%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC083-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:30:07 AM UTC 2025
% Result : Unsatisfiable 1.46s 1.65s
% Output : Proof 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 95
% Syntax : Number of formulae : 250 ( 83 unt; 0 typ; 0 def)
% Number of atoms : 1511 ( 214 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 2338 (1141 ~;1066 |; 0 &)
% ( 131 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 64 ( 64 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 : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 418 ( 386 !; 0 ?; 418 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk7_type,type,
sk7: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/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,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(7,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(12,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(17,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[17,14,7]) ).
tff(19,plain,
( ( app(app(sk5,sk6),sk7) = sk3 )
<=> ( app(app(sk5,sk6),sk7) = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
app(app(sk5,sk6),sk7) = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(21,plain,
app(app(sk5,sk6),sk7) = sk3,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
app(app(app(sk5,sk6),sk7),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
app(app(app(sk5,sk6),sk7),nil) = sk1,
inference(transitivity,[status(thm)],[22,18,4]) ).
tff(24,plain,
( segmentP(app(app(app(sk5,sk6),sk7),nil),sk7)
<=> segmentP(sk1,sk7) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
app(app(app(sk5,sk6),sk7),nil) = sk3,
inference(transitivity,[status(thm)],[22,18]) ).
tff(26,plain,
( ssList(app(app(app(sk5,sk6),sk7),nil))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ssList(sk3)
<=> ssList(app(app(app(sk5,sk6),sk7),nil)) ),
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
ssList(app(app(app(sk5,sk6),sk7),nil)),
inference(modus_ponens,[status(thm)],[7,27]) ).
tff(29,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(31,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(34,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(36,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ssList(app(V,U)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
tff(41,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ssList(app(sk5,sk6)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ssList(app(sk5,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ssList(sk6)
| ssList(app(sk5,sk6))
| ~ ssList(sk5) )
<=> ( ~ ssList(sk5)
| ~ ssList(sk6)
| ssList(app(sk5,sk6)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ssList(app(sk5,sk6))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ssList(app(sk5,sk6)) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ssList(app(sk5,sk6))
| ~ ssList(sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ssList(app(sk5,sk6)) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ssList(app(sk5,sk6))
| ~ ssList(sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ssList(app(sk5,sk6)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
ssList(app(sk5,sk6)),
inference(unit_resolution,[status(thm)],[50,44,34,31]) ).
tff(52,plain,
( ssList(sk7)
<=> ssList(sk7) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(54,plain,
ssList(sk7),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
^ [W: $i,V: $i,U: $i] :
rewrite(( ( ~ ssList(app(app(U,V),W))
| ~ ssList(U)
| ~ ssList(V)
| segmentP(app(app(U,V),W),V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(app(U,V),W))
| ~ ssList(U)
| ~ ssList(V)
| segmentP(app(app(U,V),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(app(U,V),W))
| ~ ssList(U)
| ~ ssList(V)
| segmentP(app(app(U,V),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(app(U,V),W))
| ~ ssList(U)
| ~ ssList(V)
| segmentP(app(app(U,V),W),V)
| ~ ssList(W) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(61,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(app(app(U,V),W))
| ~ ssList(U)
| ~ ssList(V)
| segmentP(app(app(U,V),W),V)
| ~ ssList(W) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(62,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(app(app(U,V),W))
| ~ ssList(U)
| ~ ssList(V)
| segmentP(app(app(U,V),W),V)
| ~ ssList(W) ) ),
inference(transitivity,[status(thm)],[61,60]) ).
tff(63,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ) ),
inference(transitivity,[status(thm)],[62,59]) ).
tff(64,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ( app(app(U,V),W) != X )
| ~ ssList(W) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(U,V),W) != X )
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
( ( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| segmentP(X,V)
| ~ ssList(W)
| ( app(app(U,V),W) != X ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ( app(app(U,V),W) != X )
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| segmentP(X,V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
tff(68,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ),
inference(modus_ponens,[status(thm)],[68,57]) ).
tff(70,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) ),
inference(modus_ponens,[status(thm)],[70,56]) ).
tff(72,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(74,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(app(sk5,sk6))
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(app(sk5,sk6))
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( ~ ssList(app(sk5,sk6))
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) )
<=> ( ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(app(sk5,sk6))
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(app(sk5,sk6))
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(app(sk5,sk6))
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(app(sk5,sk6))
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(app(sk5,sk6))
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(app(sk5,sk6))
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ~ ssList(app(sk5,sk6))
| ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ ssList(app(app(app(sk5,sk6),sk7),nil))
| segmentP(app(app(app(sk5,sk6),sk7),nil),sk7) ),
inference(unit_resolution,[status(thm)],[80,74,71,54,51]) ).
