%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC051-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:30:02 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 54 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 207 ( 9 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 295 ( 151 ~; 121 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 30 ( 27 !; 0 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(rearsegP_type,type,
rearsegP: ( $i * $i ) > $o ).
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/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(7,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[7,4]) ).
tff(9,plain,
( ( ~ neq(sk4,nil)
| neq(sk3,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(11,plain,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
neq(sk3,nil),
inference(unit_resolution,[status(thm)],[11,8]) ).
tff(13,plain,
( rearsegP(sk2,sk3)
<=> rearsegP(sk4,sk3) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(14,plain,
( rearsegP(sk4,sk3)
<=> rearsegP(sk2,sk3) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk4,sk3) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
( ~ neq(sk4,nil)
| rearsegP(sk4,sk3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(17,plain,
( ~ neq(sk4,nil)
| rearsegP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
rearsegP(sk4,sk3),
inference(unit_resolution,[status(thm)],[17,8]) ).
tff(19,plain,
rearsegP(sk2,sk3),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(22,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( rearsegP(sk3,sk3)
<=> rearsegP(sk1,sk3) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(27,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| rearsegP(U,U) )
<=> ( ~ ssList(U)
| rearsegP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause59) ).
tff(32,plain,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) ),
inference(modus_ponens,[status(thm)],[33,29]) ).
tff(35,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) )
| ~ ssList(sk3)
| rearsegP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) )
| ~ ssList(sk3)
| rearsegP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) )
| ~ ssList(sk3)
| rearsegP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,U) )
| ~ ssList(sk3)
| rearsegP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
rearsegP(sk3,sk3),
inference(unit_resolution,[status(thm)],[37,34,27]) ).
tff(39,plain,
rearsegP(sk1,sk3),
inference(modus_ponens,[status(thm)],[38,24]) ).
tff(40,plain,
^ [A: $i] :
refl(( ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [A: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) )),
rewrite(( ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(46,plain,
! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
| ~ ssList(sk3)
| ~ rearsegP(sk2,sk3)
| ~ neq(sk3,nil)
| ~ rearsegP(sk1,sk3) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
| ~ ssList(sk3)
| ~ rearsegP(sk2,sk3)
| ~ neq(sk3,nil)
| ~ rearsegP(sk1,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
| ~ ssList(sk3)
| ~ rearsegP(sk2,sk3)
| ~ neq(sk3,nil)
| ~ rearsegP(sk1,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ rearsegP(sk1,A) )
| ~ ssList(sk3)
| ~ rearsegP(sk2,sk3)
| ~ neq(sk3,nil)
| ~ rearsegP(sk1,sk3) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ rearsegP(sk2,sk3)
| ~ neq(sk3,nil)
| ~ rearsegP(sk1,sk3) ),
inference(unit_resolution,[status(thm)],[52,27,49]) ).
tff(54,plain,
$false,
inference(unit_resolution,[status(thm)],[53,39,19,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SWC051-1 : TPTP v9.0.0. Released v2.4.0.
% 0.01/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n007.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 08:09:35 EDT 2025
% 0.11/0.33 % 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
%------------------------------------------------------------------------------