%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC068-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:30:04 AM UTC 2025
% Result : Unsatisfiable 3.23s 3.41s
% Output : Proof 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 54
% Syntax : Number of formulae : 141 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 885 ( 202 equ)
% Maximal formula atoms : 19 ( 6 avg)
% Number of connectives : 1325 ( 639 ~; 599 |; 0 &)
% ( 87 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 58 ( 58 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 209 ( 189 !; 0 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk3_type,type,
sk3: $i ).
tff(1,plain,
( ( sk2 = nil )
<=> ( nil = sk2 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(2,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(4,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( sk4 = nil )
<=> ( sk2 = nil ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( ( sk4 = nil )
<=> ( nil = sk2 ) ),
inference(transitivity,[status(thm)],[6,1]) ).
tff(8,plain,
( segmentP(sk4,sk4)
<=> segmentP(sk2,sk4) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(9,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
ssList(sk4),
file('/export/starexec/sandbox/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)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(16,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk4)
| segmentP(sk4,sk4) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk4)
| segmentP(sk4,sk4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk4)
| segmentP(sk4,sk4) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk4)
| segmentP(sk4,sk4) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
segmentP(sk4,sk4),
inference(unit_resolution,[status(thm)],[21,18,11]) ).
tff(23,plain,
segmentP(sk2,sk4),
inference(modus_ponens,[status(thm)],[22,8]) ).
tff(24,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(26,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
ssList(sk3),
file('/export/starexec/sandbox/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)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(35,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[40,37,30]) ).
tff(42,plain,
( ( app(sk4,sk4) = sk3 )
<=> ( app(sk4,sk4) = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
app(sk4,sk4) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(44,plain,
app(sk4,sk4) = sk3,
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
app(app(sk4,sk4),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
app(app(sk4,sk4),nil) = sk1,
inference(transitivity,[status(thm)],[45,41,27]) ).
tff(47,plain,
( segmentP(app(app(sk4,sk4),nil),sk4)
<=> segmentP(sk1,sk4) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
app(app(sk4,sk4),nil) = sk3,
inference(transitivity,[status(thm)],[45,41]) ).
tff(49,plain,
( ssList(app(app(sk4,sk4),nil))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[48]) ).
tff(50,plain,
( ssList(sk3)
<=> ssList(app(app(sk4,sk4),nil)) ),
inference(symmetry,[status(thm)],[49]) ).
tff(51,plain,
ssList(app(app(sk4,sk4),nil)),
inference(modus_ponens,[status(thm)],[30,50]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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(56,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)],[55]) ).
tff(57,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(58,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(59,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)],[58,57]) ).
tff(60,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)],[59,56]) ).
tff(61,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(62,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)],[61]) ).
tff(63,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)],[62,60]) ).
tff(64,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(65,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)],[64,63]) ).
tff(66,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)],[65,54]) ).
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) ),
inference(skolemize,[status(sab)],[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) ),
inference(modus_ponens,[status(thm)],[67,53]) ).
tff(69,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(71,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,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(sk4)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) )
<=> ( ~ ! [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(sk4)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) )
<=> ( ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,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(sk4)
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) )
<=> ( ~ ! [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(sk4)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(sk4)
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) )
<=> ( ~ ! [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(sk4)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,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(sk4)
| ~ ssList(sk4)
| ~ ssList(nil)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [W: $i,V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ ssList(app(app(U,V),W))
| segmentP(app(app(U,V),W),V) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ~ ssList(app(app(sk4,sk4),nil))
| segmentP(app(app(sk4,sk4),nil),sk4) ),
inference(unit_resolution,[status(thm)],[77,71,68,11]) ).
tff(79,plain,
segmentP(app(app(sk4,sk4),nil),sk4),
inference(unit_resolution,[status(thm)],[78,51]) ).
tff(80,plain,
segmentP(sk1,sk4),
inference(modus_ponens,[status(thm)],[79,47]) ).
tff(81,plain,
^ [A: $i] :
refl(( ( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
^ [A: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ) )),
rewrite(( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(87,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ),
inference(modus_ponens,[status(thm)],[87,83]) ).
tff(89,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ),
inference(skolemize,[status(sab)],[88]) ).
tff(90,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) ),
inference(modus_ponens,[status(thm)],[89,82]) ).
