TSTP Solution File: SWC304-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC304-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:56:58 EDT 2022
% Result : Unsatisfiable 0.46s 0.62s
% Output : Proof 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 99
% Syntax : Number of formulae : 207 ( 59 unt; 15 typ; 0 def)
% Number of atoms : 1687 ( 248 equ)
% Maximal formula atoms : 36 ( 8 avg)
% Number of connectives : 2764 (1363 ~;1277 |; 0 &)
% ( 124 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of FOOLs : 94 ( 94 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 461 ( 419 !; 0 ?; 461 :)
% Comments :
%------------------------------------------------------------------------------
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk11_type,type,
sk11: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk10_type,type,
sk10: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk9_type,type,
sk9: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ssItem(sk7)
<=> ssItem(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
ssItem(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(3,plain,
ssItem(sk7),
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(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(18,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(19,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)],[18,17]) ).
tff(20,plain,
ssList(cons(sk7,nil)),
inference(unit_resolution,[status(thm)],[19,16,13,3]) ).
tff(21,plain,
( ssList(sk9)
<=> ssList(sk9) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
ssList(sk9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(23,plain,
ssList(sk9),
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(sk9)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) )
<=> ( ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil))) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil)))
| ~ ssList(sk9) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk9)
| ~ ssList(cons(sk7,nil))
| ssList(app(sk9,cons(sk7,nil))) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
ssList(app(sk9,cons(sk7,nil))),
inference(unit_resolution,[status(thm)],[39,33,23,20]) ).
tff(41,plain,
( ssList(sk10)
<=> ssList(sk10) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
ssList(sk10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(43,plain,
ssList(sk10),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ~ ssList(app(sk9,cons(sk7,nil))) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk10)
| ~ ssList(app(sk9,cons(sk7,nil)))
| ssList(app(app(sk9,cons(sk7,nil)),sk10)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
ssList(app(app(sk9,cons(sk7,nil)),sk10)),
inference(unit_resolution,[status(thm)],[49,33,43,40]) ).
tff(51,plain,
( ssItem(sk8)
<=> ssItem(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(52,axiom,
ssItem(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(53,plain,
ssItem(sk8),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk8)
| ~ ssList(nil)
| ssList(cons(sk8,nil)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
ssList(cons(sk8,nil)),
inference(unit_resolution,[status(thm)],[56,16,13,53]) ).
tff(58,plain,
( ssList(sk11)
<=> ssList(sk11) ),
inference(rewrite,[status(thm)],]) ).
tff(59,axiom,
ssList(sk11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(60,plain,
ssList(sk11),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,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(62,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)],[61]) ).
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)) ) )
<=> ! [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(64,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(65,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)],[64]) ).
tff(66,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(67,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)],[66,65]) ).
tff(68,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)],[67,63]) ).
tff(69,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)],[68]) ).
tff(70,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)],[69,62]) ).
tff(71,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk11)
| ~ ssList(cons(sk8,nil))
| ~ ssList(app(app(sk9,cons(sk7,nil)),sk10))
| ( app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)),
inference(unit_resolution,[status(thm)],[73,70,60,57,50]) ).
tff(75,plain,
app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)) = app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11),
inference(symmetry,[status(thm)],[74]) ).
tff(76,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(77,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)],[76]) ).
tff(78,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(79,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(80,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)],[79]) ).
tff(81,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(82,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk8)
| ~ ssList(sk11)
| ( app(cons(sk8,nil),sk11) = cons(sk8,sk11) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
app(cons(sk8,nil),sk11) = cons(sk8,sk11),
inference(unit_resolution,[status(thm)],[88,85,53,60]) ).
tff(90,plain,
cons(sk8,sk11) = app(cons(sk8,nil),sk11),
inference(symmetry,[status(thm)],[89]) ).
tff(91,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(sk10)
| ~ ssList(cons(sk7,nil))
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) )
<=> ( ~ ! [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(sk10)
| ~ ssList(cons(sk7,nil))
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) )
<=> ( ~ ssList(sk9)
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) )
<=> ( ~ ! [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(sk10)
| ~ ssList(cons(sk7,nil))
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) )
<=> ( ~ ! [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(sk10)
| ~ ssList(cons(sk7,nil))
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ) ),
inference(transitivity,[status(thm)],[93,91]) ).
