%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC254-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:30:41 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 24
% Syntax : Number of formulae : 58 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 221 ( 38 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 281 ( 132 ~; 118 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 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; 6 con; 0-2 aty)
% Number of variables : 34 ( 31 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
tff(ssList_type,type,
ssList: $i > $o ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $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(singletonP_type,type,
singletonP: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssItem_type,type,
ssItem: $i > $o ).
tff(1,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( neq(sk2,nil)
| 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(sk2,nil),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[9,4]) ).
tff(11,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(14,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[15,10]) ).
tff(17,plain,
( ssList(cons(sk5,nil))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[16]) ).
tff(18,plain,
( ssList(sk3)
<=> ssList(cons(sk5,nil)) ),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(21,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
ssList(cons(sk5,nil)),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(25,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
cons(sk5,nil) = sk1,
inference(transitivity,[status(thm)],[16,26]) ).
tff(28,plain,
( singletonP(cons(sk5,nil))
<=> singletonP(sk1) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( singletonP(sk1)
<=> singletonP(cons(sk5,nil)) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ singletonP(sk1)
<=> ~ singletonP(cons(sk5,nil)) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ singletonP(sk1)
| ~ neq(sk4,nil) )
<=> ( ~ singletonP(sk1)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
( ~ singletonP(sk1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(33,plain,
( ~ singletonP(sk1)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ singletonP(sk1),
inference(unit_resolution,[status(thm)],[33,10]) ).
tff(35,plain,
~ singletonP(cons(sk5,nil)),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(38,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[38,10]) ).
tff(40,plain,
^ [U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
<=> ( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(44,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(45,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ) ),
inference(transitivity,[status(thm)],[44,43]) ).
tff(46,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( cons(U,nil) != V )
| ~ ssItem(U) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssItem(U)
| ( cons(U,nil) != V )
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) ) )),
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ( cons(U,nil) != V )
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
( ( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| singletonP(V)
| ( cons(U,nil) != V ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) )
<=> ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,axiom,
! [V: $i,U: $i] :
( ( cons(U,nil) != V )
| ~ ssItem(U)
| ~ ssList(V)
| singletonP(V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
tff(50,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ),
inference(modus_ponens,[status(thm)],[50,42]) ).
tff(52,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) ),
inference(modus_ponens,[status(thm)],[52,41]) ).
tff(54,plain,
( ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| singletonP(cons(sk5,nil)) )
<=> ( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| singletonP(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| singletonP(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [U: $i] :
( ~ ssItem(U)
| ~ ssList(cons(U,nil))
| singletonP(cons(U,nil)) )
| ~ ssItem(sk5)
| ~ ssList(cons(sk5,nil))
| singletonP(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ ssList(cons(sk5,nil))
| singletonP(cons(sk5,nil)) ),
inference(unit_resolution,[status(thm)],[56,53,39]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,35,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC254-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 08:44:37 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.45 % SZS status Unsatisfiable
% 0.20/0.45 % SZS output start Proof
% See solution above
% 0.20/0.47 % E exiting
%------------------------------------------------------------------------------