TSTP Solution File: SWC171-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC171-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:55:49 EDT 2022
% Result : Unsatisfiable 1.02s 0.91s
% Output : Proof 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 138
% Syntax : Number of formulae : 303 ( 72 unt; 18 typ; 0 def)
% Number of atoms : 2387 ( 451 equ)
% Maximal formula atoms : 35 ( 8 avg)
% Number of connectives : 3785 (1836 ~;1755 |; 0 &)
% ( 194 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 153 ( 153 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 10 >; 6 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 611 ( 550 !; 0 ?; 611 :)
% Comments :
%------------------------------------------------------------------------------
tff(strictorderedP_type,type,
strictorderedP: $i > $o ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk9_type,type,
sk9: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(singletonP_type,type,
singletonP: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(1,plain,
( ( nil = cons(sk6,nil) )
<=> ( cons(sk6,nil) = nil ) ),
inference(commutativity,[status(thm)],]) ).
tff(2,plain,
( ( cons(sk6,nil) = nil )
<=> ( nil = cons(sk6,nil) ) ),
inference(symmetry,[status(thm)],[1]) ).
tff(3,plain,
( ( cons(sk6,nil) != nil )
<=> ( nil != cons(sk6,nil) ) ),
inference(monotonicity,[status(thm)],[2]) ).
tff(4,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(6,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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(11,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)],[10]) ).
tff(12,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(13,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ~ singletonP(nil)
<=> ~ singletonP(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause11) ).
tff(19,plain,
~ singletonP(nil),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(22,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| ~ ssItem(sk6)
| ~ ssList(nil)
| singletonP(nil)
| ( cons(sk6,nil) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
| singletonP(nil)
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( cons(sk6,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
cons(sk6,nil) != nil,
inference(unit_resolution,[status(thm)],[28,22,19,16,6]) ).
tff(30,plain,
nil != cons(sk6,nil),
inference(modus_ponens,[status(thm)],[29,3]) ).
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(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(42,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(43,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)],[42,41]) ).
tff(44,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[43,22,40,6]) ).
tff(45,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ segmentP(nil,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause80) ).
tff(51,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(57,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(cons(sk6,nil))
| ( nil = cons(sk6,nil) )
| ~ segmentP(nil,cons(sk6,nil)) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
~ segmentP(nil,cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[57,54,44,30]) ).
tff(59,plain,
( ssItem(sk5)
<=> ssItem(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(60,axiom,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(61,plain,
ssItem(sk5),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,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(63,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(64,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)],[63,62]) ).
tff(65,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[64,22,40,61]) ).
tff(66,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(68,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,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(70,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)],[69]) ).
tff(71,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(72,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(73,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)],[72]) ).
tff(74,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[77,70]) ).
tff(79,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(80,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(81,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)],[80]) ).
tff(82,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)],[81,79]) ).
tff(83,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(84,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)],[83,82]) ).
tff(85,plain,
ssList(app(sk7,cons(sk5,nil))),
inference(unit_resolution,[status(thm)],[84,78,68,65]) ).
tff(86,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(87,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(88,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(app(U,V),W) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) ) )),
rewrite(
( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
tff(95,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk6,nil))
| segmentP(nil,cons(sk6,nil))
| ~ ssList(sk8)
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil )
| segmentP(nil,cons(sk6,nil)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) != nil,
inference(unit_resolution,[status(thm)],[104,22,98,88,44,85,58]) ).
tff(106,plain,
( ssList(sk3)
<=> ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(110,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[110,107]) ).
tff(112,plain,
ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(modus_ponens,[status(thm)],[111,106]) ).
tff(113,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| frontsegP(U,nil) )
<=> ( ~ ssList(U)
| frontsegP(U,nil) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,axiom,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
tff(117,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,nil) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil),
inference(unit_resolution,[status(thm)],[122,119,112]) ).
tff(124,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ( V = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ frontsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause129) ).
tff(130,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(monotonicity,[status(thm)],[135]) ).
tff(137,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ) ),
inference(transitivity,[status(thm)],[136,134]) ).
tff(138,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil)
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil )
| ~ frontsegP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),nil) ),
inference(modus_ponens,[status(thm)],[138,137]) ).
tff(140,plain,
( ~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = nil ) ),
inference(unit_resolution,[status(thm)],[139,22,133,112,123]) ).
tff(141,plain,
~ frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(unit_resolution,[status(thm)],[140,105]) ).
tff(142,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(143,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
( ( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,axiom,
! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| frontsegP(nil,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause83) ).
tff(148,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[150,143]) ).
tff(152,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(quant_inst,[status(thm)],]) ).
tff(154,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil != U )
| frontsegP(nil,U) )
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
( ( nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| frontsegP(nil,app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(unit_resolution,[status(thm)],[154,151,112]) ).
tff(156,plain,
nil != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(unit_resolution,[status(thm)],[155,141]) ).
