%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC075-1 : 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 05:30:05 AM UTC 2025
% Result : Unsatisfiable 28.12s 28.34s
% Output : Proof 28.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 72
% Syntax : Number of formulae : 203 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 1152 ( 204 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 1745 ( 841 ~; 807 |; 0 &)
% ( 97 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 45 ( 45 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 : 273 ( 255 !; 0 ?; 273 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk2_type,type,
sk2: $i ).
tff(nil_type,type,
nil: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk1_type,type,
sk1: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk3_type,type,
sk3: $i ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( sk5 = sk4 )
<=> ( sk4 = sk5 ) ),
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_5) ).
tff(4,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( ( sk1 = sk3 )
<=> ( sk1 = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
tff(7,plain,
sk1 = sk3,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
sk3 = sk1,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(11,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ( ~ ssList(U)
| ( app(U,nil) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
tff(16,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk3)
| ( app(sk3,nil) = sk3 ) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
app(sk3,nil) = sk3,
inference(unit_resolution,[status(thm)],[21,18,11]) ).
tff(23,plain,
( ( app(sk6,sk5) = sk3 )
<=> ( app(sk6,sk5) = sk3 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
app(sk6,sk5) = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
tff(25,plain,
app(sk6,sk5) = sk3,
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
app(app(sk6,sk5),nil) = app(sk3,nil),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
app(app(sk6,sk5),nil) = sk1,
inference(transitivity,[status(thm)],[26,22,8]) ).
tff(28,plain,
( segmentP(app(app(sk6,sk5),nil),sk5)
<=> segmentP(sk1,sk5) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
app(app(sk6,sk5),nil) = sk3,
inference(transitivity,[status(thm)],[26,22]) ).
tff(30,plain,
( ssList(app(app(sk6,sk5),nil))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ssList(sk3)
<=> ssList(app(app(sk6,sk5),nil)) ),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
ssList(app(app(sk6,sk5),nil)),
inference(modus_ponens,[status(thm)],[11,31]) ).
tff(33,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(35,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(38,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,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(40,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)],[39]) ).
tff(41,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(42,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(43,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)],[42]) ).
tff(44,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(45,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(46,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)],[45,44]) ).
tff(47,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)],[46,43]) ).
tff(48,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(49,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)],[48]) ).
tff(50,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)],[49,47]) ).
tff(51,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(52,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)],[51,50]) ).
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) ),
inference(modus_ponens,[status(thm)],[52,41]) ).
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) ),
inference(skolemize,[status(sab)],[53]) ).
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) ),
inference(modus_ponens,[status(thm)],[54,40]) ).
tff(56,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(58,plain,
ssList(nil),
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) )
| ~ 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(60,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(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) )
| ~ 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)],[60]) ).
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(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)],[61,59]) ).
tff(63,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(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(nil)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
( ~ ssList(app(app(sk6,sk5),nil))
| segmentP(app(app(sk6,sk5),nil),sk5) ),
inference(unit_resolution,[status(thm)],[64,58,55,38,35]) ).
tff(66,plain,
segmentP(app(app(sk6,sk5),nil),sk5),
inference(unit_resolution,[status(thm)],[65,32]) ).
tff(67,plain,
segmentP(sk1,sk5),
inference(modus_ponens,[status(thm)],[66,28]) ).
tff(68,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[4]) ).
tff(69,plain,
( ( app(sk5,sk6) = sk4 )
<=> ( app(sk5,sk6) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
app(sk5,sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(71,plain,
app(sk5,sk6) = sk4,
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ( ~ ssList(U)
| ( app(nil,U) = U ) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
<=> ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
tff(76,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(skolemize,[status(sab)],[76]) ).
tff(78,plain,
! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,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(80,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk5)
| ( app(nil,sk5) = sk5 ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
app(nil,sk5) = sk5,
inference(unit_resolution,[status(thm)],[81,78,38]) ).
tff(83,plain,
app(app(nil,sk5),sk6) = app(sk5,sk6),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
app(app(nil,sk5),sk6) = sk2,
inference(transitivity,[status(thm)],[83,71,68]) ).
tff(85,plain,
( segmentP(app(app(nil,sk5),sk6),sk5)
<=> segmentP(sk2,sk5) ),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
app(app(nil,sk5),sk6) = sk4,
inference(transitivity,[status(thm)],[83,71]) ).
tff(87,plain,
( ssList(app(app(nil,sk5),sk6))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ssList(sk4)
<=> ssList(app(app(nil,sk5),sk6)) ),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ssList(sk4)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
tff(91,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
ssList(app(app(nil,sk5),sk6)),
inference(modus_ponens,[status(thm)],[91,88]) ).
tff(93,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(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(nil)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) ),
inference(quant_inst,[status(thm)],[]) ).
