%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC381-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:31:05 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 22
% Syntax : Number of formulae : 52 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 227 ( 57 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 348 ( 181 ~; 143 |; 0 &)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 8 ( 8 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 : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(memberP_type,type,
memberP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $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/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( memberP(sk2,sk5)
<=> memberP(sk4,sk5) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( memberP(sk4,sk5)
<=> memberP(sk2,sk5) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(7,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(10,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[11,6]) ).
tff(13,plain,
( ( ~ neq(sk4,nil)
| memberP(sk4,sk5) )
<=> ( ~ neq(sk4,nil)
| memberP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,plain,
( ( memberP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| memberP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
( memberP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
tff(16,plain,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ~ neq(sk4,nil)
| memberP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
memberP(sk4,sk5),
inference(unit_resolution,[status(thm)],[17,12]) ).
tff(19,plain,
memberP(sk2,sk5),
inference(modus_ponens,[status(thm)],[18,5]) ).
tff(20,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(22,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
( ( cons(sk5,nil) = sk3 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(27,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ neq(sk4,nil)
| ( cons(sk5,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
cons(sk5,nil) = sk3,
inference(unit_resolution,[status(thm)],[28,12]) ).
tff(30,plain,
cons(sk5,nil) = sk1,
inference(transitivity,[status(thm)],[29,23]) ).
tff(31,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [A: $i] :
trans(monotonicity(rewrite(( ( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
<=> ( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ) )),
( ( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A)
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ) )),
( ( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A)
| ~ neq(sk4,nil) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [A: $i] :
( ~ ssItem(A)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(37,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(43,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[43,12]) ).
tff(45,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) )
<=> ( ~ neq(sk4,nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( cons(A,nil) != sk1 )
| ~ memberP(sk2,A) )
| ~ neq(sk4,nil)
| ~ ssItem(sk5)
| ( cons(sk5,nil) != sk1 )
| ~ memberP(sk2,sk5) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
~ memberP(sk2,sk5),
inference(unit_resolution,[status(thm)],[50,12,44,40,30]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC381-1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 09:09:20 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
%------------------------------------------------------------------------------