%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC090-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:08 AM UTC 2025
% Result : Unsatisfiable 0.82s 1.02s
% Output : Proof 0.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 79
% Syntax : Number of formulae : 212 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 1255 ( 184 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1942 ( 953 ~; 880 |; 0 &)
% ( 109 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 54 ( 54 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 : 313 ( 291 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(nil_type,type,
nil: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk6_type,type,
sk6: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk4_type,type,
sk4: $i ).
tff(1,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/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,
( ( app(sk6,sk5) = sk3 )
<=> ( app(sk6,sk5) = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
app(sk6,sk5) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(7,plain,
app(sk6,sk5) = sk3,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(10,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(15,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
app(nil,sk6) = sk6,
inference(unit_resolution,[status(thm)],[20,17,10]) ).
tff(22,plain,
app(app(nil,sk6),sk5) = app(sk6,sk5),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
app(app(nil,sk6),sk5) = sk1,
inference(transitivity,[status(thm)],[22,7,4]) ).
tff(24,plain,
( segmentP(app(app(nil,sk6),sk5),sk6)
<=> segmentP(sk1,sk6) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
app(app(nil,sk6),sk5) = sk3,
inference(transitivity,[status(thm)],[22,7]) ).
tff(26,plain,
( ssList(app(app(nil,sk6),sk5))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ssList(sk3)
<=> ssList(app(app(nil,sk6),sk5)) ),
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,
ssList(app(app(nil,sk6),sk5)),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(34,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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(39,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)],[38]) ).
tff(40,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(41,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(42,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)],[41,40]) ).
tff(43,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)],[42,39]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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)],[45,43]) ).
tff(47,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(48,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)],[47,46]) ).
tff(49,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)],[48,37]) ).
tff(50,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)],[49]) ).
tff(51,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)],[50,36]) ).
tff(52,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(54,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ( ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) )
<=> ( ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,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(sk6)
| ~ ssList(sk5)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ) ),
inference(monotonicity,[status(thm)],[56]) ).
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) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
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) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ),
inference(quant_inst,[status(thm)],[]) ).
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) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ),
inference(unit_resolution,[status(thm)],[60,54,51,34,10]) ).
tff(62,plain,
segmentP(app(app(nil,sk6),sk5),sk6),
inference(unit_resolution,[status(thm)],[61,31]) ).
tff(63,plain,
segmentP(sk1,sk6),
inference(modus_ponens,[status(thm)],[62,24]) ).
tff(64,plain,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(66,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[66]) ).
tff(68,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(70,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(75,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[75]) ).
tff(77,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[76,72]) ).
tff(78,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(79,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
app(sk4,nil) = sk4,
inference(unit_resolution,[status(thm)],[80,77,70]) ).
tff(82,plain,
( ( app(sk5,sk6) = sk4 )
<=> ( app(sk5,sk6) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
app(sk5,sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(84,plain,
app(sk5,sk6) = sk4,
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
app(app(sk5,sk6),nil) = app(sk4,nil),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
app(app(sk5,sk6),nil) = sk2,
inference(transitivity,[status(thm)],[85,81,67]) ).
tff(87,plain,
( segmentP(app(app(sk5,sk6),nil),sk6)
<=> segmentP(sk2,sk6) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
app(app(sk5,sk6),nil) = sk4,
inference(transitivity,[status(thm)],[85,81]) ).
tff(89,plain,
( ssList(app(app(sk5,sk6),nil))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ssList(sk4)
<=> ssList(app(app(sk5,sk6),nil)) ),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
ssList(app(app(sk5,sk6),nil)),
inference(modus_ponens,[status(thm)],[70,90]) ).
tff(92,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ( ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) )
<=> ( ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,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(sk6)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,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(sk6)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,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(sk6)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ),
inference(unit_resolution,[status(thm)],[97,54,51,34,10]) ).
tff(99,plain,
segmentP(app(app(sk5,sk6),nil),sk6),
inference(unit_resolution,[status(thm)],[98,91]) ).
tff(100,plain,
segmentP(sk2,sk6),
inference(modus_ponens,[status(thm)],[99,87]) ).
