%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWW423-1 : TPTP v9.0.0. Released v5.2.0.
% 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 05:36:57 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 49 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 64 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 151 ( 55 ~; 76 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 117 ( 106 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
tff(heap_type,type,
heap: $i > $o ).
tff(sep_type,type,
sep: ( $i * $i ) > $i ).
tff(emp_type,type,
emp: $i ).
tff(lseg_type,type,
lseg: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(x3_type,type,
x3: $i ).
tff(x2_type,type,
x2: $i ).
tff(next_type,type,
next: ( $i * $i ) > $i ).
tff(x1_type,type,
x1: $i ).
tff(1,plain,
^ [Sigma: $i,S: $i,T: $i] :
refl(( ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
<=> ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV013-0.ax',associative_commutative) ).
tff(5,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x3,nil),sep(next(x1,x2),emp)) = sep(next(x1,x2),sep(lseg(x3,nil),emp)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
sep(lseg(x3,nil),sep(next(x1,x2),emp)) = sep(next(x1,x2),sep(lseg(x3,nil),emp)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
sep(next(x1,x2),sep(lseg(x3,nil),emp)) = sep(lseg(x3,nil),sep(next(x1,x2),emp)),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
sep(lseg(x2,nil),sep(next(x1,x2),sep(lseg(x3,nil),emp))) = sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp))),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ~ ! [Sigma: $i,S: $i,T: $i] : ( sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)) )
| ( sep(lseg(x2,nil),sep(next(x1,x2),sep(lseg(x3,nil),emp))) = sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
sep(lseg(x2,nil),sep(next(x1,x2),sep(lseg(x3,nil),emp))) = sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp))),
inference(unit_resolution,[status(thm)],[12,7]) ).
tff(14,plain,
sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp))) = sep(lseg(x2,nil),sep(next(x1,x2),sep(lseg(x3,nil),emp))),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp))) = sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp))),
inference(transitivity,[status(thm)],[14,11]) ).
tff(16,plain,
( heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp))))
<=> heap(sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp)))) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( heap(sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp))))
<=> heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( heap(sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp))))
<=> heap(sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
heap(sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_4) ).
tff(20,plain,
heap(sep(lseg(x2,nil),sep(lseg(x3,nil),sep(next(x1,x2),emp)))),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( ( x1 = x2 )
<=> ( x2 = x1 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(23,plain,
( ( x2 = x1 )
<=> ( x1 = x2 ) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ( x2 != x1 )
<=> ( x1 != x2 ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( x2 != x1 )
<=> ( x2 != x1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
x2 != x1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_2) ).
tff(27,plain,
x2 != x1,
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
x1 != x2,
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
( ~ heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
<=> ~ heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp))) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
~ heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_1) ).
tff(31,plain,
~ heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp))),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [Sigma: $i,Z: $i,Y: $i,X: $i] :
refl(( ( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
<=> ( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
<=> ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
<=> ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [Sigma: $i,Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma)))
| ( X = Y )
| heap(sep(lseg(X,Z),Sigma)) )
<=> ( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma)))
| ( X = Y )
| heap(sep(lseg(X,Z),Sigma)) )
<=> ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma)))
| ( X = Y )
| heap(sep(lseg(X,Z),Sigma)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV013-0.ax',unfolding_2) ).
tff(38,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ( x1 = x2 )
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ( x1 = x2 )
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ( x1 = x2 )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) )
<=> ( heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ( x1 = x2 )
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| ( x1 = x2 )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ( x1 = x2 )
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| ( x1 = x2 )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) )
<=> ( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ( x1 = x2 )
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| ( x1 = x2 )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Sigma: $i,Z: $i,Y: $i,X: $i] :
( ( X = Y )
| heap(sep(lseg(X,Z),Sigma))
| ~ heap(sep(next(X,Y),sep(lseg(Y,Z),Sigma))) )
| heap(sep(lseg(x1,nil),sep(lseg(x3,nil),emp)))
| ( x1 = x2 )
| ~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ heap(sep(next(x1,x2),sep(lseg(x2,nil),sep(lseg(x3,nil),emp)))),
inference(unit_resolution,[status(thm)],[47,41,31,28]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW423-1 : TPTP v9.0.0. Released v5.2.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 11:42:57 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
% 0.18/0.39 % E exiting
%------------------------------------------------------------------------------