%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC373-1 : 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 05:31:03 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 42
% Syntax : Number of formulae : 95 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 616 ( 69 equ)
% Maximal formula atoms : 23 ( 6 avg)
% Number of connectives : 934 ( 456 ~; 421 |; 0 &)
% ( 57 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 43 ( 43 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 172 ( 156 !; 0 ?; 172 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(skaf46_type,type,
skaf46: ( $i * $i ) > $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(rearsegP_type,type,
rearsegP: ( $i * $i ) > $o ).
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,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
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,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
tff(11,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(16,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,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(20,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
app(sk4,nil) = sk4,
inference(unit_resolution,[status(thm)],[21,18,11]) ).
tff(23,plain,
( rearsegP(sk4,sk3)
<=> rearsegP(sk4,sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
rearsegP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(25,plain,
rearsegP(sk4,sk3),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(28,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ~ rearsegP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ rearsegP(U,V) ) )),
( ( ~ rearsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ~ rearsegP(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ~ rearsegP(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V) ) )),
( ( ~ rearsegP(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V) ) )),
( ( ~ rearsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(skaf46(U,V),V) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ) )),
( ( ~ rearsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(skaf46(U,V),V) = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V: $i,U: $i] :
( ~ rearsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(skaf46(U,V),V) = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V: $i,U: $i] :
( ~ rearsegP(U,V)
| ~ ssList(V)
| ~ ssList(U)
| ( app(skaf46(U,V),V) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).
tff(35,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk3)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk4)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk4)
| ~ ssList(sk3)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V)
| ( app(skaf46(U,V),V) = U ) )
| ~ ssList(sk3)
| ~ ssList(sk4)
| ~ rearsegP(sk4,sk3)
| ( app(skaf46(sk4,sk3),sk3) = sk4 ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
app(skaf46(sk4,sk3),sk3) = sk4,
inference(unit_resolution,[status(thm)],[44,38,28,11,25]) ).
tff(46,plain,
app(app(skaf46(sk4,sk3),sk3),nil) = app(sk4,nil),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
app(app(skaf46(sk4,sk3),sk3),nil) = sk2,
inference(transitivity,[status(thm)],[46,22,8]) ).
tff(48,plain,
( segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
<=> segmentP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[47,4]) ).
tff(49,plain,
( segmentP(sk2,sk1)
<=> segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3) ),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk2,sk1) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
~ segmentP(sk2,sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(53,plain,
~ segmentP(sk2,sk1),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3),
inference(modus_ponens,[status(thm)],[53,50]) ).
tff(55,plain,
^ [V: $i,U: $i] :
refl(( ssList(skaf46(U,V))
<=> ssList(skaf46(U,V)) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V: $i,U: $i] : ssList(skaf46(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf46(U,V)) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [V: $i,U: $i] : ssList(skaf46(U,V))
<=> ! [V: $i,U: $i] : ssList(skaf46(U,V)) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
! [V: $i,U: $i] : ssList(skaf46(U,V)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
tff(59,plain,
! [V: $i,U: $i] : ssList(skaf46(U,V)),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [V: $i,U: $i] : ssList(skaf46(U,V)),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [V: $i,U: $i] : ssList(skaf46(U,V)),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
( ~ ! [V: $i,U: $i] : ssList(skaf46(U,V))
| ssList(skaf46(sk4,sk3)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
ssList(skaf46(sk4,sk3)),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(68,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,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(72,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[73,70,28]) ).
tff(75,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(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) )
<=> ! [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)],[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) )
<=> ! [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(78,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(79,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)],[78]) ).
tff(80,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(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) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
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) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
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) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,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)],[83,76]) ).
tff(85,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(87,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,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(nil)
| ~ ssList(sk3)
| ~ ssList(skaf46(sk4,sk3))
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ segmentP(sk3,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(nil)
| ~ ssList(sk3)
| ~ ssList(skaf46(sk4,sk3))
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ ssList(skaf46(sk4,sk3))
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ ssList(nil) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(skaf46(sk4,sk3))
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,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(skaf46(sk4,sk3))
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ ssList(nil) )
<=> ( ~ ! [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(nil)
| ~ ssList(sk3)
| ~ ssList(skaf46(sk4,sk3))
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,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(skaf46(sk4,sk3))
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ ssList(nil) )
<=> ( ~ ! [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(nil)
| ~ ssList(sk3)
| ~ ssList(skaf46(sk4,sk3))
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,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(skaf46(sk4,sk3))
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ ssList(nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,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(nil)
| ~ ssList(sk3)
| ~ ssList(skaf46(sk4,sk3))
| segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3)
| ~ segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
segmentP(app(app(skaf46(sk4,sk3),sk3),nil),sk3),
inference(unit_resolution,[status(thm)],[93,87,84,28,74,63]) ).
tff(95,plain,
$false,
inference(unit_resolution,[status(thm)],[94,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC373-1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 09:09:03 EDT 2025
% 0.12/0.33 % 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
%------------------------------------------------------------------------------