%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC038-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:29:59 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 44 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 162 ( 63 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 204 ( 94 ~; 88 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 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 : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $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_6) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( nil = sk2 )
<=> ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
nil = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(6,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
nil = sk4,
inference(transitivity,[status(thm)],[6,3]) ).
tff(8,plain,
( frontsegP(nil,sk3)
<=> frontsegP(sk4,sk3) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( frontsegP(sk4,sk3)
<=> frontsegP(nil,sk3) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(12,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(17,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[17,14]) ).
tff(19,plain,
( ( ( nil = sk3 )
| frontsegP(sk4,sk3) )
<=> ( ( nil = sk3 )
| frontsegP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( ( nil = sk3 )
| frontsegP(sk4,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(21,plain,
( ( nil = sk3 )
| frontsegP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
frontsegP(sk4,sk3),
inference(unit_resolution,[status(thm)],[21,18]) ).
tff(23,plain,
frontsegP(nil,sk3),
inference(modus_ponens,[status(thm)],[22,9]) ).
tff(24,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(26,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ frontsegP(nil,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ frontsegP(nil,U) ) )),
( ( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ frontsegP(nil,U)
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ frontsegP(nil,U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) )),
( ( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [U: $i] :
( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,axiom,
! [U: $i] :
( ~ frontsegP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause84) ).
tff(33,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(skolemize,[status(sab)],[34]) ).
tff(36,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ~ frontsegP(nil,sk3) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ frontsegP(nil,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ frontsegP(nil,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ frontsegP(nil,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ frontsegP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ frontsegP(nil,sk3),
inference(unit_resolution,[status(thm)],[42,36,26,18]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC038-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 08:06:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% See solution above
% 0.20/0.43 % E exiting
%------------------------------------------------------------------------------