%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC355-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:30:59 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 42
% Syntax : Number of formulae : 97 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 534 ( 39 equ)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 793 ( 386 ~; 357 |; 0 &)
% ( 50 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 30 ( 30 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 : 144 ( 130 !; 0 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(cons_type,type,
cons: ( $i * $i ) > $i ).
tff(nil_type,type,
nil: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(ssItem_type,type,
ssItem: $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,
( neq(sk2,nil)
<=> neq(sk4,nil) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(10,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ( neq(sk2,nil)
| neq(sk2,nil) )
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
( neq(sk2,nil)
| neq(sk2,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(13,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
neq(sk4,nil),
inference(modus_ponens,[status(thm)],[14,9]) ).
tff(16,plain,
( ( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) )
<=> ( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
( ( ( app(sk3,cons(sk5,nil)) = sk4 )
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
( ( app(sk3,cons(sk5,nil)) = sk4 )
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(19,plain,
( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ neq(sk4,nil)
| ( app(sk3,cons(sk5,nil)) = sk4 ) ),
inference(modus_ponens,[status(thm)],[19,16]) ).
tff(21,plain,
app(sk3,cons(sk5,nil)) = sk4,
inference(unit_resolution,[status(thm)],[20,15]) ).
tff(22,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
tff(24,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(26,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(29,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[30,26]) ).
tff(32,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk3)
| ( app(nil,sk3) = sk3 ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
app(nil,sk3) = sk3,
inference(unit_resolution,[status(thm)],[34,31,24]) ).
tff(36,plain,
app(app(nil,sk3),cons(sk5,nil)) = app(sk3,cons(sk5,nil)),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
app(app(nil,sk3),cons(sk5,nil)) = sk2,
inference(transitivity,[status(thm)],[36,21,8]) ).
tff(38,plain,
( segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
<=> segmentP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[37,4]) ).
tff(39,plain,
( segmentP(sk2,sk1)
<=> segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3) ),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) )
<=> ( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ segmentP(sk2,sk1)
| ~ neq(sk4,nil) )
<=> ( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
( ~ segmentP(sk2,sk1)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(44,plain,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[44,41]) ).
tff(46,plain,
~ segmentP(sk2,sk1),
inference(unit_resolution,[status(thm)],[45,15]) ).
tff(47,plain,
~ segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3),
inference(modus_ponens,[status(thm)],[46,40]) ).
tff(48,plain,
( ( ssItem(sk5)
| ~ neq(sk4,nil) )
<=> ( ssItem(sk5)
| ~ neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(50,plain,
( ssItem(sk5)
| ~ neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
ssItem(sk5),
inference(unit_resolution,[status(thm)],[50,15]) ).
tff(52,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [V: $i,U: $i] :
rewrite(( ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
<=> ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
tff(58,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(64,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssItem(U)
| ~ ssList(V)
| ssList(cons(U,V)) )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ssList(cons(sk5,nil)) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
ssList(cons(sk5,nil)),
inference(unit_resolution,[status(thm)],[67,64,61,51]) ).
tff(69,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(73,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[74,70]) ).
tff(76,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(77,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[78,75,24]) ).
tff(80,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(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) )
<=> ! [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)],[80]) ).
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) )
<=> ! [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(83,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(84,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)],[83]) ).
tff(85,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(86,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)],[85,84]) ).
tff(87,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)],[86,82]) ).
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) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,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)],[88,81]) ).
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(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| segmentP(app(app(nil,sk3),cons(sk5,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(cons(sk5,nil))
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ ssList(cons(sk5,nil)) )
<=> ( ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(cons(sk5,nil))
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
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(nil)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ ssList(cons(sk5,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(cons(sk5,nil))
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(monotonicity,[status(thm)],[91]) ).
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(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ ssList(cons(sk5,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(cons(sk5,nil))
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,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(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ ssList(cons(sk5,nil)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,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(cons(sk5,nil))
| segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3)
| ~ segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
segmentP(app(app(nil,sk3),cons(sk5,nil)),sk3),
inference(unit_resolution,[status(thm)],[95,64,89,24,79,68]) ).
tff(97,plain,
$false,
inference(unit_resolution,[status(thm)],[96,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC355-1 : TPTP v9.0.0. Released v2.4.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.10/0.32 % Computer : n007.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Fri Jun 20 09:08:35 EDT 2025
% 0.10/0.32 % CPUTime :
% 0.18/0.42 % SZS status Unsatisfiable
% 0.18/0.42 % SZS output start Proof
% See solution above
% 0.18/0.44 % E exiting
%------------------------------------------------------------------------------