tff(82,plain,
segmentP(app(app(app(sk5,sk6),sk7),nil),sk7),
inference(unit_resolution,[status(thm)],[81,28]) ).
tff(83,plain,
segmentP(sk1,sk7),
inference(modus_ponens,[status(thm)],[82,24]) ).
tff(84,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(86,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[86]) ).
tff(88,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,axiom,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
tff(90,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
app(sk4,nil) = sk4,
inference(unit_resolution,[status(thm)],[93,14,90]) ).
tff(95,plain,
( ( app(sk5,sk7) = sk4 )
<=> ( app(sk5,sk7) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,axiom,
app(sk5,sk7) = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(97,plain,
app(sk5,sk7) = sk4,
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
app(app(sk5,sk7),nil) = app(sk4,nil),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
app(app(sk5,sk7),nil) = sk2,
inference(transitivity,[status(thm)],[98,94,87]) ).
tff(100,plain,
( segmentP(app(app(sk5,sk7),nil),sk7)
<=> segmentP(sk2,sk7) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,plain,
app(app(sk5,sk7),nil) = sk4,
inference(transitivity,[status(thm)],[98,94]) ).
tff(102,plain,
( ssList(app(app(sk5,sk7),nil))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ssList(sk4)
<=> ssList(app(app(sk5,sk7),nil)) ),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
ssList(app(app(sk5,sk7),nil)),
inference(modus_ponens,[status(thm)],[90,103]) ).
tff(105,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) )
<=> ( ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) ) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) ) ),
inference(transitivity,[status(thm)],[107,105]) ).
tff(109,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
( ~ ssList(app(app(sk5,sk7),nil))
| segmentP(app(app(sk5,sk7),nil),sk7) ),
inference(unit_resolution,[status(thm)],[110,74,71,34,54]) ).
tff(112,plain,
segmentP(app(app(sk5,sk7),nil),sk7),
inference(unit_resolution,[status(thm)],[111,104]) ).
tff(113,plain,
segmentP(sk2,sk7),
inference(modus_ponens,[status(thm)],[112,100]) ).
tff(114,plain,
^ [A: $i] :
refl(( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
inference(bind,[status(th)],[]) ).
tff(115,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[114]) ).
tff(116,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
^ [A: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
rewrite(( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
inference(bind,[status(th)],[]) ).
tff(118,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(120,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk7)
| ~ segmentP(sk2,sk7)
| ~ neq(sk7,nil)
| ~ segmentP(sk1,sk7) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk7)
| ~ segmentP(sk2,sk7)
| ~ neq(sk7,nil)
| ~ segmentP(sk1,sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk7)
| ~ segmentP(sk2,sk7)
| ~ neq(sk7,nil)
| ~ segmentP(sk1,sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk7)
| ~ segmentP(sk2,sk7)
| ~ neq(sk7,nil)
| ~ segmentP(sk1,sk7) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ segmentP(sk2,sk7)
| ~ neq(sk7,nil)
| ~ segmentP(sk1,sk7) ),
inference(unit_resolution,[status(thm)],[126,123,54]) ).
tff(128,plain,
~ neq(sk7,nil),
inference(unit_resolution,[status(thm)],[127,113,83]) ).
tff(129,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(133,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[132]) ).
tff(134,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(135,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[135,131]) ).
tff(137,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[136]) ).
tff(138,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[137,130]) ).
tff(139,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ( sk7 = nil )
| neq(sk7,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ( sk7 = nil )
| neq(sk7,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ( sk7 = nil )
| neq(sk7,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(141,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk7)
| ( sk7 = nil )
| neq(sk7,nil) ),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
sk7 = nil,
inference(unit_resolution,[status(thm)],[141,74,138,54,128]) ).
tff(143,plain,
nil = sk7,
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
^ [W: $i,V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
^ [W: $i,V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
<=> ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause149) ).
tff(150,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ( ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) )
<=> ( ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(156,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) ) ),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) ) ),
inference(transitivity,[status(thm)],[156,154]) ).
tff(158,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk7)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ( app(app(W,V),U) = app(W,app(V,U)) ) )
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ( app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)) ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
app(app(sk5,sk6),sk7) = app(sk5,app(sk6,sk7)),
inference(unit_resolution,[status(thm)],[159,153,34,31,54]) ).