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(nil)
| ~ ssList(sk5)
| ~ ssList(sk6)
| ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ ssList(app(app(nil,sk5),sk6))
| segmentP(app(app(nil,sk5),sk6),sk5) ),
inference(unit_resolution,[status(thm)],[95,58,55,38,35]) ).
tff(97,plain,
segmentP(app(app(nil,sk5),sk6),sk5),
inference(unit_resolution,[status(thm)],[96,92]) ).
tff(98,plain,
segmentP(sk2,sk5),
inference(modus_ponens,[status(thm)],[97,85]) ).
tff(99,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(100,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)],[99]) ).
tff(101,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(102,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(103,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)],[102]) ).
tff(104,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(A,nil)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(105,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ segmentP(sk1,sk5)
| ~ neq(sk5,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ segmentP(sk1,sk5)
| ~ neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ segmentP(sk1,sk5)
| ~ neq(sk5,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(111,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk5)
| ~ segmentP(sk2,sk5)
| ~ segmentP(sk1,sk5)
| ~ neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
( ~ segmentP(sk2,sk5)
| ~ segmentP(sk1,sk5)
| ~ neq(sk5,nil) ),
inference(unit_resolution,[status(thm)],[111,108,38]) ).
tff(113,plain,
~ neq(sk5,nil),
inference(unit_resolution,[status(thm)],[112,98,67]) ).
tff(114,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(115,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)],[114]) ).
tff(116,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(117,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(118,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)],[117]) ).
tff(119,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(120,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[120,116]) ).
tff(122,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(skolemize,[status(sab)],[121]) ).
tff(123,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| neq(V,U) ),
inference(modus_ponens,[status(thm)],[122,115]) ).
tff(124,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(125,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(126,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)],[125,124]) ).
tff(127,plain,
sk5 = nil,
inference(unit_resolution,[status(thm)],[126,58,123,38,113]) ).
tff(128,plain,
nil = sk5,
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
( ( nil = sk2 )
<=> ( sk5 = sk4 ) ),
inference(monotonicity,[status(thm)],[128,4]) ).
tff(130,plain,
( ( nil = sk2 )
<=> ( sk4 = sk5 ) ),
inference(transitivity,[status(thm)],[129,1]) ).
tff(131,plain,
( ( sk4 = sk5 )
<=> ( nil = sk2 ) ),
inference(symmetry,[status(thm)],[130]) ).
tff(132,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(133,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk4)
| ( app(sk4,nil) = sk4 ) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
app(sk4,nil) = sk4,
inference(unit_resolution,[status(thm)],[134,18,91]) ).
tff(136,plain,
app(app(sk5,sk6),nil) = app(sk4,nil),
inference(monotonicity,[status(thm)],[71]) ).
tff(137,plain,
app(app(sk5,sk6),nil) = sk2,
inference(transitivity,[status(thm)],[136,135,68]) ).
tff(138,plain,
( segmentP(app(app(sk5,sk6),nil),sk6)
<=> segmentP(sk2,sk6) ),
inference(monotonicity,[status(thm)],[137]) ).
tff(139,plain,
app(app(sk5,sk6),nil) = sk4,
inference(transitivity,[status(thm)],[136,135]) ).
tff(140,plain,
( ssList(app(app(sk5,sk6),nil))
<=> ssList(sk4) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ssList(sk4)
<=> ssList(app(app(sk5,sk6),nil)) ),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
ssList(app(app(sk5,sk6),nil)),
inference(modus_ponens,[status(thm)],[91,141]) ).
tff(143,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(144,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(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(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)],[144]) ).
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(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)],[145,143]) ).
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(sk5)
| ~ ssList(sk6)
| ~ ssList(nil)
| ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(148,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)],[147,146]) ).
tff(149,plain,
( ~ ssList(app(app(sk5,sk6),nil))
| segmentP(app(app(sk5,sk6),nil),sk6) ),
inference(unit_resolution,[status(thm)],[148,58,55,38,35]) ).
tff(150,plain,
segmentP(app(app(sk5,sk6),nil),sk6),
inference(unit_resolution,[status(thm)],[149,142]) ).
tff(151,plain,
segmentP(sk2,sk6),
inference(modus_ponens,[status(thm)],[150,138]) ).
tff(152,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(153,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(nil,U) = U ) )
| ~ ssList(sk6)
| ( app(nil,sk6) = sk6 ) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
app(nil,sk6) = sk6,
inference(unit_resolution,[status(thm)],[154,78,35]) ).
tff(156,plain,
app(app(nil,sk6),sk5) = app(sk6,sk5),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
app(app(nil,sk6),sk5) = sk1,
inference(transitivity,[status(thm)],[156,25,8]) ).
tff(158,plain,
( segmentP(app(app(nil,sk6),sk5),sk6)
<=> segmentP(sk1,sk6) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
app(app(nil,sk6),sk5) = sk3,
inference(transitivity,[status(thm)],[156,25]) ).
tff(160,plain,
( ssList(app(app(nil,sk6),sk5))
<=> ssList(sk3) ),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ssList(sk3)
<=> ssList(app(app(nil,sk6),sk5)) ),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
ssList(app(app(nil,sk6),sk5)),
inference(modus_ponens,[status(thm)],[11,161]) ).
