%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV543-1.004 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:34:52 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.37s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 58
% Syntax : Number of formulae : 165 ( 133 unt; 0 typ; 0 def)
% Number of atoms : 199 ( 197 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 41 ( 8 ~; 4 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 29 con; 0-3 aty)
% Number of variables : 63 ( 60 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(a_440_type,type,
a_440: $i ).
tff(a_430_type,type,
a_430: $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(e_439_type,type,
e_439: $i ).
tff(i2_type,type,
i2: $i ).
tff(a_438_type,type,
a_438: $i ).
tff(select_type,type,
select: ( $i * $i ) > $i ).
tff(i0_type,type,
i0: $i ).
tff(e_425_type,type,
e_425: $i ).
tff(a_424_type,type,
a_424: $i ).
tff(a_426_type,type,
a_426: $i ).
tff(a_436_type,type,
a_436: $i ).
tff(e_435_type,type,
e_435: $i ).
tff(a_434_type,type,
a_434: $i ).
tff(i3_type,type,
i3: $i ).
tff(a_422_type,type,
a_422: $i ).
tff(a_432_type,type,
a_432: $i ).
tff(e_421_type,type,
e_421: $i ).
tff(a_420_type,type,
a_420: $i ).
tff(e_416_type,type,
e_416: $i ).
tff(i1_type,type,
i1: $i ).
tff(a_417_type,type,
a_417: $i ).
tff(a_418_type,type,
a_418: $i ).
tff(e_419_type,type,
e_419: $i ).
tff(a_431_type,type,
a_431: $i ).
tff(e_423_type,type,
e_423: $i ).
tff(e_433_type,type,
e_433: $i ).
tff(e_437_type,type,
e_437: $i ).
tff(e_429_type,type,
e_429: $i ).
tff(a_428_type,type,
a_428: $i ).
tff(e_427_type,type,
e_427: $i ).
tff(1,plain,
( ( a_440 = store(a_438,i2,e_439) )
<=> ( a_440 = store(a_438,i2,e_439) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
a_440 = store(a_438,i2,e_439),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(3,plain,
a_440 = store(a_438,i2,e_439),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
store(a_438,i2,e_439) = a_440,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( ( a_426 = store(a_424,i2,e_425) )
<=> ( a_426 = store(a_424,i2,e_425) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(6,axiom,
a_426 = store(a_424,i2,e_425),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(7,plain,
a_426 = store(a_424,i2,e_425),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
store(a_424,i2,e_425) = a_426,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
select(store(a_424,i2,e_425),i0) = select(a_426,i0),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
select(a_426,i0) = select(store(a_424,i2,e_425),i0),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( ( e_425 = select(a_422,i3) )
<=> ( e_425 = select(a_422,i3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
e_425 = select(a_422,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp18) ).
tff(13,plain,
e_425 = select(a_422,i3),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
select(a_422,i3) = e_425,
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
( ( a_422 = store(a_420,i3,e_421) )
<=> ( a_422 = store(a_420,i3,e_421) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,axiom,
a_422 = store(a_420,i3,e_421),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(17,plain,
a_422 = store(a_420,i3,e_421),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
store(a_420,i3,e_421) = a_422,
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( ( e_421 = select(a_418,i0) )
<=> ( e_421 = select(a_418,i0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
e_421 = select(a_418,i0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(21,plain,
e_421 = select(a_418,i0),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
select(a_418,i0) = e_421,
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( ( a_418 = store(a_417,i1,e_416) )
<=> ( a_418 = store(a_417,i1,e_416) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
a_418 = store(a_417,i1,e_416),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(25,plain,
a_418 = store(a_417,i1,e_416),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
store(a_417,i1,e_416) = a_418,
inference(symmetry,[status(thm)],[25]) ).
tff(27,plain,
select(store(a_417,i1,e_416),i0) = select(a_418,i0),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
select(store(a_417,i1,e_416),i0) = e_421,
inference(transitivity,[status(thm)],[27,22]) ).
