TSTP Solution File: SWC333-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC333-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 11:57:10 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 51
% Syntax : Number of formulae : 111 ( 12 unt; 9 typ; 0 def)
% Number of atoms : 511 ( 0 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 749 ( 354 ~; 328 |; 0 &)
% ( 67 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 17 ( 15 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(totalorderedP_type,type,
totalorderedP: $i > $o ).
tff(sk5_type,type,
sk5: $i ).
tff(segmentP_type,type,
segmentP: ( $i * $i ) > $o ).
tff(sk3_type,type,
sk3: $i ).
tff(sk4_type,type,
sk4: $i ).
tff(sk1_type,type,
sk1: $i ).
tff(sk2_type,type,
sk2: $i ).
tff(neq_type,type,
neq: ( $i * $i ) > $o ).
tff(ssList_type,type,
ssList: $i > $o ).
tff(1,plain,
( ( totalorderedP(sk5)
| $false
| $false )
<=> totalorderedP(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( segmentP(sk4,sk3)
<=> segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
segmentP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
tff(5,plain,
segmentP(sk4,sk3),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
( segmentP(sk4,sk3)
<=> $true ),
inference(iff_true,[status(thm)],[5]) ).
tff(7,plain,
( ~ segmentP(sk4,sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ~ segmentP(sk4,sk3)
<=> $false ),
inference(transitivity,[status(thm)],[7,2]) ).
tff(9,plain,
( totalorderedP(sk3)
<=> totalorderedP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
totalorderedP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
tff(11,plain,
totalorderedP(sk3),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
( totalorderedP(sk3)
<=> $true ),
inference(iff_true,[status(thm)],[11]) ).
tff(13,plain,
( ~ totalorderedP(sk3)
<=> ~ $true ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ~ totalorderedP(sk3)
<=> $false ),
inference(transitivity,[status(thm)],[13,2]) ).
tff(15,plain,
( ( totalorderedP(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) )
<=> ( totalorderedP(sk5)
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[14,8]) ).
tff(16,plain,
( ( totalorderedP(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) )
<=> totalorderedP(sk5) ),
inference(transitivity,[status(thm)],[15,1]) ).
tff(17,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| totalorderedP(sk5) )
<=> ( totalorderedP(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ segmentP(sk2,sk1)
<=> ~ segmentP(sk4,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(19,plain,
( ~ totalorderedP(sk1)
<=> ~ totalorderedP(sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) )
<=> ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| totalorderedP(sk5) ) ),
inference(monotonicity,[status(thm)],[19,18]) ).
tff(21,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) )
<=> ( totalorderedP(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) ) ),
inference(transitivity,[status(thm)],[20,17]) ).
tff(22,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( totalorderedP(sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
( totalorderedP(sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
tff(25,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| totalorderedP(sk5) ),
inference(modus_ponens,[status(thm)],[27,22]) ).
tff(29,plain,
( totalorderedP(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
totalorderedP(sk5),
inference(modus_ponens,[status(thm)],[29,16]) ).
tff(31,plain,
( ( $false
| $false
| segmentP(sk5,sk3) )
<=> segmentP(sk5,sk3) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk5,sk3) )
<=> ( $false
| $false
| segmentP(sk5,sk3) ) ),
inference(monotonicity,[status(thm)],[14,8]) ).
tff(33,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk5,sk3) )
<=> segmentP(sk5,sk3) ),
inference(transitivity,[status(thm)],[32,31]) ).
tff(34,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) )
<=> ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk5,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( segmentP(sk5,sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( segmentP(sk5,sk1)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1)
| ~ totalorderedP(sk1) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( segmentP(sk5,sk1)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,axiom,
( segmentP(sk5,sk1)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
tff(41,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| segmentP(sk5,sk1) ),
inference(modus_ponens,[status(thm)],[41,35]) ).
tff(43,plain,
( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk5,sk3) ),
inference(modus_ponens,[status(thm)],[42,34]) ).
tff(44,plain,
segmentP(sk5,sk3),
inference(modus_ponens,[status(thm)],[43,33]) ).
tff(45,plain,
( ( $false
| $false
| segmentP(sk4,sk5) )
<=> segmentP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk4,sk5) )
<=> ( $false
| $false
| segmentP(sk4,sk5) ) ),
inference(monotonicity,[status(thm)],[14,8]) ).
tff(47,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk4,sk5) )
<=> segmentP(sk4,sk5) ),
inference(transitivity,[status(thm)],[46,45]) ).
tff(48,plain,
( ( segmentP(sk4,sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) )
<=> ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk4,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( segmentP(sk2,sk5)
<=> segmentP(sk4,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( segmentP(sk4,sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) ) ),
inference(monotonicity,[status(thm)],[49,19,18]) ).
tff(51,plain,
( ( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk4,sk5) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ( segmentP(sk2,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(54,plain,
( ( segmentP(sk2,sk5)
| ~ segmentP(sk2,sk1) )
<=> ( segmentP(sk2,sk5)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
( ( segmentP(sk2,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( segmentP(sk2,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ) ),
inference(monotonicity,[status(thm)],[54]) ).
tff(56,plain,
( ( segmentP(sk2,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(transitivity,[status(thm)],[55,53]) ).
tff(57,axiom,
( segmentP(sk2,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
tff(58,plain,
( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[58,52]) ).
tff(60,plain,
( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
( segmentP(sk2,sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[60,52]) ).
tff(62,plain,
( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| segmentP(sk4,sk5) ),
inference(modus_ponens,[status(thm)],[61,51]) ).
