TSTP Solution File: SWC037-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC037-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Tue Sep 20 11:54:48 EDT 2022
% Result : Unsatisfiable 0.21s 0.46s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 48
% Syntax : Number of formulae : 98 ( 18 unt; 8 typ; 0 def)
% Number of atoms : 536 ( 118 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 804 ( 382 ~; 367 |; 0 &)
% ( 55 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 24 ( 24 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 101 ( 91 !; 0 ?; 101 :)
% Comments :
%------------------------------------------------------------------------------
tff(sk4_type,type,
sk4: $i ).
tff(sk5_type,type,
sk5: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(nil_type,type,
nil: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(1,plain,
( ( ssList(sk5)
| $false )
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( nil != sk1 )
<=> ( sk4 != sk3 ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( nil != sk1 )
<=> ( nil != sk1 ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
nil != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(5,plain,
nil != sk1,
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
sk4 != sk3,
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
( ( sk4 = sk3 )
<=> $false ),
inference(iff_false,[status(thm)],[6]) ).
tff(8,plain,
( ( ssList(sk5)
| ( sk4 = sk3 ) )
<=> ( ssList(sk5)
| $false ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( ( ssList(sk5)
| ( sk4 = sk3 ) )
<=> ssList(sk5) ),
inference(transitivity,[status(thm)],[8,1]) ).
tff(10,plain,
( ( ssList(sk5)
| ( nil = sk3 ) )
<=> ( ssList(sk5)
| ( sk4 = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ( ssList(sk5)
| ( nil = sk3 ) )
<=> ( ssList(sk5)
| ( nil = sk3 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
( ssList(sk5)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(13,plain,
( ssList(sk5)
| ( nil = sk3 ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ssList(sk5)
| ( sk4 = sk3 ) ),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[14,9]) ).
tff(16,plain,
^ [U: $i] :
refl(
( ( ~ ssList(U)
| segmentP(U,sk4) )
<=> ( ~ ssList(U)
| segmentP(U,sk4) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [U: $i] :
rewrite(
( ( ~ ssList(U)
| segmentP(U,nil) )
<=> ( ~ ssList(U)
| segmentP(U,sk4) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) )
<=> ! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
tff(22,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,nil) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) ),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,plain,
( ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) )
| ~ ssList(sk5)
| segmentP(sk5,sk4) )
<=> ( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) )
| ~ ssList(sk5)
| segmentP(sk5,sk4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) )
| ~ ssList(sk5)
| segmentP(sk5,sk4) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [U: $i] :
( ~ ssList(U)
| segmentP(U,sk4) )
| ~ ssList(sk5)
| segmentP(sk5,sk4) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
segmentP(sk5,sk4),
inference(unit_resolution,[status(thm)],[28,25,15]) ).
tff(30,plain,
( ( $false
| segmentP(sk4,sk5) )
<=> segmentP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ( ( sk4 = sk3 )
| segmentP(sk4,sk5) )
<=> ( $false
| segmentP(sk4,sk5) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(32,plain,
( ( ( sk4 = sk3 )
| segmentP(sk4,sk5) )
<=> segmentP(sk4,sk5) ),
inference(transitivity,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ( nil = sk3 )
| segmentP(sk4,sk5) )
<=> ( ( sk4 = sk3 )
| segmentP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ( ( nil = sk3 )
| segmentP(sk4,sk5) )
<=> ( ( nil = sk3 )
| segmentP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( segmentP(sk4,sk5)
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| segmentP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
( segmentP(sk4,sk5)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
tff(37,plain,
( ( nil = sk3 )
| segmentP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( nil = sk3 )
| segmentP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[37,34]) ).
tff(39,plain,
( ( sk4 = sk3 )
| segmentP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[38,33]) ).
tff(40,plain,
segmentP(sk4,sk5),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(42,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
^ [V: $i,U: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U) )
<=> ( ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) ) )),
rewrite(
( ( ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U)
| ~ ssList(V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ( V = U ) ) )),
rewrite(
( ( ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) )),
( ( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(45,plain,
( ! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [V: $i,U: $i] :
( ~ segmentP(U,V)
| ~ segmentP(V,U)
| ~ ssList(U)
| ~ ssList(V)
| ( V = U ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause127) ).
tff(47,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ssList(nil)
<=> ssList(sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ssList(nil)
<=> ssList(nil) ),
inference(rewrite,[status(thm)],]) ).
tff(53,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
tff(54,plain,
ssList(nil),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
ssList(sk4),
inference(modus_ponens,[status(thm)],[54,51]) ).
tff(56,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ segmentP(sk4,sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ segmentP(sk4,sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ( ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4)
| ~ segmentP(sk4,sk5) )
<=> ( ~ ssList(sk4)
| ~ ssList(sk5)
| ~ segmentP(sk4,sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4)
| ~ segmentP(sk4,sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ segmentP(sk4,sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4)
| ~ segmentP(sk4,sk5) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ segmentP(sk4,sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4)
| ~ segmentP(sk4,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( V = U )
| ~ segmentP(V,U)
| ~ segmentP(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ~ segmentP(sk4,sk5)
| ( sk5 = sk4 )
| ~ segmentP(sk5,sk4) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
sk5 = sk4,
inference(unit_resolution,[status(thm)],[61,55,50,15,40,29]) ).
tff(63,plain,
( ( $false
| neq(sk5,sk4) )
<=> neq(sk5,sk4) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ( sk4 = sk3 )
| neq(sk5,sk4) )
<=> ( $false
| neq(sk5,sk4) ) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(65,plain,
( ( ( sk4 = sk3 )
| neq(sk5,sk4) )
<=> neq(sk5,sk4) ),
inference(transitivity,[status(thm)],[64,63]) ).
tff(66,plain,
( ( ( nil = sk3 )
| neq(sk5,nil) )
<=> ( ( sk4 = sk3 )
| neq(sk5,sk4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ( nil = sk3 )
| neq(sk5,nil) )
<=> ( ( nil = sk3 )
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( neq(sk5,nil)
| ( nil = sk3 ) )
<=> ( ( nil = sk3 )
| neq(sk5,nil) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,axiom,
( neq(sk5,nil)
| ( nil = sk3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(70,plain,
( ( nil = sk3 )
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( nil = sk3 )
| neq(sk5,nil) ),
inference(modus_ponens,[status(thm)],[70,67]) ).
tff(72,plain,
( ( sk4 = sk3 )
| neq(sk5,sk4) ),
inference(modus_ponens,[status(thm)],[71,66]) ).
tff(73,plain,
neq(sk5,sk4),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
^ [V: $i,U: $i] :
refl(
( ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
<=> ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,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(78,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)],[77]) ).
tff(79,axiom,
! [V: $i,U: $i] :
( ( U != V )
| ~ neq(U,V)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause115) ).
tff(80,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,plain,
( ( ~ ssList(sk5)
| ~ ssList(sk4)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) )
<=> ( ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk5)
| ~ ssList(sk4)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk5)
| ~ ssList(sk4)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) )
<=> ( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk5)
| ~ ssList(sk4)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [V: $i,U: $i] :
( ~ ssList(U)
| ~ ssList(V)
| ( U != V )
| ~ neq(U,V) )
| ~ ssList(sk4)
| ~ ssList(sk5)
| ( sk5 != sk4 )
| ~ neq(sk5,sk4) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
$false,
inference(unit_resolution,[status(thm)],[89,55,83,15,73,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC037-1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 20:57:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.21/0.46 % SZS status Unsatisfiable
% 0.21/0.46 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------