tff(29,plain,
( ( a_420 = store(a_418,i0,e_419) )
<=> ( a_420 = store(a_418,i0,e_419) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
a_420 = store(a_418,i0,e_419),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
tff(31,plain,
a_420 = store(a_418,i0,e_419),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
store(a_418,i0,e_419) = a_420,
inference(symmetry,[status(thm)],[31]) ).
tff(33,plain,
( ( e_419 = select(a_418,i3) )
<=> ( e_419 = select(a_418,i3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
e_419 = select(a_418,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp15) ).
tff(35,plain,
e_419 = select(a_418,i3),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
select(a_418,i3) = e_419,
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
select(store(a_417,i1,e_416),i3) = select(a_418,i3),
inference(monotonicity,[status(thm)],[26]) ).
tff(38,plain,
select(store(a_417,i1,e_416),i3) = e_419,
inference(transitivity,[status(thm)],[37,36]) ).
tff(39,plain,
store(store(a_417,i1,e_416),i0,select(store(a_417,i1,e_416),i3)) = store(a_418,i0,e_419),
inference(monotonicity,[status(thm)],[26,38]) ).
tff(40,plain,
store(store(a_417,i1,e_416),i0,select(store(a_417,i1,e_416),i3)) = a_420,
inference(transitivity,[status(thm)],[39,32]) ).
tff(41,plain,
store(store(store(a_417,i1,e_416),i0,select(store(a_417,i1,e_416),i3)),i3,select(store(a_417,i1,e_416),i0)) = store(a_420,i3,e_421),
inference(monotonicity,[status(thm)],[40,28]) ).
tff(42,plain,
^ [I: $i,A: $i,J: $i] :
refl(( ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) )
<=> ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) )
<=> ! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) )
<=> ! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,axiom,
! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
tff(46,plain,
! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( ~ ! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) )
| ( store(store(store(a_417,i1,e_416),i0,select(store(a_417,i1,e_416),i3)),i3,select(store(a_417,i1,e_416),i0)) = store(store(store(a_417,i1,e_416),i3,select(store(a_417,i1,e_416),i0)),i0,select(store(a_417,i1,e_416),i3)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
store(store(store(a_417,i1,e_416),i0,select(store(a_417,i1,e_416),i3)),i3,select(store(a_417,i1,e_416),i0)) = store(store(store(a_417,i1,e_416),i3,select(store(a_417,i1,e_416),i0)),i0,select(store(a_417,i1,e_416),i3)),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
store(store(store(a_417,i1,e_416),i3,select(store(a_417,i1,e_416),i0)),i0,select(store(a_417,i1,e_416),i3)) = store(store(store(a_417,i1,e_416),i0,select(store(a_417,i1,e_416),i3)),i3,select(store(a_417,i1,e_416),i0)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
select(a_418,i3) = select(store(a_417,i1,e_416),i3),
inference(symmetry,[status(thm)],[37]) ).
tff(53,plain,
e_419 = select(store(a_417,i1,e_416),i3),
inference(transitivity,[status(thm)],[35,52]) ).
tff(54,plain,
store(store(a_417,i1,e_416),i3,select(store(a_417,i1,e_416),i0)) = store(a_418,i3,e_421),
inference(monotonicity,[status(thm)],[26,28]) ).
tff(55,plain,
store(a_418,i3,e_421) = store(store(a_417,i1,e_416),i3,select(store(a_417,i1,e_416),i0)),
inference(symmetry,[status(thm)],[54]) ).
tff(56,plain,
( ( a_431 = store(a_418,i3,e_421) )
<=> ( a_431 = store(a_418,i3,e_421) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
a_431 = store(a_418,i3,e_421),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp8) ).
tff(58,plain,
a_431 = store(a_418,i3,e_421),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
a_431 = store(store(a_417,i1,e_416),i3,select(store(a_417,i1,e_416),i0)),
inference(transitivity,[status(thm)],[58,55]) ).