tff(63,plain,
segmentP(sk4,sk5),
inference(modus_ponens,[status(thm)],[62,47]) ).
tff(64,plain,
( ( $false
| $false
| neq(sk3,sk5) )
<=> neq(sk3,sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| neq(sk3,sk5) )
<=> ( $false
| $false
| neq(sk3,sk5) ) ),
inference(monotonicity,[status(thm)],[14,8]) ).
tff(66,plain,
( ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| neq(sk3,sk5) )
<=> neq(sk3,sk5) ),
inference(transitivity,[status(thm)],[65,64]) ).
tff(67,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) )
<=> ( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| neq(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ segmentP(sk2,sk1)
| neq(sk1,sk5)
| ~ totalorderedP(sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( neq(sk1,sk5)
| ~ segmentP(sk2,sk1) )
<=> ( ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( neq(sk1,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ segmentP(sk2,sk1)
| neq(sk1,sk5)
| ~ totalorderedP(sk1) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( neq(sk1,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,axiom,
( neq(sk1,sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
tff(74,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
( ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1)
| neq(sk1,sk5) ),
inference(modus_ponens,[status(thm)],[74,68]) ).
tff(76,plain,
( ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3)
| neq(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[75,67]) ).
tff(77,plain,
neq(sk3,sk5),
inference(modus_ponens,[status(thm)],[76,66]) ).
tff(78,plain,
( ( ssList(sk5)
| $false
| $false )
<=> ssList(sk5) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ssList(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) )
<=> ( ssList(sk5)
| $false
| $false ) ),
inference(monotonicity,[status(thm)],[14,8]) ).
tff(80,plain,
( ( ssList(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) )
<=> ssList(sk5) ),
inference(transitivity,[status(thm)],[79,78]) ).
tff(81,plain,
( ( ssList(sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ssList(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ssList(sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) )
<=> ( ssList(sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ssList(sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) )
<=> ( ssList(sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
( ssList(sk5)
| ~ segmentP(sk2,sk1)
| ~ totalorderedP(sk1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
tff(85,plain,
( ssList(sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ssList(sk5)
| ~ totalorderedP(sk1)
| ~ segmentP(sk2,sk1) ),
inference(modus_ponens,[status(thm)],[85,82]) ).
tff(87,plain,
( ssList(sk5)
| ~ totalorderedP(sk3)
| ~ segmentP(sk4,sk3) ),
inference(modus_ponens,[status(thm)],[86,81]) ).
tff(88,plain,
ssList(sk5),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
^ [A: $i] :
refl(
( ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) )
<=> ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [A: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ ssList(A)
| ~ neq(sk3,A)
| ~ segmentP(sk4,A) )
<=> ( ~ ssList(A)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A) ) )),
( ( ~ ssList(A)
| ~ neq(sk3,A)
| ~ segmentP(sk4,A)
| ~ segmentP(A,sk3) )
<=> ( ~ ssList(A)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A)
| ~ segmentP(A,sk3) ) )),
rewrite(
( ( ~ ssList(A)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A)
| ~ segmentP(A,sk3) )
<=> ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A) ) )),
( ( ~ ssList(A)
| ~ neq(sk3,A)
| ~ segmentP(sk4,A)
| ~ segmentP(A,sk3) )
<=> ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A) ) )),
( ( ~ ssList(A)
| ~ neq(sk3,A)
| ~ segmentP(sk4,A)
| ~ segmentP(A,sk3)
| ~ totalorderedP(A) )
<=> ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A)
| ~ totalorderedP(A) ) )),
rewrite(
( ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ neq(sk3,A)
| ~ totalorderedP(A) )
<=> ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ) )),
( ( ~ ssList(A)
| ~ neq(sk3,A)
| ~ segmentP(sk4,A)
| ~ segmentP(A,sk3)
| ~ totalorderedP(A) )
<=> ( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [A: $i] :
( ~ ssList(A)
| ~ neq(sk3,A)
| ~ segmentP(sk4,A)
| ~ segmentP(A,sk3)
| ~ totalorderedP(A) )
<=> ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [A: $i] :
( ~ ssList(A)
| ~ neq(sk3,A)
| ~ segmentP(sk4,A)
| ~ segmentP(A,sk3)
| ~ totalorderedP(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
tff(95,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) )
| ~ ssList(sk5)
| ~ segmentP(sk5,sk3)
| ~ segmentP(sk4,sk5)
| ~ totalorderedP(sk5)
| ~ neq(sk3,sk5) )
<=> ( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) )
| ~ ssList(sk5)
| ~ segmentP(sk5,sk3)
| ~ segmentP(sk4,sk5)
| ~ totalorderedP(sk5)
| ~ neq(sk3,sk5) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) )
| ~ ssList(sk5)
| ~ segmentP(sk5,sk3)
| ~ segmentP(sk4,sk5)
| ~ totalorderedP(sk5)
| ~ neq(sk3,sk5) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [A: $i] :
( ~ ssList(A)
| ~ segmentP(A,sk3)
| ~ segmentP(sk4,A)
| ~ totalorderedP(A)
| ~ neq(sk3,A) )
| ~ ssList(sk5)
| ~ segmentP(sk5,sk3)
| ~ segmentP(sk4,sk5)
| ~ totalorderedP(sk5)
| ~ neq(sk3,sk5) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
$false,
inference(unit_resolution,[status(thm)],[101,98,88,77,63,44,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC333-1 : TPTP v8.1.0. Released v2.4.0.
% 0.13/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 00:27:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------