tff(91,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
| ~ ssList(sk4)
| ~ segmentP(sk1,sk4)
| ~ neq(sk4,nil)
| ~ segmentP(sk2,sk4) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
| ~ ssList(sk4)
| ~ segmentP(sk1,sk4)
| ~ neq(sk4,nil)
| ~ segmentP(sk2,sk4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
| ~ ssList(sk4)
| ~ segmentP(sk1,sk4)
| ~ neq(sk4,nil)
| ~ segmentP(sk2,sk4) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A) )
| ~ ssList(sk4)
| ~ segmentP(sk1,sk4)
| ~ neq(sk4,nil)
| ~ segmentP(sk2,sk4) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
( ~ segmentP(sk1,sk4)
| ~ neq(sk4,nil)
| ~ segmentP(sk2,sk4) ),
inference(unit_resolution,[status(thm)],[93,11,90]) ).
tff(95,plain,
~ neq(sk4,nil),
inference(unit_resolution,[status(thm)],[94,80,23]) ).
tff(96,plain,
^ [V: $i,U: $i] :
refl(( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ) )),
rewrite(( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
( ( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| neq(V,U)
| ( V = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
tff(102,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk4)
| ( sk4 = nil )
| neq(sk4,nil) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
sk4 = nil,
inference(unit_resolution,[status(thm)],[108,71,105,11,95]) ).
tff(110,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[109,7]) ).
tff(111,plain,
( ( sk4 = sk3 )
<=> ( sk3 = sk4 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(112,plain,
nil = sk4,
inference(symmetry,[status(thm)],[109]) ).
tff(113,plain,
( ( nil = sk1 )
<=> ( sk4 = sk3 ) ),
inference(monotonicity,[status(thm)],[112,26]) ).
tff(114,plain,
( ( nil = sk1 )
<=> ( sk3 = sk4 ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
( ( sk3 = sk4 )
<=> ( nil = sk1 ) ),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ! [V: $i,U: $i] :
( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) )
<=> ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(119,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(120,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ( ~ ssList(nil)
| ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[119,118]) ).
tff(121,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[120,117]) ).
tff(122,plain,
^ [V: $i,U: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( nil != U )
| ( nil != V )
| ~ ssList(V) )
<=> ( ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ~ ssList(U) ) )),
rewrite(( ( ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ( app(U,V) = nil ) ) )),
rewrite(( ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( nil != V )
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) )),
( ( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ( nil != U )
| ~ ssList(V)
| ( app(U,V) = nil )
| ( nil != V ) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) )
<=> ( ~ ssList(nil)
| ( app(nil,nil) = nil ) ) ),
inference(transitivity,[status(thm)],[123,121]) ).
tff(125,axiom,
! [V: $i,U: $i] :
( ( nil != U )
| ( nil != V )
| ~ ssList(V)
| ~ ssList(U)
| ( app(U,V) = nil ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause145) ).
tff(126,plain,
( ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ ssList(nil)
| ( app(nil,nil) = nil ) ),
inference(modus_ponens,[status(thm)],[126,116]) ).
tff(128,plain,
app(nil,nil) = nil,
inference(unit_resolution,[status(thm)],[127,71]) ).
tff(129,plain,
app(nil,nil) = app(sk4,sk4),
inference(monotonicity,[status(thm)],[112,112]) ).
tff(130,plain,
app(sk4,sk4) = app(nil,nil),
inference(symmetry,[status(thm)],[129]) ).
tff(131,plain,
sk3 = app(sk4,sk4),
inference(symmetry,[status(thm)],[44]) ).
tff(132,plain,
sk3 = sk4,
inference(transitivity,[status(thm)],[131,130,128,112]) ).
tff(133,plain,
nil = sk1,
inference(modus_ponens,[status(thm)],[132,115]) ).
tff(134,plain,
( ( ( nil != sk2 )
| ( nil != sk1 ) )
<=> ( ( nil != sk2 )
| ( nil != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,axiom,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(136,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[136,134]) ).
tff(138,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[137,134]) ).
tff(139,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[138,134]) ).
tff(140,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[139,134]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,133,110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC068-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:12:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 3.23/3.41 % SZS status Unsatisfiable
% 3.23/3.41 % SZS output start Proof
% See solution above
% 3.23/3.42 % E exiting
%------------------------------------------------------------------------------