TSTP Solution File: SWC419-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC419-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 11:57:51 EDT 2022
% Result : Unsatisfiable 0.18s 0.49s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 67
% Syntax : Number of formulae : 150 ( 33 unt; 12 typ; 0 def)
% Number of atoms : 721 ( 216 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1079 ( 531 ~; 474 |; 0 &)
% ( 74 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 198 ( 177 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
tff(4,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
( ( ( app(sk6,cons(sk5,nil)) = sk3 )
| $false )
<=> ( app(sk6,cons(sk5,nil)) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(22,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[23]) ).
tff(25,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[25,18]) ).
tff(27,plain,
( ( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ( app(sk6,cons(sk5,nil)) = sk3 )
| $false ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) )
<=> ( app(sk6,cons(sk5,nil)) = sk3 ) ),
inference(transitivity,[status(thm)],[27,17]) ).
tff(29,plain,
( ( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(31,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[32,29]) ).
tff(34,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[34,29]) ).
tff(36,plain,
( ( app(sk6,cons(sk5,nil)) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[35,29]) ).
tff(37,plain,
app(sk6,cons(sk5,nil)) = sk3,
inference(modus_ponens,[status(thm)],[36,28]) ).
tff(38,plain,
app(app(sk6,cons(sk5,nil)),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
app(app(sk6,cons(sk5,nil)),nil) = sk3,
inference(transitivity,[status(thm)],[38,16]) ).
tff(40,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
tff(43,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[43,40]) ).
tff(45,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(49,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk4)
| ( app(nil,sk4) = sk4 ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
app(nil,sk4) = sk4,
inference(unit_resolution,[status(thm)],[54,51,44]) ).
tff(56,plain,
( ( ( app(cons(sk5,nil),sk6) = sk4 )
| $false )
<=> ( app(cons(sk5,nil),sk6) = sk4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ( app(cons(sk5,nil),sk6) = sk4 )
| $false ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(58,plain,
( ( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) )
<=> ( app(cons(sk5,nil),sk6) = sk4 ) ),
inference(transitivity,[status(thm)],[57,56]) ).
tff(59,plain,
( ( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(61,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[61,59]) ).
tff(63,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[62,59]) ).
tff(64,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[64,59]) ).
tff(66,plain,
( ( app(cons(sk5,nil),sk6) = sk4 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[65,59]) ).
tff(67,plain,
app(cons(sk5,nil),sk6) = sk4,
inference(modus_ponens,[status(thm)],[66,58]) ).
tff(68,plain,
app(nil,app(cons(sk5,nil),sk6)) = app(nil,sk4),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ssItem(sk5)
| $false )
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(71,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ssItem(sk5) ),
inference(transitivity,[status(thm)],[70,69]) ).
tff(72,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(74,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[74,71]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,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)],[79]) ).
tff(81,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(88,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[91,88,85,75]) ).
tff(93,plain,
( ( ssList(sk6)
| $false )
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ( ssList(sk6)
| $false ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(95,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ssList(sk6) ),
inference(transitivity,[status(thm)],[94,93]) ).
tff(96,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ( ssList(sk6)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(98,plain,
( ssList(sk6)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[98,95]) ).
tff(100,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(101,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)],[100]) ).
tff(102,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(103,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(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(quant_intro,[status(thm)],[103]) ).
tff(105,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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
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)) ) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,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)],[106,102]) ).
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(skolemize,[status(sab)],[107]) ).
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)],[108,101]) ).
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)) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(rewrite,[status(thm)],]) ).
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(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ) ),
inference(transitivity,[status(thm)],[112,110]) ).
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(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ),
inference(quant_inst,[status(thm)],]) ).
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(nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ( app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
app(app(nil,cons(sk5,nil)),sk6) = app(nil,app(cons(sk5,nil),sk6)),
inference(unit_resolution,[status(thm)],[115,88,109,99,92]) ).
tff(117,plain,
app(app(nil,cons(sk5,nil)),sk6) = sk4,
inference(transitivity,[status(thm)],[116,68,55]) ).
tff(118,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(app(C,cons(A,nil)),B) != sk1 )
<=> ( app(app(C,cons(A,nil)),B) != sk3 ) )),
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk2 )
<=> ( app(app(B,cons(A,nil)),C) != sk4 ) )),
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
inference(bind,[status(th)],]) ).
tff(124,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[123]) ).
tff(125,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(app(C,cons(A,nil)),B) != sk1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(126,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[126,122]) ).
tff(128,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[127,121]) ).
tff(129,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[129,119]) ).
tff(131,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,plain,
( ( ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) ) ),
inference(transitivity,[status(thm)],[133,131]) ).
tff(135,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(C,cons(A,nil)),B) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssItem(sk5)
| ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
( ( app(app(sk6,cons(sk5,nil)),nil) != sk3 )
| ( app(app(nil,cons(sk5,nil)),sk6) != sk4 ) ),
inference(unit_resolution,[status(thm)],[136,88,130,75,99]) ).
tff(138,plain,
$false,
inference(unit_resolution,[status(thm)],[137,117,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWC419-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n005.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 00:51:33 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.18/0.49 % SZS status Unsatisfiable
% 0.18/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------