%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC106-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:30:11 AM UTC 2025
% Result : Unsatisfiable 0.94s 1.14s
% Output : Proof 0.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 48
% Syntax : Number of formulae : 125 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 610 ( 127 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 865 ( 416 ~; 381 |; 0 &)
% ( 68 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 36 ( 36 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; 7 con; 0-2 aty)
% Number of variables : 135 ( 122 !; 0 ?; 135 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(rearsegP_type,type,
rearsegP: ( $i * $i ) > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $i > $o ).
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,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(10,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(15,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[16,11]) ).
tff(18,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[10]) ).
tff(19,plain,
( ( ~ neq(sk4,nil)
| ( app(sk6,cons(sk5,nil)) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(sk6,cons(sk5,nil)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ( ( app(sk6,cons(sk5,nil)) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(sk6,cons(sk5,nil)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
( ( app(sk6,cons(sk5,nil)) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(22,plain,
( ~ neq(sk4,nil)
| ( app(sk6,cons(sk5,nil)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ~ neq(sk4,nil)
| ( app(sk6,cons(sk5,nil)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
app(sk6,cons(sk5,nil)) = sk4,
inference(unit_resolution,[status(thm)],[23,17]) ).
tff(25,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(28,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[29,17]) ).
tff(31,plain,
sk3 = cons(sk5,nil),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
app(sk6,sk3) = app(sk6,cons(sk5,nil)),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
app(sk6,sk3) = sk2,
inference(transitivity,[status(thm)],[32,24,18]) ).
tff(34,plain,
( rearsegP(app(sk6,sk3),sk3)
<=> rearsegP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[33,4]) ).
tff(35,plain,
app(sk6,sk3) = sk4,
inference(transitivity,[status(thm)],[32,24]) ).
tff(36,plain,
( ssList(app(sk6,sk3))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ssList(sk4)
<=> ssList(app(sk6,sk3)) ),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(40,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
ssList(app(sk6,sk3)),
inference(modus_ponens,[status(thm)],[40,37]) ).
tff(42,plain,
( ( ssList(sk6)
| ~ neq(sk4,nil) )
<=> ( ssList(sk6)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
( ssList(sk6)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(44,plain,
( ssList(sk6)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
ssList(sk6),
inference(unit_resolution,[status(thm)],[44,17]) ).
tff(46,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(48,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(53,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V)
| ( app(U,V) != W ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(54,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V)
| ( app(U,V) != W ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ) ),
inference(transitivity,[status(thm)],[53,52]) ).
tff(55,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(U,V) != W )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ( app(U,V) != W )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(U)
| ( app(U,V) != W )
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(W) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ( app(U,V) != W )
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| rearsegP(W,V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(U,V) != W )
| rearsegP(W,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V)
| ( app(U,V) != W ) ) )),
( ( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V)
| ( app(U,V) != W ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V)
| ( app(U,V) != W ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,axiom,
! [W: $i,V: $i,U: $i] :
( ( app(U,V) != W )
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| rearsegP(W,V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause143) ).
tff(59,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ),
inference(modus_ponens,[status(thm)],[59,51]) ).
tff(61,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) ),
inference(modus_ponens,[status(thm)],[61,50]) ).
tff(63,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(app(U,V))
| rearsegP(app(U,V),V) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ ssList(app(sk6,sk3))
| rearsegP(app(sk6,sk3),sk3) ),
inference(unit_resolution,[status(thm)],[68,62,48,45]) ).
tff(70,plain,
rearsegP(app(sk6,sk3),sk3),
inference(unit_resolution,[status(thm)],[69,41]) ).
tff(71,plain,
rearsegP(sk2,sk1),
inference(modus_ponens,[status(thm)],[70,34]) ).
tff(72,plain,
( ( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) )
<=> ( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ neq(sk1,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
( ~ neq(sk1,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(75,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[77,72]) ).
tff(79,plain,
( ~ neq(sk4,nil)
| ~ rearsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[78,72]) ).
tff(80,plain,
~ neq(sk1,nil),
inference(unit_resolution,[status(thm)],[79,71,17]) ).
tff(81,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[80,7]) ).
tff(82,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(83,plain,
( ( nil = sk3 )
<=> ( sk3 = nil ) ),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ( nil != sk3 )
<=> ( sk3 != nil ) ),
inference(monotonicity,[status(thm)],[83]) ).
tff(85,plain,
( ( cons(sk5,nil) = nil )
<=> ( sk3 = nil ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(86,plain,
( ( cons(sk5,nil) = nil )
<=> ( nil = sk3 ) ),
inference(transitivity,[status(thm)],[85,82]) ).
tff(87,plain,
( ( cons(sk5,nil) != nil )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(90,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[90,17]) ).
tff(92,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(93,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)],[92]) ).
tff(94,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(95,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(96,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)],[95]) ).
tff(97,axiom,
! [V: $i,U: $i] :
( ( cons(U,V) != V )
| ~ ssItem(U)
| ~ ssList(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause99) ).
tff(98,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,V) != V ) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(104,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,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(106,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(107,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)],[106,105]) ).
tff(108,plain,
cons(sk5,nil) != nil,
inference(unit_resolution,[status(thm)],[107,104,101,91]) ).
tff(109,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[108,87]) ).
tff(110,plain,
sk3 != nil,
inference(modus_ponens,[status(thm)],[109,84]) ).
tff(111,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(112,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)],[111]) ).
tff(113,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(114,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(115,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)],[114]) ).
tff(116,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(117,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[117,113]) ).
tff(119,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[119,112]) ).
tff(121,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(122,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(123,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)],[122,121]) ).
tff(124,plain,
neq(sk3,nil),
inference(unit_resolution,[status(thm)],[123,104,120,48,110]) ).
tff(125,plain,
$false,
inference(unit_resolution,[status(thm)],[124,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC106-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.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 08:20:17 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.94/1.14 % SZS status Unsatisfiable
% 0.94/1.14 % SZS output start Proof
% See solution above
% 0.94/1.15 % E exiting
%------------------------------------------------------------------------------