%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC076-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.76s 0.95s
% Output : Proof 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 49
% Syntax : Number of formulae : 123 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 737 ( 123 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1102 ( 532 ~; 499 |; 0 &)
% ( 71 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 44 ( 44 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 : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 176 ( 159 !; 0 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $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,
( ( nil = sk2 )
<=> ( nil = sk4 ) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( ( nil = sk4 )
<=> ( nil = sk2 ) ),
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( sk3 = nil )
<=> ( nil = sk3 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(7,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(9,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( segmentP(sk3,sk3)
<=> segmentP(sk1,sk3) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(14,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(19,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,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(23,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[24,21,14]) ).
tff(26,plain,
segmentP(sk1,sk3),
inference(modus_ponens,[status(thm)],[25,11]) ).
tff(27,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[3]) ).
tff(28,plain,
( ( app(app(sk5,sk3),sk6) = sk4 )
<=> ( app(app(sk5,sk3),sk6) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(30,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
app(app(sk5,sk3),sk6) = sk2,
inference(transitivity,[status(thm)],[30,27]) ).
tff(32,plain,
( segmentP(app(app(sk5,sk3),sk6),sk3)
<=> segmentP(sk2,sk3) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ssList(app(app(sk5,sk3),sk6))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(34,plain,
( ssList(sk4)
<=> ssList(app(app(sk5,sk3),sk6)) ),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(37,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
ssList(app(app(sk5,sk3),sk6)),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(41,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(44,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,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(49,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)],[48]) ).
tff(50,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(51,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(52,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)],[51,50]) ).
tff(53,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)],[52,49]) ).
tff(54,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(55,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)],[54]) ).
tff(56,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)],[55,53]) ).
tff(57,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(58,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)],[57,56]) ).
tff(59,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)],[58,47]) ).
tff(60,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)],[59]) ).
tff(61,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)],[60,46]) ).
tff(62,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(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) )
<=> ( ~ ! [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(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,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(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) )
<=> ( ~ ! [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(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) ) ),
inference(monotonicity,[status(thm)],[63]) ).
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) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) )
<=> ( ~ ! [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(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
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) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(quant_inst,[status(thm)],[]) ).
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) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ ssList(app(app(sk5,sk3),sk6))
| segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(unit_resolution,[status(thm)],[67,61,14,44,41]) ).
tff(69,plain,
segmentP(app(app(sk5,sk3),sk6),sk3),
inference(unit_resolution,[status(thm)],[68,38]) ).
tff(70,plain,
segmentP(sk2,sk3),
inference(modus_ponens,[status(thm)],[69,32]) ).
tff(71,plain,
^ [A: $i] :
refl(( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
^ [A: $i] :
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(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(77,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk3)
| ~ segmentP(sk2,sk3)
| ~ segmentP(sk1,sk3)
| ~ neq(sk3,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk3)
| ~ segmentP(sk2,sk3)
| ~ segmentP(sk1,sk3)
| ~ neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk3)
| ~ segmentP(sk2,sk3)
| ~ segmentP(sk1,sk3)
| ~ neq(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk3)
| ~ segmentP(sk2,sk3)
| ~ segmentP(sk1,sk3)
| ~ neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
( ~ segmentP(sk2,sk3)
| ~ segmentP(sk1,sk3)
| ~ neq(sk3,nil) ),
inference(unit_resolution,[status(thm)],[83,14,80]) ).
tff(85,plain,
~ neq(sk3,nil),
inference(unit_resolution,[status(thm)],[84,70,26]) ).
tff(86,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(87,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)],[86]) ).
tff(88,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(89,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(90,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)],[89]) ).
tff(91,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(92,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[94,87]) ).
tff(96,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(98,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 = nil )
| neq(sk3,nil) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
sk3 = nil,
inference(unit_resolution,[status(thm)],[101,98,95,14,85]) ).
tff(103,plain,
nil = sk3,
inference(modus_ponens,[status(thm)],[102,6]) ).
tff(104,plain,
( ( ( nil != sk3 )
| ( nil = sk4 ) )
<=> ( ( nil != sk3 )
| ( nil = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( ( nil = sk4 )
| ( nil != sk3 ) )
<=> ( ( nil != sk3 )
| ( nil = sk4 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
( ( nil = sk4 )
| ( nil != sk3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(107,plain,
( ( nil != sk3 )
| ( nil = sk4 ) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( ( nil != sk3 )
| ( nil = sk4 ) ),
inference(modus_ponens,[status(thm)],[107,104]) ).
tff(109,plain,
nil = sk4,
inference(unit_resolution,[status(thm)],[108,103]) ).
tff(110,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[109,5]) ).
tff(111,plain,
( ( nil = sk1 )
<=> ( nil = sk3 ) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(112,plain,
( ( nil = sk3 )
<=> ( nil = sk1 ) ),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
( ( sk3 = nil )
<=> ( nil = sk1 ) ),
inference(transitivity,[status(thm)],[6,112]) ).
tff(114,plain,
nil = sk1,
inference(modus_ponens,[status(thm)],[102,113]) ).
tff(115,plain,
( ( ( nil != sk2 )
| ( nil != sk1 ) )
<=> ( ( nil != sk2 )
| ( nil != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
tff(117,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[117,115]) ).
tff(119,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[118,115]) ).
tff(120,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[120,115]) ).
tff(122,plain,
nil != sk2,
inference(unit_resolution,[status(thm)],[121,114]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14 % Problem : SWC076-1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.12/0.35 % Computer : n014.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Jun 20 08:14:55 EDT 2025
% 0.18/0.36 % CPUTime :
% 0.76/0.95 % SZS status Unsatisfiable
% 0.76/0.95 % SZS output start Proof
% See solution above
% 0.79/0.97 % E exiting
%------------------------------------------------------------------------------