TSTP Solution File: SWC175-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC175-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 11:55:51 EDT 2022
% Result : Unsatisfiable 0.20s 0.57s
% Output : Proof 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 80
% Syntax : Number of formulae : 163 ( 49 unt; 14 typ; 0 def)
% Number of atoms : 1202 ( 173 equ)
% Maximal formula atoms : 35 ( 8 avg)
% Number of connectives : 1912 ( 927 ~; 895 |; 0 &)
% ( 90 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 68 ( 68 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 7 >; 4 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 354 ( 318 !; 0 ?; 354 :)
% Comments :
%------------------------------------------------------------------------------
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk9_type,type,
sk9: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(strictorderedP_type,type,
strictorderedP: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ssItem(sk6)
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(3,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(10,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(16,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(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(18,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(19,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)],[18,17]) ).
tff(20,plain,
ssList(cons(sk6,nil)),
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
tff(21,plain,
( ssList(sk8)
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(23,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
^ [V: $i,U: $i] :
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(30,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) )
<=> ( ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil))) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil)))
| ~ ssList(sk8) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk8)
| ~ ssList(cons(sk6,nil))
| ssList(app(sk8,cons(sk6,nil))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
ssList(app(sk8,cons(sk6,nil))),
inference(unit_resolution,[status(thm)],[39,33,23,20]) ).
tff(41,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(43,plain,
ssItem(sk7),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk7)
| ~ ssList(nil)
| ssList(cons(sk7,nil)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
ssList(cons(sk7,nil)),
inference(unit_resolution,[status(thm)],[46,16,13,43]) ).
tff(48,plain,
( ssList(sk9)
<=> ssList(sk9) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(50,plain,
ssList(sk9),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
^ [W: $i,V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
^ [W: $i,V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(57,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(sk8,cons(sk6,nil)))
| ( app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) = app(app(sk8,cons(sk6,nil)),app(cons(sk7,nil),sk9)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(sk8,cons(sk6,nil)))
| ( app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) = app(app(sk8,cons(sk6,nil)),app(cons(sk7,nil),sk9)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(sk8,cons(sk6,nil)))
| ( app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) = app(app(sk8,cons(sk6,nil)),app(cons(sk7,nil),sk9)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ~ ssList(app(sk8,cons(sk6,nil)))
| ( app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) = app(app(sk8,cons(sk6,nil)),app(cons(sk7,nil),sk9)) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) = app(app(sk8,cons(sk6,nil)),app(cons(sk7,nil),sk9)),
inference(unit_resolution,[status(thm)],[63,60,50,47,40]) ).
tff(65,plain,
app(app(sk8,cons(sk6,nil)),app(cons(sk7,nil),sk9)) = app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9),
inference(symmetry,[status(thm)],[64]) ).
tff(66,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(67,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)],[66]) ).
tff(68,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(69,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(70,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)],[69]) ).
tff(71,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(72,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk9)
| ( app(cons(sk7,nil),sk9) = cons(sk7,sk9) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk9)
| ( app(cons(sk7,nil),sk9) = cons(sk7,sk9) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk9)
| ( app(cons(sk7,nil),sk9) = cons(sk7,sk9) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk9)
| ( app(cons(sk7,nil),sk9) = cons(sk7,sk9) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
app(cons(sk7,nil),sk9) = cons(sk7,sk9),
inference(unit_resolution,[status(thm)],[78,75,43,50]) ).
tff(80,plain,
cons(sk7,sk9) = app(cons(sk7,nil),sk9),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
( ~ neq(sk6,sk7)
<=> ~ neq(sk6,sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(82,axiom,
~ neq(sk6,sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(83,plain,
~ neq(sk6,sk7),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,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(85,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)],[84]) ).
tff(86,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(87,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(88,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)],[87]) ).