tff(95,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk10)
| ~ ssList(cons(sk7,nil))
| ~ ssList(sk9)
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,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(sk10)
| ~ ssList(cons(sk7,nil))
| ( app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)) ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
app(app(sk9,cons(sk7,nil)),sk10) = app(sk9,app(cons(sk7,nil),sk10)),
inference(unit_resolution,[status(thm)],[96,70,23,43,20]) ).
tff(98,plain,
app(sk9,app(cons(sk7,nil),sk10)) = app(app(sk9,cons(sk7,nil)),sk10),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( app(cons(U,nil),V) = cons(U,V) ) )
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(cons(sk7,nil),sk10) = cons(sk7,sk10) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
app(cons(sk7,nil),sk10) = cons(sk7,sk10),
inference(unit_resolution,[status(thm)],[101,85,3,43]) ).
tff(103,plain,
cons(sk7,sk10) = app(cons(sk7,nil),sk10),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
app(sk9,cons(sk7,sk10)) = app(sk9,app(cons(sk7,nil),sk10)),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
app(sk9,cons(sk7,sk10)) = app(app(sk9,cons(sk7,nil)),sk10),
inference(transitivity,[status(thm)],[104,98]) ).
tff(106,plain,
app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) = app(app(app(sk9,cons(sk7,nil)),sk10),app(cons(sk8,nil),sk11)),
inference(monotonicity,[status(thm)],[105,90]) ).
tff(107,plain,
app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) = app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11),
inference(transitivity,[status(thm)],[106,75]) ).
tff(108,plain,
( ( sk7 = sk8 )
<=> ( sk8 = sk7 ) ),
inference(commutativity,[status(thm)],]) ).
tff(109,plain,
( ( sk8 = sk7 )
<=> ( sk7 = sk8 ) ),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ( sk8 != sk7 )
<=> ( sk7 != sk8 ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( lt(sk8,sk7)
<=> lt(sk8,sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
lt(sk8,sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_19) ).
tff(113,plain,
lt(sk8,sk7),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
inference(bind,[status(th)],]) ).
tff(115,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V )
| ~ ssItem(U) ) )),
rewrite(
( ( ~ ssItem(V)
| ~ lt(U,V)
| ( U != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
( ( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) )),
inference(bind,[status(th)],]) ).
tff(118,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause111) ).
tff(120,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,plain,
( ( ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) )
<=> ( ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(126,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) ) ),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) ) ),
inference(transitivity,[status(thm)],[126,124]) ).
tff(128,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk8)
| ~ ssItem(sk7)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ( U != V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk8,sk7)
| ( sk8 != sk7 ) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
sk8 != sk7,
inference(unit_resolution,[status(thm)],[129,123,3,53,113]) ).
tff(131,plain,
sk7 != sk8,
inference(modus_ponens,[status(thm)],[130,110]) ).
tff(132,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(133,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
rewrite(
( ( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
( ( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(V) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
( ( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,axiom,
! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ lt(V,U)
| ~ ssItem(U)
| ~ ssItem(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause114) ).
tff(138,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) ),
inference(modus_ponens,[status(thm)],[140,133]) ).
tff(142,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk7,sk8)
| ~ lt(sk8,sk7) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk7,sk8)
| ~ lt(sk8,sk7) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk7,sk8)
| ~ lt(sk8,sk7) ),
inference(quant_inst,[status(thm)],]) ).
tff(144,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| ~ lt(V,U) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| ~ lt(sk7,sk8)
| ~ lt(sk8,sk7) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
~ lt(sk7,sk8),
inference(unit_resolution,[status(thm)],[144,141,3,53,113]) ).
tff(146,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
inference(bind,[status(th)],]) ).
tff(147,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ leq(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(U) ) )),
rewrite(
( ( ~ ssItem(V)
| ~ leq(U,V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| lt(U,V) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ leq(U,V)
| lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
rewrite(
( ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
( ( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) )),
inference(bind,[status(th)],]) ).
tff(150,plain,
( ! [V: $i,U: $i] :
( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ) ),
inference(quant_intro,[status(thm)],[149]) ).
tff(151,axiom,
! [V: $i,U: $i] :
( ~ leq(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| lt(U,V)
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause121) ).
tff(152,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) ),
inference(modus_ponens,[status(thm)],[154,147]) ).
