TSTP Solution File: SWC085-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC085-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 11:55:08 EDT 2022
% Result : Unsatisfiable 0.51s 0.57s
% Output : Proof 0.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 69
% Syntax : Number of formulae : 144 ( 40 unt; 11 typ; 0 def)
% Number of atoms : 963 ( 171 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1548 ( 786 ~; 677 |; 0 &)
% ( 85 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 68 ( 68 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 235 ( 212 !; 0 ?; 235 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk4_type,type,
sk4: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf45_type,type,
skaf45: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(nil_type,type,
nil: $i ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk4 = nil )
<=> ( nil = sk4 ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( sk4 != nil )
<=> ( nil != sk4 ) ),
inference(monotonicity,[status(thm)],[1]) ).
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/sandbox2/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,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
tff(11,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[11,8]) ).
tff(13,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(14,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)],[13]) ).
tff(15,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(16,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(17,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)],[16]) ).
tff(18,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(19,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(25,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ neq(sk4,nil)
| ( sk4 != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ neq(sk4,nil)
| ( sk4 != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ( ~ ssList(sk4)
| ~ ssList(nil)
| ( sk4 != nil )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(nil)
| ~ ssList(sk4)
| ~ neq(sk4,nil)
| ( sk4 != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,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) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ neq(sk4,nil)
| ( sk4 != nil ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,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) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ neq(sk4,nil)
| ( sk4 != nil ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,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(31,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ neq(sk4,nil)
| ( sk4 != nil ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
sk4 != nil,
inference(unit_resolution,[status(thm)],[31,25,22,12,7]) ).
tff(33,plain,
nil != sk4,
inference(modus_ponens,[status(thm)],[32,2]) ).
tff(34,plain,
( ( ( nil = sk4 )
| frontsegP(sk4,sk3) )
<=> ( ( nil = sk4 )
| frontsegP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,axiom,
( ( nil = sk4 )
| frontsegP(sk4,sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(36,plain,
( ( nil = sk4 )
| frontsegP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
frontsegP(sk4,sk3),
inference(unit_resolution,[status(thm)],[36,33]) ).
tff(38,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(41,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ frontsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,axiom,
! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[51,44]) ).
tff(53,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ frontsegP(sk4,sk3)
| ( app(sk3,skaf45(sk4,sk3)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
app(sk3,skaf45(sk4,sk3)) = sk4,
inference(unit_resolution,[status(thm)],[58,52,42,12,37]) ).
tff(60,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(64,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[69,66,42]) ).
tff(71,plain,
app(app(nil,sk3),skaf45(sk4,sk3)) = app(sk3,skaf45(sk4,sk3)),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
app(app(nil,sk3),skaf45(sk4,sk3)) = sk4,
inference(transitivity,[status(thm)],[71,59]) ).
tff(73,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf45(U,V))
<=> ssList(skaf45(U,V)) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
tff(77,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf45(U,V))
| ssList(skaf45(sk4,sk3)) ),
inference(quant_inst,[status(thm)],]) ).
tff(81,plain,
ssList(skaf45(sk4,sk3)),
inference(unit_resolution,[status(thm)],[80,79]) ).
tff(82,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(83,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(86,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[91,88,42]) ).
tff(93,plain,
( ( ( nil = sk4 )
| neq(sk3,nil) )
<=> ( ( nil = sk4 )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
( ( nil = sk4 )
| neq(sk3,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(95,plain,
( ( nil = sk4 )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
neq(sk3,nil),
inference(unit_resolution,[status(thm)],[95,33]) ).
tff(97,plain,
^ [A: $i] :
refl(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [A: $i] :
trans(
monotonicity(
rewrite(
( ~ segmentP(sk2,A)
<=> ~ segmentP(sk4,A) )),
rewrite(
( ~ segmentP(sk1,A)
<=> ~ segmentP(sk3,A) )),
( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ segmentP(sk3,A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ segmentP(sk4,A)
| ~ neq(A,nil)
| ~ segmentP(sk3,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) )),
( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
^ [A: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(105,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ),
inference(modus_ponens,[status(thm)],[106,100]) ).
tff(108,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(112,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk4,A)
| ~ segmentP(sk3,A) )
| ~ ssList(sk3)
| ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ neq(sk3,nil)
| ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3) ),
inference(unit_resolution,[status(thm)],[112,42,109]) ).
tff(114,plain,
~ segmentP(sk4,sk3),
inference(unit_resolution,[status(thm)],[113,96,92]) ).
tff(115,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(116,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)],[115]) ).
tff(117,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(118,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(119,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)],[118]) ).
tff(120,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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
tff(121,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)],[120,119]) ).
tff(122,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)],[121,117]) ).
tff(123,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)],[122]) ).
tff(124,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)],[123,116]) ).
tff(125,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(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != 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 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ~ ssList(sk4)
| ~ ssList(nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
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 ) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != 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 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,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(nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != 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 ) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) ) ),
inference(transitivity,[status(thm)],[127,125]) ).
tff(129,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(nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,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(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
( ~ ssList(skaf45(sk4,sk3))
| ( app(app(nil,sk3),skaf45(sk4,sk3)) != sk4 ) ),
inference(unit_resolution,[status(thm)],[130,25,124,42,12,114]) ).
tff(132,plain,
app(app(nil,sk3),skaf45(sk4,sk3)) != sk4,
inference(unit_resolution,[status(thm)],[131,81]) ).
tff(133,plain,
$false,
inference(unit_resolution,[status(thm)],[132,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC085-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n002.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 21:34:17 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.36 Usage: tptp [options] [-file:]file
% 0.21/0.36 -h, -? prints this message.
% 0.21/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.36 -m, -model generate model.
% 0.21/0.36 -p, -proof generate proof.
% 0.21/0.36 -c, -core generate unsat core of named formulas.
% 0.21/0.36 -st, -statistics display statistics.
% 0.21/0.36 -t:timeout set timeout (in second).
% 0.21/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.36 -<param>:<value> configuration parameter and value.
% 0.21/0.36 -o:<output-file> file to place output in.
% 0.51/0.57 % SZS status Unsatisfiable
% 0.51/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------