%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC080-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:30:06 AM UTC 2025
% Result : Unsatisfiable 0.56s 0.77s
% Output : Proof 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 60
% Syntax : Number of formulae : 147 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 920 ( 105 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 1422 ( 706 ~; 634 |; 0 &)
% ( 82 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 57 ( 57 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 210 ( 191 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(skaf45_type,type,
skaf45: ( $i * $i ) > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(nil_type,type,
nil: $i ).
tff(frontsegP_type,type,
frontsegP: ( $i * $i ) > $o ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(1,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(6,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(9,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[10,5]) ).
tff(12,plain,
( ( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) )
<=> ( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( frontsegP(sk4,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
( frontsegP(sk4,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_17) ).
tff(15,plain,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ neq(sk4,nil)
| frontsegP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
frontsegP(sk4,sk5),
inference(unit_resolution,[status(thm)],[16,11]) ).
tff(18,plain,
( ( ssList(sk5)
| ~ neq(sk4,nil) )
<=> ( ssList(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
( ssList(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(20,plain,
( ssList(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
ssList(sk5),
inference(unit_resolution,[status(thm)],[20,11]) ).
tff(22,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(24,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ frontsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ frontsegP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
( ( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [V: $i,U: $i] :
( ~ frontsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(V,skaf45(U,V)) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).
tff(31,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ frontsegP(sk4,sk5)
| ( app(sk5,skaf45(sk4,sk5)) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ frontsegP(sk4,sk5)
| ( app(sk5,skaf45(sk4,sk5)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ frontsegP(sk4,sk5)
| ( app(sk5,skaf45(sk4,sk5)) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ frontsegP(sk4,sk5)
| ( app(sk5,skaf45(sk4,sk5)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
app(sk5,skaf45(sk4,sk5)) = sk4,
inference(unit_resolution,[status(thm)],[37,34,24,21,17]) ).
tff(39,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(43,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,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(47,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
app(nil,sk5) = sk5,
inference(unit_resolution,[status(thm)],[48,45,21]) ).
tff(50,plain,
app(app(nil,sk5),skaf45(sk4,sk5)) = app(sk5,skaf45(sk4,sk5)),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
app(app(nil,sk5),skaf45(sk4,sk5)) = sk2,
inference(transitivity,[status(thm)],[50,38,4]) ).
tff(52,plain,
( segmentP(app(app(nil,sk5),skaf45(sk4,sk5)),sk5)
<=> segmentP(sk2,sk5) ),
inference(monotonicity,[status(thm)],[51]) ).
tff(53,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf45(U,V))
<=> ssList(skaf45(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [V: $i,U: $i] : ssList(skaf45(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf45(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
tff(57,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [V: $i,U: $i] : ssList(skaf45(U,V)),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf45(U,V))
| ssList(skaf45(sk4,sk5)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
ssList(skaf45(sk4,sk5)),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
app(app(nil,sk5),skaf45(sk4,sk5)) = sk4,
inference(transitivity,[status(thm)],[50,38]) ).
tff(63,plain,
( ssList(app(app(nil,sk5),skaf45(sk4,sk5)))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ssList(sk4)
<=> ssList(app(app(nil,sk5),skaf45(sk4,sk5))) ),
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
ssList(app(app(nil,sk5),skaf45(sk4,sk5))),
inference(modus_ponens,[status(thm)],[24,64]) ).
tff(66,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(67,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)],[66]) ).
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) )
<=> ! [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(69,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(70,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)],[69]) ).
tff(71,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(72,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(73,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)],[72,71]) ).
tff(74,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)],[73,70]) ).
tff(75,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(76,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)],[75]) ).
tff(77,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)],[76,74]) ).
tff(78,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/sandbox/benchmark/Axioms/SWC001-0.ax',clause173) ).
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) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
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) ),
inference(modus_ponens,[status(thm)],[79,68]) ).
tff(81,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)],[80]) ).
tff(82,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)],[81,67]) ).
tff(83,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(85,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,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(skaf45(sk4,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk4,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk4,sk5)),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(skaf45(sk4,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk4,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk4,sk5)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,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(skaf45(sk4,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk4,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk4,sk5)),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(88,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(skaf45(sk4,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk4,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk4,sk5)),sk5) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ ssList(skaf45(sk4,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk4,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk4,sk5)),sk5) ),
inference(unit_resolution,[status(thm)],[88,85,82,21]) ).
tff(90,plain,
segmentP(app(app(nil,sk5),skaf45(sk4,sk5)),sk5),
inference(unit_resolution,[status(thm)],[89,65,61]) ).
tff(91,plain,
segmentP(sk2,sk5),
inference(modus_ponens,[status(thm)],[90,52]) ).
