%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC102-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : 8
% Number of leaves : 17
% Syntax : Number of formulae : 46 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 91 ( 17 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 86 ( 42 ~; 30 |; 0 &)
% ( 14 <=>; 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(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $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,
sk3 = sk1,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(7,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( sk4 = sk3 )
<=> ( sk4 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
sk4 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(11,plain,
sk4 = sk3,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
sk3 = sk4,
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
sk3 = sk2,
inference(transitivity,[status(thm)],[12,8]) ).
tff(14,plain,
( frontsegP(sk3,sk3)
<=> frontsegP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[13,4]) ).
tff(15,plain,
( frontsegP(sk2,sk1)
<=> frontsegP(sk3,sk3) ),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
( ~ frontsegP(sk2,sk1)
<=> ~ frontsegP(sk3,sk3) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
sk2 = sk1,
inference(transitivity,[status(thm)],[7,11,4]) ).
tff(18,plain,
( neq(sk2,nil)
<=> neq(sk1,nil) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(21,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
neq(sk1,nil),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
( ( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) )
<=> ( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(25,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ neq(sk1,nil)
| ~ frontsegP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[28,23]) ).
tff(30,plain,
~ frontsegP(sk2,sk1),
inference(unit_resolution,[status(thm)],[29,22]) ).
tff(31,plain,
~ frontsegP(sk3,sk3),
inference(modus_ponens,[status(thm)],[30,16]) ).
tff(32,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(34,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| frontsegP(U,U) )
<=> ( ~ ssList(U)
| frontsegP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause61) ).
tff(39,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| frontsegP(U,U) )
| ~ ssList(sk3)
| frontsegP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
frontsegP(sk3,sk3),
inference(unit_resolution,[status(thm)],[44,41,34]) ).
tff(46,plain,
$false,
inference(unit_resolution,[status(thm)],[45,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC102-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 08:19:07 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.44 % E exiting
%------------------------------------------------------------------------------