%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC205-1 : 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 05:30:30 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 30
% Syntax : Number of formulae : 77 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 312 ( 76 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 423 ( 205 ~; 179 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 74 ( 66 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/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,
( neq(sk3,nil)
<=> neq(sk1,nil) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( neq(sk1,nil)
<=> neq(sk3,nil) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk1,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
~ neq(sk1,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(10,plain,
~ neq(sk1,nil),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(14,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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(19,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)],[18]) ).
tff(20,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(21,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(27,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,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(29,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(30,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)],[29,28]) ).
tff(31,plain,
( ( sk3 = nil )
| neq(sk3,nil) ),
inference(unit_resolution,[status(thm)],[30,27,24,14]) ).
tff(32,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[31,11]) ).
tff(33,plain,
nil = sk3,
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(35,plain,
nil = sk3,
inference(modus_ponens,[status(thm)],[32,34]) ).
tff(36,plain,
( ( ( nil = sk4 )
| ( nil != sk3 ) )
<=> ( ( nil = sk4 )
| ( nil != sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
( ( nil = sk4 )
| ( nil != sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(38,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[38,36]) ).
tff(40,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( nil = sk4 )
| ( nil != sk3 ) ),
inference(modus_ponens,[status(thm)],[41,36]) ).
tff(43,plain,
nil = sk4,
inference(unit_resolution,[status(thm)],[42,35]) ).
tff(44,plain,
sk4 = nil,
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(47,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
sk2 = sk3,
inference(transitivity,[status(thm)],[47,44,33]) ).
tff(49,plain,
( neq(sk2,nil)
<=> neq(sk3,sk3) ),
inference(monotonicity,[status(thm)],[48,33]) ).
tff(50,plain,
( neq(sk3,sk3)
<=> neq(sk2,nil) ),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
( ~ neq(sk3,sk3)
<=> ~ neq(sk2,nil) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
^ [V: $i] :
refl(( ( ~ ssList(V)
| ~ neq(V,V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [V: $i] :
rewrite(( ( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [V: $i,U: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(58,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(59,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(transitivity,[status(thm)],[58,57]) ).
tff(60,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(transitivity,[status(thm)],[59,56]) ).
tff(61,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(65,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[65,54]) ).
tff(67,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[67,53]) ).
tff(69,plain,
( ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk3)
| ~ neq(sk3,sk3) )
<=> ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk3)
| ~ neq(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk3)
| ~ neq(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk3)
| ~ neq(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
~ neq(sk3,sk3),
inference(unit_resolution,[status(thm)],[71,68,14]) ).
tff(73,plain,
~ neq(sk2,nil),
inference(modus_ponens,[status(thm)],[72,51]) ).
tff(74,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(76,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
$false,
inference(unit_resolution,[status(thm)],[76,73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC205-1 : 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 08:38:09 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------