%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC328-1 : 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 05:30:54 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 45 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 17 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 85 ( 40 ~; 29 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 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 : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 13 ( 12 !; 0 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(equalelemsP_type,type,
equalelemsP: $i > $o ).
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_7) ).
tff(3,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( nil = sk3 )
<=> ( nil = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
nil = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(7,plain,
nil = sk3,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
nil = sk1,
inference(transitivity,[status(thm)],[7,4]) ).
tff(9,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(11,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( segmentP(sk4,nil)
<=> segmentP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[12,8]) ).
tff(14,plain,
( segmentP(sk2,sk1)
<=> segmentP(sk4,nil) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk4,nil) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
sk3 = nil,
inference(symmetry,[status(thm)],[7]) ).
tff(17,plain,
sk1 = nil,
inference(transitivity,[status(thm)],[3,16]) ).
tff(18,plain,
( equalelemsP(sk1)
<=> equalelemsP(nil) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( equalelemsP(nil)
<=> equalelemsP(sk1) ),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( equalelemsP(nil)
<=> equalelemsP(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause1) ).
tff(22,plain,
equalelemsP(nil),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
equalelemsP(sk1),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
( ( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ segmentP(sk2,sk1)
| ~ equalelemsP(sk1) )
<=> ( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
( ~ segmentP(sk2,sk1)
| ~ equalelemsP(sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(27,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
( ~ equalelemsP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[27,24]) ).
tff(29,plain,
~ segmentP(sk2,sk1),
inference(unit_resolution,[status(thm)],[28,23]) ).
tff(30,plain,
~ segmentP(sk4,nil),
inference(modus_ponens,[status(thm)],[29,15]) ).
tff(31,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(33,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| segmentP(U,nil) )
<=> ( ~ ssList(U)
| segmentP(U,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
tff(38,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
| ~ ssList(sk4)
| segmentP(sk4,nil) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
segmentP(sk4,nil),
inference(unit_resolution,[status(thm)],[43,40,33]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWC328-1 : 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 09:03:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.42 % SZS status Unsatisfiable
% 0.19/0.42 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------