TSTP Solution File: SWC374-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC374-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:57:30 EDT 2022
% Result : Unsatisfiable 2.07s 1.57s
% Output : Proof 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 85
% Syntax : Number of formulae : 186 ( 51 unt; 14 typ; 0 def)
% Number of atoms : 1248 ( 225 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 1920 ( 925 ~; 893 |; 0 &)
% ( 102 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 81 ( 81 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 352 ( 317 !; 0 ?; 352 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk4_type,type,
sk4: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf43_type,type,
skaf43: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(skaf42_type,type,
skaf42: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ssList(sk2)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ssList(sk2)
<=> ssList(sk2) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
tff(4,plain,
ssList(sk2),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| segmentP(U,nil) )
<=> ( ~ ssList(U)
| segmentP(U,nil) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) ),
inference(quant_inst,[status(thm)],]) ).
tff(15,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
segmentP(sk4,nil),
inference(unit_resolution,[status(thm)],[15,12,5]) ).
tff(17,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk2,sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
~ segmentP(sk2,sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(20,plain,
~ segmentP(sk2,sk1),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
~ segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(25,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ ssList(V) ) )),
rewrite(
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(U,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W)
| segmentP(U,W) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ segmentP(V,W)
| segmentP(U,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(U,W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(U,W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [W: $i,V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ segmentP(V,W)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(U,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause152) ).
tff(33,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(39,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(nil,sk3)
| ~ segmentP(sk4,nil) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(nil,sk3)
| ~ segmentP(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ssList(sk4)
| ~ ssList(nil)
| ~ segmentP(sk4,nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ segmentP(nil,sk3) )
<=> ( segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(nil,sk3)
| ~ segmentP(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ segmentP(sk4,nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ segmentP(nil,sk3) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(nil,sk3)
| ~ segmentP(sk4,nil) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ segmentP(sk4,nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ segmentP(nil,sk3) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(nil,sk3)
| ~ segmentP(sk4,nil) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ segmentP(sk4,nil)
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ segmentP(nil,sk3) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(U,W)
| ~ segmentP(V,W) )
| segmentP(sk4,sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ segmentP(nil,sk3)
| ~ segmentP(sk4,nil) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ segmentP(nil,sk3),
inference(unit_resolution,[status(thm)],[45,39,36,26,5,21,16]) ).
tff(47,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
<=> ( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
^ [U: $i] :
trans(
monotonicity(
rewrite(
( ( ( nil != U )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| segmentP(nil,U) )
<=> ( ~ ssList(U)
| ( nil != U )
| segmentP(nil,U) ) )),
rewrite(
( ( ~ ssList(U)
| ( nil != U )
| segmentP(nil,U) )
<=> ( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ) )),
( ( ( nil != U )
| ~ ssList(U)
| segmentP(nil,U) )
<=> ( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [U: $i] :
( ( nil != U )
| ~ ssList(U)
| segmentP(nil,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).
tff(53,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| ( nil != sk3 )
| segmentP(nil,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| ( nil != sk3 )
| segmentP(nil,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ ssList(sk3)
| segmentP(nil,sk3)
| ( nil != sk3 ) )
<=> ( ~ ssList(sk3)
| ( nil != sk3 )
| segmentP(nil,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| segmentP(nil,sk3)
| ( nil != sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| ( nil != sk3 )
| segmentP(nil,sk3) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| segmentP(nil,sk3)
| ( nil != sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| ( nil != sk3 )
| segmentP(nil,sk3) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| segmentP(nil,sk3)
| ( nil != sk3 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(nil,U)
| ( nil != U ) )
| ~ ssList(sk3)
| ( nil != sk3 )
| segmentP(nil,sk3) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
( ( nil != sk3 )
| segmentP(nil,sk3) ),
inference(unit_resolution,[status(thm)],[62,56,26]) ).
tff(64,plain,
nil != sk3,
inference(unit_resolution,[status(thm)],[63,46]) ).
tff(65,plain,
( ( memberP(sk4,sk5)
| ( nil = sk3 ) )
<=> ( memberP(sk4,sk5)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(67,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[67,65]) ).
tff(69,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[70,65]) ).
tff(72,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[71,65]) ).
tff(73,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[73,65]) ).
tff(75,plain,
( memberP(sk4,sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[74,65]) ).
tff(76,plain,
memberP(sk4,sk5),
inference(unit_resolution,[status(thm)],[75,64]) ).
tff(77,plain,
( ( ssItem(sk5)
| ( nil = sk3 ) )
<=> ( ssItem(sk5)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,axiom,
( ssItem(sk5)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(79,plain,
( ssItem(sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[79,64]) ).
