%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC044-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:30:01 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 26
% Syntax : Number of formulae : 58 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 304 ( 62 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 446 ( 215 ~; 200 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 15 ( 15 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 : 55 ( 50 !; 0 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
tff(rearsegP_type,type,
rearsegP: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(1,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(3,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| rearsegP(U,nil) )
<=> ( ~ ssList(U)
| rearsegP(U,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause58) ).
tff(8,plain,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) )
| ~ ssList(sk3)
| rearsegP(sk3,nil) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) )
| ~ ssList(sk3)
| rearsegP(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) )
| ~ ssList(sk3)
| rearsegP(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(13,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| rearsegP(U,nil) )
| ~ ssList(sk3)
| rearsegP(sk3,nil) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
rearsegP(sk3,nil),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(17,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
( ( nil = sk2 )
<=> ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
nil = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(20,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
nil = sk4,
inference(transitivity,[status(thm)],[20,17]) ).
tff(22,plain,
( rearsegP(nil,sk3)
<=> rearsegP(sk4,sk3) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( rearsegP(sk4,sk3)
<=> rearsegP(nil,sk3) ),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( rearsegP(sk4,sk3)
<=> rearsegP(sk4,sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
rearsegP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(26,plain,
rearsegP(sk4,sk3),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
rearsegP(nil,sk3),
inference(modus_ponens,[status(thm)],[26,23]) ).
tff(28,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(30,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ( nil = sk3 )
<=> ( nil = sk1 ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(symmetry,[status(thm)],[32]) ).
tff(34,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(37,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) )),
( ( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(U)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) )),
( ( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) )),
( ( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) )),
( ( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [V: $i,U: $i] :
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [V: $i,U: $i] :
( ~ rearsegP(U,V)
| ~ rearsegP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause128) ).
tff(45,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(51,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ssList(sk3)
| ~ ssList(nil)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) ) ),
inference(monotonicity,[status(thm)],[53]) ).
tff(55,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(sk3)
| ~ ssList(nil)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ rearsegP(nil,sk3)
| ~ rearsegP(sk3,nil) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,51,48,3,38,27,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC044-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 08:06:39 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
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------