tff(161,plain,
app(sk5,app(sk6,sk7)) = app(app(sk5,sk6),sk7),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(163,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(166,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(171,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
app(nil,sk5) = sk5,
inference(unit_resolution,[status(thm)],[171,168,34]) ).
tff(173,plain,
app(app(nil,sk5),app(sk6,sk7)) = app(sk5,app(sk6,sk7)),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
app(app(nil,sk5),app(sk6,sk7)) = sk1,
inference(transitivity,[status(thm)],[173,161,21,4]) ).
tff(175,plain,
( segmentP(app(app(nil,sk5),app(sk6,sk7)),sk5)
<=> segmentP(sk1,sk5) ),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ~ ssList(sk7)
| ssList(app(sk6,sk7)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ~ ssList(sk7)
| ssList(app(sk6,sk7)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(177,plain,
( ( ~ ssList(sk7)
| ssList(app(sk6,sk7))
| ~ ssList(sk6) )
<=> ( ~ ssList(sk6)
| ~ ssList(sk7)
| ssList(app(sk6,sk7)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ssList(app(sk6,sk7))
| ~ ssList(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ~ ssList(sk7)
| ssList(app(sk6,sk7)) ) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ssList(app(sk6,sk7))
| ~ ssList(sk6) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ~ ssList(sk7)
| ssList(app(sk6,sk7)) ) ),
inference(transitivity,[status(thm)],[178,176]) ).
tff(180,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk7)
| ssList(app(sk6,sk7))
| ~ ssList(sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ssList(app(V,U))
| ~ ssList(V) )
| ~ ssList(sk6)
| ~ ssList(sk7)
| ssList(app(sk6,sk7)) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
ssList(app(sk6,sk7)),
inference(unit_resolution,[status(thm)],[181,44,31,54]) ).
tff(183,plain,
app(app(nil,sk5),app(sk6,sk7)) = sk3,
inference(transitivity,[status(thm)],[173,161,21]) ).
tff(184,plain,
( ssList(app(app(nil,sk5),app(sk6,sk7)))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ssList(sk3)
<=> ssList(app(app(nil,sk5),app(sk6,sk7))) ),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
ssList(app(app(nil,sk5),app(sk6,sk7))),
inference(modus_ponens,[status(thm)],[7,185]) ).
tff(187,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(app(sk6,sk7))
| ~ ssList(app(app(nil,sk5),app(sk6,sk7)))
| segmentP(app(app(nil,sk5),app(sk6,sk7)),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(app(sk6,sk7))
| ~ ssList(app(app(nil,sk5),app(sk6,sk7)))
| segmentP(app(app(nil,sk5),app(sk6,sk7)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(app(sk6,sk7))
| ~ ssList(app(app(nil,sk5),app(sk6,sk7)))
| segmentP(app(app(nil,sk5),app(sk6,sk7)),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(app(sk6,sk7))
| ~ ssList(app(app(nil,sk5),app(sk6,sk7)))
| segmentP(app(app(nil,sk5),app(sk6,sk7)),sk5) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
( ~ ssList(app(sk6,sk7))
| ~ ssList(app(app(nil,sk5),app(sk6,sk7)))
| segmentP(app(app(nil,sk5),app(sk6,sk7)),sk5) ),
inference(unit_resolution,[status(thm)],[189,74,71,34]) ).
tff(191,plain,
segmentP(app(app(nil,sk5),app(sk6,sk7)),sk5),
inference(unit_resolution,[status(thm)],[190,186,182]) ).
tff(192,plain,
segmentP(sk1,sk5),
inference(modus_ponens,[status(thm)],[191,175]) ).
tff(193,plain,
app(app(nil,sk5),sk7) = app(sk5,sk7),
inference(monotonicity,[status(thm)],[172]) ).
tff(194,plain,
app(app(nil,sk5),sk7) = sk2,
inference(transitivity,[status(thm)],[193,97,87]) ).
tff(195,plain,
( segmentP(app(app(nil,sk5),sk7),sk5)
<=> segmentP(sk2,sk5) ),
inference(monotonicity,[status(thm)],[194]) ).
tff(196,plain,
app(app(nil,sk5),sk7) = sk4,
inference(transitivity,[status(thm)],[193,97]) ).
tff(197,plain,
( ssList(app(app(nil,sk5),sk7))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
( ssList(sk4)
<=> ssList(app(app(nil,sk5),sk7)) ),
inference(symmetry,[status(thm)],[197]) ).
