%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC339-1 : 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 05:30:56 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 29
% Syntax : Number of formulae : 65 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 403 ( 15 equ)
% Maximal formula atoms : 23 ( 6 avg)
% Number of connectives : 614 ( 303 ~; 272 |; 0 &)
% ( 39 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 27 ( 27 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 : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 97 ( 88 !; 0 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(app_type,type,
app: ( $i * $i ) > $i ).
tff(sk6_type,type,
sk6: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
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,
( ( sk2 = sk4 )
<=> ( sk2 = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
tff(7,plain,
sk2 = sk4,
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
sk4 = sk2,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( app(app(sk5,sk3),sk6) = sk4 )
<=> ( app(app(sk5,sk3),sk6) = sk4 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
app(app(sk5,sk3),sk6) = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
tff(11,plain,
app(app(sk5,sk3),sk6) = sk4,
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
app(app(sk5,sk3),sk6) = sk2,
inference(transitivity,[status(thm)],[11,8]) ).
tff(13,plain,
( segmentP(app(app(sk5,sk3),sk6),sk3)
<=> segmentP(sk2,sk1) ),
inference(monotonicity,[status(thm)],[12,4]) ).
tff(14,plain,
( segmentP(sk2,sk1)
<=> segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(app(app(sk5,sk3),sk6),sk3) ),
inference(monotonicity,[status(thm)],[14]) ).
tff(16,plain,
( totalorderedP(sk1)
<=> totalorderedP(sk3) ),
inference(monotonicity,[status(thm)],[3]) ).
tff(17,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk1) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
totalorderedP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
tff(20,plain,
totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
totalorderedP(sk1),
inference(modus_ponens,[status(thm)],[20,17]) ).
tff(22,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,plain,
( ( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
( ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
tff(25,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
~ segmentP(sk2,sk1),
inference(unit_resolution,[status(thm)],[26,21]) ).
tff(28,plain,
~ segmentP(app(app(sk5,sk3),sk6),sk3),
inference(modus_ponens,[status(thm)],[27,15]) ).
tff(29,plain,
( ssList(sk3)
<=> ssList(sk3) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
tff(31,plain,
ssList(sk3),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
^ [U: $i] :
refl(( ( ~ ssList(U)
| segmentP(U,U) )
<=> ( ~ ssList(U)
| segmentP(U,U) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
tff(36,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,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(40,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,U) )
| ~ ssList(sk3)
| segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
segmentP(sk3,sk3),
inference(unit_resolution,[status(thm)],[41,38,31]) ).
tff(43,plain,
( ssList(sk6)
<=> ssList(sk6) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
tff(45,plain,
ssList(sk6),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ssList(sk5)
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,axiom,
ssList(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
tff(48,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
refl(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
^ [W: $i,V: $i,U: $i,X: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( ~ segmentP(U,V)
| ~ ssList(W) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) ) )),
rewrite(( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) ) )),
rewrite(( ( ~ ssList(X)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) ) )),
rewrite(( ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| ~ ssList(W)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
( ( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) )
<=> ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,axiom,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ segmentP(U,V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| segmentP(app(app(X,U),W),V) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause172) ).
tff(55,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[54,53]) ).
tff(56,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[55,51]) ).
tff(57,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) ),
inference(modus_ponens,[status(thm)],[57,50]) ).
tff(59,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ segmentP(sk3,sk3) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) )
<=> ( ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) )
<=> ( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ segmentP(sk3,sk3) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk5)
| ~ ssList(sk3)
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ ssList(sk6) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [W: $i,V: $i,U: $i,X: $i] :
( ~ ssList(X)
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V)
| segmentP(app(app(X,U),W),V)
| ~ ssList(W) )
| ~ ssList(sk3)
| ~ ssList(sk5)
| ~ ssList(sk6)
| segmentP(app(app(sk5,sk3),sk6),sk3)
| ~ segmentP(sk3,sk3) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
$false,
inference(unit_resolution,[status(thm)],[64,58,31,48,45,42,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC339-1 : TPTP v9.0.0. Released v2.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 09:03:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44 % SZS output start Proof
% See solution above
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------