tff(92,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(94,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) )
<=> ( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ( frontsegP(sk3,sk5)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
( frontsegP(sk3,sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_18) ).
tff(99,plain,
( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ neq(sk4,nil)
| frontsegP(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[99,96]) ).
tff(101,plain,
frontsegP(sk3,sk5),
inference(unit_resolution,[status(thm)],[100,11]) ).
tff(102,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(103,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(104,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ frontsegP(sk3,sk5)
| ( app(sk5,skaf45(sk3,sk5)) = sk3 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ frontsegP(sk3,sk5)
| ( app(sk5,skaf45(sk3,sk5)) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ frontsegP(sk3,sk5)
| ( app(sk5,skaf45(sk3,sk5)) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V)
| ( app(V,skaf45(U,V)) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ frontsegP(sk3,sk5)
| ( app(sk5,skaf45(sk3,sk5)) = sk3 ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
app(sk5,skaf45(sk3,sk5)) = sk3,
inference(unit_resolution,[status(thm)],[107,34,104,21,101]) ).
tff(109,plain,
app(app(nil,sk5),skaf45(sk3,sk5)) = app(sk5,skaf45(sk3,sk5)),
inference(monotonicity,[status(thm)],[49]) ).
tff(110,plain,
app(app(nil,sk5),skaf45(sk3,sk5)) = sk1,
inference(transitivity,[status(thm)],[109,108,95]) ).
tff(111,plain,
( segmentP(app(app(nil,sk5),skaf45(sk3,sk5)),sk5)
<=> segmentP(sk1,sk5) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf45(U,V))
| ssList(skaf45(sk3,sk5)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
ssList(skaf45(sk3,sk5)),
inference(unit_resolution,[status(thm)],[112,59]) ).
tff(114,plain,
app(app(nil,sk5),skaf45(sk3,sk5)) = sk3,
inference(transitivity,[status(thm)],[109,108]) ).
tff(115,plain,
( ssList(app(app(nil,sk5),skaf45(sk3,sk5)))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ssList(sk3)
<=> ssList(app(app(nil,sk5),skaf45(sk3,sk5))) ),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
ssList(app(app(nil,sk5),skaf45(sk3,sk5))),
inference(modus_ponens,[status(thm)],[104,116]) ).
tff(118,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(skaf45(sk3,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk3,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk3,sk5)),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(skaf45(sk3,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk3,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk3,sk5)),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,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(skaf45(sk3,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk3,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk3,sk5)),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,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(skaf45(sk3,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk3,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk3,sk5)),sk5) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( ~ ssList(skaf45(sk3,sk5))
| ~ ssList(app(app(nil,sk5),skaf45(sk3,sk5)))
| segmentP(app(app(nil,sk5),skaf45(sk3,sk5)),sk5) ),
inference(unit_resolution,[status(thm)],[120,85,82,21]) ).
tff(122,plain,
segmentP(app(app(nil,sk5),skaf45(sk3,sk5)),sk5),
inference(unit_resolution,[status(thm)],[121,117,113]) ).
tff(123,plain,
segmentP(sk1,sk5),
inference(modus_ponens,[status(thm)],[122,111]) ).
tff(124,plain,
^ [A: $i] :
refl(( ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
^ [A: $i] :
trans(monotonicity(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(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ neq(sk4,nil) ) )),
rewrite(( ( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(sk4,nil) )
<=> ( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(sk4,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(130,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
( ( ~ neq(sk4,nil)
| neq(sk5,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( neq(sk5,nil)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
( neq(sk5,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
tff(137,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[137,134]) ).
tff(139,plain,
neq(sk5,nil),
inference(unit_resolution,[status(thm)],[138,11]) ).
tff(140,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(monotonicity,[status(thm)],[141]) ).
tff(143,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ) ),
inference(transitivity,[status(thm)],[142,140]) ).
tff(144,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk4,nil)
| ~ segmentP(sk1,A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil) )
| ~ neq(sk4,nil)
| ~ ssList(sk5)
| ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ segmentP(sk1,sk5)
| ~ segmentP(sk2,sk5) ),
inference(unit_resolution,[status(thm)],[145,11,21,139,133]) ).
tff(147,plain,
$false,
inference(unit_resolution,[status(thm)],[146,123,91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SWC080-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.15 % Command : run_E %s %d THM
% 0.12/0.37 % Computer : n012.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Jun 20 08:13:10 EDT 2025
% 0.12/0.37 % CPUTime :
% 0.56/0.77 % SZS status Unsatisfiable
% 0.56/0.77 % SZS output start Proof
% See solution above
% 0.56/0.79 % E exiting
%------------------------------------------------------------------------------