%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC103-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:30:10 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 31 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 58 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 49 ( 22 ~; 15 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(frontsegP_type,type,
frontsegP: ( $i * $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(sk3,nil)
<=> neq(sk1,nil) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(8,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(12,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
( ( ~ neq(sk4,nil)
| neq(sk3,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(16,plain,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
neq(sk3,nil),
inference(unit_resolution,[status(thm)],[16,13]) ).
tff(18,plain,
neq(sk1,nil),
inference(modus_ponens,[status(thm)],[17,5]) ).
tff(19,plain,
( frontsegP(sk2,sk1)
<=> frontsegP(sk4,sk3) ),
inference(monotonicity,[status(thm)],[8,3]) ).
tff(20,plain,
( frontsegP(sk4,sk3)
<=> frontsegP(sk2,sk1) ),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
( ( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) )
<=> ( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(23,plain,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
frontsegP(sk4,sk3),
inference(unit_resolution,[status(thm)],[23,13]) ).
tff(25,plain,
frontsegP(sk2,sk1),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) )
<=> ( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) )
<=> ( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(29,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil) ),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
$false,
inference(unit_resolution,[status(thm)],[30,25,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC103-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.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 08:19:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------