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,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(164,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(165,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)],[164]) ).
tff(166,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)],[165,163]) ).
tff(167,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(168,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)],[167,166]) ).
tff(169,plain,
( ~ ssList(app(app(nil,sk6),sk5))
| segmentP(app(app(nil,sk6),sk5),sk6) ),
inference(unit_resolution,[status(thm)],[168,58,55,38,35]) ).
tff(170,plain,
segmentP(app(app(nil,sk6),sk5),sk6),
inference(unit_resolution,[status(thm)],[169,162]) ).
tff(171,plain,
segmentP(sk1,sk6),
inference(modus_ponens,[status(thm)],[170,158]) ).
tff(172,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ segmentP(sk1,sk6)
| ~ neq(sk6,nil) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ segmentP(sk1,sk6)
| ~ neq(sk6,nil) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ segmentP(sk1,sk6)
| ~ neq(sk6,nil) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(sk2,A)
| ~ segmentP(sk1,A)
| ~ neq(A,nil) )
| ~ ssList(sk6)
| ~ segmentP(sk2,sk6)
| ~ segmentP(sk1,sk6)
| ~ neq(sk6,nil) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
( ~ segmentP(sk2,sk6)
| ~ segmentP(sk1,sk6)
| ~ neq(sk6,nil) ),
inference(unit_resolution,[status(thm)],[174,108,35]) ).
tff(176,plain,
~ neq(sk6,nil),
inference(unit_resolution,[status(thm)],[175,171,151]) ).
tff(177,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(178,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(179,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)],[178,177]) ).
tff(180,plain,
sk6 = nil,
inference(unit_resolution,[status(thm)],[179,58,123,35,176]) ).
tff(181,plain,
app(sk5,sk6) = app(nil,sk6),
inference(monotonicity,[status(thm)],[127]) ).
tff(182,plain,
sk4 = app(sk5,sk6),
inference(symmetry,[status(thm)],[71]) ).
tff(183,plain,
sk4 = sk5,
inference(transitivity,[status(thm)],[182,181,155,180,128]) ).
tff(184,plain,
nil = sk2,
inference(modus_ponens,[status(thm)],[183,131]) ).
tff(185,plain,
( ( sk1 = nil )
<=> ( nil = sk1 ) ),
inference(commutativity,[status(thm)],[]) ).
tff(186,plain,
( ( sk3 = sk5 )
<=> ( sk1 = nil ) ),
inference(monotonicity,[status(thm)],[8,127]) ).
tff(187,plain,
( ( sk3 = sk5 )
<=> ( nil = sk1 ) ),
inference(transitivity,[status(thm)],[186,185]) ).
tff(188,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk6)
| ( app(sk6,nil) = sk6 ) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk6)
| ( app(sk6,nil) = sk6 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(189,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk6)
| ( app(sk6,nil) = sk6 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(190,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| ( app(U,nil) = U ) )
| ~ ssList(sk6)
| ( app(sk6,nil) = sk6 ) ),
inference(modus_ponens,[status(thm)],[189,188]) ).
tff(191,plain,
app(sk6,nil) = sk6,
inference(unit_resolution,[status(thm)],[190,18,35]) ).
tff(192,plain,
app(sk6,sk5) = app(sk6,nil),
inference(monotonicity,[status(thm)],[127]) ).
tff(193,plain,
sk3 = app(sk6,sk5),
inference(symmetry,[status(thm)],[25]) ).
tff(194,plain,
sk3 = sk5,
inference(transitivity,[status(thm)],[193,192,191,180,128]) ).
tff(195,plain,
nil = sk1,
inference(modus_ponens,[status(thm)],[194,187]) ).
tff(196,plain,
( ( ( nil != sk2 )
| ( nil != sk1 ) )
<=> ( ( nil != sk2 )
| ( nil != sk1 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,axiom,
( ( nil != sk2 )
| ( nil != sk1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
tff(198,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[198,196]) ).
tff(200,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[199,196]) ).
tff(201,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[200,196]) ).
tff(202,plain,
( ( nil != sk2 )
| ( nil != sk1 ) ),
inference(modus_ponens,[status(thm)],[201,196]) ).
tff(203,plain,
$false,
inference(unit_resolution,[status(thm)],[202,195,184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : SWC075-1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.15 % Command : run_E %s %d THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8042.1875MB
% 0.11/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Jun 20 08:14:09 EDT 2025
% 0.11/0.37 % CPUTime :
% 28.12/28.34 % SZS status Unsatisfiable
% 28.12/28.34 % SZS output start Proof
% See solution above
% 28.12/28.36 % E exiting
%------------------------------------------------------------------------------