%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC097-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:30:09 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 18
% Syntax : Number of formulae : 41 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 120 ( 43 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 162 ( 85 ~; 63 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
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,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(6,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(9,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
( ( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ( app(sk3,cons(sk5,nil)) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
( ( app(sk3,cons(sk5,nil)) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(15,plain,
( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
app(sk3,cons(sk5,nil)) = sk4,
inference(unit_resolution,[status(thm)],[16,11]) ).
tff(18,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(20,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
app(sk1,cons(sk5,nil)) = app(sk3,cons(sk5,nil)),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
app(sk1,cons(sk5,nil)) = sk2,
inference(transitivity,[status(thm)],[21,17,4]) ).
tff(23,plain,
^ [A: $i] :
refl(( ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(24,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
^ [A: $i] :
rewrite(( ( ~ ssItem(A)
| ( app(sk1,cons(A,nil)) != sk2 )
| ~ neq(sk4,nil) )
<=> ( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [A: $i] :
( ~ ssItem(A)
| ( app(sk1,cons(A,nil)) != sk2 )
| ~ neq(sk4,nil) )
<=> ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,axiom,
! [A: $i] :
( ~ ssItem(A)
| ( app(sk1,cons(A,nil)) != sk2 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(29,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,plain,
! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) ),
inference(modus_ponens,[status(thm)],[31,24]) ).
tff(33,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
tff(35,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[35,11]) ).
tff(37,plain,
( ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) )
| ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( app(sk1,cons(sk5,nil)) != sk2 ) )
<=> ( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) )
| ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( app(sk1,cons(sk5,nil)) != sk2 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) )
| ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( app(sk1,cons(sk5,nil)) != sk2 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [A: $i] :
( ~ ssItem(A)
| ~ neq(sk4,nil)
| ( app(sk1,cons(A,nil)) != sk2 ) )
| ~ ssItem(sk5)
| ~ neq(sk4,nil)
| ( app(sk1,cons(sk5,nil)) != sk2 ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
app(sk1,cons(sk5,nil)) != sk2,
inference(unit_resolution,[status(thm)],[39,11,36,32]) ).
tff(41,plain,
$false,
inference(unit_resolution,[status(thm)],[40,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWC097-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:17:55 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------