%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC209-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:30:31 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 50 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 171 ( 30 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 247 ( 135 ~; 85 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 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 : 40 ( 36 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $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,
( neq(sk1,nil)
<=> neq(sk3,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk3,nil) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( ~ neq(sk1,nil)
<=> ~ neq(sk1,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
~ neq(sk1,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(8,plain,
~ neq(sk1,nil),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
~ neq(sk3,nil),
inference(modus_ponens,[status(thm)],[8,5]) ).
tff(10,plain,
( ( ( nil = sk4 )
| neq(sk3,nil) )
<=> ( ( nil = sk4 )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
( ( nil = sk4 )
| neq(sk3,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(12,plain,
( ( nil = sk4 )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
nil = sk4,
inference(unit_resolution,[status(thm)],[12,9]) ).
tff(14,plain,
sk4 = nil,
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(17,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
sk2 = nil,
inference(transitivity,[status(thm)],[17,14]) ).
tff(19,plain,
( neq(sk2,nil)
<=> neq(nil,nil) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( neq(nil,nil)
<=> neq(sk2,nil) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ~ neq(nil,nil)
<=> ~ neq(sk2,nil) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
^ [V: $i] :
refl(( ( ~ ssList(V)
| ~ neq(V,V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
^ [V: $i] :
rewrite(( ( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,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(28,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(29,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)],[28,27]) ).
tff(30,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)],[29,26]) ).
tff(31,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(32,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)],[31]) ).
tff(33,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)],[32,30]) ).
tff(34,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(35,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[35,24]) ).
tff(37,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[37,23]) ).
tff(39,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(41,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(nil)
| ~ neq(nil,nil) )
<=> ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(nil)
| ~ neq(nil,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(nil)
| ~ neq(nil,nil) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ neq(nil,nil),
inference(unit_resolution,[status(thm)],[44,41,38]) ).
tff(46,plain,
~ neq(sk2,nil),
inference(modus_ponens,[status(thm)],[45,21]) ).
tff(47,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(49,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWC209-1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 08:39:57 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
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------