TSTP Solution File: SWC363-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC363-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 11:57:24 EDT 2022
% Result : Unsatisfiable 0.52s 0.58s
% Output : Proof 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 71
% Syntax : Number of formulae : 156 ( 44 unt; 15 typ; 0 def)
% Number of atoms : 832 ( 169 equ)
% Maximal formula atoms : 24 ( 5 avg)
% Number of connectives : 1232 ( 593 ~; 558 |; 0 &)
% ( 81 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 52 ( 52 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 255 ( 229 !; 0 ?; 255 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk4_type,type,
sk4: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(1,plain,
( ( memberP(sk4,sk5)
| $false )
<=> memberP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(6,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[7]) ).
tff(9,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[9,2]) ).
tff(11,plain,
( ( memberP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( memberP(sk4,sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ( memberP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> memberP(sk4,sk5) ),
inference(transitivity,[status(thm)],[11,1]) ).
tff(13,plain,
( ( memberP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( memberP(sk4,sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(15,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[18,13]) ).
tff(20,plain,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
memberP(sk4,sk5),
inference(modus_ponens,[status(thm)],[20,12]) ).
tff(22,plain,
( ( ssItem(sk5)
| $false )
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(24,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ssItem(sk5) ),
inference(transitivity,[status(thm)],[23,22]) ).
tff(25,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(27,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(32,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
tff(40,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4,
inference(unit_resolution,[status(thm)],[46,43,33,28,21]) ).
tff(48,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(52,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5,sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
ssList(skaf43(sk5,sk4)),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,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(58,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)],[57]) ).
tff(59,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(60,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(61,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)],[60]) ).
tff(62,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(63,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(unit_resolution,[status(thm)],[69,66,28]) ).
tff(71,plain,
app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)),
inference(unit_resolution,[status(thm)],[70,56]) ).
tff(72,plain,
( ( ( cons(sk5,nil) = sk3 )
| $false )
<=> ( cons(sk5,nil) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ( cons(sk5,nil) = sk3 )
| $false ) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(74,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( cons(sk5,nil) = sk3 ) ),
inference(transitivity,[status(thm)],[73,72]) ).
tff(75,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(77,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[77,75]) ).
tff(79,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[78,75]) ).
tff(80,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[80,75]) ).
tff(82,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[81,75]) ).
tff(83,plain,
cons(sk5,nil) = sk3,
inference(modus_ponens,[status(thm)],[82,74]) ).
tff(84,plain,
sk3 = cons(sk5,nil),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
app(sk3,skaf43(sk5,sk4)) = app(cons(sk5,nil),skaf43(sk5,sk4)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
app(sk3,skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)),
inference(transitivity,[status(thm)],[85,71]) ).
tff(87,plain,
app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) = app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(91,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(92,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[92]) ).
tff(94,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[93,89]) ).
tff(95,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk4,sk5)) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
ssList(skaf42(sk4,sk5)),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(99,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(100,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[100,97]) ).
tff(102,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(108,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[108,104]) ).
tff(110,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
( ( ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ssList(sk3)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))),
inference(unit_resolution,[status(thm)],[117,111,101,56,96]) ).
tff(119,plain,
app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = sk4,
inference(transitivity,[status(thm)],[118,87,47]) ).
tff(120,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk2,sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(122,axiom,
~ segmentP(sk2,sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(123,plain,
~ segmentP(sk2,sk1),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
~ segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[123,120]) ).
tff(125,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(app(U,V),W) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
tff(131,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(transitivity,[status(thm)],[137,135]) ).
tff(139,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,134,101,33,124,56,96,119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC363-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 23:46:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.52/0.58 % SZS status Unsatisfiable
% 0.52/0.58 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------