%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC050-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 0.21s 0.45s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 59 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 310 ( 8 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 487 ( 250 ~; 206 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 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 : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 21 ( 19 !; 0 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(rearsegP_type,type,
rearsegP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $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,
( rearsegP(sk1,sk5)
<=> rearsegP(sk3,sk5) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( rearsegP(sk3,sk5)
<=> rearsegP(sk1,sk5) ),
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,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(13,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[14,9]) ).
tff(16,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ( rearsegP(sk3,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
( rearsegP(sk3,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(19,plain,
( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ neq(sk4,nil)
| rearsegP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
rearsegP(sk3,sk5),
inference(unit_resolution,[status(thm)],[20,15]) ).
tff(22,plain,
rearsegP(sk1,sk5),
inference(modus_ponens,[status(thm)],[21,5]) ).
tff(23,plain,
( rearsegP(sk2,sk5)
<=> rearsegP(sk4,sk5) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(24,plain,
( rearsegP(sk4,sk5)
<=> rearsegP(sk2,sk5) ),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( rearsegP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
( rearsegP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(28,plain,
( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ~ neq(sk4,nil)
| rearsegP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[28,25]) ).
tff(30,plain,
rearsegP(sk4,sk5),
inference(unit_resolution,[status(thm)],[29,15]) ).
tff(31,plain,
rearsegP(sk2,sk5),
inference(modus_ponens,[status(thm)],[30,24]) ).
tff(32,plain,
^ [A: $i] :
refl(( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,plain,
^ [A: $i] :
trans(monotonicity(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(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssList(A)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ rearsegP(sk2,A)
| ~ rearsegP(sk1,A)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(38,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( neq(sk5,nil)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(45,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[45,42]) ).
tff(47,plain,
neq(sk5,nil),
inference(unit_resolution,[status(thm)],[46,15]) ).
tff(48,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
( ssList(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(50,plain,
( ssList(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
ssList(sk5),
inference(unit_resolution,[status(thm)],[50,15]) ).
tff(52,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ rearsegP(sk1,A)
| ~ rearsegP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5)
| ~ neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ rearsegP(sk1,sk5)
| ~ rearsegP(sk2,sk5) ),
inference(unit_resolution,[status(thm)],[57,15,51,47,41]) ).
tff(59,plain,
$false,
inference(unit_resolution,[status(thm)],[58,31,22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC050-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.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 08:06:35 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.21/0.45 % SZS status Unsatisfiable
% 0.21/0.45 % SZS output start Proof
% See solution above
% 0.21/0.47 % E exiting
%------------------------------------------------------------------------------