tff(199,plain,
ssList(app(app(nil,sk5),sk7)),
inference(modus_ponens,[status(thm)],[90,198]) ).
tff(200,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(nil,sk5),sk7))
| segmentP(app(app(nil,sk5),sk7),sk5) )
<=> ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(nil,sk5),sk7))
| segmentP(app(app(nil,sk5),sk7),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(nil,sk5),sk7))
| segmentP(app(app(nil,sk5),sk7),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(202,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk7)
| ~ ssList(app(app(nil,sk5),sk7))
| segmentP(app(app(nil,sk5),sk7),sk5) ),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
( ~ ssList(app(app(nil,sk5),sk7))
| segmentP(app(app(nil,sk5),sk7),sk5) ),
inference(unit_resolution,[status(thm)],[202,74,71,34,54]) ).
tff(204,plain,
segmentP(app(app(nil,sk5),sk7),sk5),
inference(unit_resolution,[status(thm)],[203,199]) ).
tff(205,plain,
segmentP(sk2,sk5),
inference(modus_ponens,[status(thm)],[204,195]) ).
tff(206,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(207,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(208,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ),
inference(modus_ponens,[status(thm)],[207,206]) ).
tff(209,plain,
( ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ),
inference(unit_resolution,[status(thm)],[208,123,34]) ).
tff(210,plain,
~ neq(sk5,nil),
inference(unit_resolution,[status(thm)],[209,205,192]) ).
tff(211,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(212,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(213,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[212,211]) ).
tff(214,plain,
sk5 = nil,
inference(unit_resolution,[status(thm)],[213,74,138,34,210]) ).
tff(215,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(216,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) ),
inference(modus_ponens,[status(thm)],[216,215]) ).
tff(218,plain,
app(sk5,nil) = sk5,
inference(unit_resolution,[status(thm)],[217,14,34]) ).
tff(219,plain,
app(sk5,sk7) = app(sk5,nil),
inference(monotonicity,[status(thm)],[142]) ).
tff(220,plain,
sk4 = app(sk5,sk7),
inference(symmetry,[status(thm)],[97]) ).
tff(221,plain,
sk2 = sk7,
inference(transitivity,[status(thm)],[86,220,219,218,214,143]) ).
tff(222,plain,
( neq(sk2,nil)
<=> neq(sk7,sk7) ),
inference(monotonicity,[status(thm)],[221,143]) ).
tff(223,plain,
( neq(sk7,sk7)
<=> neq(sk2,nil) ),
inference(symmetry,[status(thm)],[222]) ).
tff(224,plain,
( ~ neq(sk7,sk7)
<=> ~ neq(sk2,nil) ),
inference(monotonicity,[status(thm)],[223]) ).
tff(225,plain,
^ [V: $i] :
refl(( ( ~ ssList(V)
| ~ neq(V,V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(226,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[225]) ).
tff(227,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(228,plain,
^ [V: $i] :
rewrite(( ( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(229,plain,
( ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[228]) ).
tff(230,plain,
( ! [V: $i,U: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(231,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(232,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(transitivity,[status(thm)],[231,230]) ).
tff(233,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(transitivity,[status(thm)],[232,229]) ).
tff(234,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(235,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[234]) ).
tff(236,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(transitivity,[status(thm)],[235,233]) ).
tff(237,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(238,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[238,227]) ).
tff(240,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(skolemize,[status(sab)],[239]) ).
tff(241,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[240,226]) ).
tff(242,plain,
( ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk7)
| ~ neq(sk7,sk7) )
<=> ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk7)
| ~ neq(sk7,sk7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(243,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk7)
| ~ neq(sk7,sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(244,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk7)
| ~ neq(sk7,sk7) ),
inference(modus_ponens,[status(thm)],[243,242]) ).
tff(245,plain,
~ neq(sk7,sk7),
inference(unit_resolution,[status(thm)],[244,241,54]) ).
tff(246,plain,
~ neq(sk2,nil),
inference(modus_ponens,[status(thm)],[245,224]) ).
tff(247,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(248,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(249,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[248,247]) ).
tff(250,plain,
$false,
inference(unit_resolution,[status(thm)],[249,246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC083-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n008.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:15:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.46/1.65 % SZS status Unsatisfiable
% 1.46/1.65 % SZS output start Proof
% See solution above
% 1.53/1.68 % E exiting
%------------------------------------------------------------------------------