tff(60,plain,
store(a_431,i0,e_419) = store(store(store(a_417,i1,e_416),i3,select(store(a_417,i1,e_416),i0)),i0,select(store(a_417,i1,e_416),i3)),
inference(monotonicity,[status(thm)],[59,53]) ).
tff(61,plain,
( ( a_432 = store(a_431,i0,e_419) )
<=> ( a_432 = store(a_431,i0,e_419) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,axiom,
a_432 = store(a_431,i0,e_419),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(63,plain,
a_432 = store(a_431,i0,e_419),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
a_432 = a_422,
inference(transitivity,[status(thm)],[63,60,51,41,18]) ).
tff(65,plain,
select(a_432,i3) = select(a_422,i3),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( e_435 = select(a_432,i3) )
<=> ( e_435 = select(a_432,i3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
e_435 = select(a_432,i3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp22) ).
tff(68,plain,
e_435 = select(a_432,i3),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
e_435 = e_425,
inference(transitivity,[status(thm)],[68,65,14]) ).
tff(70,plain,
( ( a_424 = store(a_422,i3,e_423) )
<=> ( a_424 = store(a_422,i3,e_423) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
a_424 = store(a_422,i3,e_423),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp4) ).
tff(72,plain,
a_424 = store(a_422,i3,e_423),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
store(a_422,i3,e_423) = a_424,
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ( e_423 = select(a_422,i2) )
<=> ( e_423 = select(a_422,i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
e_423 = select(a_422,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp17) ).
tff(76,plain,
e_423 = select(a_422,i2),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
select(a_422,i2) = e_423,
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
select(a_432,i2) = select(a_422,i2),
inference(monotonicity,[status(thm)],[64]) ).
tff(79,plain,
( ( e_433 = select(a_432,i2) )
<=> ( e_433 = select(a_432,i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
e_433 = select(a_432,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp21) ).
tff(81,plain,
e_433 = select(a_432,i2),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
e_433 = e_423,
inference(transitivity,[status(thm)],[81,78,77]) ).
tff(83,plain,
store(a_432,i3,e_433) = store(a_422,i3,e_423),
inference(monotonicity,[status(thm)],[64,82]) ).
tff(84,plain,
( ( a_434 = store(a_432,i3,e_433) )
<=> ( a_434 = store(a_432,i3,e_433) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
a_434 = store(a_432,i3,e_433),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp10) ).
tff(86,plain,
a_434 = store(a_432,i3,e_433),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
a_434 = a_424,
inference(transitivity,[status(thm)],[86,83,73]) ).
tff(88,plain,
store(a_434,i2,e_435) = store(a_424,i2,e_425),
inference(monotonicity,[status(thm)],[87,69]) ).
tff(89,plain,
( ( a_436 = store(a_434,i2,e_435) )
<=> ( a_436 = store(a_434,i2,e_435) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
a_436 = store(a_434,i2,e_435),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(91,plain,
a_436 = store(a_434,i2,e_435),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
a_436 = a_426,
inference(transitivity,[status(thm)],[91,88,8]) ).
tff(93,plain,
select(a_436,i0) = select(a_426,i0),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( e_439 = select(a_436,i0) )
<=> ( e_439 = select(a_436,i0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,axiom,
e_439 = select(a_436,i0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp24) ).
tff(96,plain,
e_439 = select(a_436,i0),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
e_439 = select(store(a_424,i2,e_425),i0),
inference(transitivity,[status(thm)],[96,93,10]) ).
tff(98,plain,
( ( e_437 = select(a_436,i2) )
<=> ( e_437 = select(a_436,i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,axiom,
e_437 = select(a_436,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp23) ).
tff(100,plain,
e_437 = select(a_436,i2),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
select(a_436,i2) = e_437,
inference(symmetry,[status(thm)],[100]) ).
tff(102,plain,
select(a_432,i3) = e_435,
inference(symmetry,[status(thm)],[68]) ).
tff(103,plain,
store(a_432,i3,e_433) = a_434,
inference(symmetry,[status(thm)],[86]) ).
