1,B) != A )
<=> ( app(sk3,B) != A ) )),
rewrite(
( ( tl(sk2) != B )
<=> ( tl(sk4) != B ) )),
rewrite(
( ( sk2 != A )
<=> ( sk4 != A ) )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) )),
rewrite(
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) )),
( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) )),
inference(bind,[status(th)],]) ).
tff(113,plain,
( ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) )
<=> ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) )
<=> ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
^ [B: $i,A: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( sk2 != A )
| ( tl(sk2) != B ) ) )),
rewrite(
( ( ~ ssList(A)
| ~ ssList(B)
| ( sk2 != A )
| ( tl(sk2) != B ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( tl(sk2) != B )
| ( sk2 != A )
| ( app(sk1,B) != A ) ) )),
rewrite(
( ( ~ ssList(A)
| ~ ssList(B)
| ( tl(sk2) != B )
| ( sk2 != A )
| ( app(sk1,B) != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A ) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A )
| ~ neq(nil,sk2) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A )
| ~ neq(nil,sk2) ) )),
rewrite(
( ( ~ ssList(A)
| ~ ssList(B)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A )
| ~ neq(nil,sk2) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A )
| ~ neq(nil,sk2) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A )
| ~ neq(sk4,nil) ) )),
rewrite(
( ( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
( ( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [B: $i,A: $i] :
( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,axiom,
! [B: $i,A: $i] :
( ~ ssList(A)
| ( sk2 != A )
| ~ ssList(B)
| ( tl(sk2) != B )
| ( app(sk1,B) != A )
| ~ neq(nil,sk2)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(118,plain,
! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk2)
| ( app(sk1,B) != A )
| ( tl(sk2) != B )
| ( sk2 != A ) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
! [B: $i,A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ),
inference(modus_ponens,[status(thm)],[119,113]) ).
tff(121,plain,
! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ),
inference(modus_ponens,[status(thm)],[120,111]) ).
tff(122,plain,
! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) ),
inference(modus_ponens,[status(thm)],[122,109]) ).
tff(124,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ neq(nil,sk4)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ( tl(sk4) != sk6 )
| ( app(sk3,sk6) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ neq(nil,sk4)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ( tl(sk4) != sk6 )
| ( app(sk3,sk6) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk6)
| ~ neq(nil,sk4)
| ( app(sk3,sk6) != sk4 )
| ( tl(sk4) != sk6 )
| $false )
<=> ( ~ neq(nil,sk4)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ( tl(sk4) != sk6 )
| ( app(sk3,sk6) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( sk4 = sk4 )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ( sk4 != sk4 )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
( ( sk4 != sk4 )
<=> $false ),
inference(transitivity,[status(thm)],[127,38]) ).
tff(129,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk6)
| ~ neq(nil,sk4)
| ( app(sk3,sk6) != sk4 )
| ( tl(sk4) != sk6 )
| ( sk4 != sk4 ) )
<=> ( ~ ssList(sk4)
| ~ ssList(sk6)
| ~ neq(nil,sk4)
| ( app(sk3,sk6) != sk4 )
| ( tl(sk4) != sk6 )
| $false ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk6)
| ~ neq(nil,sk4)
| ( app(sk3,sk6) != sk4 )
| ( tl(sk4) != sk6 )
| ( sk4 != sk4 ) )
<=> ( ~ neq(nil,sk4)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ( tl(sk4) != sk6 )
| ( app(sk3,sk6) != sk4 ) ) ),
inference(transitivity,[status(thm)],[129,125]) ).
tff(131,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ ssList(sk4)
| ~ ssList(sk6)
| ~ neq(nil,sk4)
| ( app(sk3,sk6) != sk4 )
| ( tl(sk4) != sk6 )
| ( sk4 != sk4 ) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ neq(nil,sk4)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ( tl(sk4) != sk6 )
| ( app(sk3,sk6) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
( ( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ ssList(sk4)
| ~ ssList(sk6)
| ~ neq(nil,sk4)
| ( app(sk3,sk6) != sk4 )
| ( tl(sk4) != sk6 )
| ( sk4 != sk4 ) )
<=> ( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ neq(nil,sk4)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ( tl(sk4) != sk6 )
| ( app(sk3,sk6) != sk4 ) ) ),
inference(transitivity,[status(thm)],[131,124]) ).
tff(133,plain,
( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ ssList(sk4)
| ~ ssList(sk6)
| ~ neq(nil,sk4)
| ( app(sk3,sk6) != sk4 )
| ( tl(sk4) != sk6 )
| ( sk4 != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
( ~ ! [B: $i,A: $i] :
( ~ ssList(A)
| ~ ssList(B)
| ~ neq(nil,sk4)
| ( app(sk3,B) != A )
| ( tl(sk4) != B )
| ( sk4 != A ) )
| ~ neq(nil,sk4)
| ~ ssList(sk6)
| ~ ssList(sk4)
| ( tl(sk4) != sk6 )
| ( app(sk3,sk6) != sk4 ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( ~ neq(nil,sk4)
| ( tl(sk4) != sk6 ) ),
inference(unit_resolution,[status(thm)],[134,15,123,47,103]) ).
tff(136,plain,
~ neq(nil,sk4),
inference(unit_resolution,[status(thm)],[135,107]) ).
tff(137,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(143,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[144]) ).
tff(146,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[145,138]) ).
tff(147,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| neq(nil,sk4)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| neq(nil,sk4)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ( ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) )
<=> ( neq(nil,sk4)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| neq(nil,sk4)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 ) ) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| neq(nil,sk4)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 ) ) ),
inference(transitivity,[status(thm)],[149,147]) ).
tff(151,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ( nil = sk4 )
| neq(nil,sk4) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| neq(nil,sk4)
| ~ ssList(nil)
| ~ ssList(sk4)
| ( nil = sk4 ) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
$false,
inference(unit_resolution,[status(thm)],[152,28,146,15,136,36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC014-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 21:01:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.55/0.63 % SZS status Unsatisfiable
% 0.55/0.63 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------