%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC241-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Sat Jun 21 05:30:38 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.48s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 41
% Syntax : Number of formulae : 105 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 924 ( 176 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 1507 ( 744 ~; 694 |; 0 &)
% ( 69 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 56 ( 56 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 231 ( 209 !; 0 ?; 231 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssItem_type,type,
ssItem: $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(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(lt_type,type,
lt: ( $i * $i ) > $o ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(6,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(9,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( ( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) )
<=> ( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
tff(13,plain,
( ( nil = sk3 )
| ( app(app(sk7,cons(sk6,nil)),sk8) = sk3 ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk3,
inference(unit_resolution,[status(thm)],[13,10]) ).
tff(15,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk1,
inference(transitivity,[status(thm)],[14,4]) ).
tff(16,plain,
( ( ( nil = sk3 )
| ssList(sk8) )
<=> ( ( nil = sk3 )
| ssList(sk8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
( ( nil = sk3 )
| ssList(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(18,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[18,16]) ).
tff(20,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( nil = sk3 )
| ssList(sk8) ),
inference(modus_ponens,[status(thm)],[21,16]) ).
tff(23,plain,
ssList(sk8),
inference(unit_resolution,[status(thm)],[22,10]) ).
tff(24,plain,
( ( ssList(sk7)
| ( nil = sk3 ) )
<=> ( ssList(sk7)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ( nil = sk3 )
| ssList(sk7) )
<=> ( ssList(sk7)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
( ( nil = sk3 )
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(27,plain,
( ssList(sk7)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ssList(sk7)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
ssList(sk7),
inference(unit_resolution,[status(thm)],[28,10]) ).
tff(30,plain,
( ( ( nil = sk3 )
| ssItem(sk6) )
<=> ( ( nil = sk3 )
| ssItem(sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
( ( nil = sk3 )
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(32,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[32,30]) ).
tff(34,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( nil = sk3 )
| ssItem(sk6) ),
inference(modus_ponens,[status(thm)],[35,30]) ).
tff(37,plain,
ssItem(sk6),
inference(unit_resolution,[status(thm)],[36,10]) ).
tff(38,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [B: $i,A: $i,C: $i] :
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) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ssItem(sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(44,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ssItem(sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 ) )
<=> ( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 ) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ssItem(sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ssItem(sk5(sk8,sk7,sk6))
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ssItem(sk5(C,B,A))
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ssItem(sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
ssItem(sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[53,47,37,29,23,15]) ).
tff(55,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
^ [B: $i,A: $i,C: $i] :
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) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,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) != sk1 )
| lt(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,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) != sk1 )
| lt(A,sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(61,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| lt(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
lt(sk6,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[70,64,37,29,23,15]) ).
tff(72,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [B: $i,A: $i,C: $i] :
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) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 ) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 ) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
rewrite(( ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
( ( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
<=> ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [B: $i,A: $i,C: $i] :
( ~ ssItem(A)
| ~ ssList(B)
| ~ ssList(C)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(78,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ( ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[84,82]) ).
tff(86,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssList(sk8)
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i,C: $i] :
( ~ ssList(C)
| ~ ssItem(A)
| ~ ssList(B)
| ( app(app(B,cons(A,nil)),C) != sk1 )
| ~ leq(A,sk5(C,B,A)) )
| ~ ssItem(sk6)
| ~ ssList(sk7)
| ~ ssList(sk8)
| ( app(app(sk7,cons(sk6,nil)),sk8) != sk1 )
| ~ leq(sk6,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
~ leq(sk6,sk5(sk8,sk7,sk6)),
inference(unit_resolution,[status(thm)],[87,81,37,29,23,15]) ).
tff(89,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ lt(U,V)
| ~ ssItem(V) )
<=> ( ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) ) )),
rewrite(( ( ~ ssItem(V)
| ~ lt(U,V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
( ( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [V: $i,U: $i] :
( ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U)
| leq(U,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause103) ).
tff(95,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ( ~ ssItem(sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| ~ ssItem(sk5(sk8,sk7,sk6))
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(sk8,sk7,sk6))
| ~ ssItem(sk5(sk8,sk7,sk6))
| ~ lt(sk6,sk5(sk8,sk7,sk6)) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,98,37,88,71,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC241-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:42:10 EDT 2025
% 0.18/0.34 % CPUTime :
% 0.20/0.48 % SZS status Unsatisfiable
% 0.20/0.48 % SZS output start Proof
% See solution above
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------