TSTP Solution File: SWC002-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC002-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 11:54:32 EDT 2022
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 81
% Syntax : Number of formulae : 175 ( 32 unt; 16 typ; 0 def)
% Number of atoms : 2409 ( 710 equ)
% Maximal formula atoms : 24 ( 15 avg)
% Number of connectives : 3839 (1880 ~;1754 |; 0 &)
% ( 205 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 291 ( 291 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 17 ( 14 usr; 2 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 369 ( 318 !; 0 ?; 369 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk8_type,type,
sk8: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(geq_type,type,
geq: ( $i * $i ) > $o ).
tff(1,plain,
( ( $false
| ( app(sk7,sk8) = sk3 ) )
<=> ( app(sk7,sk8) = sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(5,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],]) ).
tff(6,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(7,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
( neq(sk4,nil)
<=> $true ),
inference(iff_true,[status(thm)],[9]) ).
tff(11,plain,
( ~ neq(sk4,nil)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ neq(sk4,nil)
<=> $false ),
inference(transitivity,[status(thm)],[11,2]) ).
tff(13,plain,
( ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) )
<=> ( $false
| ( app(sk7,sk8) = sk3 ) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) )
<=> ( app(sk7,sk8) = sk3 ) ),
inference(transitivity,[status(thm)],[13,1]) ).
tff(15,plain,
( ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( ( app(sk7,sk8) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
( ( app(sk7,sk8) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_27) ).
tff(18,plain,
( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ neq(sk4,nil)
| ( app(sk7,sk8) = sk3 ) ),
inference(modus_ponens,[status(thm)],[18,15]) ).
tff(20,plain,
app(sk7,sk8) = sk3,
inference(modus_ponens,[status(thm)],[19,14]) ).
tff(21,plain,
( ( $false
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) )
<=> ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) )
<=> ( $false
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(23,plain,
( ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) )
<=> ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ),
inference(transitivity,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,axiom,
( ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_26) ).
tff(27,plain,
( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ neq(sk4,nil)
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk4 ) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk4,
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
( ( ssList(sk8)
| $false )
<=> ssList(sk8) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ssList(sk8)
| ~ neq(sk4,nil) )
<=> ( ssList(sk8)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(32,plain,
( ( ssList(sk8)
| ~ neq(sk4,nil) )
<=> ssList(sk8) ),
inference(transitivity,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ssList(sk8)
| ~ neq(sk4,nil) )
<=> ( ssList(sk8)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
( ssList(sk8)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_25) ).
tff(35,plain,
( ssList(sk8)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
ssList(sk8),
inference(modus_ponens,[status(thm)],[35,32]) ).
tff(37,plain,
( ( ssList(sk7)
| $false )
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ssList(sk7)
| ~ neq(sk4,nil) )
<=> ( ssList(sk7)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(39,plain,
( ( ssList(sk7)
| ~ neq(sk4,nil) )
<=> ssList(sk7) ),
inference(transitivity,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ssList(sk7)
| ~ neq(sk4,nil) )
<=> ( ssList(sk7)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
( ssList(sk7)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_24) ).
tff(42,plain,
( ssList(sk7)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
( ( ssItem(sk6)
| $false )
<=> ssItem(sk6) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ssItem(sk6)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk6)
| $false ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(46,plain,
( ( ssItem(sk6)
| ~ neq(sk4,nil) )
<=> ssItem(sk6) ),
inference(transitivity,[status(thm)],[45,44]) ).
tff(47,plain,
( ( ssItem(sk6)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk6)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_23) ).
tff(49,plain,
( ssItem(sk6)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
ssItem(sk6),
inference(modus_ponens,[status(thm)],[49,46]) ).
tff(51,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(
mp(
mp(
mp(
asserted(
( neq(sk2,nil)
| neq(sk2,nil) )),
rewrite(
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk4,nil) )),
neq(sk4,nil)),
( neq(sk4,nil)
<=> $true )),
( ~ neq(sk4,nil)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ neq(sk4,nil)
<=> $false )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(B,C) != sk1 )
<=> ( app(B,C) != sk3 ) )),
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk2 )
<=> ( app(app(B,cons(A,nil)),C) != sk4 ) )),
rewrite(
( memberP(sk2,sk5(C,B,A))
<=> memberP(sk4,sk5(C,B,A)) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| memberP(sk2,sk5(C,B,A))
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| memberP(sk2,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[62,56]) ).
tff(64,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[63,54]) ).
tff(65,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[65,52]) ).
tff(67,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| memberP(sk4,sk5(C,B,A)) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| memberP(sk4,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
memberP(sk4,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[72,66,50,43,36,29,20]) ).
tff(74,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(
mp(
mp(
mp(
asserted(
( neq(sk2,nil)
| neq(sk2,nil) )),
rewrite(
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk4,nil) )),
neq(sk4,nil)),
( neq(sk4,nil)
<=> $true )),
( ~ neq(sk4,nil)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ neq(sk4,nil)
<=> $false )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
rewrite(
( ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(B,C) != sk1 )
<=> ( app(B,C) != sk3 ) )),
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk2 )
<=> ( app(app(B,cons(A,nil)),C) != sk4 ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ssItem(sk5(C,B,A)) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ~ neq(sk4,nil) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ssItem(sk5(C,B,A))
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
tff(84,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[85,79]) ).
tff(87,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[86,77]) ).