tff(81,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ memberP(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) ) )),
rewrite(
( ( ~ ssItem(V)
| ~ memberP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
( ( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) )),
inference(bind,[status(th)],]) ).
tff(85,plain,
( ! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [V: $i,U: $i] :
( ~ memberP(U,V)
| ~ ssItem(V)
| ~ ssList(U)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
tff(87,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssItem(V)
| ~ memberP(U,V)
| ( app(skaf42(U,V),cons(V,skaf43(V,U))) = U ) )
| ~ ssList(sk4)
| ~ ssItem(sk5)
| ~ memberP(sk4,sk5)
| ( app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4 ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))) = sk4,
inference(unit_resolution,[status(thm)],[93,90,5,80,76]) ).
tff(95,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf43(U,V))
<=> ssList(skaf43(U,V)) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [V: $i,U: $i] : ssList(skaf43(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf43(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
tff(99,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [V: $i,U: $i] : ssList(skaf43(U,V)),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf43(U,V))
| ssList(skaf43(sk5,sk4)) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
ssList(skaf43(sk5,sk4)),
inference(unit_resolution,[status(thm)],[102,101]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,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(108,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)],[107]) ).
tff(109,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(110,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[112,105]) ).
tff(114,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(116,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk5)
| ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
( ~ ssList(skaf43(sk5,sk4))
| ( app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)) ) ),
inference(unit_resolution,[status(thm)],[116,113,80]) ).
tff(118,plain,
app(cons(sk5,nil),skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)),
inference(unit_resolution,[status(thm)],[117,103]) ).
tff(119,plain,
( ( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
( ( cons(sk5,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(122,plain,
( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
( ( nil = sk3 )
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[122,119]) ).
tff(124,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[123,64]) ).
tff(125,plain,
sk3 = cons(sk5,nil),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
app(sk3,skaf43(sk5,sk4)) = app(cons(sk5,nil),skaf43(sk5,sk4)),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
app(sk3,skaf43(sk5,sk4)) = cons(sk5,skaf43(sk5,sk4)),
inference(transitivity,[status(thm)],[126,118]) ).
tff(128,plain,
app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) = app(skaf42(sk4,sk5),cons(sk5,skaf43(sk5,sk4))),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
^ [V: $i,U: $i] :
refl(
( ssList(skaf42(U,V))
<=> ssList(skaf42(U,V)) )),
inference(bind,[status(th)],]) ).
tff(130,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [V: $i,U: $i] : ssList(skaf42(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf42(U,V)) ),
inference(rewrite,[status(thm)],]) ).
tff(132,axiom,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
tff(133,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [V: $i,U: $i] : ssList(skaf42(U,V)),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf42(U,V))
| ssList(skaf42(sk4,sk5)) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
ssList(skaf42(sk4,sk5)),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,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(139,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)],[138]) ).
tff(140,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(141,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(142,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)],[141]) ).
tff(143,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(144,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)],[143,142]) ).
tff(145,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)],[144,140]) ).
tff(146,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)],[145]) ).
tff(147,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)],[146,139]) ).
tff(148,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ( ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(monotonicity,[status(thm)],[149]) ).
tff(151,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ) ),
inference(transitivity,[status(thm)],[150,148]) ).
tff(152,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(skaf43(sk5,sk4))
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk3)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))) ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = app(skaf42(sk4,sk5),app(sk3,skaf43(sk5,sk4))),
inference(unit_resolution,[status(thm)],[153,147,26,137,103]) ).
tff(155,plain,
app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) = sk4,
inference(transitivity,[status(thm)],[154,128,94]) ).
tff(156,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(157,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)],[156]) ).
tff(158,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(159,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(160,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)],[159]) ).
tff(161,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(162,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)],[161,160]) ).
tff(163,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)],[162,158]) ).
tff(164,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)],[163]) ).
tff(165,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)],[164,157]) ).
tff(166,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 ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( ~ ! [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 ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
( ( ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(168,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(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( ~ ! [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 ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[167]) ).
tff(169,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(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) )
<=> ( ~ ! [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 ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ) ),
inference(transitivity,[status(thm)],[168,166]) ).
tff(170,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(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(sk3)
| segmentP(sk4,sk3)
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,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 ) )
| segmentP(sk4,sk3)
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ ssList(skaf42(sk4,sk5))
| ~ ssList(skaf43(sk5,sk4))
| ( app(app(skaf42(sk4,sk5),sk3),skaf43(sk5,sk4)) != sk4 ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
$false,
inference(unit_resolution,[status(thm)],[171,165,26,5,21,137,103,155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SWC374-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.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 : Sun Sep 4 00:38:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.07/1.57 % SZS status Unsatisfiable
% 2.07/1.57 % SZS output start Proof
% See solution above
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