TSTP Solution File: SWC191-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC191-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 11:56:00 EDT 2022
% Result : Unsatisfiable 2.31s 1.72s
% Output : Proof 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 83
% Syntax : Number of formulae : 175 ( 52 unt; 12 typ; 0 def)
% Number of atoms : 1301 ( 258 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 2103 (1025 ~; 984 |; 0 &)
% ( 94 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 60 ( 60 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 409 ( 375 !; 0 ?; 409 :)
% Comments :
%------------------------------------------------------------------------------
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk8_type,type,
sk8: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(equalelemsP_type,type,
equalelemsP: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(3,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,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(5,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)],[4]) ).
tff(6,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(7,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(8,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)],[7]) ).
tff(9,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(10,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(16,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,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(18,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(19,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)],[18,17]) ).
tff(20,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
tff(21,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(23,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,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(25,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)],[24]) ).
tff(26,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(27,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(28,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)],[27]) ).
tff(29,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(30,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) )
<=> ( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(sk7) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ssList(app(sk7,cons(sk5,nil))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
ssList(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[39,33,23,20]) ).
tff(41,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(43,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssList(cons(sk6,nil)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[46,16,13,43]) ).
tff(48,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(50,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,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(52,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)],[51]) ).
tff(53,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(54,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(55,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)],[54]) ).
tff(56,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(57,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)],[56,55]) ).
tff(58,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)],[57,53]) ).
tff(59,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)],[58]) ).
tff(60,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)],[59,52]) ).
tff(61,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),
inference(unit_resolution,[status(thm)],[63,60,50,47,40]) ).
tff(65,plain,
app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) )
<=> ( ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk6,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(cons(sk6,nil),sk8)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
ssList(app(cons(sk6,nil),sk8)),
inference(unit_resolution,[status(thm)],[71,33,50,47]) ).
tff(73,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk6,nil),sk8))
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk6,nil),sk8))
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
( ( ~ ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) )
<=> ( ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk6,nil),sk8))
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk6,nil),sk8))
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk6,nil),sk8))
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(app(cons(sk6,nil),sk8))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk6,nil),sk8))
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ssList(app(cons(sk6,nil),sk8))
| ( app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) ) ),
inference(unit_resolution,[status(thm)],[78,60,23,20]) ).
tff(80,plain,
app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))),
inference(unit_resolution,[status(thm)],[79,72]) ).
tff(81,plain,
app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) )
<=> ( ~ ssList(sk8)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(cons(sk5,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk8)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk6,nil))
| ( app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
app(app(cons(sk5,nil),cons(sk6,nil)),sk8) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)),
inference(unit_resolution,[status(thm)],[87,60,50,20,47]) ).
tff(89,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause120) ).
tff(95,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( app(cons(sk5,nil),cons(sk6,nil)) = cons(sk5,cons(sk6,nil)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( app(cons(sk5,nil),cons(sk6,nil)) = cons(sk5,cons(sk6,nil)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( app(cons(sk5,nil),cons(sk6,nil)) = cons(sk5,cons(sk6,nil)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( app(cons(sk5,nil),cons(sk6,nil)) = cons(sk5,cons(sk6,nil)) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
app(cons(sk5,nil),cons(sk6,nil)) = cons(sk5,cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[101,98,3,47]) ).
tff(103,plain,
cons(sk5,cons(sk6,nil)) = app(cons(sk5,nil),cons(sk6,nil)),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
app(cons(sk5,cons(sk6,nil)),sk8) = app(app(cons(sk5,nil),cons(sk6,nil)),sk8),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
( ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).
tff(111,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ( ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) )
<=> ( ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) ) ),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ~ ssList(sk8)
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ~ ssList(W)
| ( cons(U,app(V,W)) = app(cons(U,V),W) ) )
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssList(cons(sk6,nil))
| ( cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8) ) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
cons(sk5,app(cons(sk6,nil),sk8)) = app(cons(sk5,cons(sk6,nil)),sk8),
inference(unit_resolution,[status(thm)],[120,114,3,50,47]) ).
tff(122,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk6)
| ~ ssList(sk8)
| ( app(cons(sk6,nil),sk8) = cons(sk6,sk8) ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
app(cons(sk6,nil),sk8) = cons(sk6,sk8),
inference(unit_resolution,[status(thm)],[124,98,43,50]) ).
tff(126,plain,
cons(sk6,sk8) = app(cons(sk6,nil),sk8),
inference(symmetry,[status(thm)],[125]) ).
tff(127,plain,
cons(sk5,cons(sk6,sk8)) = cons(sk5,app(cons(sk6,nil),sk8)),
inference(monotonicity,[status(thm)],[126]) ).
tff(128,plain,
cons(sk5,cons(sk6,sk8)) = app(cons(sk5,nil),app(cons(sk6,nil),sk8)),
inference(transitivity,[status(thm)],[127,121,104,88]) ).
tff(129,plain,
app(sk7,cons(sk5,cons(sk6,sk8))) = app(sk7,app(cons(sk5,nil),app(cons(sk6,nil),sk8))),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,plain,
app(sk7,cons(sk5,cons(sk6,sk8))) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(transitivity,[status(thm)],[129,81,65]) ).
tff(131,plain,
( ( sk5 != sk6 )
<=> ( sk5 != sk6 ) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
sk5 != sk6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(133,plain,
sk5 != sk6,
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
( equalelemsP(sk3)
<=> equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( equalelemsP(sk3)
<=> equalelemsP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(136,axiom,
equalelemsP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(137,plain,
equalelemsP(sk3),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(modus_ponens,[status(thm)],[137,134]) ).
tff(139,plain,
( ssList(sk3)
<=> ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(rewrite,[status(thm)],]) ).
tff(140,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(141,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(142,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(143,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[143,140]) ).
tff(145,plain,
ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(modus_ponens,[status(thm)],[144,139]) ).
tff(146,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(147,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
^ [W: $i,V: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(X)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(W) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ equalelemsP(Y) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ equalelemsP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(Y) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ( V = W ) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y )
| ( V = W ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
( ( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) )
<=> ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,axiom,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ( app(U,cons(V,cons(W,X))) != Y )
| ~ ssList(X)
| ~ ssList(U)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ equalelemsP(Y)
| ~ ssList(Y)
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause180) ).
tff(152,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) ),
inference(modus_ponens,[status(thm)],[154,147]) ).
tff(156,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ( sk5 = sk6 )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ( sk5 = sk6 )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ( ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk5)
| ( sk5 = sk6 )
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ( sk5 = sk6 )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk5)
| ( sk5 = sk6 )
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ( sk5 = sk6 )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk5)
| ( sk5 = sk6 )
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ( sk5 = sk6 )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(transitivity,[status(thm)],[158,156]) ).
tff(160,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ~ ssList(sk8)
| ~ ssList(sk7)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk5)
| ( sk5 = sk6 )
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
( ~ ! [W: $i,V: $i,Y: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ( V = W )
| ~ equalelemsP(Y)
| ~ ssItem(W)
| ( app(U,cons(V,cons(W,X))) != Y ) )
| ( sk5 = sk6 )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ~ equalelemsP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
app(sk7,cons(sk5,cons(sk6,sk8))) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(unit_resolution,[status(thm)],[161,155,145,138,3,43,23,50,133]) ).
tff(163,plain,
$false,
inference(unit_resolution,[status(thm)],[162,130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC191-1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n007.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 22:09:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 2.31/1.72 % SZS status Unsatisfiable
% 2.31/1.72 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------