%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC039-1 : 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 05:30:00 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 36
% Syntax : Number of formulae : 85 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 535 ( 84 equ)
% Maximal formula atoms : 23 ( 6 avg)
% Number of connectives : 797 ( 382 ~; 364 |; 0 &)
% ( 51 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 35 ( 35 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 118 ( 107 !; 0 ?; 118 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk7_type,type,
sk7: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( nil = sk2 )
<=> ( nil = sk2 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
nil = sk2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
tff(3,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sk2 = nil,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
tff(7,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(11,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ( nil != sk1 )
<=> ( nil != sk3 ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(16,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
nil != sk3,
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
( ( ( nil = sk3 )
| ( app(app(sk6,sk3),sk7) = sk4 ) )
<=> ( ( nil = sk3 )
| ( app(app(sk6,sk3),sk7) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ( app(app(sk6,sk3),sk7) = sk4 )
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| ( app(app(sk6,sk3),sk7) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( ( app(app(sk6,sk3),sk7) = sk4 )
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_20) ).
tff(21,plain,
( ( nil = sk3 )
| ( app(app(sk6,sk3),sk7) = sk4 ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
( ( nil = sk3 )
| ( app(app(sk6,sk3),sk7) = sk4 ) ),
inference(modus_ponens,[status(thm)],[21,18]) ).
tff(23,plain,
app(app(sk6,sk3),sk7) = sk4,
inference(unit_resolution,[status(thm)],[22,17]) ).
tff(24,plain,
app(app(sk6,sk3),sk7) = nil,
inference(transitivity,[status(thm)],[23,8,4]) ).
tff(25,plain,
( segmentP(app(app(sk6,sk3),sk7),sk3)
<=> segmentP(nil,sk3) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( segmentP(nil,sk3)
<=> segmentP(app(app(sk6,sk3),sk7),sk3) ),
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
( ~ segmentP(nil,sk3)
<=> ~ segmentP(app(app(sk6,sk3),sk7),sk3) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(30,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [U: $i] :
trans(monotonicity(rewrite(( ( ~ segmentP(nil,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ segmentP(nil,U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
( ( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [U: $i] :
( ~ segmentP(nil,U)
| ~ ssList(U)
| ( nil = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause80) ).
tff(37,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ssList(sk3)
| ( nil = sk3 )
| ~ segmentP(nil,sk3) )
<=> ( ( nil = sk3 )
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ segmentP(nil,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ segmentP(nil,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ~ ssList(sk3)
| ( nil = sk3 )
| ~ segmentP(nil,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( nil = U )
| ~ segmentP(nil,U) )
| ( nil = sk3 )
| ~ ssList(sk3)
| ~ segmentP(nil,sk3) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
~ segmentP(nil,sk3),
inference(unit_resolution,[status(thm)],[46,40,30,17]) ).
tff(48,plain,
~ segmentP(app(app(sk6,sk3),sk7),sk3),
inference(modus_ponens,[status(thm)],[47,27]) ).
tff(49,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(53,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[58,55,30]) ).
tff(60,plain,
( ( ssList(sk7)
| ( nil = sk3 ) )
<=> ( ssList(sk7)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
( ssList(sk7)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
tff(62,plain,
( ssList(sk7)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
ssList(sk7),
inference(unit_resolution,[status(thm)],[62,17]) ).
tff(64,plain,
( ( ssList(sk6)
| ( nil = sk3 ) )
<=> ( ssList(sk6)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
( ssList(sk6)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
tff(66,plain,
( ssList(sk6)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
ssList(sk6),
inference(unit_resolution,[status(thm)],[66,17]) ).
tff(68,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ segmentP(U,V)
| ~ ssList(W) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) ) )),
rewrite(( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause172) ).
tff(74,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[76,69]) ).
tff(78,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3)
| ~ ssList(sk7) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3)
| ~ ssList(sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3)
| ~ ssList(sk7) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk6)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3)
| ~ ssList(sk7) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(sk7)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk6,sk3),sk7),sk3) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
segmentP(app(app(sk6,sk3),sk7),sk3),
inference(unit_resolution,[status(thm)],[83,77,30,67,63,59]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC039-1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n003.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 08:06:09 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------