tff(157,plain,
( ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) )
<=> ( ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| ( cons(sk9,nil) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ( ( cons(sk9,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,axiom,
( ( cons(sk9,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(161,plain,
( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
( ( nil = sk3 )
| ( cons(sk9,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[161,158]) ).
tff(163,plain,
( ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) )
| ( cons(sk9,nil) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(modus_ponens,[status(thm)],[162,157]) ).
tff(164,plain,
cons(sk9,nil) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(unit_resolution,[status(thm)],[163,156]) ).
tff(165,plain,
( strictorderedP(cons(sk9,nil))
<=> strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)) ),
inference(monotonicity,[status(thm)],[164]) ).
tff(166,plain,
( strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
<=> strictorderedP(cons(sk9,nil)) ),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
( ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
<=> ~ strictorderedP(cons(sk9,nil)) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,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(169,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)],[168]) ).
tff(170,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(171,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(172,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)],[171]) ).
tff(173,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(174,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)],[173,172]) ).
tff(175,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)],[174,170]) ).
tff(176,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)],[175]) ).
tff(177,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)],[176,169]) ).
tff(178,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(179,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(180,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)],[179,178]) ).
tff(181,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)],[180,177,88,44,85]) ).
tff(182,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)],[181]) ).
tff(183,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(184,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)],[183]) ).
tff(185,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(186,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(187,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)],[186]) ).
tff(188,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(189,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[189,185]) ).
tff(191,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[190]) ).
tff(192,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[191,184]) ).
tff(193,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(194,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(195,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)],[194,193]) ).
tff(196,plain,
app(cons(sk6,nil),sk8) = cons(sk6,sk8),
inference(unit_resolution,[status(thm)],[195,192,6,88]) ).
tff(197,plain,
cons(sk6,sk8) = app(cons(sk6,nil),sk8),
inference(symmetry,[status(thm)],[196]) ).
tff(198,plain,
( ~ neq(sk5,sk6)
<=> ~ neq(sk5,sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(199,axiom,
~ neq(sk5,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(200,plain,
~ neq(sk5,sk6),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) )),
inference(bind,[status(th)],]) ).
tff(202,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(204,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U) )
<=> ( ~ ssItem(U)
| neq(V,U)
| ~ ssItem(V) ) )),
( ( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssItem(U)
| neq(V,U)
| ~ ssItem(V)
| ( V = U ) ) )),
rewrite(
( ( ~ ssItem(U)
| neq(V,U)
| ~ ssItem(V)
| ( V = U ) )
<=> ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) )),
( ( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) )),
inference(bind,[status(th)],]) ).
tff(205,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ) ),
inference(quant_intro,[status(thm)],[204]) ).
tff(206,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause102) ).
tff(207,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[206,205]) ).
tff(208,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[207,203]) ).
tff(209,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(skolemize,[status(sab)],[208]) ).
tff(210,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[209,202]) ).
tff(211,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(212,plain,
( ( ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) )
<=> ( neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(213,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(monotonicity,[status(thm)],[212]) ).
tff(214,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ) ),
inference(transitivity,[status(thm)],[213,211]) ).
tff(215,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk6)
| ( sk5 = sk6 )
| neq(sk5,sk6)
| ~ ssItem(sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(216,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk5,sk6)
| ~ ssItem(sk5)
| ~ ssItem(sk6)
| ( sk5 = sk6 ) ),
inference(modus_ponens,[status(thm)],[215,214]) ).
tff(217,plain,
sk5 = sk6,
inference(unit_resolution,[status(thm)],[216,210,61,6,200]) ).
tff(218,plain,
cons(sk5,nil) = cons(sk6,nil),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
cons(sk6,nil) = cons(sk5,nil),
inference(symmetry,[status(thm)],[218]) ).
tff(220,plain,
app(sk7,cons(sk6,nil)) = app(sk7,cons(sk5,nil)),
inference(monotonicity,[status(thm)],[219]) ).
tff(221,plain,
app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) = app(app(sk7,cons(sk5,nil)),app(cons(sk6,nil),sk8)),
inference(monotonicity,[status(thm)],[220,197]) ).
tff(222,plain,
app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(transitivity,[status(thm)],[221,182]) ).
tff(223,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ lt(U,U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(224,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[223]) ).
tff(225,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(226,plain,
^ [U: $i] :
rewrite(
( ( ~ lt(U,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(227,plain,
( ! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[226]) ).
tff(228,axiom,
! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause63) ).
tff(229,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[228,227]) ).
tff(230,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[229,225]) ).
tff(231,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemize,[status(sab)],[230]) ).
tff(232,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[231,224]) ).
tff(233,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(234,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(235,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk6)
| ~ lt(sk6,sk6) ),
inference(modus_ponens,[status(thm)],[234,233]) ).
