TSTP Solution File: SWC218-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC218-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 11:56:13 EDT 2022
% Result : Unsatisfiable 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 67
% Syntax : Number of formulae : 136 ( 36 unt; 11 typ; 0 def)
% Number of atoms : 837 ( 231 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 1250 ( 592 ~; 580 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 54 ( 54 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 228 ( 204 !; 0 ?; 228 :)
% Comments :
%------------------------------------------------------------------------------
tff(nil_type,type,
nil: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(1,plain,
( ~ neq(sk1,nil)
<=> ~ neq(app(app(sk5,cons(sk7,nil)),sk6),nil) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk1,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ neq(sk1,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(4,plain,
~ neq(sk1,nil),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ neq(app(app(sk5,cons(sk7,nil)),sk6),nil),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( ssList(sk1)
<=> ssList(app(app(sk5,cons(sk7,nil)),sk6)) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(9,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
ssList(app(app(sk5,cons(sk7,nil)),sk6)),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,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(12,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)],[11]) ).
tff(13,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(14,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(15,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)],[14]) ).
tff(16,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(17,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(23,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,cons(sk7,nil)),sk6))
| ( app(app(sk5,cons(sk7,nil)),sk6) = nil )
| neq(app(app(sk5,cons(sk7,nil)),sk6),nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,cons(sk7,nil)),sk6))
| ( app(app(sk5,cons(sk7,nil)),sk6) = nil )
| neq(app(app(sk5,cons(sk7,nil)),sk6),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,cons(sk7,nil)),sk6))
| ( app(app(sk5,cons(sk7,nil)),sk6) = nil )
| neq(app(app(sk5,cons(sk7,nil)),sk6),nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(app(app(sk5,cons(sk7,nil)),sk6))
| ( app(app(sk5,cons(sk7,nil)),sk6) = nil )
| neq(app(app(sk5,cons(sk7,nil)),sk6),nil) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
app(app(sk5,cons(sk7,nil)),sk6) = nil,
inference(unit_resolution,[status(thm)],[26,23,20,10,5]) ).
tff(28,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(30,plain,
ssItem(sk7),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
ssList(cons(sk7,nil)),
inference(unit_resolution,[status(thm)],[43,23,40,30]) ).
tff(45,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(47,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(54,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[56,49]) ).
tff(58,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) )
<=> ( ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil))) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil)))
| ~ ssList(sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk5,cons(sk7,nil))) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
ssList(app(sk5,cons(sk7,nil))),
inference(unit_resolution,[status(thm)],[63,57,47,44]) ).
tff(65,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(67,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause118) ).
tff(74,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) )
<=> ( ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ~ ssList(sk6)
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ ssList(V)
| ( app(U,V) != nil ) )
| ~ ssList(sk6)
| ~ ssList(app(sk5,cons(sk7,nil)))
| ( nil = app(sk5,cons(sk7,nil)) )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ( nil = app(sk5,cons(sk7,nil)) )
| ( app(app(sk5,cons(sk7,nil)),sk6) != nil ) ),
inference(unit_resolution,[status(thm)],[83,77,67,64]) ).
tff(85,plain,
nil = app(sk5,cons(sk7,nil)),
inference(unit_resolution,[status(thm)],[84,27]) ).
tff(86,plain,
app(sk5,cons(sk7,nil)) = nil,
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
( ( nil = cons(sk7,nil) )
<=> ( cons(sk7,nil) = nil ) ),
inference(commutativity,[status(thm)],]) ).
tff(88,plain,
( ( cons(sk7,nil) = nil )
<=> ( nil = cons(sk7,nil) ) ),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ( cons(sk7,nil) != nil )
<=> ( nil != cons(sk7,nil) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
inference(bind,[status(th)],]) ).
tff(91,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( cons(U,nil) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,axiom,
! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
tff(96,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[96,92]) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[98,91]) ).
tff(100,plain,
( ~ singletonP(nil)
<=> ~ singletonP(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(101,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause11) ).
tff(102,plain,
~ singletonP(nil),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk7)
| ( cons(sk7,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk7)
| ( cons(sk7,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( ~ ssItem(sk7)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk7,nil) != nil ) )
<=> ( singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk7)
| ( cons(sk7,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk7,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk7)
| ( cons(sk7,nil) != nil ) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk7,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk7)
| ( cons(sk7,nil) != nil ) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk7,nil) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk7)
| ( cons(sk7,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
cons(sk7,nil) != nil,
inference(unit_resolution,[status(thm)],[108,23,102,99,30]) ).
tff(110,plain,
nil != cons(sk7,nil),
inference(modus_ponens,[status(thm)],[109,89]) ).
tff(111,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],]) ).
tff(112,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,V) != nil )
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ( app(U,V) != nil )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
( ( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,axiom,
! [V: $i,U: $i] :
( ( app(U,V) != nil )
| ~ ssList(V)
| ~ ssList(U)
| ( nil = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
tff(117,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != nil )
| ( nil = V ) )
| ~ ssList(sk5)
| ~ ssList(cons(sk7,nil))
| ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( ( app(sk5,cons(sk7,nil)) != nil )
| ( nil = cons(sk7,nil) ) ),
inference(unit_resolution,[status(thm)],[123,120,47,44]) ).
tff(125,plain,
$false,
inference(unit_resolution,[status(thm)],[124,110,86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC218-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 22:57:21 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.45 % SZS status Unsatisfiable
% 0.19/0.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------