tff(104,plain,
store(store(a_432,i3,e_433),i2,select(a_432,i3)) = store(a_434,i2,e_435),
inference(monotonicity,[status(thm)],[103,102]) ).
tff(105,plain,
store(a_434,i2,e_435) = store(store(a_432,i3,e_433),i2,select(a_432,i3)),
inference(symmetry,[status(thm)],[104]) ).
tff(106,plain,
a_436 = store(store(a_432,i3,e_433),i2,select(a_432,i3)),
inference(transitivity,[status(thm)],[91,105]) ).
tff(107,plain,
select(a_436,i2) = select(store(store(a_432,i3,e_433),i2,select(a_432,i3)),i2),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
select(store(store(a_432,i3,e_433),i2,select(a_432,i3)),i2) = select(a_436,i2),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(112,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[113,109]) ).
tff(115,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a_432,i3,e_433),i2,select(a_432,i3)),i2) = select(a_432,i3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(116,plain,
select(store(store(a_432,i3,e_433),i2,select(a_432,i3)),i2) = select(a_432,i3),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
select(a_432,i3) = select(store(store(a_432,i3,e_433),i2,select(a_432,i3)),i2),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
select(a_422,i3) = select(a_432,i3),
inference(symmetry,[status(thm)],[65]) ).
tff(119,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(store(a_422,i3,e_423),i2,select(a_422,i3)),i2) = select(a_422,i3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
select(store(store(a_422,i3,e_423),i2,select(a_422,i3)),i2) = select(a_422,i3),
inference(unit_resolution,[status(thm)],[119,114]) ).
tff(121,plain,
store(store(a_422,i3,e_423),i2,select(a_422,i3)) = store(a_424,i2,e_425),
inference(monotonicity,[status(thm)],[73,14]) ).
tff(122,plain,
store(a_424,i2,e_425) = store(store(a_422,i3,e_423),i2,select(a_422,i3)),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
a_426 = store(store(a_422,i3,e_423),i2,select(a_422,i3)),
inference(transitivity,[status(thm)],[7,122]) ).
tff(124,plain,
select(a_426,i2) = select(store(store(a_422,i3,e_423),i2,select(a_422,i3)),i2),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
select(store(a_424,i2,e_425),i2) = select(a_426,i2),
inference(monotonicity,[status(thm)],[8]) ).
tff(126,plain,
select(store(a_424,i2,e_425),i2) = e_437,
inference(transitivity,[status(thm)],[125,124,120,118,117,108,101]) ).
tff(127,plain,
store(a_434,i2,e_435) = a_436,
inference(symmetry,[status(thm)],[91]) ).
tff(128,plain,
store(a_424,i2,e_425) = store(a_434,i2,e_435),
inference(symmetry,[status(thm)],[88]) ).
tff(129,plain,
store(a_424,i2,e_425) = a_436,
inference(transitivity,[status(thm)],[128,127]) ).
tff(130,plain,
store(store(a_424,i2,e_425),i0,select(store(a_424,i2,e_425),i2)) = store(a_436,i0,e_437),
inference(monotonicity,[status(thm)],[129,126]) ).
tff(131,plain,
store(a_436,i0,e_437) = store(store(a_424,i2,e_425),i0,select(store(a_424,i2,e_425),i2)),
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
( ( a_438 = store(a_436,i0,e_437) )
<=> ( a_438 = store(a_436,i0,e_437) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,axiom,
a_438 = store(a_436,i0,e_437),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp12) ).
tff(134,plain,
a_438 = store(a_436,i0,e_437),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
a_438 = store(store(a_424,i2,e_425),i0,select(store(a_424,i2,e_425),i2)),
inference(transitivity,[status(thm)],[134,131]) ).
tff(136,plain,
store(a_438,i2,e_439) = store(store(store(a_424,i2,e_425),i0,select(store(a_424,i2,e_425),i2)),i2,select(store(a_424,i2,e_425),i0)),
inference(monotonicity,[status(thm)],[135,97]) ).