tff(101,plain,
^ [A: $i] :
refl(( ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,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)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
( ( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(107,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ neq(sk6,nil)
| ~ segmentP(sk1,sk6) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ neq(sk6,nil)
| ~ segmentP(sk1,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ neq(sk6,nil)
| ~ segmentP(sk1,sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ neq(sk6,nil)
| ~ segmentP(sk1,sk6) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
( ~ segmentP(sk2,sk6)
| ~ neq(sk6,nil)
| ~ segmentP(sk1,sk6) ),
inference(unit_resolution,[status(thm)],[113,110,10]) ).
tff(115,plain,
~ neq(sk6,nil),
inference(unit_resolution,[status(thm)],[114,100,63]) ).
tff(116,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(117,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)],[116]) ).
tff(118,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(119,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(120,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)],[119]) ).
tff(121,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(122,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ( sk6 = nil )
| neq(sk6,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ( sk6 = nil )
| neq(sk6,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ( sk6 = nil )
| neq(sk6,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk6)
| ( sk6 = nil )
| neq(sk6,nil) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
sk6 = nil,
inference(unit_resolution,[status(thm)],[128,54,125,10,115]) ).
tff(130,plain,
nil = sk6,
inference(symmetry,[status(thm)],[129]) ).
tff(131,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(132,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[133,77,30]) ).
tff(135,plain,
app(app(sk6,sk5),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[7]) ).
tff(136,plain,
app(app(sk6,sk5),nil) = sk1,
inference(transitivity,[status(thm)],[135,134,4]) ).
tff(137,plain,
( segmentP(app(app(sk6,sk5),nil),sk5)
<=> segmentP(sk1,sk5) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
app(app(sk6,sk5),nil) = sk3,
inference(transitivity,[status(thm)],[135,134]) ).
tff(139,plain,
( ssList(app(app(sk6,sk5),nil))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[138]) ).
tff(140,plain,
( ssList(sk3)
<=> ssList(app(app(sk6,sk5),nil)) ),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
ssList(app(app(sk6,sk5),nil)),
inference(modus_ponens,[status(thm)],[30,140]) ).
tff(142,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( ~ ssList(sk6)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) )
<=> ( ~ ssList(nil)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,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(sk6)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,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(sk6)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ) ),
inference(transitivity,[status(thm)],[144,142]) ).
tff(146,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(sk6)
| ~ ssList(sk5)
| ~ ssList(nil)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
( ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ),
inference(unit_resolution,[status(thm)],[147,54,51,34,10]) ).
tff(149,plain,
segmentP(app(app(sk6,sk5),nil),sk5),
inference(unit_resolution,[status(thm)],[148,141]) ).
tff(150,plain,
segmentP(sk1,sk5),
inference(modus_ponens,[status(thm)],[149,137]) ).
tff(151,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
app(nil,sk5) = sk5,
inference(unit_resolution,[status(thm)],[153,17,34]) ).
tff(155,plain,
app(app(nil,sk5),sk6) = app(sk5,sk6),
inference(monotonicity,[status(thm)],[154]) ).
tff(156,plain,
app(app(nil,sk5),sk6) = sk2,
inference(transitivity,[status(thm)],[155,84,67]) ).
tff(157,plain,
( segmentP(app(app(nil,sk5),sk6),sk5)
<=> segmentP(sk2,sk5) ),
inference(monotonicity,[status(thm)],[156]) ).
tff(158,plain,
app(app(nil,sk5),sk6) = sk4,
inference(transitivity,[status(thm)],[155,84]) ).
tff(159,plain,
( ssList(app(app(nil,sk5),sk6))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[158]) ).
tff(160,plain,
( ssList(sk4)
<=> ssList(app(app(nil,sk5),sk6)) ),
inference(symmetry,[status(thm)],[159]) ).
tff(161,plain,
ssList(app(app(nil,sk5),sk6)),
inference(modus_ponens,[status(thm)],[70,160]) ).
tff(162,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) )
<=> ( ~ ! [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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,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(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
( ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) ),
inference(unit_resolution,[status(thm)],[164,54,51,34,10]) ).
tff(166,plain,
segmentP(app(app(nil,sk5),sk6),sk5),
inference(unit_resolution,[status(thm)],[165,161]) ).
