%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC239-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 0.22s 0.54s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 50
% Syntax : Number of formulae : 125 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 967 ( 209 equ)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 1558 ( 774 ~; 708 |; 0 &)
% ( 76 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 58 ( 58 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 257 ( 233 !; 0 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(sk5_type,type,
sk5: ( $i * $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $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,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(7,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(23,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[28,25,7]) ).
tff(30,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(31,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(34,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
( ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) )
<=> ( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
tff(38,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[38,36]) ).
tff(40,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( cons(sk6,nil) = sk3 )
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[41,36]) ).
tff(43,plain,
cons(sk6,nil) = sk3,
inference(unit_resolution,[status(thm)],[42,35]) ).
tff(44,plain,
app(nil,cons(sk6,nil)) = app(nil,sk3),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
app(nil,cons(sk6,nil)) = sk3,
inference(transitivity,[status(thm)],[44,29]) ).
tff(46,plain,
app(app(nil,cons(sk6,nil)),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
app(app(nil,cons(sk6,nil)),nil) = sk1,
inference(transitivity,[status(thm)],[46,18,4]) ).
tff(48,plain,
( ( ssItem(sk6)
| ( nil = sk3 ) )
<=> ( ssItem(sk6)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
( ssItem(sk6)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(50,plain,
( ssItem(sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
ssItem(sk6),
inference(unit_resolution,[status(thm)],[50,35]) ).
tff(52,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(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 ) )
<=> ! [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)],[52]) ).
tff(54,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(55,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(56,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)],[55]) ).
tff(57,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(58,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)],[57,56]) ).
tff(59,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)],[58,54]) ).
tff(60,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)],[59]) ).
tff(61,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)],[60,53]) ).
tff(62,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(64,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,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(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ssItem(sk5(nil,nil,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 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 ) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != 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 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != 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 ) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ssItem(sk5(nil,nil,sk6)) ) ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ssItem(sk5(nil,nil,sk6))
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,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(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ssItem(sk5(nil,nil,sk6)) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ssItem(sk5(nil,nil,sk6)) ),
inference(unit_resolution,[status(thm)],[70,64,61,51]) ).
tff(72,plain,
ssItem(sk5(nil,nil,sk6)),
inference(unit_resolution,[status(thm)],[71,47]) ).
tff(73,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(74,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)],[73]) ).
tff(75,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(76,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(77,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)],[76]) ).
tff(78,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(79,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)],[78,77]) ).
tff(80,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)],[79,75]) ).
tff(81,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)],[80]) ).
tff(82,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)],[81,74]) ).
tff(83,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(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,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)) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,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)) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,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)) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(transitivity,[status(thm)],[85,83]) ).
tff(87,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,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(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| lt(sk6,sk5(nil,nil,sk6)) ),
inference(unit_resolution,[status(thm)],[88,64,82,51]) ).
tff(90,plain,
lt(sk6,sk5(nil,nil,sk6)),
inference(unit_resolution,[status(thm)],[89,47]) ).
tff(91,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(92,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)],[91]) ).
tff(93,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(94,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(95,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)],[94]) ).
tff(96,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(97,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)],[96,95]) ).
tff(98,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)],[97,93]) ).
tff(99,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)],[98]) ).
tff(100,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)],[99,92]) ).
tff(101,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(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,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)) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ ssList(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) )
<=> ( ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,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)) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,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)) )
| ~ ssList(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
tff(105,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(nil)
| ~ ssItem(sk6)
| ~ ssList(nil)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(106,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(nil)
| ~ ssItem(sk6)
| ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
( ( app(app(nil,cons(sk6,nil)),nil) != sk1 )
| ~ leq(sk6,sk5(nil,nil,sk6)) ),
inference(unit_resolution,[status(thm)],[106,64,100,51]) ).
tff(108,plain,
~ leq(sk6,sk5(nil,nil,sk6)),
inference(unit_resolution,[status(thm)],[107,47]) ).
tff(109,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(110,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)],[109]) ).
tff(111,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(112,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(113,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)],[112]) ).
tff(114,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(115,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(skolemize,[status(sab)],[116]) ).
tff(118,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) ),
inference(modus_ponens,[status(thm)],[117,110]) ).
tff(119,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(nil,nil,sk6))
| ~ ssItem(sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(nil,nil,sk6))
| ~ ssItem(sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(120,plain,
( ( ~ ssItem(sk6)
| ~ ssItem(sk5(nil,nil,sk6))
| leq(sk6,sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) )
<=> ( ~ ssItem(sk6)
| leq(sk6,sk5(nil,nil,sk6))
| ~ ssItem(sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| ~ ssItem(sk5(nil,nil,sk6))
| leq(sk6,sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(nil,nil,sk6))
| ~ ssItem(sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(monotonicity,[status(thm)],[120]) ).
tff(122,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| ~ ssItem(sk5(nil,nil,sk6))
| leq(sk6,sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(nil,nil,sk6))
| ~ ssItem(sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) ) ),
inference(transitivity,[status(thm)],[121,119]) ).
tff(123,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| ~ ssItem(sk5(nil,nil,sk6))
| leq(sk6,sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssItem(V)
| leq(U,V)
| ~ lt(U,V) )
| ~ ssItem(sk6)
| leq(sk6,sk5(nil,nil,sk6))
| ~ ssItem(sk5(nil,nil,sk6))
| ~ lt(sk6,sk5(nil,nil,sk6)) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
$false,
inference(unit_resolution,[status(thm)],[124,118,51,108,90,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWC239-1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 08:42:23 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.22/0.54 % SZS status Unsatisfiable
% 0.22/0.54 % SZS output start Proof
% See solution above
% 0.22/0.56 % E exiting
%------------------------------------------------------------------------------