tff(236,plain,
~ lt(sk6,sk6),
inference(unit_resolution,[status(thm)],[235,232,6]) ).
tff(237,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
inference(bind,[status(th)],]) ).
tff(238,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ),
inference(quant_intro,[status(thm)],[237]) ).
tff(239,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(240,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y) )
<=> ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(W) ) )),
rewrite(
( ( ~ ssList(Y)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X) )
<=> ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(X) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ strictorderedP(Z) ) )),
rewrite(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Z) ) )),
rewrite(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| lt(V,X) ) )),
rewrite(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) )),
inference(bind,[status(th)],]) ).
tff(241,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ),
inference(quant_intro,[status(thm)],[240]) ).
tff(242,axiom,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ strictorderedP(Z)
| ~ ssList(Z)
| lt(V,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause181) ).
tff(243,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(modus_ponens,[status(thm)],[242,241]) ).
tff(244,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(modus_ponens,[status(thm)],[243,239]) ).
tff(245,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(skolemize,[status(sab)],[244]) ).
tff(246,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) ),
inference(modus_ponens,[status(thm)],[245,238]) ).
tff(247,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(248,plain,
( ( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(nil)
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(249,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(nil)
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(monotonicity,[status(thm)],[248]) ).
tff(250,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(nil)
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(transitivity,[status(thm)],[249,247]) ).
tff(251,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(nil)
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(252,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| lt(V,X)
| ~ strictorderedP(Z)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z ) )
| ~ ssList(nil)
| ~ ssList(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| lt(sk6,sk6)
| ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(modus_ponens,[status(thm)],[251,250]) ).
tff(253,plain,
( ~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8))
| ( app(app(sk7,cons(sk6,nil)),cons(sk6,sk8)) != app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(unit_resolution,[status(thm)],[252,22,246,112,6,68,88,236]) ).
tff(254,plain,
~ strictorderedP(app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8)),
inference(unit_resolution,[status(thm)],[253,222]) ).
tff(255,plain,
~ strictorderedP(cons(sk9,nil)),
inference(modus_ponens,[status(thm)],[254,167]) ).
tff(256,plain,
( ( ssItem(sk9)
| ( nil = sk3 ) )
<=> ( ssItem(sk9)
| ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(257,plain,
( ( ssItem(sk9)
| ( nil = sk3 ) )
<=> ( ssItem(sk9)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(258,axiom,
( ssItem(sk9)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(259,plain,
( ssItem(sk9)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[258,257]) ).
tff(260,plain,
( ssItem(sk9)
| ( nil = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) ) ),
inference(modus_ponens,[status(thm)],[259,256]) ).
tff(261,plain,
ssItem(sk9),
inference(unit_resolution,[status(thm)],[260,156]) ).
tff(262,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
inference(bind,[status(th)],]) ).
tff(263,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ),
inference(quant_intro,[status(thm)],[262]) ).
tff(264,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(265,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
( ( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) )),
inference(bind,[status(th)],]) ).
tff(266,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ) ),
inference(quant_intro,[status(thm)],[265]) ).
tff(267,axiom,
! [V: $i,U: $i] :
( ( nil != U )
| ~ ssList(U)
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause112) ).
tff(268,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(modus_ponens,[status(thm)],[267,266]) ).
tff(269,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(modus_ponens,[status(thm)],[268,264]) ).
tff(270,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(skolemize,[status(sab)],[269]) ).
tff(271,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) ),
inference(modus_ponens,[status(thm)],[270,263]) ).
tff(272,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(273,plain,
( ( ~ ssList(nil)
| $false
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(274,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(275,plain,
( ( nil = nil )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(276,plain,
( ( nil != nil )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[275]) ).
tff(277,plain,
( ( nil != nil )
<=> $false ),
inference(transitivity,[status(thm)],[276,274]) ).
tff(278,plain,
( ( ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) )
<=> ( ~ ssList(nil)
| $false
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ) ),
inference(monotonicity,[status(thm)],[277]) ).
tff(279,plain,
( ( ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ) ),
inference(transitivity,[status(thm)],[278,273]) ).
tff(280,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ) ),
inference(monotonicity,[status(thm)],[279]) ).
tff(281,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ) ),
inference(transitivity,[status(thm)],[280,272]) ).
tff(282,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ( nil != nil )
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(283,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssItem(V)
| strictorderedP(cons(V,U)) )
| ~ ssList(nil)
| ~ ssItem(sk9)
| strictorderedP(cons(sk9,nil)) ),
inference(modus_ponens,[status(thm)],[282,281]) ).
tff(284,plain,
strictorderedP(cons(sk9,nil)),
inference(unit_resolution,[status(thm)],[283,22,271,261]) ).
tff(285,plain,
$false,
inference(unit_resolution,[status(thm)],[284,255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC171-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n024.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 22:13:03 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.
% 1.02/0.91 % SZS status Unsatisfiable
% 1.02/0.91 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------