tff(156,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ( sk7 = sk8 )
| ~ leq(sk7,sk8) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ( sk7 = sk8 )
| ~ leq(sk7,sk8) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ( ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ~ leq(sk7,sk8)
| ( sk7 = sk8 ) )
<=> ( ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ( sk7 = sk8 )
| ~ leq(sk7,sk8) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ~ leq(sk7,sk8)
| ( sk7 = sk8 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ( sk7 = sk8 )
| ~ leq(sk7,sk8) ) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ~ leq(sk7,sk8)
| ( sk7 = sk8 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ( sk7 = sk8 )
| ~ leq(sk7,sk8) ) ),
inference(transitivity,[status(thm)],[158,156]) ).
tff(160,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ~ leq(sk7,sk8)
| ( sk7 = sk8 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(161,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| lt(U,V)
| ~ leq(U,V)
| ( U = V ) )
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| lt(sk7,sk8)
| ( sk7 = sk8 )
| ~ leq(sk7,sk8) ),
inference(modus_ponens,[status(thm)],[160,159]) ).
tff(162,plain,
~ leq(sk7,sk8),
inference(unit_resolution,[status(thm)],[161,155,3,53,145,131]) ).
tff(163,plain,
( totalorderedP(sk3)
<=> totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)) ),
inference(rewrite,[status(thm)],]) ).
tff(164,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(165,axiom,
totalorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(166,plain,
totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)),
inference(modus_ponens,[status(thm)],[166,163]) ).
tff(168,plain,
( ssList(sk3)
<=> ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)) ),
inference(rewrite,[status(thm)],]) ).
tff(169,plain,
( ssList(sk1)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ssList(sk1)
<=> ssList(sk1) ),
inference(rewrite,[status(thm)],]) ).
tff(171,axiom,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
tff(172,plain,
ssList(sk1),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[172,169]) ).
tff(174,plain,
ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)),
inference(modus_ponens,[status(thm)],[173,168]) ).
tff(175,plain,
^ [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
refl(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) )),
inference(bind,[status(th)],]) ).
tff(176,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,plain,
( ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(178,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)
| ~ totalorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
rewrite(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| ~ ssList(Z) ) )),
rewrite(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| leq(V,X) ) )),
rewrite(
( ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ totalorderedP(Z)
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) )),
( ( ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| ~ ssList(Y)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssItem(X)
| ~ ssItem(V)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) )
<=> ( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) )),
inference(bind,[status(th)],]) ).
tff(179,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)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) )
<=> ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ) ),
inference(quant_intro,[status(thm)],[178]) ).
tff(180,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)
| ~ totalorderedP(Z)
| ~ ssList(Z)
| leq(V,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause182) ).
tff(181,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ),
inference(modus_ponens,[status(thm)],[181,177]) ).
tff(183,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ),
inference(skolemize,[status(sab)],[182]) ).
tff(184,plain,
! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) ),
inference(modus_ponens,[status(thm)],[183,176]) ).
tff(185,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) ) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(186,plain,
( ( ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) )
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)) )
<=> ( ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) )
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) ) ) ),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) )
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)) )
<=> ( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) ) ) ),
inference(transitivity,[status(thm)],[187,185]) ).
tff(189,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssItem(sk8)
| ~ ssList(sk9)
| ~ ssList(sk11)
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssItem(sk7)
| ~ ssList(sk10)
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) )
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11)) ),
inference(quant_inst,[status(thm)],]) ).
tff(190,plain,
( ~ ! [W: $i,V: $i,Z: $i,Y: $i,U: $i,X: $i] :
( ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(Y)
| ~ ssList(Z)
| ~ ssItem(V)
| ~ ssList(W)
| ( app(app(U,cons(V,W)),cons(X,Y)) != Z )
| leq(V,X)
| ~ totalorderedP(Z) )
| ~ ssList(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ~ ssList(sk9)
| ~ ssList(sk10)
| ~ ssList(sk11)
| ~ ssItem(sk7)
| ~ ssItem(sk8)
| leq(sk7,sk8)
| ~ totalorderedP(app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11))
| ( app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11) ) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
app(app(sk9,cons(sk7,sk10)),cons(sk8,sk11)) != app(app(app(app(sk9,cons(sk7,nil)),sk10),cons(sk8,nil)),sk11),
inference(unit_resolution,[status(thm)],[190,184,174,167,3,53,23,43,60,162]) ).
tff(192,plain,
$false,
inference(unit_resolution,[status(thm)],[191,107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC304-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n004.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 23:42:34 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.
% 0.46/0.62 % SZS status Unsatisfiable
% 0.46/0.62 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------