tff(88,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[88,75]) ).
tff(90,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| ssItem(sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| ssItem(sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[95,89,50,43,36,29,20]) ).
tff(97,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(
mp(
mp(
mp(
asserted(
( neq(sk2,nil)
| neq(sk2,nil) )),
rewrite(
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk4,nil) )),
neq(sk4,nil)),
( neq(sk4,nil)
<=> $true )),
( ~ neq(sk4,nil)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ neq(sk4,nil)
<=> $false )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
rewrite(
( ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(B,C) != sk1 )
<=> ( app(B,C) != sk3 ) )),
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk2 )
<=> ( app(app(B,cons(A,nil)),C) != sk4 ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| geq(sk5(C,B,A),A) ) )),
rewrite(
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| geq(sk5(C,B,A),A)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_21) ).
tff(107,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| geq(sk5(C,B,A),A) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[108,102]) ).
tff(110,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[109,100]) ).
tff(111,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[111,98]) ).
tff(113,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| geq(sk5(sk8,sk7,sk6),sk6) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| geq(sk5(sk8,sk7,sk6),sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(rewrite,[status(thm)],]) ).
tff(115,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| geq(sk5(sk8,sk7,sk6),sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| geq(sk5(sk8,sk7,sk6),sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| geq(sk5(sk8,sk7,sk6),sk6) ) ),
inference(transitivity,[status(thm)],[115,113]) ).
tff(117,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| geq(sk5(sk8,sk7,sk6),sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| geq(sk5(C,B,A),A)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 )
| geq(sk5(sk8,sk7,sk6),sk6) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
geq(sk5(sk8,sk7,sk6),sk6),
inference(unit_resolution,[status(thm)],[118,112,50,43,36,29,20]) ).
tff(120,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(121,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(
mp(
mp(
mp(
asserted(
( neq(sk2,nil)
| neq(sk2,nil) )),
rewrite(
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk4,nil) )),
neq(sk4,nil)),
( neq(sk4,nil)
<=> $true )),
( ~ neq(sk4,nil)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ neq(sk4,nil)
<=> $false )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
rewrite(
( ( ~ ssList(C)
| $false
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( app(B,C) != sk1 )
<=> ( app(B,C) != sk3 ) )),
rewrite(
( ( app(app(B,cons(A,nil)),C) != sk2 )
<=> ( app(app(B,cons(A,nil)),C) != sk4 ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| ( A != sk5(C,B,A) ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
( ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
^ [B: $i,A: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) ) )),
rewrite(
( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( app(B,C) != sk1 )
| ( A != sk5(C,B,A) )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_22) ).
tff(130,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(B,C) != sk1 )
| ( app(app(B,cons(A,nil)),C) != sk2 )
| ( A != sk5(C,B,A) ) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ neq(sk4,nil)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[131,125]) ).
tff(133,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[132,123]) ).
tff(134,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) ),
inference(modus_ponens,[status(thm)],[134,121]) ).
tff(136,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(138,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ) ),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ) ),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(141,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( A != sk5(C,B,A) )
| ( app(B,C) != sk3 )
| ( app(app(B,cons(A,nil)),C) != sk4 ) )
| ~ ssList(sk7)
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ( sk6 != sk5(sk8,sk7,sk6) )
| ( app(sk7,sk8) != sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk4 ) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
sk6 != sk5(sk8,sk7,sk6),
inference(unit_resolution,[status(thm)],[141,135,50,43,36,29,20]) ).
tff(143,plain,
^ [A: $i] :
refl(
( ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
^ [A: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(
mp(
mp(
mp(
asserted(
( neq(sk2,nil)
| neq(sk2,nil) )),
rewrite(
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk2,nil) )),
neq(sk2,nil)),
rewrite(
( neq(sk2,nil)
<=> neq(sk4,nil) )),
neq(sk4,nil)),
( neq(sk4,nil)
<=> $true )),
( ~ neq(sk4,nil)
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ neq(sk4,nil)
<=> $false )),
( ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ( ~ ssItem(A)
| $false
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
rewrite(
( ( ~ ssItem(A)
| $false
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
inference(bind,[status(th)],]) ).
tff(146,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
^ [A: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A) )
<=> ( ~ ssItem(A)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ geq(A,sk6) ) )),
rewrite(
( ( ~ ssItem(A)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ geq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ neq(sk4,nil) ) )),
rewrite(
( ( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A )
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
( ( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) )),
inference(bind,[status(th)],]) ).
tff(149,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,axiom,
! [A: $i] :
( ~ ssItem(A)
| ( sk6 = A )
| ~ memberP(sk4,A)
| ~ geq(A,sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_28) ).
tff(151,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(modus_ponens,[status(thm)],[151,147]) ).
tff(153,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(modus_ponens,[status(thm)],[152,146]) ).
tff(154,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(skolemize,[status(sab)],[153]) ).
tff(155,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) ),
inference(modus_ponens,[status(thm)],[154,144]) ).
tff(156,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ geq(A,sk6)
| ~ memberP(sk4,A)
| ( sk6 = A ) )
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ geq(sk5(sk8,sk7,sk6),sk6)
| ~ memberP(sk4,sk5(sk8,sk7,sk6))
| ( sk6 = sk5(sk8,sk7,sk6) ) ),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
$false,
inference(unit_resolution,[status(thm)],[158,155,142,119,96,73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC002-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Sep 3 20:49:21 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------