tff(137,plain,
store(store(store(a_424,i2,e_425),i0,select(store(a_424,i2,e_425),i2)),i2,select(store(a_424,i2,e_425),i0)) = store(a_438,i2,e_439),
inference(symmetry,[status(thm)],[136]) ).
tff(138,plain,
( ~ ! [I: $i,A: $i,J: $i] : ( store(store(A,I,select(A,J)),J,select(A,I)) = store(store(A,J,select(A,I)),I,select(A,J)) )
| ( store(store(store(a_424,i2,e_425),i2,select(store(a_424,i2,e_425),i0)),i0,select(store(a_424,i2,e_425),i2)) = store(store(store(a_424,i2,e_425),i0,select(store(a_424,i2,e_425),i2)),i2,select(store(a_424,i2,e_425),i0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
store(store(store(a_424,i2,e_425),i2,select(store(a_424,i2,e_425),i0)),i0,select(store(a_424,i2,e_425),i2)) = store(store(store(a_424,i2,e_425),i0,select(store(a_424,i2,e_425),i2)),i2,select(store(a_424,i2,e_425),i0)),
inference(unit_resolution,[status(thm)],[138,48]) ).
tff(140,plain,
( ( e_429 = select(a_426,i2) )
<=> ( e_429 = select(a_426,i2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,axiom,
e_429 = select(a_426,i2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp20) ).
tff(142,plain,
e_429 = select(a_426,i2),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
select(a_426,i2) = e_429,
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
select(store(a_424,i2,e_425),i2) = e_429,
inference(transitivity,[status(thm)],[125,143]) ).
tff(145,plain,
( ( a_428 = store(a_426,i2,e_427) )
<=> ( a_428 = store(a_426,i2,e_427) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(146,axiom,
a_428 = store(a_426,i2,e_427),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp6) ).
tff(147,plain,
a_428 = store(a_426,i2,e_427),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
store(a_426,i2,e_427) = a_428,
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
( ( e_427 = select(a_426,i0) )
<=> ( e_427 = select(a_426,i0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
e_427 = select(a_426,i0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp19) ).
tff(151,plain,
e_427 = select(a_426,i0),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
select(a_426,i0) = e_427,
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
select(store(a_424,i2,e_425),i0) = e_427,
inference(transitivity,[status(thm)],[9,152]) ).
tff(154,plain,
store(store(a_424,i2,e_425),i2,select(store(a_424,i2,e_425),i0)) = store(a_426,i2,e_427),
inference(monotonicity,[status(thm)],[8,153]) ).
tff(155,plain,
store(store(a_424,i2,e_425),i2,select(store(a_424,i2,e_425),i0)) = a_428,
inference(transitivity,[status(thm)],[154,148]) ).
tff(156,plain,
store(store(store(a_424,i2,e_425),i2,select(store(a_424,i2,e_425),i0)),i0,select(store(a_424,i2,e_425),i2)) = store(a_428,i0,e_429),
inference(monotonicity,[status(thm)],[155,144]) ).
tff(157,plain,
store(a_428,i0,e_429) = store(store(store(a_424,i2,e_425),i2,select(store(a_424,i2,e_425),i0)),i0,select(store(a_424,i2,e_425),i2)),
inference(symmetry,[status(thm)],[156]) ).
tff(158,plain,
( ( a_430 = store(a_428,i0,e_429) )
<=> ( a_430 = store(a_428,i0,e_429) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
a_430 = store(a_428,i0,e_429),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(160,plain,
a_430 = store(a_428,i0,e_429),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
a_430 = a_440,
inference(transitivity,[status(thm)],[160,157,139,137,4]) ).
tff(162,plain,
( ( a_430 != a_440 )
<=> ( a_430 != a_440 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,axiom,
a_430 != a_440,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(164,plain,
a_430 != a_440,
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
$false,
inference(unit_resolution,[status(thm)],[164,161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV543-1.004 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n009.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 : Fri Jun 20 10:14:33 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.13/0.37 % SZS status Unsatisfiable
% 0.13/0.37 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------