tff(89,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(90,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk6,sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ( sk6 = sk7 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk6,sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ( sk6 = sk7 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
( ( ~ ssItem(sk7)
| ( sk6 = sk7 )
| neq(sk6,sk7)
| ~ ssItem(sk6) )
<=> ( neq(sk6,sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ( sk6 = sk7 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk7)
| ( sk6 = sk7 )
| neq(sk6,sk7)
| ~ ssItem(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk6,sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ( sk6 = sk7 ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk7)
| ( sk6 = sk7 )
| neq(sk6,sk7)
| ~ ssItem(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk6,sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ( sk6 = sk7 ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| ~ ssItem(sk7)
| ( sk6 = sk7 )
| neq(sk6,sk7)
| ~ ssItem(sk6) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ( V = U )
| neq(V,U)
| ~ ssItem(V) )
| neq(sk6,sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk7)
| ( sk6 = sk7 ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
sk6 = sk7,
inference(unit_resolution,[status(thm)],[99,93,3,43,83]) ).
tff(101,plain,
cons(sk6,nil) = cons(sk7,nil),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
cons(sk7,nil) = cons(sk6,nil),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
app(sk8,cons(sk7,nil)) = app(sk8,cons(sk6,nil)),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) = app(app(sk8,cons(sk6,nil)),app(cons(sk7,nil),sk9)),
inference(monotonicity,[status(thm)],[103,80]) ).
tff(105,plain,
app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) = app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9),
inference(transitivity,[status(thm)],[104,65]) ).
tff(106,plain,
^ [U: $i] :
refl(
( ( ~ ssItem(U)
| ~ lt(U,U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
^ [U: $i] :
rewrite(
( ( ~ lt(U,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ lt(U,U) ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,axiom,
! [U: $i] :
( ~ lt(U,U)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause63) ).
tff(112,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[112,108]) ).
tff(114,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(modus_ponens,[status(thm)],[114,107]) ).
tff(116,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ lt(U,U) )
| ~ ssItem(sk7)
| ~ lt(sk7,sk7) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
~ lt(sk7,sk7),
inference(unit_resolution,[status(thm)],[118,115,43]) ).
tff(120,plain,
( strictorderedP(sk3)
<=> strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9)) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
( strictorderedP(sk3)
<=> strictorderedP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(122,axiom,
strictorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(123,plain,
strictorderedP(sk3),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9)),
inference(modus_ponens,[status(thm)],[123,120]) ).
tff(125,plain,
( ssList(sk3)
<=> ssList(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9)) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(128,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(129,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[129,126]) ).
tff(131,plain,
ssList(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9)),
inference(modus_ponens,[status(thm)],[130,125]) ).
tff(132,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(133,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)],[132]) ).
tff(134,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(135,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(136,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)],[135]) ).
tff(137,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(138,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)],[137,136]) ).
tff(139,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)],[138,134]) ).
tff(140,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)],[139]) ).
tff(141,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)],[140,133]) ).
tff(142,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(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) )
<=> ( ~ ! [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(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ( ~ ssItem(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(nil)
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) )
<=> ( ~ ssList(nil)
| ~ ssList(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,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(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(nil)
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) )
<=> ( ~ ! [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(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,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(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(nil)
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) )
<=> ( ~ ! [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(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) ) ),
inference(transitivity,[status(thm)],[144,142]) ).
tff(146,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(sk7)
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssList(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(nil)
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(147,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(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ~ ssList(sk8)
| ~ ssList(sk9)
| ~ ssItem(sk7)
| lt(sk7,sk7)
| ~ strictorderedP(app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9))
| ( app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
app(app(sk8,cons(sk7,nil)),cons(sk7,sk9)) != app(app(app(sk8,cons(sk6,nil)),cons(sk7,nil)),sk9),
inference(unit_resolution,[status(thm)],[147,16,141,131,124,43,23,50,119]) ).
tff(149,plain,
$false,
inference(unit_resolution,[status(thm)],[148,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC175-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 22:17:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.57 % SZS status Unsatisfiable
% 0.20/0.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------