tff(167,plain,
segmentP(sk2,sk5),
inference(modus_ponens,[status(thm)],[166,157]) ).
tff(168,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ neq(A,nil)
| ~ segmentP(sk1,A) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
( ~ segmentP(sk2,sk5)
| ~ neq(sk5,nil)
| ~ segmentP(sk1,sk5) ),
inference(unit_resolution,[status(thm)],[170,110,34]) ).
tff(172,plain,
~ neq(sk5,nil),
inference(unit_resolution,[status(thm)],[171,167,150]) ).
tff(173,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(175,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) )
| ~ ssList(nil)
| ~ ssList(sk5)
| ( sk5 = nil )
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
sk5 = nil,
inference(unit_resolution,[status(thm)],[175,54,125,34,172]) ).
tff(177,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk5)
| ( app(sk5,nil) = sk5 ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
app(sk5,nil) = sk5,
inference(unit_resolution,[status(thm)],[179,77,34]) ).
tff(181,plain,
app(sk5,sk6) = app(sk5,nil),
inference(monotonicity,[status(thm)],[129]) ).
tff(182,plain,
sk4 = app(sk5,sk6),
inference(symmetry,[status(thm)],[84]) ).
tff(183,plain,
sk2 = sk6,
inference(transitivity,[status(thm)],[66,182,181,180,176,130]) ).
tff(184,plain,
( neq(sk2,nil)
<=> neq(sk6,sk6) ),
inference(monotonicity,[status(thm)],[183,130]) ).
tff(185,plain,
( neq(sk6,sk6)
<=> neq(sk2,nil) ),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
( ~ neq(sk6,sk6)
<=> ~ neq(sk2,nil) ),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
^ [V: $i] :
refl(( ( ~ ssList(V)
| ~ neq(V,V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(188,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[187]) ).
tff(189,plain,
( ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(190,plain,
^ [V: $i] :
rewrite(( ( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ~ neq(V,V) ) )),
inference(bind,[status(th)],[]) ).
tff(191,plain,
( ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(quant_intro,[status(thm)],[190]) ).
tff(192,plain,
( ! [V: $i,U: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) )
<=> ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(elim_unused_vars,[status(thm)],[]) ).
tff(193,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(destructive_equality_resolution,[status(thm)],[]) ).
tff(194,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i] :
( ~ neq(V,V)
| ~ ssList(V)
| ~ ssList(V) ) ),
inference(transitivity,[status(thm)],[193,192]) ).
tff(195,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(transitivity,[status(thm)],[194,191]) ).
tff(196,plain,
^ [V: $i,U: $i] :
trans(monotonicity(rewrite(( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(V)
| ( U != V )
| ~ neq(U,V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
( ( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],[]) ).
tff(197,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
( ! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) )
<=> ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ) ),
inference(transitivity,[status(thm)],[197,195]) ).
tff(199,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(200,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[200,189]) ).
tff(202,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(skolemize,[status(sab)],[201]) ).
tff(203,plain,
! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) ),
inference(modus_ponens,[status(thm)],[202,188]) ).
tff(204,plain,
( ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk6)
| ~ neq(sk6,sk6) )
<=> ( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk6)
| ~ neq(sk6,sk6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk6)
| ~ neq(sk6,sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(206,plain,
( ~ ! [V: $i] :
( ~ ssList(V)
| ~ neq(V,V) )
| ~ ssList(sk6)
| ~ neq(sk6,sk6) ),
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
~ neq(sk6,sk6),
inference(unit_resolution,[status(thm)],[206,203,10]) ).
tff(208,plain,
~ neq(sk2,nil),
inference(modus_ponens,[status(thm)],[207,186]) ).
tff(209,plain,
( neq(sk2,nil)
<=> neq(sk2,nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,axiom,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(211,plain,
neq(sk2,nil),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
$false,
inference(unit_resolution,[status(thm)],[211,208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC090-1 : TPTP v9.0.0. Released v2.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 08:16:54 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.82/1.02 % SZS status Unsatisfiable
% 0.82/1.02 % SZS output start Proof
% See solution above
% 0.89/1.04 % E exiting
%------------------------------------------------------------------------------