TSTP Solution File: SWC206-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC206-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 11:56:07 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 50
% Syntax : Number of formulae : 115 ( 26 unt; 9 typ; 0 def)
% Number of atoms : 494 ( 102 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 694 ( 330 ~; 307 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 93 ( 83 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk5_type,type,
sk5: $i ).
tff(nil_type,type,
nil: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ( sk5 = nil )
<=> ( nil = sk5 ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( sk5 != nil )
<=> ( nil != sk5 ) ),
inference(monotonicity,[status(thm)],[1]) ).
tff(3,plain,
( ( neq(sk5,nil)
| $false )
<=> neq(sk5,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(8,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[9]) ).
tff(11,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[11,4]) ).
tff(13,plain,
( ( neq(sk5,nil)
| ~ neq(sk4,nil) )
<=> ( neq(sk5,nil)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( neq(sk5,nil)
| ~ neq(sk4,nil) )
<=> neq(sk5,nil) ),
inference(transitivity,[status(thm)],[13,3]) ).
tff(15,plain,
( ( neq(sk5,nil)
| ~ neq(sk4,nil) )
<=> ( neq(sk5,nil)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(17,plain,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,plain,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[20,15]) ).
tff(22,plain,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[21,15]) ).
tff(23,plain,
neq(sk5,nil),
inference(modus_ponens,[status(thm)],[22,14]) ).
tff(24,plain,
( ( ssList(sk5)
| $false )
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(26,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ssList(sk5) ),
inference(transitivity,[status(thm)],[25,24]) ).
tff(27,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
( ssList(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(29,plain,
( ssList(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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(34,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(35,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)],[34]) ).
tff(36,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(43,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 != nil )
| ~ neq(sk5,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 != nil )
| ~ neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ssList(sk5)
| ~ ssList(nil)
| ( sk5 != nil )
| ~ neq(sk5,nil) )
<=> ( ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 != nil )
| ~ neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk5)
| ~ ssList(nil)
| ( sk5 != nil )
| ~ neq(sk5,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 != nil )
| ~ neq(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk5)
| ~ ssList(nil)
| ( sk5 != nil )
| ~ neq(sk5,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 != nil )
| ~ neq(sk5,nil) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk5)
| ~ ssList(nil)
| ( sk5 != nil )
| ~ neq(sk5,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 != nil )
| ~ neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
sk5 != nil,
inference(unit_resolution,[status(thm)],[49,43,40,30,23]) ).
tff(51,plain,
nil != sk5,
inference(modus_ponens,[status(thm)],[50,2]) ).
tff(52,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk1,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(54,axiom,
~ neq(sk1,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(55,plain,
~ neq(sk1,nil),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[55,52]) ).
tff(57,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(60,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[60,57]) ).
tff(62,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(63,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)],[62]) ).
tff(64,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(65,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(66,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)],[65]) ).
tff(67,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(68,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[74,43,71,61,56]) ).
tff(76,plain,
nil = sk3,
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( segmentP(nil,sk5)
<=> segmentP(sk3,sk5) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( segmentP(sk3,sk5)
<=> segmentP(nil,sk5) ),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ( segmentP(sk3,sk5)
| $false )
<=> segmentP(sk3,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( segmentP(sk3,sk5)
| ~ neq(sk4,nil) )
<=> ( segmentP(sk3,sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(81,plain,
( ( segmentP(sk3,sk5)
| ~ neq(sk4,nil) )
<=> segmentP(sk3,sk5) ),
inference(transitivity,[status(thm)],[80,79]) ).
tff(82,plain,
( ( segmentP(sk3,sk5)
| ~ neq(sk4,nil) )
<=> ( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(84,plain,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[84,82]) ).
tff(86,plain,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[85,82]) ).
tff(87,plain,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[87,82]) ).
tff(89,plain,
( segmentP(sk3,sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[88,82]) ).
tff(90,plain,
segmentP(sk3,sk5),
inference(modus_ponens,[status(thm)],[89,81]) ).
tff(91,plain,
segmentP(nil,sk5),
inference(modus_ponens,[status(thm)],[90,78]) ).
tff(92,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ segmentP(nil,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
tff(98,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(sk5)
| ( nil = sk5 )
| ~ segmentP(nil,sk5) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(sk5)
| ( nil = sk5 )
| ~ segmentP(nil,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(sk5)
| ( nil = sk5 )
| ~ segmentP(nil,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(sk5)
| ( nil = sk5 )
| ~ segmentP(nil,sk5) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ( nil = sk5 )
| ~ segmentP(nil,sk5) ),
inference(unit_resolution,[status(thm)],[104,101,30]) ).
tff(106,plain,
$false,
inference(unit_resolution,[status(thm)],[105,91,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC206-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n014.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 22:38:00 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.
% 0.20/0.46 % SZS status Unsatisfiable
% 0.20/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------