%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC217-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:30:33 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 73 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 285 ( 87 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 367 ( 171 ~; 162 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 68 ( 60 !; 0 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
tff(nil_type,type,
nil: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(4,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(8,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(12,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[12,10]) ).
tff(14,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[16,9]) ).
tff(18,plain,
( ( cons(sk5,nil) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( cons(sk5,nil) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[18,1]) ).
tff(20,plain,
( ( nil = sk3 )
<=> ( cons(sk5,nil) = nil ) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(23,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( neq(sk3,nil)
<=> neq(sk1,nil) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( neq(sk1,nil)
<=> neq(sk3,nil) ),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk1,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
~ neq(sk1,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(30,plain,
~ neq(sk1,nil),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(34,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(41,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(47,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ( sk3 = nil )
| neq(sk3,nil) ),
inference(unit_resolution,[status(thm)],[50,47,44,34]) ).
tff(52,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[51,31]) ).
tff(53,plain,
nil = sk3,
inference(modus_ponens,[status(thm)],[52,1]) ).
tff(54,plain,
cons(sk5,nil) = nil,
inference(modus_ponens,[status(thm)],[53,20]) ).
tff(55,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(57,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[57,9]) ).
tff(59,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( cons(U,V) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,V) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
( ( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(65,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[65,61]) ).
tff(67,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[67,60]) ).
tff(69,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ( cons(sk5,nil) != nil ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
cons(sk5,nil) != nil,
inference(unit_resolution,[status(thm)],[71,47,68,58]) ).
tff(73,plain,
$false,
inference(unit_resolution,[status(thm)],[72,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC217-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:38:54 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% See solution above
% 0.20/0.45 % E exiting
%------------------------------------------------------------------------------